Campo, M. A.; Lopez, J. J.; Rebole, J. P.
2012-04-01
This work was carried out in north of Spain. San Sebastian A meteorological station, where there are available precipitation records every ten minutes was selected. Precipitation data covers from October of 1927 to September of 1997. Pulse models describe the temporal process of rainfall as a succession of rainy cells, main storm, whose origins are distributed in time according to a Poisson process and a secondary process that generates a random number of cells of rain within each storm. Among different pulse models, the Bartlett-Lewis was used. On the other hand, alternative renewal processes and Markov chains describe the way in which the process will evolve in the future depending only on the current state. Therefore they are nor dependant on past events. Two basic processes are considered when describing the occurrence of rain: the alternation of wet and dry periods and temporal distribution of rainfall in each rain event, which determines the rainwater collected in each of the intervals that make up the rain. This allows the introduction of alternative renewal processes and Markov chains of three states, where interstorm time is given by either of the two dry states, short or long. Thus, the stochastic model of Markov chains tries to reproduce the basis of pulse models: the succession of storms, each one composed for a series of rain, separated by a short interval of time without theoretical complexity of these. In a first step, we analyzed all variables involved in the sequential process of the rain: rain event duration, event duration of non-rain, average rainfall intensity in rain events, and finally, temporal distribution of rainfall within the rain event. Additionally, for pulse Bartlett-Lewis model calibration, main descriptive statistics were calculated for each month, considering the process of seasonal rainfall in each month. In a second step, both models were calibrated. Finally, synthetic series were simulated with calibration parameters; series
Stochastic modelling of daily rainfall sequences
Buishand, T.A.
1977-01-01
Rainfall series of different climatic regions were analysed with the aim of generating daily rainfall sequences. A survey of the data is given in I, 1. When analysing daily rainfall sequences one must be aware of the following points:
a. Seasonality. Because of seasonal variation
Parameter estimation in stochastic rainfall-runoff models
DEFF Research Database (Denmark)
Jonsdottir, Harpa; Madsen, Henrik; Palsson, Olafur Petur
2006-01-01
A parameter estimation method for stochastic rainfall-runoff models is presented. The model considered in the paper is a conceptual stochastic model, formulated in continuous-discrete state space form. The model is small and a fully automatic optimization is, therefore, possible for estimating all...... the parameter values are optimal for simulation or prediction. The data originates from Iceland and the model is designed for Icelandic conditions, including a snow routine for mountainous areas. The model demands only two input data series, precipitation and temperature and one output data series...
A Stochastic Fractional Dynamics Model of Rainfall Statistics
Kundu, Prasun; Travis, James
2013-04-01
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is designed to faithfully reflect the scale dependence and is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. The main restriction is the assumption that the statistics of the precipitation field is spatially homogeneous and isotropic and stationary in time. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of the radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment. Some data sets containing periods of non-stationary behavior that involves occasional anomalously correlated rain events, present a challenge for the model.
Stochastic modeling of hourly rainfall times series in Campania (Italy)
Giorgio, M.; Greco, R.
2009-04-01
Occurrence of flowslides and floods in small catchments is uneasy to predict, since it is affected by a number of variables, such as mechanical and hydraulic soil properties, slope morphology, vegetation coverage, rainfall spatial and temporal variability. Consequently, landslide risk assessment procedures and early warning systems still rely on simple empirical models based on correlation between recorded rainfall data and observed landslides and/or river discharges. Effectiveness of such systems could be improved by reliable quantitative rainfall prediction, which can allow gaining larger lead-times. Analysis of on-site recorded rainfall height time series represents the most effective approach for a reliable prediction of local temporal evolution of rainfall. Hydrological time series analysis is a widely studied field in hydrology, often carried out by means of autoregressive models, such as AR, ARMA, ARX, ARMAX (e.g. Salas [1992]). Such models gave the best results when applied to the analysis of autocorrelated hydrological time series, like river flow or level time series. Conversely, they are not able to model the behaviour of intermittent time series, like point rainfall height series usually are, especially when recorded with short sampling time intervals. More useful for this issue are the so-called DRIP (Disaggregated Rectangular Intensity Pulse) and NSRP (Neymann-Scott Rectangular Pulse) model [Heneker et al., 2001; Cowpertwait et al., 2002], usually adopted to generate synthetic point rainfall series. In this paper, the DRIP model approach is adopted, in which the sequence of rain storms and dry intervals constituting the structure of rainfall time series is modeled as an alternating renewal process. Final aim of the study is to provide a useful tool to implement an early warning system for hydrogeological risk management. Model calibration has been carried out with hourly rainfall hieght data provided by the rain gauges of Campania Region civil
Peleg, Nadav; Blumensaat, Frank; Molnar, Peter; Fatichi, Simone; Burlando, Paolo
2016-04-01
Urban drainage response is highly dependent on the spatial and temporal structure of rainfall. Therefore, measuring and simulating rainfall at a high spatial and temporal resolution is a fundamental step to fully assess urban drainage system reliability and related uncertainties. This is even more relevant when considering extreme rainfall events. However, the current space-time rainfall models have limitations in capturing extreme rainfall intensity statistics for short durations. Here, we use the STREAP (Space-Time Realizations of Areal Precipitation) model, which is a novel stochastic rainfall generator for simulating high-resolution rainfall fields that preserve the spatio-temporal structure of rainfall and its statistical characteristics. The model enables a generation of rain fields at 102 m and minute scales in a fast and computer-efficient way matching the requirements for hydrological analysis of urban drainage systems. The STREAP model was applied successfully in the past to generate high-resolution extreme rainfall intensities over a small domain. A sub-catchment in the city of Luzern (Switzerland) was chosen as a case study to: (i) evaluate the ability of STREAP to disaggregate extreme rainfall intensities for urban drainage applications; (ii) assessing the role of stochastic climate variability of rainfall in flow response and (iii) evaluate the degree of non-linearity between extreme rainfall intensity and system response (i.e. flow) for a small urban catchment. The channel flow at the catchment outlet is simulated by means of a calibrated hydrodynamic sewer model.
Chowdhury, A. F. M. K.; Lockart, N.; Willgoose, G. R.; Kuczera, G. A.; Kiem, A.; Nadeeka, P. M.
2016-12-01
One of the key objectives of stochastic rainfall modelling is to capture the full variability of climate system for future drought and flood risk assessment. However, it is not clear how well these models can capture the future climate variability when they are calibrated to Global/Regional Climate Model data (GCM/RCM) as these datasets are usually available for very short future period/s (e.g. 20 years). This study has assessed the ability of two stochastic daily rainfall models to capture climate variability by calibrating them to a dynamically downscaled RCM dataset in an east Australian catchment for 1990-2010, 2020-2040, and 2060-2080 epochs. The two stochastic models are: (1) a hierarchical Markov Chain (MC) model, which we developed in a previous study and (2) a semi-parametric MC model developed by Mehrotra and Sharma (2007). Our hierarchical model uses stochastic parameters of MC and Gamma distribution, while the semi-parametric model uses a modified MC process with memory of past periods and kernel density estimation. This study has generated multiple realizations of rainfall series by using parameters of each model calibrated to the RCM dataset for each epoch. The generated rainfall series are used to generate synthetic streamflow by using a SimHyd hydrology model. Assessing the synthetic rainfall and streamflow series, this study has found that both stochastic models can incorporate a range of variability in rainfall as well as streamflow generation for both current and future periods. However, the hierarchical model tends to overestimate the multiyear variability of wet spell lengths (therefore, is less likely to simulate long periods of drought and flood), while the semi-parametric model tends to overestimate the mean annual rainfall depths and streamflow volumes (hence, simulated droughts are likely to be less severe). Sensitivity of these limitations of both stochastic models in terms of future drought and flood risk assessment will be discussed.
A coupled stochastic rainfall-evapotranspiration model for hydrological impact analysis
Pham, Minh Tu; Vernieuwe, Hilde; De Baets, Bernard; Verhoest, Niko E. C.
2018-02-01
A hydrological impact analysis concerns the study of the consequences of certain scenarios on one or more variables or fluxes in the hydrological cycle. In such an exercise, discharge is often considered, as floods originating from extremely high discharges often cause damage. Investigating the impact of extreme discharges generally requires long time series of precipitation and evapotranspiration to be used to force a rainfall-runoff model. However, such kinds of data may not be available and one should resort to stochastically generated time series, even though the impact of using such data on the overall discharge, and especially on the extreme discharge events, is not well studied. In this paper, stochastically generated rainfall and corresponding evapotranspiration time series, generated by means of vine copulas, are used to force a simple conceptual hydrological model. The results obtained are comparable to the modelled discharge using observed forcing data. Yet, uncertainties in the modelled discharge increase with an increasing number of stochastically generated time series used. Notwithstanding this finding, it can be concluded that using a coupled stochastic rainfall-evapotranspiration model has great potential for hydrological impact analysis.
Regionalization of the Modified Bartlett-Lewis Rectangular Pulse Stochastic Rainfall Model
Dongkyun Kim; Francisco Olivera; Huidae Cho; Scott A. Socolofsky
2013-01-01
Parameters of the Modified Bartlett-Lewis Rectangular Pulse (MBLRP) stochastic rainfall simulation model were regionalized across the contiguous United States. Three thousand four hundred forty-four National Climate Data Center (NCDC) rain gauges were used to obtain spatial and seasonal patterns of the model parameters. The MBLRP model was calibrated to minimize the discrepancy between the precipitation depth statistics between the observed and MBLRP-generated precipitation time series. These...
Development and evaluation of a stochastic daily rainfall model with long-term variability
Kamal Chowdhury, A. F. M.; Lockart, Natalie; Willgoose, Garry; Kuczera, George; Kiem, Anthony S.; Parana Manage, Nadeeka
2017-12-01
The primary objective of this study is to develop a stochastic rainfall generation model that can match not only the short resolution (daily) variability but also the longer resolution (monthly to multiyear) variability of observed rainfall. This study has developed a Markov chain (MC) model, which uses a two-state MC process with two parameters (wet-to-wet and dry-to-dry transition probabilities) to simulate rainfall occurrence and a gamma distribution with two parameters (mean and standard deviation of wet day rainfall) to simulate wet day rainfall depths. Starting with the traditional MC-gamma model with deterministic parameters, this study has developed and assessed four other variants of the MC-gamma model with different parameterisations. The key finding is that if the parameters of the gamma distribution are randomly sampled each year from fitted distributions rather than fixed parameters with time, the variability of rainfall depths at both short and longer temporal resolutions can be preserved, while the variability of wet periods (i.e. number of wet days and mean length of wet spell) can be preserved by decadally varied MC parameters. This is a straightforward enhancement to the traditional simplest MC model and is both objective and parsimonious.
Costa, Veber; Fernandes, Wilson
2017-11-01
Extreme flood estimation has been a key research topic in hydrological sciences. Reliable estimates of such events are necessary as structures for flood conveyance are continuously evolving in size and complexity and, as a result, their failure-associated hazards become more and more pronounced. Due to this fact, several estimation techniques intended to improve flood frequency analysis and reducing uncertainty in extreme quantile estimation have been addressed in the literature in the last decades. In this paper, we develop a Bayesian framework for the indirect estimation of extreme flood quantiles from rainfall-runoff models. In the proposed approach, an ensemble of long daily rainfall series is simulated with a stochastic generator, which models extreme rainfall amounts with an upper-bounded distribution function, namely, the 4-parameter lognormal model. The rationale behind the generation model is that physical limits for rainfall amounts, and consequently for floods, exist and, by imposing an appropriate upper bound for the probabilistic model, more plausible estimates can be obtained for those rainfall quantiles with very low exceedance probabilities. Daily rainfall time series are converted into streamflows by routing each realization of the synthetic ensemble through a conceptual hydrologic model, the Rio Grande rainfall-runoff model. Calibration of parameters is performed through a nonlinear regression model, by means of the specification of a statistical model for the residuals that is able to accommodate autocorrelation, heteroscedasticity and nonnormality. By combining the outlined steps in a Bayesian structure of analysis, one is able to properly summarize the resulting uncertainty and estimating more accurate credible intervals for a set of flood quantiles of interest. The method for extreme flood indirect estimation was applied to the American river catchment, at the Folsom dam, in the state of California, USA. Results show that most floods
Towards large scale stochastic rainfall models for flood risk assessment in trans-national basins
Serinaldi, F.; Kilsby, C. G.
2012-04-01
While extensive research has been devoted to rainfall-runoff modelling for risk assessment in small and medium size watersheds, less attention has been paid, so far, to large scale trans-national basins, where flood events have severe societal and economic impacts with magnitudes quantified in billions of Euros. As an example, in the April 2006 flood events along the Danube basin at least 10 people lost their lives and up to 30 000 people were displaced, with overall damages estimated at more than half a billion Euros. In this context, refined analytical methods are fundamental to improve the risk assessment and, then, the design of structural and non structural measures of protection, such as hydraulic works and insurance/reinsurance policies. Since flood events are mainly driven by exceptional rainfall events, suitable characterization and modelling of space-time properties of rainfall fields is a key issue to perform a reliable flood risk analysis based on alternative precipitation scenarios to be fed in a new generation of large scale rainfall-runoff models. Ultimately, this approach should be extended to a global flood risk model. However, as the need of rainfall models able to account for and simulate spatio-temporal properties of rainfall fields over large areas is rather new, the development of new rainfall simulation frameworks is a challenging task involving that faces with the problem of overcoming the drawbacks of the existing modelling schemes (devised for smaller spatial scales), but keeping the desirable properties. In this study, we critically summarize the most widely used approaches for rainfall simulation. Focusing on stochastic approaches, we stress the importance of introducing suitable climate forcings in these simulation schemes in order to account for the physical coherence of rainfall fields over wide areas. Based on preliminary considerations, we suggest a modelling framework relying on the Generalized Additive Models for Location, Scale
Cowden, Joshua R.; Watkins, David W., Jr.; Mihelcic, James R.
2008-10-01
SummarySeveral parsimonious stochastic rainfall models are developed and compared for application to domestic rainwater harvesting (DRWH) assessment in West Africa. Worldwide, improved water access rates are lowest for Sub-Saharan Africa, including the West African region, and these low rates have important implications on the health and economy of the region. Domestic rainwater harvesting (DRWH) is proposed as a potential mechanism for water supply enhancement, especially for the poor urban households in the region, which is essential for development planning and poverty alleviation initiatives. The stochastic rainfall models examined are Markov models and LARS-WG, selected due to availability and ease of use for water planners in the developing world. A first-order Markov occurrence model with a mixed exponential amount model is selected as the best option for unconditioned Markov models. However, there is no clear advantage in selecting Markov models over the LARS-WG model for DRWH in West Africa, with each model having distinct strengths and weaknesses. A multi-model approach is used in assessing DRWH in the region to illustrate the variability associated with the rainfall models. It is clear DRWH can be successfully used as a water enhancement mechanism in West Africa for certain times of the year. A 200 L drum storage capacity could potentially optimize these simple, small roof area systems for many locations in the region.
Regionalization of the Modified Bartlett-Lewis Rectangular Pulse Stochastic Rainfall Model
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Dongkyun Kim
2013-01-01
Full Text Available Parameters of the Modified Bartlett-Lewis Rectangular Pulse (MBLRP stochastic rainfall simulation model were regionalized across the contiguous United States. Three thousand four hundred forty-four National Climate Data Center (NCDC rain gauges were used to obtain spatial and seasonal patterns of the model parameters. The MBLRP model was calibrated to minimize the discrepancy between the precipitation depth statistics between the observed and MBLRP-generated precipitation time series. These statistics included the mean, variance, probability of zero rainfall and autocorrelation at 1-, 3-, 12- and 24-hour accumulation intervals. The Ordinary Kriging interpolation technique was used to generate maps of the six MBLRP model parameters for each of the 12 months of the year. All parameters had clear to discernible regional tendencies; except for one related to rain cell duration distribution. Parameter seasonality was not obvious and it was more apparent in some locations than in others, depending on the seasonality of the rainfall statistics. Cross-validation was used to assess the validity of the parameter maps. The results indicate that the suggested maps reproduce well the observed rainfall statistics for different accumulation intervals, except for the lag-1 autocorrelation coefficient. The boundaries of the expected residual, with 95% confidence, between the observed rainfall statistics and the simulated rainfall statistics based on the map parameters were approximately ±0.064 mm hr-1, ±1.63 mm2 hr-2, ±0.16, and ±0.030 for the mean, variance, lag-1 autocorrelation and probability of zero rainfall at hourly accumulation levels, respectively. The estimated parameter values were also used to estimate the storm and rain cell characteristics.
Aronica, G. T.; Candela, A.
2007-12-01
SummaryIn this paper a Monte Carlo procedure for deriving frequency distributions of peak flows using a semi-distributed stochastic rainfall-runoff model is presented. The rainfall-runoff model here used is very simple one, with a limited number of parameters and practically does not require any calibration, resulting in a robust tool for those catchments which are partially or poorly gauged. The procedure is based on three modules: a stochastic rainfall generator module, a hydrologic loss module and a flood routing module. In the rainfall generator module the rainfall storm, i.e. the maximum rainfall depth for a fixed duration, is assumed to follow the two components extreme value (TCEV) distribution whose parameters have been estimated at regional scale for Sicily. The catchment response has been modelled by using the Soil Conservation Service-Curve Number (SCS-CN) method, in a semi-distributed form, for the transformation of total rainfall to effective rainfall and simple form of IUH for the flood routing. Here, SCS-CN method is implemented in probabilistic form with respect to prior-to-storm conditions, allowing to relax the classical iso-frequency assumption between rainfall and peak flow. The procedure is tested on six practical case studies where synthetic FFC (flood frequency curve) were obtained starting from model variables distributions by simulating 5000 flood events combining 5000 values of total rainfall depth for the storm duration and AMC (antecedent moisture conditions) conditions. The application of this procedure showed how Monte Carlo simulation technique can reproduce the observed flood frequency curves with reasonable accuracy over a wide range of return periods using a simple and parsimonious approach, limited data input and without any calibration of the rainfall-runoff model.
Haberlandt, U.; Radtke, I.
2014-01-01
Derived flood frequency analysis allows the estimation of design floods with hydrological modeling for poorly observed basins considering change and taking into account flood protection measures. There are several possible choices regarding precipitation input, discharge output and consequently the calibration of the model. The objective of this study is to compare different calibration strategies for a hydrological model considering various types of rainfall input and runoff output data sets and to propose the most suitable approach. Event based and continuous, observed hourly rainfall data as well as disaggregated daily rainfall and stochastically generated hourly rainfall data are used as input for the model. As output, short hourly and longer daily continuous flow time series as well as probability distributions of annual maximum peak flow series are employed. The performance of the strategies is evaluated using the obtained different model parameter sets for continuous simulation of discharge in an independent validation period and by comparing the model derived flood frequency distributions with the observed one. The investigations are carried out for three mesoscale catchments in northern Germany with the hydrological model HEC-HMS (Hydrologic Engineering Center's Hydrologic Modeling System). The results show that (I) the same type of precipitation input data should be used for calibration and application of the hydrological model, (II) a model calibrated using a small sample of extreme values works quite well for the simulation of continuous time series with moderate length but not vice versa, and (III) the best performance with small uncertainty is obtained when stochastic precipitation data and the observed probability distribution of peak flows are used for model calibration. This outcome suggests to calibrate a hydrological model directly on probability distributions of observed peak flows using stochastic rainfall as input if its purpose is the
Directory of Open Access Journals (Sweden)
Ibrahim Suliman Hanaish
2011-01-01
Full Text Available Three versions of Bartlett Lewis rectangular pulse rainfall models, namely, the Original Bartlett Lewis (OBL, Modified Bartlett Lewis (MBL, and 2N-cell-type Bartlett Lewis model (BL2n, are considered. These models are fitted to the hourly rainfall data from 1970 to 2008 obtained from Petaling Jaya rain gauge station, located in Peninsular Malaysia. The generalized method of moments is used to estimate the model parameters. Under this method, minimization of two different objective functions which involve different weight functions, one weight is inversely proportional to the variance and another one is inversely proportional to the mean squared, is carried out using Nelder-Mead optimization technique. For the purpose of comparison of the performance of the three different models, the results found for the months of July and November are used for illustration. This performance is assessed based on the goodness of fit of the models. In addition, the sensitivity of the parameter estimates to the choice of the objective function is also investigated. It is found that BL2n slightly outperforms OBL. However, the best model is the Modified Bartlett Lewis MBL, particularly when the objective function considered involves weight which is inversely proportional to the variance.
Rainfall height stochastic modelling as a support tool for landslides early warning
Capparelli, G.; Giorgio, M.; Greco, R.; Versace, P.
2009-04-01
Occurrence of landslides is uneasy to predict, since it is affected by a number of variables, such as mechanical and hydraulic soil properties, slope morphology, vegetation coverage, rainfall spatial and temporal variability. Although heavy landslides frequently occurred in Campania, southern Italy, during the last decade, no complete data sets are available for natural slopes where landslides occurred. As a consequence, landslide risk assessment procedures and early warning systems in Campania still rely on simple empirical models based on correlation between daily rainfall records and observed landslides, like FLAIR model [Versace et al., 2003]. Effectiveness of such systems could be improved by reliable quantitative rainfall prediction. In mountainous areas, rainfall spatial and temporal variability are very pronounced due to orographic effects, making predictions even more complicated. Existing rain gauge networks are not dense enough to resolve the small scale spatial variability, and the same limitation of spatial resolution affects rainfall height maps provided by radar sensors as well as by meteorological physically based models. Therefore, analysis of on-site recorded rainfall height time series still represents the most effective approach for a reliable prediction of local temporal evolution of rainfall. Hydrological time series analysis is a widely studied field in hydrology, often carried out by means of autoregressive models, such as AR and ARMA [Box and Jenkins, 1976]. Sometimes exogenous information coming from additional series of observations is also taken into account, and the models are called ARX and ARMAX (e.g. Salas [1992]). Such models gave the best results when applied to the analysis of autocorrelated hydrological time series, like river flow or level time series. Conversely, they are not able to model the behaviour of intermittent time series, like point rainfall height series usually are, especially when recorded with short sampling time
Abas, Norzaida; Daud, Zalina M.; Yusof, Fadhilah
2014-11-01
A stochastic rainfall model is presented for the generation of hourly rainfall data in an urban area in Malaysia. In view of the high temporal and spatial variability of rainfall within the tropical rain belt, the Spatial-Temporal Neyman-Scott Rectangular Pulse model was used. The model, which is governed by the Neyman-Scott process, employs a reasonable number of parameters to represent the physical attributes of rainfall. A common approach is to attach each attribute to a mathematical distribution. With respect to rain cell intensity, this study proposes the use of a mixed exponential distribution. The performance of the proposed model was compared to a model that employs the Weibull distribution. Hourly and daily rainfall data from four stations in the Damansara River basin in Malaysia were used as input to the models, and simulations of hourly series were performed for an independent site within the basin. The performance of the models was assessed based on how closely the statistical characteristics of the simulated series resembled the statistics of the observed series. The findings obtained based on graphical representation revealed that the statistical characteristics of the simulated series for both models compared reasonably well with the observed series. However, a further assessment using the AIC, BIC and RMSE showed that the proposed model yields better results. The results of this study indicate that for tropical climates, the proposed model, using a mixed exponential distribution, is the best choice for generation of synthetic data for ungauged sites or for sites with insufficient data within the limit of the fitted region.
A Stochastic Model of Space-Time Variability of Tropical Rainfall: I. Statistics of Spatial Averages
Kundu, Prasun K.; Bell, Thomas L.; Lau, William K. M. (Technical Monitor)
2002-01-01
Global maps of rainfall are of great importance in connection with modeling of the earth s climate. Comparison between the maps of rainfall predicted by computer-generated climate models with observation provides a sensitive test for these models. To make such a comparison, one typically needs the total precipitation amount over a large area, which could be hundreds of kilometers in size over extended periods of time of order days or months. This presents a difficult problem since rain varies greatly from place to place as well as in time. Remote sensing methods using ground radar or satellites detect rain over a large area by essentially taking a series of snapshots at infrequent intervals and indirectly deriving the average rain intensity within a collection of pixels , usually several kilometers in size. They measure area average of rain at a particular instant. Rain gauges, on the other hand, record rain accumulation continuously in time but only over a very small area tens of centimeters across, say, the size of a dinner plate. They measure only a time average at a single location. In making use of either method one needs to fill in the gaps in the observation - either the gaps in the area covered or the gaps in time of observation. This involves using statistical models to obtain information about the rain that is missed from what is actually detected. This paper investigates such a statistical model and validates it with rain data collected over the tropical Western Pacific from ship borne radars during TOGA COARE (Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment). The model incorporates a number of commonly observed features of rain. While rain varies rapidly with location and time, the variability diminishes when averaged over larger areas or longer periods of time. Moreover, rain is patchy in nature - at any instant on the average only a certain fraction of the observed pixels contain rain. The fraction of area covered by
Delgado, Oihane; Campo-Bescós, Miguel A.; López, J. Javier
2017-04-01
Frequently, when we are trying to solve certain hydrological engineering problems, it is often necessary to know rain intensity values related to a specific probability or return period, T. Based on analyses of extreme rainfall events at different time scale aggregation, we can deduce the relationships among Intensity-Duration-Frequency (IDF), that are widely used in hydraulic infrastructure design. However, the lack of long time series of rainfall intensities for smaller time periods, minutes or hours, leads to use mathematical expressions to characterize and extend these curves. One way to deduce them is through the development of synthetic rainfall time series generated from stochastic models, which is evaluated in this work. From recorded accumulated rainfall time series every 10 min in the pluviograph of Igueldo (San Sebastian, Spain) for the time period between 1927-2005, their homogeneity has been checked and possible statistically significant increasing or decreasing trends have also been shown. Subsequently, two models have been calibrated: Bartlett-Lewis and Markov chains models, which are based on the successions of storms, composed for a series of rainfall events, separated by a short interval of time each. Finally, synthetic ten-minute rainfall time series are generated, which allow to estimate detailed IDF curves and compare them with the estimated IDF based on the recorded data.
Stochastic rainfall synthesis for urban applications using different regionalization methods
Callau Poduje, A. C.; Leimbach, S.; Haberlandt, U.
2017-12-01
The proper design and efficient operation of urban drainage systems require long and continuous rainfall series in a high temporal resolution. Unfortunately, these time series are usually available in a few locations and it is therefore suitable to develop a stochastic precipitation model to generate rainfall in locations without observations. The model presented is based on an alternating renewal process and involves an external and an internal structure. The members of these structures are described by probability distributions which are site specific. Different regionalization methods based on site descriptors are presented which are used for estimating the distributions for locations without observations. Regional frequency analysis, multiple linear regressions and a vine-copula method are applied for this purpose. An area located in the north-west of Germany is used to compare the different methods and involves a total of 81 stations with 5 min rainfall records. The site descriptors include information available for the whole region: position, topography and hydrometeorologic characteristics which are estimated from long term observations. The methods are compared directly by cross validation of different rainfall statistics. Given that the model is stochastic the evaluation is performed based on ensembles of many long synthetic time series which are compared with observed ones. The performance is as well indirectly evaluated by setting up a fictional urban hydrological system to test the capability of the different methods regarding flooding and overflow characteristics. The results show a good representation of the seasonal variability and good performance in reproducing the sample statistics of the rainfall characteristics. The copula based method shows to be the most robust of the three methods. Advantages and disadvantages of the different methods are presented and discussed.
Stochastic bias-correction of daily rainfall scenarios for hydrological applications
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I. Portoghese
2011-09-01
Full Text Available The accuracy of rainfall predictions provided by climate models is crucial for the assessment of climate change impacts on hydrological processes. In fact, the presence of bias in downscaled precipitation may produce large bias in the assessment of soil moisture dynamics, river flows and groundwater recharge.
In this study, a comparison between statistical properties of rainfall observations and model control simulations from a Regional Climate Model (RCM was performed through a robust and meaningful representation of the precipitation process. The output of the adopted RCM was analysed and re-scaled exploiting the structure of a stochastic model of the point rainfall process. In particular, the stochastic model is able to adequately reproduce the rainfall intermittency at the synoptic scale, which is one of the crucial aspects for the Mediterranean environments. Possible alteration in the local rainfall regime was investigated by means of the historical daily time-series from a dense rain-gauge network, which were also used for the analysis of the RCM bias in terms of dry and wet periods and storm intensity. The result is a stochastic scheme for bias-correction at the RCM-cell scale, which produces a realistic representation of the daily rainfall intermittency and precipitation depths, though a residual bias in the storm intensity of longer storm events persists.
Directory of Open Access Journals (Sweden)
Dongkyun Kim
2014-01-01
Full Text Available A novel approach for a Poisson cluster stochastic rainfall generator was validated in its ability to reproduce important rainfall and watershed response characteristics at 104 locations in the United States. The suggested novel approach, The Hybrid Model (THM, as compared to the traditional Poisson cluster rainfall modeling approaches, has an additional capability to account for the interannual variability of rainfall statistics. THM and a traditional approach of Poisson cluster rainfall model (modified Bartlett-Lewis rectangular pulse model were compared in their ability to reproduce the characteristics of extreme rainfall and watershed response variables such as runoff and peak flow. The results of the comparison indicate that THM generally outperforms the traditional approach in reproducing the distributions of peak rainfall, peak flow, and runoff volume. In addition, THM significantly outperformed the traditional approach in reproducing extreme rainfall by 2.3% to 66% and extreme flow values by 32% to 71%.
Prediction of Annual Rainfall Pattern Using Hidden Markov Model ...
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ADOWIE PERE
Hidden Markov model is very influential in stochastic world because of its ... the earth from the clouds. The usual ... Rainfall modelling and ... Markov Models have become popular tools ... environment sciences, University of Jos, plateau state,.
Lanchier, Nicolas
2017-01-01
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the ...
Stochastic Urban Pluvial Flood Hazard Maps Based upon a Spatial-Temporal Rainfall Generator
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Nuno Eduardo Simões
2015-06-01
Full Text Available It is a common practice to assign the return period of a given storm event to the urban pluvial flood event that such storm generates. However, this approach may be inappropriate as rainfall events with the same return period can produce different urban pluvial flooding events, i.e., with different associated flood extent, water levels and return periods. This depends on the characteristics of the rainfall events, such as spatial variability, and on other characteristics of the sewer system and the catchment. To address this, the paper presents an innovative contribution to produce stochastic urban pluvial flood hazard maps. A stochastic rainfall generator for urban-scale applications was employed to generate an ensemble of spatially—and temporally—variable design storms with similar return period. These were used as input to the urban drainage model of a pilot urban catchment (~9 km2 located in London, UK. Stochastic flood hazard maps were generated through a frequency analysis of the flooding generated by the various storm events. The stochastic flood hazard maps obtained show that rainfall spatial-temporal variability is an important factor in the estimation of flood likelihood in urban areas. Moreover, as compared to the flood hazard maps obtained by using a single spatially-uniform storm event, the stochastic maps generated in this study provide a more comprehensive assessment of flood hazard which enables better informed flood risk management decisions.
A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall
Lombardo, F.; Volpi, E.; Koutsoyiannis, D.; Serinaldi, F.
2017-06-01
Generating fine-scale time series of intermittent rainfall that are fully consistent with any given coarse-scale totals is a key and open issue in many hydrological problems. We propose a stationary disaggregation method that simulates rainfall time series with given dependence structure, wet/dry probability, and marginal distribution at a target finer (lower-level) time scale, preserving full consistency with variables at a parent coarser (higher-level) time scale. We account for the intermittent character of rainfall at fine time scales by merging a discrete stochastic representation of intermittency and a continuous one of rainfall depths. This approach yields a unique and parsimonious mathematical framework providing general analytical formulations of mean, variance, and autocorrelation function (ACF) for a mixed-type stochastic process in terms of mean, variance, and ACFs of both continuous and discrete components, respectively. To achieve the full consistency between variables at finer and coarser time scales in terms of marginal distribution and coarse-scale totals, the generated lower-level series are adjusted according to a procedure that does not affect the stochastic structure implied by the original model. To assess model performance, we study rainfall process as intermittent with both independent and dependent occurrences, where dependence is quantified by the probability that two consecutive time intervals are dry. In either case, we provide analytical formulations of main statistics of our mixed-type disaggregation model and show their clear accordance with Monte Carlo simulations. An application to rainfall time series from real world is shown as a proof of concept.
Greenwood, Priscilla E
2016-01-01
This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...
Stochastic modeling of soil salinity
Suweis, S.; Porporato, A. M.; Daly, E.; van der Zee, S.; Maritan, A.; Rinaldo, A.
2010-12-01
A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The equations for the probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equations to a single stochastic differential equation (generalized Langevin equation) driven by multiplicative Poisson noise. Generalized Langevin equations with multiplicative white Poisson noise pose the usual Ito (I) or Stratonovich (S) prescription dilemma. Different interpretations lead to different results and then choosing between the I and S prescriptions is crucial to describe correctly the dynamics of the model systems. We show how this choice can be determined by physical information about the timescales involved in the process. We also show that when the multiplicative noise is at most linear in the random variable one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We then apply these results to the generalized Langevin equation that drives the salt mass dynamics. The stationary analytical solutions for the probability density functions of salt mass and concentration provide insight on the interplay of the main soil, plant and climate parameters responsible for long term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in longterm soil salinization trends, with significant consequences, e.g. for climate change impacts on rain fed agriculture.
Stochastic modelling of turbulence
DEFF Research Database (Denmark)
Sørensen, Emil Hedevang Lohse
previously been shown to be closely connected to the energy dissipation. The incorporation of the small scale dynamics into the spatial model opens the door to a fully fledged stochastic model of turbulence. Concerning the interaction of wind and wind turbine, a new method is proposed to extract wind turbine...
Stochastic Control - External Models
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
2005-01-01
This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...
Stochasticity Modeling in Memristors
Naous, Rawan; Al-Shedivat, Maruan; Salama, Khaled N.
2015-01-01
Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.
Stochasticity Modeling in Memristors
Naous, Rawan
2015-10-26
Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.
Identifiability in stochastic models
1992-01-01
The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of ""characterization problems"" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.
Simulation of daily rainfall through markov chain modeling
International Nuclear Information System (INIS)
Sadiq, N.
2015-01-01
Being an agricultural country, the inhabitants of dry land in cultivated areas mainly rely on the daily rainfall for watering their fields. A stochastic model based on first order Markov Chain was developed to simulate daily rainfall data for Multan, D. I. Khan, Nawabshah, Chilas and Barkhan for the period 1981-2010. Transitional probability matrices of first order Markov Chain was utilized to generate the daily rainfall occurrence while gamma distribution was used to generate the daily rainfall amount. In order to achieve the parametric values of mentioned cities, method of moments is used to estimate the shape and scale parameters which lead to synthetic sequence generation as per gamma distribution. In this study, unconditional and conditional probabilities of wet and dry days in sum with means and standard deviations are considered as the essential parameters for the simulated stochastic generation of daily rainfalls. It has been found that the computerized synthetic rainfall series concurred pretty well with the actual observed rainfall series. (author)
DEFF Research Database (Denmark)
Thorndahl, Søren; Korup Andersen, Aske; Larsen, Anders Badsberg
2017-01-01
Continuous and long rainfall series are a necessity in rural and urban hydrology for analysis and design purposes. Local historical point rainfall series often cover several decades, which makes it possible to estimate rainfall means at different timescales, and to assess return periods of extreme...... includes climate changes projected to a specific future period. This paper presents a framework for resampling of historical point rainfall series in order to generate synthetic rainfall series, which has the same statistical properties as an original series. Using a number of key target predictions...... for the future climate, such as winter and summer precipitation, and representation of extreme events, the resampled historical series are projected to represent rainfall properties in a future climate. Climate-projected rainfall series are simulated by brute force randomization of model parameters, which leads...
Morgan, Byron JT; Tanner, Martin Abba; Carlin, Bradley P
2008-01-01
Introduction and Examples Introduction Examples of data sets Basic Model Fitting Introduction Maximum-likelihood estimation for a geometric model Maximum-likelihood for the beta-geometric model Modelling polyspermy Which model? What is a model for? Mechanistic models Function Optimisation Introduction MATLAB: graphs and finite differences Deterministic search methods Stochastic search methods Accuracy and a hybrid approach Basic Likelihood ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributi...
Stochastic ontogenetic growth model
West, B. J.; West, D.
2012-02-01
An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
A simple stochastic rainstorm generator for simulating spatially and temporally varying rainfall
Singer, M. B.; Michaelides, K.; Nichols, M.; Nearing, M. A.
2016-12-01
In semi-arid to arid drainage basins, rainstorms often control both water supply and flood risk to marginal communities of people. They also govern the availability of water to vegetation and other ecological communities, as well as spatial patterns of sediment, nutrient, and contaminant transport and deposition on local to basin scales. All of these landscape responses are sensitive to changes in climate that are projected to occur throughout western North America. Thus, it is important to improve characterization of rainstorms in a manner that enables statistical assessment of rainfall at spatial scales below that of existing gauging networks and the prediction of plausible manifestations of climate change. Here we present a simple, stochastic rainstorm generator that was created using data from a rich and dense network of rain gauges at the Walnut Gulch Experimental Watershed (WGEW) in SE Arizona, but which is applicable anywhere. We describe our methods for assembling pdfs of relevant rainstorm characteristics including total annual rainfall, storm area, storm center location, and storm duration. We also generate five fitted intensity-duration curves and apply a spatial rainfall gradient to generate precipitation at spatial scales below gauge spacing. The model then runs by Monte Carlo simulation in which a total annual rainfall is selected before we generate rainstorms until the annual precipitation total is reached. The procedure continues for decadal simulations. Thus, we keep track of the hydrologic impact of individual storms and the integral of precipitation over multiple decades. We first test the model using ensemble predictions until we reach statistical similarity to the input data from WGEW. We then employ the model to assess decadal precipitation under simulations of climate change in which we separately vary the distribution of total annual rainfall (trend in moisture) and the intensity-duration curves used for simulation (trends in storminess). We
Stochastically-forced Decadal Variability in Australian Rainfall
Taschetto, A.
2015-12-01
Iconic Australian dry and wet periods were driven by anomalous conditions in the tropical oceans, such as the worst short-term drought in the southeast in 1982 associated with the strong El Niño and the widespread "Big Wet" in 1974 linked with a La Niña event. The association with oceanic conditions makes droughts predictable to some extent. However, prediction can be difficult when there is no clear external forcing such as El Niños. Can dry spells be triggered and maintained with no ocean memory? In this study, we investigate the potential role of internal multi-century atmospheric variability in controlling the frequency, duration and intensity of long-term dry and wet spells over Australia. Two multi-century-scale simulations were performed with the NCAR CESM: (1) a fully-coupled simulation (CPLD) and (2) an atmospheric simulation forced by a seasonal SST climatology derived from the coupled experiment (ACGM). Results reveal that droughts and wet spells can indeed be generated by internal variability of the atmosphere. Those internally generated events are less severe than those forced by oceanic variability, however the duration of dry and wet spells longer than 3 years is comparable with and without the ocean memory. Large-scale ocean modes of variability seem to play an important role in producing continental-scale rainfall impacts over Australia. While the Pacific Decadal Oscillation plays an important role in generating droughts in the fully coupled model, perturbations of monsoonal winds seem to be the main trigger of dry spells in the AGCM case. Droughts in the mid-latitude regions such as Tasmania can be driven by perturbations in the Southern Annular Mode, not necessarily linked to oceanic conditions even in the fully-coupled model. The mechanisms behind internally-driven mega-droughts and mega-wets will be discussed.
Alternative Asymmetric Stochastic Volatility Models
M. Asai (Manabu); M.J. McAleer (Michael)
2010-01-01
textabstractThe stochastic volatility model usually incorporates asymmetric effects by introducing the negative correlation between the innovations in returns and volatility. In this paper, we propose a new asymmetric stochastic volatility model, based on the leverage and size effects. The model is
A stochastic assessment of the effect of global warming on rainfall ...
African Journals Online (AJOL)
Crop production depends on rainfall, and rainfall is affected by extreme weather conditions. Markov chain and time series model are adapted for the study of the pattern of rainfall in the North Central Region of Nigeria. Results reveal the long run distributions of the dry and wet days to be 0.7841, and 0.2159 respectively.
Directory of Open Access Journals (Sweden)
R. Uijlenhoet
2008-03-01
Full Text Available As rainfall constitutes the main source of water for the terrestrial hydrological processes, accurate and reliable measurement and prediction of its spatial and temporal distribution over a wide range of scales is an important goal for hydrology. We investigate the potential of ground-based weather radar to provide such measurements through a theoretical analysis of some of the associated observation uncertainties. A stochastic model of range profiles of raindrop size distributions is employed in a Monte Carlo simulation experiment to investigate the rainfall retrieval uncertainties associated with weather radars operating at X-, C-, and S-band. We focus in particular on the errors and uncertainties associated with rain-induced signal attenuation and its correction for incoherent, non-polarimetric, single-frequency, operational weather radars. The performance of two attenuation correction schemes, the (forward Hitschfeld-Bordan algorithm and the (backward Marzoug-Amayenc algorithm, is analyzed for both moderate (assuming a 50 km path length and intense Mediterranean rainfall (for a 30 km path. A comparison shows that the backward correction algorithm is more stable and accurate than the forward algorithm (with a bias in the order of a few percent for the former, compared to tens of percent for the latter, provided reliable estimates of the total path-integrated attenuation are available. Moreover, the bias and root mean square error associated with each algorithm are quantified as a function of path-averaged rain rate and distance from the radar in order to provide a plausible order of magnitude for the uncertainty in radar-retrieved rain rates for hydrological applications.
Statistical Modelling of Extreme Rainfall in Taiwan
L-F. Chu (Lan-Fen); M.J. McAleer (Michael); C-C. Chang (Ching-Chung)
2012-01-01
textabstractIn this paper, the annual maximum daily rainfall data from 1961 to 2010 are modelled for 18 stations in Taiwan. We fit the rainfall data with stationary and non-stationary generalized extreme value distributions (GEV), and estimate their future behaviour based on the best fitting model.
Statistical Modelling of Extreme Rainfall in Taiwan
L. Chu (LanFen); M.J. McAleer (Michael); C-H. Chang (Chu-Hsiang)
2013-01-01
textabstractIn this paper, the annual maximum daily rainfall data from 1961 to 2010 are modelled for 18 stations in Taiwan. We fit the rainfall data with stationary and non-stationary generalized extreme value distributions (GEV), and estimate their future behaviour based on the best fitting model.
Stochastic Models of Polymer Systems
2016-01-01
Distribution Unlimited Final Report: Stochastic Models of Polymer Systems The views, opinions and/or findings contained in this report are those of the...ADDRESS. Princeton University PO Box 0036 87 Prospect Avenue - 2nd floor Princeton, NJ 08544 -2020 14-Mar-2014 ABSTRACT Number of Papers published in...peer-reviewed journals: Number of Papers published in non peer-reviewed journals: Final Report: Stochastic Models of Polymer Systems Report Title
Downscaling of rainfall in Peru using Generalised Linear Models
Bergin, E.; Buytaert, W.; Onof, C.; Wheater, H.
2012-04-01
The assessment of water resources in the Peruvian Andes is particularly important because the Peruvian economy relies heavily on agriculture. Much of the agricultural land is situated near to the coast and relies on large quantities of water for irrigation. The simulation of synthetic rainfall series is thus important to evaluate the reliability of water supplies for current and future scenarios of climate change. In addition to water resources concerns, there is also a need to understand extreme heavy rainfall events, as there was significant flooding in Machu Picchu in 2010. The region exhibits a reduction of rainfall in 1983, associated with El Nino Southern Oscillation (SOI). NCEP Reanalysis 1 data was used to provide weather variable data. Correlations were calculated for several weather variables using raingauge data in the Andes. These were used to evaluate teleconnections and provide suggested covariates for the downscaling model. External covariates used in the model include sea level pressure and sea surface temperature over the region of the Humboldt Current. Relative humidity and temperature data over the region are also included. The SOI teleconnection is also used. Covariates are standardised using observations for 1960-1990. The GlimClim downscaling model was used to fit a stochastic daily rainfall model to 13 sites in the Peruvian Andes. Results indicate that the model is able to reproduce rainfall statistics well, despite the large area used. Although the correlation between individual rain gauges is generally quite low, all sites are affected by similar weather patterns. This is an assumption of the GlimClim downscaling model. Climate change scenarios are considered using several GCM outputs for the A1B scenario. GCM data was corrected for bias using 1960-1990 outputs from the 20C3M scenario. Rainfall statistics for current and future scenarios are compared. The region shows an overall decrease in mean rainfall but with an increase in variance.
Stochastic Still Water Response Model
DEFF Research Database (Denmark)
Friis-Hansen, Peter; Ditlevsen, Ove Dalager
2002-01-01
In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model is...... out that an important parameter of the stochastic cargo field model is the mean number of containers delivered by each customer.......In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model...... is to establish the stochastic load field conditional on a given draft and trim of the vessel. The model contributes to a realistic modelling of the stochastic load processes to be used in a reliability evaluation of the ship hull. Emphasis is given to container vessels. The formulation of the model for obtaining...
Stochastic models: theory and simulation.
Energy Technology Data Exchange (ETDEWEB)
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Stochastic models of cell motility
DEFF Research Database (Denmark)
Gradinaru, Cristian
2012-01-01
Cell motility and migration are central to the development and maintenance of multicellular organisms, and errors during this process can lead to major diseases. Consequently, the mechanisms and phenomenology of cell motility are currently under intense study. In recent years, a new...... interdisciplinary field focusing on the study of biological processes at the nanoscale level, with a range of technological applications in medicine and biological research, has emerged. The work presented in this thesis is at the interface of cell biology, image processing, and stochastic modeling. The stochastic...... models introduced here are based on persistent random motion, which I apply to real-life studies of cell motility on flat and nanostructured surfaces. These models aim to predict the time-dependent position of cell centroids in a stochastic manner, and conversely determine directly from experimental...
Stochastic Modelling of Hydrologic Systems
DEFF Research Database (Denmark)
Jonsdottir, Harpa
2007-01-01
In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains...... an introduction and an overview of the papers published. Then an introduction to basic concepts in hydrology along with a description of hydrological data is given. Finally an introduction to stochastic modelling is given. The second part contains the research papers. In the research papers the stochastic methods...... are described, as at the time of publication these methods represent new contribution to hydrology. The second part also contains additional description of software used and a brief introduction to stiff systems. The system in one of the papers is stiff....
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Stochastic Volatility and DSGE Models
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper argues that a specification of stochastic volatility commonly used to analyze the Great Moderation in DSGE models may not be appropriate, because the level of a process with this specification does not have conditional or unconditional moments. This is unfortunate because agents may...
Stochastic-field cavitation model
International Nuclear Information System (INIS)
Dumond, J.; Magagnato, F.; Class, A.
2013-01-01
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations
Stochastic-field cavitation model
Dumond, J.; Magagnato, F.; Class, A.
2013-07-01
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
A Fractionally Integrated Wishart Stochastic Volatility Model
M. Asai (Manabu); M.J. McAleer (Michael)
2013-01-01
textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of
Transport properties of stochastic Lorentz models
Beijeren, H. van
Diffusion processes are considered for one-dimensional stochastic Lorentz models, consisting of randomly distributed fixed scatterers and one moving light particle. In waiting time Lorentz models the light particle makes instantaneous jumps between scatterers after a stochastically distributed
Peleg, Nadav; Blumensaat, Frank; Molnar, Peter; Fatichi, Simone; Burlando, Paolo
2017-03-01
The performance of urban drainage systems is typically examined using hydrological and hydrodynamic models where rainfall input is uniformly distributed, i.e., derived from a single or very few rain gauges. When models are fed with a single uniformly distributed rainfall realization, the response of the urban drainage system to the rainfall variability remains unexplored. The goal of this study was to understand how climate variability and spatial rainfall variability, jointly or individually considered, affect the response of a calibrated hydrodynamic urban drainage model. A stochastic spatially distributed rainfall generator (STREAP - Space-Time Realizations of Areal Precipitation) was used to simulate many realizations of rainfall for a 30-year period, accounting for both climate variability and spatial rainfall variability. The generated rainfall ensemble was used as input into a calibrated hydrodynamic model (EPA SWMM - the US EPA's Storm Water Management Model) to simulate surface runoff and channel flow in a small urban catchment in the city of Lucerne, Switzerland. The variability of peak flows in response to rainfall of different return periods was evaluated at three different locations in the urban drainage network and partitioned among its sources. The main contribution to the total flow variability was found to originate from the natural climate variability (on average over 74 %). In addition, the relative contribution of the spatial rainfall variability to the total flow variability was found to increase with longer return periods. This suggests that while the use of spatially distributed rainfall data can supply valuable information for sewer network design (typically based on rainfall with return periods from 5 to 15 years), there is a more pronounced relevance when conducting flood risk assessments for larger return periods. The results show the importance of using multiple distributed rainfall realizations in urban hydrology studies to capture the
Quasi-continuous stochastic simulation framework for flood modelling
Moustakis, Yiannis; Kossieris, Panagiotis; Tsoukalas, Ioannis; Efstratiadis, Andreas
2017-04-01
Typically, flood modelling in the context of everyday engineering practices is addressed through event-based deterministic tools, e.g., the well-known SCS-CN method. A major shortcoming of such approaches is the ignorance of uncertainty, which is associated with the variability of soil moisture conditions and the variability of rainfall during the storm event.In event-based modeling, the sole expression of uncertainty is the return period of the design storm, which is assumed to represent the acceptable risk of all output quantities (flood volume, peak discharge, etc.). On the other hand, the varying antecedent soil moisture conditions across the basin are represented by means of scenarios (e.g., the three AMC types by SCS),while the temporal distribution of rainfall is represented through standard deterministic patterns (e.g., the alternative blocks method). In order to address these major inconsistencies,simultaneously preserving the simplicity and parsimony of the SCS-CN method, we have developed a quasi-continuous stochastic simulation approach, comprising the following steps: (1) generation of synthetic daily rainfall time series; (2) update of potential maximum soil moisture retention, on the basis of accumulated five-day rainfall; (3) estimation of daily runoff through the SCS-CN formula, using as inputs the daily rainfall and the updated value of soil moisture retention;(4) selection of extreme events and application of the standard SCS-CN procedure for each specific event, on the basis of synthetic rainfall.This scheme requires the use of two stochastic modelling components, namely the CastaliaR model, for the generation of synthetic daily data, and the HyetosMinute model, for the disaggregation of daily rainfall to finer temporal scales. Outcomes of this approach are a large number of synthetic flood events, allowing for expressing the design variables in statistical terms and thus properly evaluating the flood risk.
Modelling rainfall erosion resulting from climate change
Kinnell, Peter
2016-04-01
It is well known that soil erosion leads to agricultural productivity decline and contributes to water quality decline. The current widely used models for determining soil erosion for management purposes in agriculture focus on long term (~20 years) average annual soil loss and are not well suited to determining variations that occur over short timespans and as a result of climate change. Soil loss resulting from rainfall erosion is directly dependent on the product of runoff and sediment concentration both of which are likely to be influenced by climate change. This presentation demonstrates the capacity of models like the USLE, USLE-M and WEPP to predict variations in runoff and erosion associated with rainfall events eroding bare fallow plots in the USA with a view to modelling rainfall erosion in areas subject to climate change.
Stochastic diffusion models for substitutable technological innovations
Wang, L.; Hu, B.; Yu, X.
2004-01-01
Based on the analysis of firms' stochastic adoption behaviour, this paper first points out the necessity to build more practical stochastic models. And then, stochastic evolutionary models are built for substitutable innovation diffusion system. Finally, through the computer simulation of the
Research on nonlinear stochastic dynamical price model
International Nuclear Information System (INIS)
Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng
2008-01-01
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies
A space-time hybrid hourly rainfall model for derived flood frequency analysis
Directory of Open Access Journals (Sweden)
U. Haberlandt
2008-12-01
Full Text Available For derived flood frequency analysis based on hydrological modelling long continuous precipitation time series with high temporal resolution are needed. Often, the observation network with recording rainfall gauges is poor, especially regarding the limited length of the available rainfall time series. Stochastic precipitation synthesis is a good alternative either to extend or to regionalise rainfall series to provide adequate input for long-term rainfall-runoff modelling with subsequent estimation of design floods. Here, a new two step procedure for stochastic synthesis of continuous hourly space-time rainfall is proposed and tested for the extension of short observed precipitation time series.
First, a single-site alternating renewal model is presented to simulate independent hourly precipitation time series for several locations. The alternating renewal model describes wet spell durations, dry spell durations and wet spell intensities using univariate frequency distributions separately for two seasons. The dependence between wet spell intensity and duration is accounted for by 2-copulas. For disaggregation of the wet spells into hourly intensities a predefined profile is used. In the second step a multi-site resampling procedure is applied on the synthetic point rainfall event series to reproduce the spatial dependence structure of rainfall. Resampling is carried out successively on all synthetic event series using simulated annealing with an objective function considering three bivariate spatial rainfall characteristics. In a case study synthetic precipitation is generated for some locations with short observation records in two mesoscale catchments of the Bode river basin located in northern Germany. The synthetic rainfall data are then applied for derived flood frequency analysis using the hydrological model HEC-HMS. The results show good performance in reproducing average and extreme rainfall characteristics as well as in
Stochastic models for atmospheric dispersion
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2003-01-01
Simple stochastic differential equation models have been applied by several researchers to describe the dispersion of tracer particles in the planetary atmospheric boundary layer and to form the basis for computer simulations of particle paths. To obtain the drift coefficient, empirical vertical...... positions close to the boundaries. Different rules have been suggested in the literature with justifications based on simulation studies. Herein the relevant stochastic differential equation model is formulated in a particular way. The formulation is based on the marginal transformation of the position...... velocity distributions that depend on height above the ground both with respect to standard deviation and skewness are substituted into the stationary Fokker/Planck equation. The particle position distribution is taken to be uniform *the well/mixed condition( and also a given dispersion coefficient...
Further developments of the Neyman-Scott clustered point process for modeling rainfall
Cowpertwait, Paul S. P.
1991-07-01
This paper provides some useful results for modeling rainfall. It extends work on the Neyman-Scott cluster model for simulating rainfall time series. Several important properties have previously been found for the model, for example, the expectation and variance of the amount of rain captured in an arbitrary time interval (Rodriguez-Iturbe et al., 1987a), In this paper additional properties are derived, such as the probability of an arbitrary interval of any chosen length being dry. In applications this is a desirable property to have, and is often used for fitting stochastic rainfall models to field data. The model is currently being used in rainfall time series research directed toward improving sewage systems in the United Kingdom. To illustrate the model's performance an example is given, where the model is fitted to 10 years of hourly data taken from Blackpool, England.
Stochastic modeling and analysis of telecoms networks
Decreusefond, Laurent
2012-01-01
This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems.The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an
Doubly stochastic Poisson process models for precipitation at fine time-scales
Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao
2012-09-01
This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.
DEFF Research Database (Denmark)
Löwe, Roland; Mikkelsen, Peter Steen; Madsen, Henrik
2014-01-01
Probabilistic runoff forecasts generated by stochastic greybox models can be notably useful for the improvement of the decision-making process in real-time control setups for urban drainage systems because the prediction risk relationships in these systems are often highly nonlinear. To date...... the identification of models for cases with noisy in-sewer observations. For the prediction of the overflow risk, no improvement was demonstrated through the application of stochastic forecasts instead of point predictions, although this result is thought to be caused by the notably simplified setup used...
Stochastic modeling analysis and simulation
Nelson, Barry L
1995-01-01
A coherent introduction to the techniques for modeling dynamic stochastic systems, this volume also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Suitable for advanced undergraduates and graduate-level industrial engineers and management science majors, it proposes modeling systems in terms of their simulation, regardless of whether simulation is employed for analysis. Beginning with a view of the conditions that permit a mathematical-numerical analysis, the text explores Poisson and renewal processes, Markov chains in discrete and continuous time, se
Stochastic Subspace Modelling of Turbulence
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Pedersen, B. J.; Nielsen, Søren R.K.
2009-01-01
positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modelling method is proposed which allows selection of an appropriate model order......, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modelling method.......Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper...
Stochastic models, estimation, and control
Maybeck, Peter S
1982-01-01
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
Censored rainfall modelling for estimation of fine-scale extremes
Cross, David; Onof, Christian; Winter, Hugo; Bernardara, Pietro
2018-01-01
Reliable estimation of rainfall extremes is essential for drainage system design, flood mitigation, and risk quantification. However, traditional techniques lack physical realism and extrapolation can be highly uncertain. In this study, we improve the physical basis for short-duration extreme rainfall estimation by simulating the heavy portion of the rainfall record mechanistically using the Bartlett-Lewis rectangular pulse (BLRP) model. Mechanistic rainfall models have had a tendency to underestimate rainfall extremes at fine temporal scales. Despite this, the simple process representation of rectangular pulse models is appealing in the context of extreme rainfall estimation because it emulates the known phenomenology of rainfall generation. A censored approach to Bartlett-Lewis model calibration is proposed and performed for single-site rainfall from two gauges in the UK and Germany. Extreme rainfall estimation is performed for each gauge at the 5, 15, and 60 min resolutions, and considerations for censor selection discussed.
Sequential neural models with stochastic layers
DEFF Research Database (Denmark)
Fraccaro, Marco; Sønderby, Søren Kaae; Paquet, Ulrich
2016-01-01
How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural...... generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over...
A stochastic model of hormesis
International Nuclear Information System (INIS)
Yakovlev, A.Yu.; Tsodikov, A.D.; Bass, L.
1993-01-01
In order to describe the life-prolonging effect of some agents that are harmful at higher doses, ionizing radiations in particular, a stochastic model is developed in terms of accumulation and progression of intracellular lesions caused by the environment and by the agent itself. The processes of lesion repair, operating at the molecular and cellular level, are assumed to be responsible for this hormesis effect within the framework of the proposed model. Properties of lifetime distributions, derived for analysis of animal experiments with prolonged and acute irradiation, are given special attention. The model provides efficient means of interpreting experimental findings, as evidenced by its application to analysis of some published data on the hormetic effects of prolonged irradiation and of procaine on animal longevity. 51 refs., 2 figs., 1 tabs
Stochastic models for tumoral growth
Escudero, Carlos
2006-02-01
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border and the surface diffusion of cells at the growing edge. Tumor growth is thus conceived as a competition for space between the tumor and the host, and cell diffusion at the tumor border is an optimal strategy adopted for minimizing the pressure and helping tumor development. Two stochastic partial differential equations are reported in this paper in order to correctly model the physical properties of tumoral growth in (1+1) and (2+1) dimensions. The advantage of these models is that they reproduce the correct geometry of the tumor and are defined in terms of polar variables. An analysis of these models allows us to quantitatively estimate the response of the tumor to an unfavorable perturbation during growth.
The modified turning bands (MTB) model for space-time rainfall. I. Model definition and properties
Mellor, Dale
1996-02-01
A new stochastic model of space-time rainfall, the Modified Turning Bands (MTB) model, is proposed which reproduces, in particular, the movements and developments of rainbands, cluster potential regions and raincells, as well as their respective interactions. The ensemble correlation structure is unsuitable for practical estimation of the model parameters because the model is not ergodic in this statistic, and hence it cannot easily be measured from a single real storm. Thus, some general theory on the internal covariance structure of a class of stochastic models is presented, of which the MTB model is an example. It is noted that, for the MTB model, the internal covariance structure may be measured from a single storm, and can thus be used for model identification.
Temporal rainfall estimation using input data reduction and model inversion
Wright, A. J.; Vrugt, J. A.; Walker, J. P.; Pauwels, V. R. N.
2016-12-01
Floods are devastating natural hazards. To provide accurate, precise and timely flood forecasts there is a need to understand the uncertainties associated with temporal rainfall and model parameters. The estimation of temporal rainfall and model parameter distributions from streamflow observations in complex dynamic catchments adds skill to current areal rainfall estimation methods, allows for the uncertainty of rainfall input to be considered when estimating model parameters and provides the ability to estimate rainfall from poorly gauged catchments. Current methods to estimate temporal rainfall distributions from streamflow are unable to adequately explain and invert complex non-linear hydrologic systems. This study uses the Discrete Wavelet Transform (DWT) to reduce rainfall dimensionality for the catchment of Warwick, Queensland, Australia. The reduction of rainfall to DWT coefficients allows the input rainfall time series to be simultaneously estimated along with model parameters. The estimation process is conducted using multi-chain Markov chain Monte Carlo simulation with the DREAMZS algorithm. The use of a likelihood function that considers both rainfall and streamflow error allows for model parameter and temporal rainfall distributions to be estimated. Estimation of the wavelet approximation coefficients of lower order decomposition structures was able to estimate the most realistic temporal rainfall distributions. These rainfall estimates were all able to simulate streamflow that was superior to the results of a traditional calibration approach. It is shown that the choice of wavelet has a considerable impact on the robustness of the inversion. The results demonstrate that streamflow data contains sufficient information to estimate temporal rainfall and model parameter distributions. The extent and variance of rainfall time series that are able to simulate streamflow that is superior to that simulated by a traditional calibration approach is a
Stochastic hyperfine interactions modeling library
Zacate, Matthew O.; Evenson, William E.
2011-04-01
The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. In addition, example code is provided to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A can be neglected. Program summaryProgram title: SHIML Catalogue identifier: AEIF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 3 No. of lines in distributed program, including test data, etc.: 8224 No. of bytes in distributed program, including test data, etc.: 312 348 Distribution format: tar.gz Programming language: C Computer: Any Operating system: LINUX, OS X RAM: Varies Classification: 7.4 External routines: TAPP [1], BLAS [2], a C-interface to BLAS [3], and LAPACK [4] Nature of problem: In condensed matter systems, hyperfine methods such as nuclear magnetic resonance (NMR), Mössbauer effect (ME), muon spin rotation (μSR), and perturbed angular correlation spectroscopy (PAC) measure electronic and magnetic structure within Angstroms of nuclear probes through the hyperfine interaction. When
CAM Stochastic Volatility Model for Option Pricing
Directory of Open Access Journals (Sweden)
Wanwan Huang
2016-01-01
Full Text Available The coupled additive and multiplicative (CAM noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks of the model. We also derive an approximation for the characteristic function of the model.
Consistent Stochastic Modelling of Meteocean Design Parameters
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Sterndorff, M. J.
2000-01-01
Consistent stochastic models of metocean design parameters and their directional dependencies are essential for reliability assessment of offshore structures. In this paper a stochastic model for the annual maximum values of the significant wave height, and the associated wind velocity, current...
Stochastic quantization for the axial model
International Nuclear Information System (INIS)
Farina, C.; Montani, H.; Albuquerque, L.C.
1991-01-01
We use bosonization ideas to solve the axial model in the stochastic quantization framework. We obtain the fermion propagator of the theory decoupling directly the Langevin equation, instead of the Fokker-Planck equation. In the Appendix we calculate explicitly the anomalous divergence of the axial-vector current by using a regularization that does not break the Markovian character of the stochastic process
Stochastic models of intracellular transport
Bressloff, Paul C.
2013-01-09
The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an overdamped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of adenosine triphosphate hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review a wide range of analytical methods and models of intracellular transport is presented. In the case of diffusive transport, narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion are considered. In the case of active transport, Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean-field approximations are considered. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self-organization of subcellular structures. © 2013 American Physical Society.
STOCHASTIC CHARACTERISTICS AND MODELING OF RELATIVE ...
African Journals Online (AJOL)
Test
Results are highly accurate and promising for all models based on Lewis' criteria. ... hydrological cycle. Future increases in ... STOCHASTIC CHARACTERISTICS AND MODELING OF RELATIVE HUMIDITY OF OGUN BASIN, NIGERIA. 71 ...
Towards Model Checking Stochastic Process Algebra
Hermanns, H.; Grieskamp, W.; Santen, T.; Katoen, Joost P.; Stoddart, B.; Meyer-Kayser, J.; Siegle, M.
2000-01-01
Stochastic process algebras have been proven useful because they allow behaviour-oriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviour- oriented style supports composition and abstraction in a natural way. However, analysis of
Stochastic biomathematical models with applications to neuronal modeling
Batzel, Jerry; Ditlevsen, Susanne
2013-01-01
Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.
Stochasticity and determinism in models of hematopoiesis.
Kimmel, Marek
2014-01-01
This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.
Modeling and analysis of stochastic systems
Kulkarni, Vidyadhar G
2011-01-01
Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edi
Directory of Open Access Journals (Sweden)
Ibsen Chivatá Cárdenas
2008-05-01
Full Text Available This article presents a rainfall model constructed by applying non-parametric modelling and imprecise probabilities; these tools were used because there was not enough homogeneous information in the study area. The area’s hydro-logical information regarding rainfall was scarce and existing hydrological time series were not uniform. A distributed extended rainfall model was constructed from so-called probability boxes (p-boxes, multinomial probability distribu-tion and confidence intervals (a friendly algorithm was constructed for non-parametric modelling by combining the last two tools. This model confirmed the high level of uncertainty involved in local rainfall modelling. Uncertainty en-compassed the whole range (domain of probability values thereby showing the severe limitations on information, leading to the conclusion that a detailed estimation of probability would lead to significant error. Nevertheless, rele-vant information was extracted; it was estimated that maximum daily rainfall threshold (70 mm would be surpassed at least once every three years and the magnitude of uncertainty affecting hydrological parameter estimation. This paper’s conclusions may be of interest to non-parametric modellers and decisions-makers as such modelling and imprecise probability represents an alternative for hydrological variable assessment and maybe an obligatory proce-dure in the future. Its potential lies in treating scarce information and represents a robust modelling strategy for non-seasonal stochastic modelling conditions
Modelling and application of stochastic processes
1986-01-01
The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side,...
Numerical Simulation of the Heston Model under Stochastic Correlation
Directory of Open Access Journals (Sweden)
Long Teng
2017-12-01
Full Text Available Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation. We discuss the efficient algorithms for the extended Heston model by incorporating stochastic correlations. Our numerical experiments show that the proposed algorithms can efficiently provide highly accurate results for the extended Heston by including stochastic correlations. By investigating the effect of stochastic correlations on the implied volatility, we find that the performance of the Heston model can be proved by including stochastic correlations.
Maggioni, V.; Anagnostou, E. N.; Reichle, R. H.
2013-01-01
The contribution of rainfall forcing errors relative to model (structural and parameter) uncertainty in the prediction of soil moisture is investigated by integrating the NASA Catchment Land Surface Model (CLSM), forced with hydro-meteorological data, in the Oklahoma region. Rainfall-forcing uncertainty is introduced using a stochastic error model that generates ensemble rainfall fields from satellite rainfall products. The ensemble satellite rain fields are propagated through CLSM to produce soil moisture ensembles. Errors in CLSM are modeled with two different approaches: either by perturbing model parameters (representing model parameter uncertainty) or by adding randomly generated noise (representing model structure and parameter uncertainty) to the model prognostic variables. Our findings highlight that the method currently used in the NASA GEOS-5 Land Data Assimilation System to perturb CLSM variables poorly describes the uncertainty in the predicted soil moisture, even when combined with rainfall model perturbations. On the other hand, by adding model parameter perturbations to rainfall forcing perturbations, a better characterization of uncertainty in soil moisture simulations is observed. Specifically, an analysis of the rank histograms shows that the most consistent ensemble of soil moisture is obtained by combining rainfall and model parameter perturbations. When rainfall forcing and model prognostic perturbations are added, the rank histogram shows a U-shape at the domain average scale, which corresponds to a lack of variability in the forecast ensemble. The more accurate estimation of the soil moisture prediction uncertainty obtained by combining rainfall and parameter perturbations is encouraging for the application of this approach in ensemble data assimilation systems.
Mathematical and physical modeling of rainfall in centrifuge
CAICEDO, Bernardo; THOREL, Luc; TRISTANCHO, Julian
2015-01-01
Rainfall simulation in centrifuge models is important for modelling soil-atmosphere interactions. However, the presence of Coriolis force, drag forces, evaporation and wind within the centrifuge may affect the distribution of rainfall over the model. As a result, development of appropriate centrifuge rain simulators requires a demanding process of experimental trial and error. This paper highlights the key factors involved in controlling rainfall in centrifuge simulations, develops a mathemat...
Modeling Daily Rainfall Conditional on Atmospheric Predictors: An application to Western Greece
Langousis, Andreas; Kaleris, Vassilios
2013-04-01
Due to its intermittent and highly variable character, daily precipitation is the least well reproduced hydrologic variable by both General Circulation Models (GCMs) and Limited Area Models (LAMs). To that extent, several statistical procedures (usually referred to as downscaling schemes) have been suggested to generate synthetic rainfall time series conditional on predictor variables that are descriptive of the atmospheric circulation at the mesoscale. In addition to be more accurately simulated by GCMs and LAMs, large-scale atmospheric predictors are important indicators of the local weather. Currently used downscaling methods simulate rainfall series using either stable statistical relationships (usually referred to as transfer functions) between certain characteristics of the rainfall process and mesoscale atmospheric predictor variables, or simple stochastic schemes (e.g. properly transformed autoregressive models) with parameters that depend on the large-scale atmospheric conditions. The latter are determined by classifying large-scale circulation patterns into broad categories of weather states, using empirical or theoretically based classification schemes, and modeled by resampling from those categories; a process usually referred to as weather generation. In this work we propose a statistical framework to generate synthetic rainfall timeseries at a daily level, conditional on large scale atmospheric predictors. The latter include the mean sea level pressure (MSLP), the magnitude and direction of upper level geostrophic winds, and the 500 hPa geopotential height, relative vorticity and divergence. The suggested framework operates in continuous time, avoiding the use of transfer functions, and weather classification schemes. The suggested downscaling approach is validated using atmospheric data from the ERA-Interim archive (see http://www.ecmwf.int/research/era/do/get/index), and daily rainfall data from Western Greece, for the 14-year period from 01 October
Scalable inference for stochastic block models
Peng, Chengbin; Zhang, Zhihua; Wong, Ka-Chun; Zhang, Xiangliang; Keyes, David E.
2017-01-01
Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of "big data," traditional inference
Stochastic interest rates model in compounding | Galadima ...
African Journals Online (AJOL)
Stochastic interest rates model in compounding. ... in finance, real estate, insurance, accounting and other areas of business administration. The assumption that future rates are fixed and known with certainty at the beginning of an investment, ...
Moment Closure for the Stochastic Logistic Model
National Research Council Canada - National Science Library
Singh, Abhyudai; Hespanha, Joao P
2006-01-01
..., which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model...
A stochastic model of enzyme kinetics
Stefanini, Marianne; Newman, Timothy; McKane, Alan
2003-10-01
Enzyme kinetics is generally modeled by deterministic rate equations, and in the simplest case leads to the well-known Michaelis-Menten equation. It is plausible that stochastic effects will play an important role at low enzyme concentrations. We have addressed this by constructing a simple stochastic model which can be exactly solved in the steady-state. Throughout a wide range of parameter values Michaelis-Menten dynamics is replaced by a new and simple theoretical result.
Electricity price modeling with stochastic time change
International Nuclear Information System (INIS)
Borovkova, Svetlana; Schmeck, Maren Diane
2017-01-01
In this paper, we develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. This technique allows us to incorporate the characteristic features of electricity prices (such as seasonal volatility, time varying mean reversion and seasonally occurring price spikes) into the model in an elegant and economically justifiable way. The stochastic time change introduces stochastic as well as deterministic (e.g., seasonal) features in the price process' volatility and in the jump component. We specify the base process as a mean reverting jump diffusion and the time change as an absolutely continuous stochastic process with seasonal component. The activity rate of the stochastic time change can be related to the factors that influence supply and demand. Here we use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change, and show that this choice leads to realistic price paths. We derive properties of the resulting price process and develop the model calibration procedure. We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths by Monte Carlo simulations. We show that the simulated price process matches the distributional characteristics of the observed electricity prices in periods of both high and low demand. - Highlights: • We develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. • We incorporate the characteristic features of electricity prices, such as seasonal volatility and spikes into the model. • We use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change • We derive properties of the resulting price process and develop the model calibration procedure. • We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths.
Modelling Cow Behaviour Using Stochastic Automata
DEFF Research Database (Denmark)
Jónsson, Ragnar Ingi
This report covers an initial study on the modelling of cow behaviour using stochastic automata with the aim of detecting lameness. Lameness in cows is a serious problem that needs to be dealt with because it results in less profitable production units and in reduced quality of life...... for the affected livestock. By featuring training data consisting of measurements of cow activity, three different models are obtained, namely an autonomous stochastic automaton, a stochastic automaton with coinciding state and output and an autonomous stochastic automaton with coinciding state and output, all...... of which describe the cows' activity in the two regarded behavioural scenarios, non-lame and lame. Using the experimental measurement data the different behavioural relations for the two regarded behavioural scenarios are assessed. The three models comprise activity within last hour, activity within last...
A stochastic SIS epidemic model with vaccination
Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming
2017-11-01
In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while if R0s > 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.
Dynamics of a Stochastic Intraguild Predation Model
Directory of Open Access Journals (Sweden)
Zejing Xing
2016-04-01
Full Text Available Intraguild predation (IGP is a widespread ecological phenomenon which occurs when one predator species attacks another predator species with which it competes for a shared prey species. The objective of this paper is to study the dynamical properties of a stochastic intraguild predation model. We analyze stochastic persistence and extinction of the stochastic IGP model containing five cases and establish the sufficient criteria for global asymptotic stability of the positive solutions. This study shows that it is possible for the coexistence of three species under the influence of environmental noise, and that the noise may have a positive effect for IGP species. A stationary distribution of the stochastic IGP model is established and it has the ergodic property, suggesting that the time average of population size with the development of time is equal to the stationary distribution in space. Finally, we show that our results may be extended to two well-known biological systems: food chains and exploitative competition.
Computer Aided Continuous Time Stochastic Process Modelling
DEFF Research Database (Denmark)
Kristensen, N.R.; Madsen, Henrik; Jørgensen, Sten Bay
2001-01-01
A grey-box approach to process modelling that combines deterministic and stochastic modelling is advocated for identification of models for model-based control of batch and semi-batch processes. A computer-aided tool designed for supporting decision-making within the corresponding modelling cycle...
Stochastic Wake Modelling Based on POD Analysis
Directory of Open Access Journals (Sweden)
David Bastine
2018-03-01
Full Text Available In this work, large eddy simulation data is analysed to investigate a new stochastic modeling approach for the wake of a wind turbine. The data is generated by the large eddy simulation (LES model PALM combined with an actuator disk with rotation representing the turbine. After applying a proper orthogonal decomposition (POD, three different stochastic models for the weighting coefficients of the POD modes are deduced resulting in three different wake models. Their performance is investigated mainly on the basis of aeroelastic simulations of a wind turbine in the wake. Three different load cases and their statistical characteristics are compared for the original LES, truncated PODs and the stochastic wake models including different numbers of POD modes. It is shown that approximately six POD modes are enough to capture the load dynamics on large temporal scales. Modeling the weighting coefficients as independent stochastic processes leads to similar load characteristics as in the case of the truncated POD. To complete this simplified wake description, we show evidence that the small-scale dynamics can be captured by adding to our model a homogeneous turbulent field. In this way, we present a procedure to derive stochastic wake models from costly computational fluid dynamics (CFD calculations or elaborated experimental investigations. These numerically efficient models provide the added value of possible long-term studies. Depending on the aspects of interest, different minimalized models may be obtained.
DEFF Research Database (Denmark)
Löwe, Roland; Mikkelsen, Peter Steen; Madsen, Henrik
2012-01-01
We present stochastic flow forecasts to be used in a real-time control setup for urban drainage systems. The forecasts are generated using greybox models with rain gauge and radar rainfall observations as input. Predictions are evaluated as intervals rather than just mean values. We obtain...
Stochastic differential equations used to model conjugation
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo
Stochastic differential equations (SDEs) are used to model horizontal transfer of antibiotic resis- tance by conjugation. The model describes the concentration of donor, recipient, transconjugants and substrate. The strength of the SDE model over the traditional ODE models is that the noise can...
Stochastic Modeling of Traffic Air Pollution
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
2014-01-01
In this paper, modeling of traffic air pollution is discussed with special reference to infrastructures. A number of subjects related to health effects of air pollution and the different types of pollutants are briefly presented. A simple model for estimating the social cost of traffic related air...... and using simple Monte Carlo techniques to obtain a stochastic estimate of the costs of traffic air pollution for infrastructures....... pollution is derived. Several authors have published papers on this very complicated subject, but no stochastic modelling procedure have obtained general acceptance. The subject is discussed basis of a deterministic model. However, it is straightforward to modify this model to include uncertain parameters...
Stochastic differential equation model to Prendiville processes
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)
2015-10-22
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Stochastic differential equation model to Prendiville processes
International Nuclear Information System (INIS)
Granita; Bahar, Arifah
2015-01-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution
Infinite-degree-corrected stochastic block model
DEFF Research Database (Denmark)
Herlau, Tue; Schmidt, Mikkel Nørgaard; Mørup, Morten
2014-01-01
In stochastic block models, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A recent extension by Karrer and Newman [Karrer and Newman...... corrected stochastic block model as a nonparametric Bayesian model, incorporating a parameter to control the amount of degree correction that can then be inferred from data. Additionally, our formulation yields principled ways of inferring the number of groups as well as predicting missing links...
From complex to simple: interdisciplinary stochastic models
International Nuclear Information System (INIS)
Mazilu, D A; Zamora, G; Mazilu, I
2012-01-01
We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions for certain physical quantities, such as the time dependence of the length of the microtubules, and diffusion coefficients. The second one is a stochastic adsorption model with applications in surface deposition, epidemics and voter systems. We introduce the ‘empty interval method’ and show sample calculations for the time-dependent particle density. These models can serve as an introduction to the field of non-equilibrium statistical physics, and can also be used as a pedagogical tool to exemplify standard statistical physics concepts, such as random walks or the kinetic approach of the master equation. (paper)
DEFF Research Database (Denmark)
Löwe, Roland; Mikkelsen, Peter Steen; Rasmussen, Michael Robdrup
2013-01-01
Merging of radar rainfall data with rain gauge measurements is a common approach to overcome problems in deriving rain intensities from radar measurements. We extend an existing approach for adjustment of C-band radar data using state-space models and use the resulting rainfall intensities as input...... improves runoff forecasts compared with using the original radar data and that rain gauge measurements as forecast input are also outperformed. Combining the data merging approach with short-term rainfall forecasting algorithms may result in further improved runoff forecasts that can be used in real time...
Stochastic volatility models and Kelvin waves
Energy Technology Data Exchange (ETDEWEB)
Lipton, Alex [Merrill Lynch, Mlfc Main, 2 King Edward Street, London EC1A 1HQ (United Kingdom); Sepp, Artur [Merrill Lynch, 4 World Financial Center, New York, NY 10080 (United States)], E-mail: Alex_Lipton@ml.com, E-mail: Artur_Sepp@ml.com
2008-08-29
We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.
Stochastic volatility models and Kelvin waves
Lipton, Alex; Sepp, Artur
2008-08-01
We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.
Stochastic volatility models and Kelvin waves
International Nuclear Information System (INIS)
Lipton, Alex; Sepp, Artur
2008-01-01
We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics
Stochastic Modeling Of Wind Turbine Drivetrain Components
DEFF Research Database (Denmark)
Rafsanjani, Hesam Mirzaei; Sørensen, John Dalsgaard
2014-01-01
reliable components are needed for wind turbine. In this paper focus is on reliability of critical components in drivetrain such as bearings and shafts. High failure rates of these components imply a need for more reliable components. To estimate the reliability of these components, stochastic models...... are needed for initial defects and damage accumulation. In this paper, stochastic models are formulated considering some of the failure modes observed in these components. The models are based on theoretical considerations, manufacturing uncertainties, size effects of different scales. It is illustrated how...
Weather Derivatives and Stochastic Modelling of Temperature
Directory of Open Access Journals (Sweden)
Fred Espen Benth
2011-01-01
Full Text Available We propose a continuous-time autoregressive model for the temperature dynamics with volatility being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible enough to model temperature data accurately, and at the same time being analytically tractable. Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like cooling- and heating-degree days and cumulative average temperatures are computed, as well as option prices on them.
Modeling rainfall-runoff relationship using multivariate GARCH model
Modarres, R.; Ouarda, T. B. M. J.
2013-08-01
The traditional hydrologic time series approaches are used for modeling, simulating and forecasting conditional mean of hydrologic variables but neglect their time varying variance or the second order moment. This paper introduces the multivariate Generalized Autoregressive Conditional Heteroscedasticity (MGARCH) modeling approach to show how the variance-covariance relationship between hydrologic variables varies in time. These approaches are also useful to estimate the dynamic conditional correlation between hydrologic variables. To illustrate the novelty and usefulness of MGARCH models in hydrology, two major types of MGARCH models, the bivariate diagonal VECH and constant conditional correlation (CCC) models are applied to show the variance-covariance structure and cdynamic correlation in a rainfall-runoff process. The bivariate diagonal VECH-GARCH(1,1) and CCC-GARCH(1,1) models indicated both short-run and long-run persistency in the conditional variance-covariance matrix of the rainfall-runoff process. The conditional variance of rainfall appears to have a stronger persistency, especially long-run persistency, than the conditional variance of streamflow which shows a short-lived drastic increasing pattern and a stronger short-run persistency. The conditional covariance and conditional correlation coefficients have different features for each bivariate rainfall-runoff process with different degrees of stationarity and dynamic nonlinearity. The spatial and temporal pattern of variance-covariance features may reflect the signature of different physical and hydrological variables such as drainage area, topography, soil moisture and ground water fluctuations on the strength, stationarity and nonlinearity of the conditional variance-covariance for a rainfall-runoff process.
Application of the rainfall infiltration breakthrough (RIB) model for ...
African Journals Online (AJOL)
Application of the rainfall infiltration breakthrough (RIB) model for groundwater recharge estimation in west coastal South Africa. ... the data from Oudebosch with different rainfall and groundwater abstraction inputs are simulated to explore individual effects on water levels as well as recharge rate estimated on a daily basis.
PDS-Modelling and Regional Bayesian Estimation of Extreme Rainfalls
DEFF Research Database (Denmark)
Madsen, Henrik; Rosbjerg, Dan; Harremoës, Poul
1994-01-01
rainfalls. The method is applied to two variables: the total precipitation depth and the maximum 10-minute rain intensity of individual storms. On the basis of the atsite modelling a regional analysis is carried out. It is shown that the previous assumption of spatial homogeneity of extreme rainfalls...
Congo Basin rainfall climatology: can we believe the climate models?
Washington, Richard; James, Rachel; Pearce, Helen; Pokam, Wilfried M; Moufouma-Okia, Wilfran
2013-01-01
The Congo Basin is one of three key convective regions on the planet which, during the transition seasons, dominates global tropical rainfall. There is little agreement as to the distribution and quantity of rainfall across the basin with datasets differing by an order of magnitude in some seasons. The location of maximum rainfall is in the far eastern sector of the basin in some datasets but the far western edge of the basin in others during March to May. There is no consistent pattern to this rainfall distribution in satellite or model datasets. Resolving these differences is difficult without ground-based data. Moisture flux nevertheless emerges as a useful variable with which to study these differences. Climate models with weak (strong) or even divergent moisture flux over the basin are dry (wet). The paper suggests an approach, via a targeted field campaign, for generating useful climate information with which to confront rainfall products and climate models.
Stochastic Modelling Of The Repairable System
Directory of Open Access Journals (Sweden)
Andrzejczak Karol
2015-11-01
Full Text Available All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible. When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.
The stochastic resonance for the incidence function model of metapopulation
Li, Jiang-Cheng; Dong, Zhi-Wei; Zhou, Ruo-Wei; Li, Yun-Xian; Qian, Zhen-Wei
2017-06-01
A stochastic model with endogenous and exogenous periodicities is proposed in this paper on the basis of metapopulation dynamics to model the crop yield losses due to pests and diseases. The rationale is that crop yield losses occur because the physiology of the growing crop is negatively affected by pests and diseases in a dynamic way over time as crop both grows and develops. Metapopulation dynamics can thus be used to model the resultant crop yield losses. The stochastic metapopulation process is described by using the Simplified Incidence Function model (IFM). Compared to the original IFMs, endogenous and exogenous periodicities are considered in the proposed model to handle the cyclical patterns observed in pest infestations, diseases epidemics, and exogenous affecting factors such as temperature and rainfalls. Agricultural loss data in China are used to fit the proposed model. Experimental results demonstrate that: (1) Model with endogenous and exogenous periodicities is a better fit; (2) When the internal system fluctuations and external environmental fluctuations are negatively correlated, EIL or the cost of loss is monotonically increasing; when the internal system fluctuations and external environmental fluctuations are positively correlated, an outbreak of pests and diseases might occur; (3) If the internal system fluctuations and external environmental fluctuations are positively correlated, an optimal patch size can be identified which will greatly weaken the effects of external environmental influence and hence inhibit pest infestations and disease epidemics.
Dynamic Hydrological Modeling in Drylands with TRMM Based Rainfall
Directory of Open Access Journals (Sweden)
Elena Tarnavsky
2013-12-01
Full Text Available This paper introduces and evaluates DryMOD, a dynamic water balance model of the key hydrological process in drylands that is based on free, public-domain datasets. The rainfall model of DryMOD makes optimal use of spatially disaggregated Tropical Rainfall Measuring Mission (TRMM datasets to simulate hourly rainfall intensities at a spatial resolution of 1-km. Regional-scale applications of the model in seasonal catchments in Tunisia and Senegal characterize runoff and soil moisture distribution and dynamics in response to varying rainfall data inputs and soil properties. The results highlight the need for hourly-based rainfall simulation and for correcting TRMM 3B42 rainfall intensities for the fractional cover of rainfall (FCR. Without FCR correction and disaggregation to 1 km, TRMM 3B42 based rainfall intensities are too low to generate surface runoff and to induce substantial changes to soil moisture storage. The outcomes from the sensitivity analysis show that topsoil porosity is the most important soil property for simulation of runoff and soil moisture. Thus, we demonstrate the benefit of hydrological investigations at a scale, for which reliable information on soil profile characteristics exists and which is sufficiently fine to account for the heterogeneities of these. Where such information is available, application of DryMOD can assist in the spatial and temporal planning of water harvesting according to runoff-generating areas and the runoff ratio, as well as in the optimization of agricultural activities based on realistic representation of soil moisture conditions.
Compositional Modelling of Stochastic Hybrid Systems
Strubbe, S.N.
2005-01-01
In this thesis we present a modelling framework for compositional modelling of stochastic hybrid systems. Hybrid systems consist of a combination of continuous and discrete dynamics. The state space of a hybrid system is hybrid in the sense that it consists of a continuous component and a discrete
Some recent developments in stochastic volatility modelling
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Nicolato, Elisa; Shephard, N.
2002-01-01
This paper reviews and puts in context some of our recent work on stochastic volatility (SV) modelling for financial economics. Here our main focus is on: (i) the relationship between subordination and SV, (ii) OU based volatility models, (iii) exact option pricing, (iv) realized power variation...
Stochastic models for turbulent reacting flows
Energy Technology Data Exchange (ETDEWEB)
Kerstein, A. [Sandia National Laboratories, Livermore, CA (United States)
1993-12-01
The goal of this program is to develop and apply stochastic models of various processes occurring within turbulent reacting flows in order to identify the fundamental mechanisms governing these flows, to support experimental studies of these flows, and to further the development of comprehensive turbulent reacting flow models.
Gagnon, Patrick; Rousseau, Alain N.; Charron, Dominique; Fortin, Vincent; Audet, René
2017-11-01
Several businesses and industries rely on rainfall forecasts to support their day-to-day operations. To deal with the uncertainty associated with rainfall forecast, some meteorological organisations have developed products, such as ensemble forecasts. However, due to the intensive computational requirements of ensemble forecasts, the spatial resolution remains coarse. For example, Environment and Climate Change Canada's (ECCC) Global Ensemble Prediction System (GEPS) data is freely available on a 1-degree grid (about 100 km), while those of the so-called High Resolution Deterministic Prediction System (HRDPS) are available on a 2.5-km grid (about 40 times finer). Potential users are then left with the option of using either a high-resolution rainfall forecast without uncertainty estimation and/or an ensemble with a spectrum of plausible rainfall values, but at a coarser spatial scale. The objective of this study was to evaluate the added value of coupling the Gibbs Sampling Disaggregation Model (GSDM) with ECCC products to provide accurate, precise and consistent rainfall estimates at a fine spatial resolution (10-km) within a forecast framework (6-h). For 30, 6-h, rainfall events occurring within a 40,000-km2 area (Québec, Canada), results show that, using 100-km aggregated reference rainfall depths as input, statistics of the rainfall fields generated by GSDM were close to those of the 10-km reference field. However, in forecast mode, GSDM outcomes inherit of the ECCC forecast biases, resulting in a poor performance when GEPS data were used as input, mainly due to the inherent rainfall depth distribution of the latter product. Better performance was achieved when the Regional Deterministic Prediction System (RDPS), available on a 10-km grid and aggregated at 100-km, was used as input to GSDM. Nevertheless, most of the analyzed ensemble forecasts were weakly consistent. Some areas of improvement are identified herein.
Predicting Footbridge Response using Stochastic Load Models
DEFF Research Database (Denmark)
Pedersen, Lars; Frier, Christian
2013-01-01
Walking parameters such as step frequency, pedestrian mass, dynamic load factor, etc. are basically stochastic, although it is quite common to adapt deterministic models for these parameters. The present paper considers a stochastic approach to modeling the action of pedestrians, but when doing so...... decisions need to be made in terms of statistical distributions of walking parameters and in terms of the parameters describing the statistical distributions. The paper explores how sensitive computations of bridge response are to some of the decisions to be made in this respect. This is useful...
a stochastic assessment of the effect of global warming on rainfall
African Journals Online (AJOL)
PROF EKWUEME
KEYWORDS: Global Warming; Rainfall; Markov Process; Time Series; Agriculture. INTRODUCTION ... Central Region of Nigeria in the last three decades using .... r. Time. MSD: MAD: MAPE: Length: Moving Average. 68492.0. 229.3. 3806.2. 4.
A Stochastic Model for Malaria Transmission Dynamics
Directory of Open Access Journals (Sweden)
Rachel Waema Mbogo
2018-01-01
Full Text Available Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis. In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp. The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.
Modeling stochasticity in biochemical reaction networks
International Nuclear Information System (INIS)
Constantino, P H; Vlysidis, M; Smadbeck, P; Kaznessis, Y N
2016-01-01
Small biomolecular systems are inherently stochastic. Indeed, fluctuations of molecular species are substantial in living organisms and may result in significant variation in cellular phenotypes. The chemical master equation (CME) is the most detailed mathematical model that can describe stochastic behaviors. However, because of its complexity the CME has been solved for only few, very small reaction networks. As a result, the contribution of CME-based approaches to biology has been very limited. In this review we discuss the approach of solving CME by a set of differential equations of probability moments, called moment equations. We present different approaches to produce and to solve these equations, emphasizing the use of factorial moments and the zero information entropy closure scheme. We also provide information on the stability analysis of stochastic systems. Finally, we speculate on the utility of CME-based modeling formalisms, especially in the context of synthetic biology efforts. (topical review)
Seasonal predictability of Kiremt rainfall in coupled general circulation models
Gleixner, Stephanie; Keenlyside, Noel S.; Demissie, Teferi D.; Counillon, François; Wang, Yiguo; Viste, Ellen
2017-11-01
The Ethiopian economy and population is strongly dependent on rainfall. Operational seasonal predictions for the main rainy season (Kiremt, June-September) are based on statistical approaches with Pacific sea surface temperatures (SST) as the main predictor. Here we analyse dynamical predictions from 11 coupled general circulation models for the Kiremt seasons from 1985-2005 with the forecasts starting from the beginning of May. We find skillful predictions from three of the 11 models, but no model beats a simple linear prediction model based on the predicted Niño3.4 indices. The skill of the individual models for dynamically predicting Kiremt rainfall depends on the strength of the teleconnection between Kiremt rainfall and concurrent Pacific SST in the models. Models that do not simulate this teleconnection fail to capture the observed relationship between Kiremt rainfall and the large-scale Walker circulation.
Kossieris, Panagiotis; Makropoulos, Christos; Onof, Christian; Koutsoyiannis, Demetris
2018-01-01
Many hydrological applications, such as flood studies, require the use of long rainfall data at fine time scales varying from daily down to 1 min time step. However, in the real world there is limited availability of data at sub-hourly scales. To cope with this issue, stochastic disaggregation techniques are typically employed to produce possible, statistically consistent, rainfall events that aggregate up to the field data collected at coarser scales. A methodology for the stochastic disaggregation of rainfall at fine time scales was recently introduced, combining the Bartlett-Lewis process to generate rainfall events along with adjusting procedures to modify the lower-level variables (i.e., hourly) so as to be consistent with the higher-level one (i.e., daily). In the present paper, we extend the aforementioned scheme, initially designed and tested for the disaggregation of daily rainfall into hourly depths, for any sub-hourly time scale. In addition, we take advantage of the recent developments in Poisson-cluster processes incorporating in the methodology a Bartlett-Lewis model variant that introduces dependence between cell intensity and duration in order to capture the variability of rainfall at sub-hourly time scales. The disaggregation scheme is implemented in an R package, named HyetosMinute, to support disaggregation from daily down to 1-min time scale. The applicability of the methodology was assessed on a 5-min rainfall records collected in Bochum, Germany, comparing the performance of the above mentioned model variant against the original Bartlett-Lewis process (non-random with 5 parameters). The analysis shows that the disaggregation process reproduces adequately the most important statistical characteristics of rainfall at wide range of time scales, while the introduction of the model with dependent intensity-duration results in a better performance in terms of skewness, rainfall extremes and dry proportions.
Bayesian analysis of data and model error in rainfall-runoff hydrological models
Kavetski, D.; Franks, S. W.; Kuczera, G.
2004-12-01
A major unresolved issue in the identification and use of conceptual hydrologic models is realistic description of uncertainty in the data and model structure. In particular, hydrologic parameters often cannot be measured directly and must be inferred (calibrated) from observed forcing/response data (typically, rainfall and runoff). However, rainfall varies significantly in space and time, yet is often estimated from sparse gauge networks. Recent work showed that current calibration methods (e.g., standard least squares, multi-objective calibration, generalized likelihood uncertainty estimation) ignore forcing uncertainty and assume that the rainfall is known exactly. Consequently, they can yield strongly biased and misleading parameter estimates. This deficiency confounds attempts to reliably test model hypotheses, to generalize results across catchments (the regionalization problem) and to quantify predictive uncertainty when the hydrologic model is extrapolated. This paper continues the development of a Bayesian total error analysis (BATEA) methodology for the calibration and identification of hydrologic models, which explicitly incorporates the uncertainty in both the forcing and response data, and allows systematic model comparison based on residual model errors and formal Bayesian hypothesis testing (e.g., using Bayes factors). BATEA is based on explicit stochastic models for both forcing and response uncertainty, whereas current techniques focus solely on response errors. Hence, unlike existing methods, the BATEA parameter equations directly reflect the modeler's confidence in all the data. We compare several approaches to approximating the parameter distributions: a) full Markov Chain Monte Carlo methods and b) simplified approaches based on linear approximations. Studies using synthetic and real data from the US and Australia show that BATEA systematically reduces the parameter bias, leads to more meaningful model fits and allows model comparison taking
DEFF Research Database (Denmark)
Del Giudice, Dario; Löwe, Roland; Madsen, Henrik
2015-01-01
from different fields and have not yet been compared in environmental modeling. To compare the two approaches, we develop a unifying terminology, evaluate them theoretically, and apply them to conceptual rainfall-runoff modeling in the same drainage system. Our results show that both approaches can......In urban rainfall-runoff, commonly applied statistical techniques for uncertainty quantification mostly ignore systematic output errors originating from simplified models and erroneous inputs. Consequently, the resulting predictive uncertainty is often unreliable. Our objective is to present two...... approaches which use stochastic processes to describe systematic deviations and to discuss their advantages and drawbacks for urban drainage modeling. The two methodologies are an external bias description (EBD) and an internal noise description (IND, also known as stochastic gray-box modeling). They emerge...
Stochastic resonance in models of neuronal ensembles
International Nuclear Information System (INIS)
Chialvo, D.R.; Longtin, A.; Mueller-Gerkin, J.
1997-01-01
Two recently suggested mechanisms for the neuronal encoding of sensory information involving the effect of stochastic resonance with aperiodic time-varying inputs are considered. It is shown, using theoretical arguments and numerical simulations, that the nonmonotonic behavior with increasing noise of the correlation measures used for the so-called aperiodic stochastic resonance (ASR) scenario does not rely on the cooperative effect typical of stochastic resonance in bistable and excitable systems. Rather, ASR with slowly varying signals is more properly interpreted as linearization by noise. Consequently, the broadening of the open-quotes resonance curveclose quotes in the multineuron stochastic resonance without tuning scenario can also be explained by this linearization. Computation of the input-output correlation as a function of both signal frequency and noise for the model system further reveals conditions where noise-induced firing with aperiodic inputs will benefit from stochastic resonance rather than linearization by noise. Thus, our study clarifies the tuning requirements for the optimal transduction of subthreshold aperiodic signals. It also shows that a single deterministic neuron can perform as well as a network when biased into a suprathreshold regime. Finally, we show that the inclusion of a refractory period in the spike-detection scheme produces a better correlation between instantaneous firing rate and input signal. copyright 1997 The American Physical Society
Stochastic linear programming models, theory, and computation
Kall, Peter
2011-01-01
This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...
Stochastic dynamical models for ecological regime shifts
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg; Carstensen, Jacob; Madsen, Henrik
the physical and biological knowledge of the system, and nonlinearities introduced here can generate regime shifts or enhance the probability of regime shifts in the case of stochastic models, typically characterized by a threshold value for the known driver. A simple model for light competition between...... definition and stability of regimes become less subtle. Ecological regime shifts and their modeling must be viewed in a probabilistic manner, particularly if such model results are to be used in ecosystem management....
Modeling animal movements using stochastic differential equations
Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie
2004-01-01
We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...
Stochastic Load Models and Footbridge Response
DEFF Research Database (Denmark)
Pedersen, Lars; Frier, Christian
2015-01-01
Pedestrians may cause vibrations in footbridges and these vibrations may potentially be annoying. This calls for predictions of footbridge vibration levels and the paper considers a stochastic approach to modeling the action of pedestrians assuming walking parameters such as step frequency, pedes...
Stochastic Growth Models with No Discounting
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2007-01-01
Roč. 15, č. 4 (2007), s. 88-98 ISSN 0572-3043 R&D Projects: GA ČR(CZ) GA402/06/0990; GA ČR GA402/05/0115 Institutional research plan: CEZ:AV0Z10750506 Keywords : economic dynamics * stochastic version of the Ramsey growth model * Markov decision processes Subject RIV: AH - Economics
Stochastic forward and inverse groundwater flow and solute transport modeling
Janssen, G.M.C.M.
2008-01-01
Keywords: calibration, inverse modeling, stochastic modeling, nonlinear biodegradation, stochastic-convective, advective-dispersive, travel time, network design, non-Gaussian distribution, multimodal distribution, representers
This thesis offers three new approaches that contribute
Mathematical rainfall model for hydrographic demarcation of Manabi ...
African Journals Online (AJOL)
PROMOTING ACCESS TO AFRICAN RESEARCH ... To achieve this objective, the basins of the Hydrographic Demarcation of Manabí ... Keywords: multiple regression; mathematical model; GIS; Hydrology; rainfall. ... HOW TO USE AJOL.
Model simulations of rainfall over southern Africa and its eastern ...
African Journals Online (AJOL)
2016-01-01
Jan 1, 2016 ... Rainfall simulations over southern and tropical Africa in the form of low-resolution Atmospheric Model ..... provision of sea-surface temperatures and sea-ice fields of a host ...... with variability of the Atlantic Ocean. Bull.
Development of rainfall-runoff forecast model | Oyebode | Journal of ...
African Journals Online (AJOL)
... and meterological variables involved in rainfall-runoff process to improve forecast accuracy of rainfallrunoff. ... The simulation was done using MATLAB® 7.0. The simulation results showed that neurofuzzy-based model has higher coefficient ...
Stochastic models in reliability and maintenance
2002-01-01
Our daily lives can be maintained by the high-technology systems. Computer systems are typical examples of such systems. We can enjoy our modern lives by using many computer systems. Much more importantly, we have to maintain such systems without failure, but cannot predict when such systems will fail and how to fix such systems without delay. A stochastic process is a set of outcomes of a random experiment indexed by time, and is one of the key tools needed to analyze the future behavior quantitatively. Reliability and maintainability technologies are of great interest and importance to the maintenance of such systems. Many mathematical models have been and will be proposed to describe reliability and maintainability systems by using the stochastic processes. The theme of this book is "Stochastic Models in Reliability and Main tainability. " This book consists of 12 chapters on the theme above from the different viewpoints of stochastic modeling. Chapter 1 is devoted to "Renewal Processes," under which cla...
News Impact Curve for Stochastic Volatility Models
Makoto Takahashi; Yasuhiro Omori; Toshiaki Watanabe
2012-01-01
This paper proposes a new method to compute the news impact curve for stochastic volatility (SV) models. The new method incorporates the joint movement of return and volatility, which has been ignored by the extant literature, by simply adding a couple of steps to the Bayesian MCMC estimation procedures for SV models. This simple procedure is versatile and applicable to various SV type models. Contrary to the monotonic news impact functions in the extant literature, the new method gives a U-s...
Generation of a stochastic precipitation model for the tropical climate
Ng, Jing Lin; Abd Aziz, Samsuzana; Huang, Yuk Feng; Wayayok, Aimrun; Rowshon, MK
2017-06-01
A tropical country like Malaysia is characterized by intense localized precipitation with temperatures remaining relatively constant throughout the year. A stochastic modeling of precipitation in the flood-prone Kelantan River Basin is particularly challenging due to the high intermittency of precipitation events of the northeast monsoons. There is an urgent need to have long series of precipitation in modeling the hydrological responses. A single-site stochastic precipitation model that includes precipitation occurrence and an intensity model was developed, calibrated, and validated for the Kelantan River Basin. The simulation process was carried out separately for each station without considering the spatial correlation of precipitation. The Markov chains up to the fifth-order and six distributions were considered. The daily precipitation data of 17 rainfall stations for the study period of 1954-2013 were selected. The results suggested that second- and third-order Markov chains were suitable for simulating monthly and yearly precipitation occurrences, respectively. The fifth-order Markov chain resulted in overestimation of precipitation occurrences. For the mean, distribution, and standard deviation of precipitation amounts, the exponential, gamma, log-normal, skew normal, mixed exponential, and generalized Pareto distributions performed superiorly. However, for the extremes of precipitation, the exponential and log-normal distributions were better while the skew normal and generalized Pareto distributions tend to show underestimations. The log-normal distribution was chosen as the best distribution to simulate precipitation amounts. Overall, the stochastic precipitation model developed is considered a convenient tool to simulate the characteristics of precipitation in the Kelantan River Basin.
Haberlandt, U.; Radtke, I.
2013-08-01
Derived flood frequency analysis allows to estimate design floods with hydrological modelling for poorly observed basins considering change and taking into account flood protection measures. There are several possible choices about precipitation input, discharge output and consequently regarding the calibration of the model. The objective of this study is to compare different calibration strategies for a hydrological model considering various types of rainfall input and runoff output data sets. Event based and continuous observed hourly rainfall data as well as disaggregated daily rainfall and stochastically generated hourly rainfall data are used as input for the model. As output short hourly and longer daily continuous flow time series as well as probability distributions of annual maximum peak flow series are employed. The performance of the strategies is evaluated using the obtained different model parameter sets for continuous simulation of discharge in an independent validation period and by comparing the model derived flood frequency distributions with the observed one. The investigations are carried out for three mesoscale catchments in Northern Germany with the hydrological model HEC-HMS. The results show that: (i) the same type of precipitation input data should be used for calibration and application of the hydrological model, (ii) a model calibrated using a small sample of extreme values works quite well for the simulation of continuous time series with moderate length but not vice versa, (iii) the best performance with small uncertainty is obtained when stochastic precipitation data and the observed probability distribution of peak flows are used for model calibration. This outcome suggests to calibrate a hydrological model directly on probability distributions of observed peak flows using stochastic rainfall as input if its purpose is the application for derived flood frequency analysis.
Model predictive control classical, robust and stochastic
Kouvaritakis, Basil
2016-01-01
For the first time, a textbook that brings together classical predictive control with treatment of up-to-date robust and stochastic techniques. Model Predictive Control describes the development of tractable algorithms for uncertain, stochastic, constrained systems. The starting point is classical predictive control and the appropriate formulation of performance objectives and constraints to provide guarantees of closed-loop stability and performance. Moving on to robust predictive control, the text explains how similar guarantees may be obtained for cases in which the model describing the system dynamics is subject to additive disturbances and parametric uncertainties. Open- and closed-loop optimization are considered and the state of the art in computationally tractable methods based on uncertainty tubes presented for systems with additive model uncertainty. Finally, the tube framework is also applied to model predictive control problems involving hard or probabilistic constraints for the cases of multiplic...
Dynamic optimization deterministic and stochastic models
Hinderer, Karl; Stieglitz, Michael
2016-01-01
This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.
Distributed modelling of shallow landslides triggered by intense rainfall
Directory of Open Access Journals (Sweden)
G. B. Crosta
2003-01-01
Full Text Available Hazard assessment of shallow landslides represents an important aspect of land management in mountainous areas. Among all the methods proposed in the literature, physically based methods are the only ones that explicitly includes the dynamic factors that control landslide triggering (rainfall pattern, land-use. For this reason, they allow forecasting both the temporal and the spatial distribution of shallow landslides. Physically based methods for shallow landslides are based on the coupling of the infinite slope stability analysis with hydrological models. Three different grid-based distributed hydrological models are presented in this paper: a steady state model, a transient "piston-flow" wetting front model, and a transient diffusive model. A comparative test of these models was performed to simulate landslide occurred during a rainfall event (27–28 June 1997 that triggered hundreds of shallow landslides within Lecco province (central Southern Alps, Italy. In order to test the potential for a completely distributed model for rainfall-triggered landslides, radar detected rainfall intensity has been used. A new procedure for quantitative evaluation of distributed model performance is presented and used in this paper. The diffusive model results in the best model for the simulation of shallow landslide triggering after a rainfall event like the one that we have analysed. Finally, radar data available for the June 1997 event permitted greatly improving the simulation. In particular, radar data allowed to explain the non-uniform distribution of landslides within the study area.
Stochastic model of radioiodine transport
International Nuclear Information System (INIS)
Schwarz, G.; Hoffman, F.O.
1980-01-01
A research project has been underway at the Oak Ridge National Laboratory with the objective to evaluate dose assessment models and to determine the uncertainty associated with the model predictions. This has resulted in the application of methods to propagate uncertainties through models. Some techniques and results related to this problem are discussed
Raia, S.; Alvioli, M.; Rossi, M.; Baum, R.L.; Godt, J.W.; Guzzetti, F.
2013-01-01
Distributed models to forecast the spatial and temporal occurrence of rainfall-induced shallow landslides are deterministic. These models extend spatially the static stability models adopted in geotechnical engineering and adopt an infinite-slope geometry to balance the resisting and the driving forces acting on the sliding mass. An infiltration model is used to determine how rainfall changes pore-water conditions, modulating the local stability/instability conditions. A problem with the existing models is the difficulty in obtaining accurate values for the several variables that describe the material properties of the slopes. The problem is particularly severe when the models are applied over large areas, for which sufficient information on the geotechnical and hydrological conditions of the slopes is not generally available. To help solve the problem, we propose a probabilistic Monte Carlo approach to the distributed modeling of shallow rainfall-induced landslides. For the purpose, we have modified the Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability Analysis (TRIGRS) code. The new code (TRIGRS-P) adopts a stochastic approach to compute, on a cell-by-cell basis, transient pore-pressure changes and related changes in the factor of safety due to rainfall infiltration. Infiltration is modeled using analytical solutions of partial differential equations describing one-dimensional vertical flow in isotropic, homogeneous materials. Both saturated and unsaturated soil conditions can be considered. TRIGRS-P copes with the natural variability inherent to the mechanical and hydrological properties of the slope materials by allowing values of the TRIGRS model input parameters to be sampled randomly from a given probability distribution. The range of variation and the mean value of the parameters can be determined by the usual methods used for preparing the TRIGRS input parameters. The outputs of several model runs obtained varying the input parameters
Stochastic Spectral Descent for Discrete Graphical Models
International Nuclear Information System (INIS)
Carlson, David; Hsieh, Ya-Ping; Collins, Edo; Carin, Lawrence; Cevher, Volkan
2015-01-01
Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted as gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.
Brain-inspired Stochastic Models and Implementations
Al-Shedivat, Maruan
2015-05-12
One of the approaches to building artificial intelligence (AI) is to decipher the princi- ples of the brain function and to employ similar mechanisms for solving cognitive tasks, such as visual perception or natural language understanding, using machines. The recent breakthrough, named deep learning, demonstrated that large multi-layer networks of arti- ficial neural-like computing units attain remarkable performance on some of these tasks. Nevertheless, such artificial networks remain to be very loosely inspired by the brain, which rich structures and mechanisms may further suggest new algorithms or even new paradigms of computation. In this thesis, we explore brain-inspired probabilistic mechanisms, such as neural and synaptic stochasticity, in the context of generative models. The two questions we ask here are: (i) what kind of models can describe a neural learning system built of stochastic components? and (ii) how can we implement such systems e ̆ciently? To give specific answers, we consider two well known models and the corresponding neural architectures: the Naive Bayes model implemented with a winner-take-all spiking neural network and the Boltzmann machine implemented in a spiking or non-spiking fashion. We propose and analyze an e ̆cient neuromorphic implementation of the stochastic neu- ral firing mechanism and study the e ̄ects of synaptic unreliability on learning generative energy-based models implemented with neural networks.
Stochastic Modelling of Energy Systems
DEFF Research Database (Denmark)
Andersen, Klaus Kaae
2001-01-01
is that the model structure has to be adequate for practical applications, such as system simulation, fault detection and diagnosis, and design of control strategies. This also reflects on the methods used for identification of the component models. The main result from this research is the identification......In this thesis dynamic models of typical components in Danish heating systems are considered. Emphasis is made on describing and evaluating mathematical methods for identification of such models, and on presentation of component models for practical applications. The thesis consists of seven...... research papers (case studies) together with a summary report. Each case study takes it's starting point in typical heating system components and both, the applied mathematical modelling methods and the application aspects, are considered. The summary report gives an introduction to the scope...
Solvable stochastic dealer models for financial markets
Yamada, Kenta; Takayasu, Hideki; Ito, Takatoshi; Takayasu, Misako
2009-05-01
We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise generator, the model becomes fairly realistic by adding only two effects: the self-modulation of transaction intervals and a forecasting tendency, which uses a moving average of the latest market price changes. Based on the present microscopic model of markets, we find a quantitative relation with market potential forces, which have recently been discovered in the study of market price modeling based on random walks.
Modeling and Prediction Using Stochastic Differential Equations
DEFF Research Database (Denmark)
Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp
2016-01-01
Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup...... deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs...
The modification of the typhoon rainfall climatology model in Taiwan
Directory of Open Access Journals (Sweden)
C.-S. Lee
2013-01-01
Full Text Available This study is focused on the modification of a typhoon rainfall climatological model, by using the dataset up to 2006 and including data collected from rain gauge stations established after the 921 earthquake (1999. Subsequently, the climatology rainfall models for westward- and northward-moving typhoons are established by using the typhoon track classification from the Central Weather Bureau. These models are also evaluated and examined using dependent cases collected between 1989 and 2006 and independent cases collected from 2007 to 2011. For the dependent cases, the average total rainfall at all rain gauge stations forecasted using the climatology rainfall models for westward- (W-TRCM12 and northward-moving (N-TRCM12 typhoons is superior to that obtained using the original climatological model (TRCM06. Model W-TRCM12 significantly improves the precipitation underestimation of model TRCM06. The independent cases show that model W-TRCM12 provides better accumulated rainfall forecasts and distributions than model TRCM06. A climatological model for accompanied northeastern monsoons (A-TRCM12 for special typhoon types has also been established. The current A-TRCM12 model only contains five historical cases and various typhoon combinations can cause precipitation in different regions. Therefore, precipitation is likely to be significantly overestimated and high false alarm ratios are likely to occur in specific regions. For example, model A-TRCM12 significantly overestimates the rainfall forecast for Typhoon Mitag, an independent case from 2007. However, it has a higher probability of detection than model TRCM06. From a disaster prevention perspective, a high probability of detection is much more important than a high false alarm ratio. The modified models can contribute significantly to operational forecast.
Assessment of runoff contributing catchment areas in rainfall runoff modelling
DEFF Research Database (Denmark)
Thorndahl, Søren; Johansen, C.; Schaarup-Jensen, Kjeld
2006-01-01
In numerical modelling of rainfall caused runoff in urban sewer systems an essential parameter is the hydrological reduction factor which defines the percentage of the impervious area contributing to the surface flow towards the sewer. As the hydrological processes during a rainfall are difficult...... to determine with significant precision the hydrological reduction factor is implemented to account all hydrological losses except the initial loss. This paper presents an inconsistency between calculations of the hydrological reduction factor, based on measurements of rainfall and runoff, and till now...... recommended literature values for residential areas. It is proven by comparing rainfall-runoff measurements from four different residential catchments that the literature values of the hydrological reduction factor are over-estimated for this type of catchment. In addition, different catchment descriptions...
Fuzzy Stochastic Optimization Theory, Models and Applications
Wang, Shuming
2012-01-01
Covering in detail both theoretical and practical perspectives, this book is a self-contained and systematic depiction of current fuzzy stochastic optimization that deploys the fuzzy random variable as a core mathematical tool to model the integrated fuzzy random uncertainty. It proceeds in an orderly fashion from the requisite theoretical aspects of the fuzzy random variable to fuzzy stochastic optimization models and their real-life case studies. The volume reflects the fact that randomness and fuzziness (or vagueness) are two major sources of uncertainty in the real world, with significant implications in a number of settings. In industrial engineering, management and economics, the chances are high that decision makers will be confronted with information that is simultaneously probabilistically uncertain and fuzzily imprecise, and optimization in the form of a decision must be made in an environment that is doubly uncertain, characterized by a co-occurrence of randomness and fuzziness. This book begins...
Uijlenhoet, R.; Porrà, J.M.; Sempere Torres, D.; Creutin, J.D.
2006-01-01
A stochastic model of the microstructure of rainfall is used to derive explicit expressions for the magnitude of the sampling fluctuations in rainfall properties estimated from raindrop size measurements in stationary rainfall. The model is a marked point process, in which the points represent the
Stochastic models for time series
Doukhan, Paul
2018-01-01
This book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit ...
EVALUATION OF RAINFALL-RUNOFF MODELS FOR MEDITERRANEAN SUBCATCHMENTS
Directory of Open Access Journals (Sweden)
A. Cilek
2016-06-01
Full Text Available The development and the application of rainfall-runoff models have been a corner-stone of hydrological research for many decades. The amount of rainfall and its intensity and variability control the generation of runoff and the erosional processes operating at different scales. These interactions can be greatly variable in Mediterranean catchments with marked hydrological fluctuations. The aim of the study was to evaluate the performance of rainfall-runoff model, for rainfall-runoff simulation in a Mediterranean subcatchment. The Pan-European Soil Erosion Risk Assessment (PESERA, a simplified hydrological process-based approach, was used in this study to combine hydrological surface runoff factors. In total 128 input layers derived from data set includes; climate, topography, land use, crop type, planting date, and soil characteristics, are required to run the model. Initial ground cover was estimated from the Landsat ETM data provided by ESA. This hydrological model was evaluated in terms of their performance in Goksu River Watershed, Turkey. It is located at the Central Eastern Mediterranean Basin of Turkey. The area is approximately 2000 km2. The landscape is dominated by bare ground, agricultural and forests. The average annual rainfall is 636.4mm. This study has a significant importance to evaluate different model performances in a complex Mediterranean basin. The results provided comprehensive insight including advantages and limitations of modelling approaches in the Mediterranean environment.
A stochastic model for quantum measurement
International Nuclear Information System (INIS)
Budiyono, Agung
2013-01-01
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic process with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary action. We apply the statistical model to stochastically modify a classical mechanical model for the measurement of physical quantities reproducing the prediction of quantum mechanics. The system+apparatus always has a definite configuration at all times, as in classical mechanics, fluctuating randomly following a continuous trajectory. On the other hand, the wavefunction and quantum mechanical Hermitian operator corresponding to the physical quantity arise formally as artificial mathematical constructs. During a single measurement, the wavefunction of the whole system+apparatus evolves according to a Schrödinger equation and the configuration of the apparatus acts as the pointer of the measurement so that there is no wavefunction collapse. We will also show that while the outcome of each single measurement event does not reveal the actual value of the physical quantity prior to measurement, its average in an ensemble of identical measurements is equal to the average of the actual value of the physical quantity prior to measurement over the distribution of the configuration of the system. (paper)
Markov modulated Poisson process models incorporating covariates for rainfall intensity.
Thayakaran, R; Ramesh, N I
2013-01-01
Time series of rainfall bucket tip times at the Beaufort Park station, Bracknell, in the UK are modelled by a class of Markov modulated Poisson processes (MMPP) which may be thought of as a generalization of the Poisson process. Our main focus in this paper is to investigate the effects of including covariate information into the MMPP model framework on statistical properties. In particular, we look at three types of time-varying covariates namely temperature, sea level pressure, and relative humidity that are thought to be affecting the rainfall arrival process. Maximum likelihood estimation is used to obtain the parameter estimates, and likelihood ratio tests are employed in model comparison. Simulated data from the fitted model are used to make statistical inferences about the accumulated rainfall in the discrete time interval. Variability of the daily Poisson arrival rates is studied.
Stochastic Modeling of Past Volcanic Crises
Woo, Gordon
2018-01-01
The statistical foundation of disaster risk analysis is past experience. From a scientific perspective, history is just one realization of what might have happened, given the randomness and chaotic dynamics of Nature. Stochastic analysis of the past is an exploratory exercise in counterfactual history, considering alternative possible scenarios. In particular, the dynamic perturbations that might have transitioned a volcano from an unrest to an eruptive state need to be considered. The stochastic modeling of past volcanic crises leads to estimates of eruption probability that can illuminate historical volcanic crisis decisions. It can also inform future economic risk management decisions in regions where there has been some volcanic unrest, but no actual eruption for at least hundreds of years. Furthermore, the availability of a library of past eruption probabilities would provide benchmark support for estimates of eruption probability in future volcanic crises.
A stochastic model for the financial market with discontinuous prices
Directory of Open Access Journals (Sweden)
Leda D. Minkova
1996-01-01
Full Text Available This paper models some situations occurring in the financial market. The asset prices evolve according to a stochastic integral equation driven by a Gaussian martingale. A portfolio process is constrained in such a way that the wealth process covers some obligation. A solution to a linear stochastic integral equation is obtained in a class of cadlag stochastic processes.
Rainfall estimation with TFR model using Ensemble Kalman filter
Asyiqotur Rohmah, Nabila; Apriliani, Erna
2018-03-01
Rainfall fluctuation can affect condition of other environment, correlated with economic activity and public health. The increasing of global average temperature is influenced by the increasing of CO2 in the atmosphere, which caused climate change. Meanwhile, the forests as carbon sinks that help keep the carbon cycle and climate change mitigation. Climate change caused by rainfall intensity deviations can affect the economy of a region, and even countries. It encourages research on rainfall associated with an area of forest. In this study, the mathematics model that used is a model which describes the global temperatures, forest cover, and seasonal rainfall called the TFR (temperature, forest cover, and rainfall) model. The model will be discretized first, and then it will be estimated by the method of Ensemble Kalman Filter (EnKF). The result shows that the more ensembles used in estimation, the better the result is. Also, the accurateness of simulation result is influenced by measurement variable. If a variable is measurement data, the result of simulation is better.
Hidden Symmetries of Stochastic Models
Directory of Open Access Journals (Sweden)
Boyka Aneva
2007-05-01
Full Text Available In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a $SU_q(n$ quantum group action as its symmetry. Boundary processes amount to the appearance of parameter dependent linear terms in the algebraic relations and lead to a reduction of the $SU_q(n$ symmetry. We argue that the boundary operators of the asymmetric simple exclusion process generate a tridiagonal algebra whose irriducible representations are expressed in terms of the Askey-Wilson polynomials. The Askey-Wilson algebra arises as a symmetry of the boundary problem and allows to solve the model exactly.
Modeling Spatial Dependence of Rainfall Extremes Across Multiple Durations
Le, Phuong Dong; Leonard, Michael; Westra, Seth
2018-03-01
Determining the probability of a flood event in a catchment given that another flood has occurred in a nearby catchment is useful in the design of infrastructure such as road networks that have multiple river crossings. These conditional flood probabilities can be estimated by calculating conditional probabilities of extreme rainfall and then transforming rainfall to runoff through a hydrologic model. Each catchment's hydrological response times are unlikely to be the same, so in order to estimate these conditional probabilities one must consider the dependence of extreme rainfall both across space and across critical storm durations. To represent these types of dependence, this study proposes a new approach for combining extreme rainfall across different durations within a spatial extreme value model using max-stable process theory. This is achieved in a stepwise manner. The first step defines a set of common parameters for the marginal distributions across multiple durations. The parameters are then spatially interpolated to develop a spatial field. Storm-level dependence is represented through the max-stable process for rainfall extremes across different durations. The dependence model shows a reasonable fit between the observed pairwise extremal coefficients and the theoretical pairwise extremal coefficient function across all durations. The study demonstrates how the approach can be applied to develop conditional maps of the return period and return level across different durations.
Stochastic Optimization of Wind Turbine Power Factor Using Stochastic Model of Wind Power
DEFF Research Database (Denmark)
Chen, Peiyuan; Siano, Pierluigi; Bak-Jensen, Birgitte
2010-01-01
This paper proposes a stochastic optimization algorithm that aims to minimize the expectation of the system power losses by controlling wind turbine (WT) power factors. This objective of the optimization is subject to the probability constraints of bus voltage and line current requirements....... The optimization algorithm utilizes the stochastic models of wind power generation (WPG) and load demand to take into account their stochastic variation. The stochastic model of WPG is developed on the basis of a limited autoregressive integrated moving average (LARIMA) model by introducing a crosscorrelation...... structure to the LARIMA model. The proposed stochastic optimization is carried out on a 69-bus distribution system. Simulation results confirm that, under various combinations of WPG and load demand, the system power losses are considerably reduced with the optimal setting of WT power factor as compared...
Modeling stochastic frontier based on vine copulas
Constantino, Michel; Candido, Osvaldo; Tabak, Benjamin M.; da Costa, Reginaldo Brito
2017-11-01
This article models a production function and analyzes the technical efficiency of listed companies in the United States, Germany and England between 2005 and 2012 based on the vine copula approach. Traditional estimates of the stochastic frontier assume that data is multivariate normally distributed and there is no source of asymmetry. The proposed method based on vine copulas allow us to explore different types of asymmetry and multivariate distribution. Using data on product, capital and labor, we measure the relative efficiency of the vine production function and estimate the coefficient used in the stochastic frontier literature for comparison purposes. This production vine copula predicts the value added by firms with given capital and labor in a probabilistic way. It thereby stands in sharp contrast to the production function, where the output of firms is completely deterministic. The results show that, on average, S&P500 companies are more efficient than companies listed in England and Germany, which presented similar average efficiency coefficients. For comparative purposes, the traditional stochastic frontier was estimated and the results showed discrepancies between the coefficients obtained by the application of the two methods, traditional and frontier-vine, opening new paths of non-linear research.
Modelling Evolutionary Algorithms with Stochastic Differential Equations.
Heredia, Jorge Pérez
2017-11-20
There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.
Models of the stochastic activity of neurones
Holden, Arun Vivian
1976-01-01
These notes have grown from a series of seminars given at Leeds between 1972 and 1975. They represent an attempt to gather together the different kinds of model which have been proposed to account for the stochastic activity of neurones, and to provide an introduction to this area of mathematical biology. A striking feature of the electrical activity of the nervous system is that it appears stochastic: this is apparent at all levels of recording, ranging from intracellular recordings to the electroencephalogram. The chapters start with fluctuations in membrane potential, proceed through single unit and synaptic activity and end with the behaviour of large aggregates of neurones: L have chgaen this seque~~e\\/~~';uggest that the interesting behaviourr~f :the nervous system - its individuality, variability and dynamic forms - may in part result from the stochastic behaviour of its components. I would like to thank Dr. Julio Rubio for reading and commenting on the drafts, Mrs. Doris Beighton for producing the fin...
Discrete stochastic analogs of Erlang epidemic models.
Getz, Wayne M; Dougherty, Eric R
2018-12-01
Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.
Mathematical models of information and stochastic systems
Kornreich, Philipp
2008-01-01
From ancient soothsayers and astrologists to today's pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system's probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the t
Stochastic model of energetic nuclear reactor
International Nuclear Information System (INIS)
Bojko, R.V.; Ryazanov, V.V.
2002-01-01
Behaviour of nuclear reactor was treated using the theory of branching processes. As mathematical model descriptive the neutron number in time the Markov occasional process is proposed. Application of branching occasional processes with variable regime to the description of neutron behaviour in the reactor makes possible conducting strong description of critical operation regime and demonstrates the severity of the process. Three regimes of the critical behaviour depending on the sign of manipulated variables and feedbacks were discovered. Probability regularities peculiar to the behaviour of the reactor are embodied to the suggested stochastic model [ru
Predicting extinction rates in stochastic epidemic models
International Nuclear Information System (INIS)
Schwartz, Ira B; Billings, Lora; Dykman, Mark; Landsman, Alexandra
2009-01-01
We investigate the stochastic extinction processes in a class of epidemic models. Motivated by the process of natural disease extinction in epidemics, we examine the rate of extinction as a function of disease spread. We show that the effective entropic barrier for extinction in a susceptible–infected–susceptible epidemic model displays scaling with the distance to the bifurcation point, with an unusual critical exponent. We make a direct comparison between predictions and numerical simulations. We also consider the effect of non-Gaussian vaccine schedules, and show numerically how the extinction process may be enhanced when the vaccine schedules are Poisson distributed
Regionalising Parameters of a Conceptual Rainfall-Runoff Model for ...
African Journals Online (AJOL)
IHACRES, a lumped conceptual rainfall-runoff model, was calibrated to six catchments ranging in size from 49km2 to 600 km2 within the upper Tana River basin to obtain a set of model parameters that characterise the hydrological behaviour within the region. Physical catchment attributes indexing topography, soil and ...
Effect of monthly areal rainfall uncertainty on streamflow simulation
Ndiritu, J. G.; Mkhize, N.
2017-08-01
Areal rainfall is mostly obtained from point rainfall measurements that are sparsely located and several studies have shown that this results in large areal rainfall uncertainties at the daily time step. However, water resources assessment is often carried out a monthly time step and streamflow simulation is usually an essential component of this assessment. This study set out to quantify monthly areal rainfall uncertainties and assess their effect on streamflow simulation. This was achieved by; i) quantifying areal rainfall uncertainties and using these to generate stochastic monthly areal rainfalls, and ii) finding out how the quality of monthly streamflow simulation and streamflow variability change if stochastic areal rainfalls are used instead of historic areal rainfalls. Tests on monthly rainfall uncertainty were carried out using data from two South African catchments while streamflow simulation was confined to one of them. A non-parametric model that had been applied at a daily time step was used for stochastic areal rainfall generation and the Pitman catchment model calibrated using the SCE-UA optimizer was used for streamflow simulation. 100 randomly-initialised calibration-validation runs using 100 stochastic areal rainfalls were compared with 100 runs obtained using the single historic areal rainfall series. By using 4 rain gauges alternately to obtain areal rainfall, the resulting differences in areal rainfall averaged to 20% of the mean monthly areal rainfall and rainfall uncertainty was therefore highly significant. Pitman model simulations obtained coefficient of efficiencies averaging 0.66 and 0.64 in calibration and validation using historic rainfalls while the respective values using stochastic areal rainfalls were 0.59 and 0.57. Average bias was less than 5% in all cases. The streamflow ranges using historic rainfalls averaged to 29% of the mean naturalised flow in calibration and validation and the respective average ranges using stochastic
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...
Stochastic Model Checking of the Stochastic Quality Calculus
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis; Zeng, Kebin
2015-01-01
The Quality Calculus uses quality binders for input to express strategies for continuing the computation even when the desired input has not been received. The Stochastic Quality Calculus adds generally distributed delays for output actions and real-time constraints on the quality binders for input....... This gives rise to Generalised Semi-Markov Decision Processes for which few analytical techniques are available. We restrict delays on output actions to be exponentially distributed while still admitting real-time constraints on the quality binders. This facilitates developing analytical techniques based...
Modelling the stochastic behaviour of primary nucleation.
Maggioni, Giovanni Maria; Mazzotti, Marco
2015-01-01
We study the stochastic nature of primary nucleation and how it manifests itself in a crystallisation process at different scales and under different operating conditions. Such characteristics of nucleation are evident in many experiments where detection times of crystals are not identical, despite identical experimental conditions, but instead are distributed around an average value. While abundant experimental evidence has been reported in the literature, a clear theoretical understanding and an appropriate modelling of this feature is still missing. In this contribution, we present two models describing a batch cooling crystallisation, where the interplay between stochastic nucleation and deterministic crystal growth is described differently in each. The nucleation and growth rates of the two models are estimated by a comprehensive set of measurements of paracetamol crystallisation from aqueous solution in a 1 mL vessel [Kadam et al., Chemical Engineering Science, 2012, 72, 10-19]. Both models are applied to the cooling crystallisation process above under different operating conditions, i.e. different volumes, initial concentrations, cooling rates. The advantages and disadvantages of the two approaches are illustrated and discussed, with particular reference to their use across scales of nucleation rate measured in very small crystallisers.
Characterizing economic trends by Bayesian stochastic model specifi cation search
Grassi, Stefano; Proietti, Tommaso
2010-01-01
We apply a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. We illustrate that the methodology can be quite successfully applied to discriminate between stochastic and deterministic trends. In particular, we formulate autoregressive models with stochastic trends components and decide on whether a specific feature of the series, i.e. the underlying level and/or the rate...
An Overview of Rainfall-Runoff Model Types
This report explores rainfall-runoff models, their generation methods, and the categories under which they fall. Runoff plays an important role in the hydrological cycle by returning excess precipitation to the oceans and controlling how much water flows into stream systems. Mode...
DAILY RAINFALL-RUNOFF MODELLING BY NEURAL NETWORKS ...
African Journals Online (AJOL)
K. Benzineb, M. Remaoun
2016-09-01
Sep 1, 2016 ... The hydrologic behaviour modelling of w. Journal of ... i Ouahrane's basin from rainfall-runoff relation which is non-linea networks ... will allow checking efficiency of formal neural networks for flows simulation in semi-arid zone.
Scalable inference for stochastic block models
Peng, Chengbin
2017-12-08
Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of "big data," traditional inference algorithms for such a model are increasingly limited due to their high time complexity and poor scalability. In this paper, we propose a multi-stage maximum likelihood approach to recover the latent parameters of the stochastic block model, in time linear with respect to the number of edges. We also propose a parallel algorithm based on message passing. Our algorithm can overlap communication and computation, providing speedup without compromising accuracy as the number of processors grows. For example, to process a real-world graph with about 1.3 million nodes and 10 million edges, our algorithm requires about 6 seconds on 64 cores of a contemporary commodity Linux cluster. Experiments demonstrate that the algorithm can produce high quality results on both benchmark and real-world graphs. An example of finding more meaningful communities is illustrated consequently in comparison with a popular modularity maximization algorithm.
Intimate Partner Violence: A Stochastic Model.
Guidi, Elisa; Meringolo, Patrizia; Guazzini, Andrea; Bagnoli, Franco
2017-01-01
Intimate partner violence (IPV) has been a well-studied problem in the past psychological literature, especially through its classical methodology such as qualitative, quantitative and mixed methods. This article introduces two basic stochastic models as an alternative approach to simulate the short and long-term dynamics of a couple at risk of IPV. In both models, the members of the couple may assume a finite number of states, updating them in a probabilistic way at discrete time steps. After defining the transition probabilities, we first analyze the evolution of the couple in isolation and then we consider the case in which the individuals modify their behavior depending on the perceived violence from other couples in their environment or based on the perceived informal social support. While high perceived violence in other couples may converge toward the own presence of IPV by means a gender-specific transmission, the gender differences fade-out in the case of received informal social support. Despite the simplicity of the two stochastic models, they generate results which compare well with past experimental studies about IPV and they give important practical implications for prevention intervention in this field. Copyright: © 2016 by Fabrizio Serra editore, Pisa · Roma.
Directory of Open Access Journals (Sweden)
P. Cowpertwait
2013-02-01
Full Text Available A spatiotemporal point process model of rainfall is fitted to data taken from three homogeneous regions in the Basque Country, Spain. The model is the superposition of two spatiotemporal Neyman–Scott processes, in which rain cells are modelled as discs with radii that follow exponential distributions. In addition, the model includes a parameter for the radius of storm discs, so that rain only occurs when both a cell and a storm disc overlap a point. The model is fitted to data for each month, taken from each of the three homogeneous regions, using a modified method of moments procedure that ensures a smooth seasonal variation in the parameter estimates.
Daily temperature data from 23 sites are used to fit a stochastic temperature model. A principal component analysis of the maximum daily temperatures across the sites indicates that 92% of the variance is explained by the first component, implying that this component can be used to account for spatial variation. A harmonic equation with autoregressive error terms is fitted to the first principal component. The temperature model is obtained by regressing the maximum daily temperature on the first principal component, an indicator variable for the region, and altitude. This, together with scaling and a regression model of temperature range, enables hourly temperatures to be predicted. Rainfall is included as an explanatory variable but has only a marginal influence when predicting temperatures.
A distributed model (TETIS; Francés et al., 2007 is calibrated for a selected catchment. Five hundred years of data are simulated using the rainfall and temperature models and used as input to the calibrated TETIS model to obtain simulated discharges to compare with observed discharges. Kolmogorov–Smirnov tests indicate that there is no significant difference in the distributions of observed and simulated maximum flows at the same sites, thus supporting the use of the spatiotemporal
Stochastic Model of TCP SYN Attacks
Directory of Open Access Journals (Sweden)
Simona Ramanauskaitė
2011-08-01
Full Text Available A great proportion of essential services are moving into internet space making the threat of DoS attacks even more actual. To estimate the real risk of some kind of denial of service (DoS attack in real world is difficult, but mathematical and software models make this task easier. In this paper we overview the ways of implementing DoS attack models and offer a stochastic model of SYN flooding attack. It allows evaluating the potential threat of SYN flooding attacks, taking into account both the legitimate system flow as well as the possible attack power. At the same time we can assess the effect of such parameters as buffer capacity, open connection storage in the buffer or filtering efficiency on the success of different SYN flooding attacks. This model can be used for other type of memory depletion denial of service attacks.Article in Lithuanian
Stochastic approaches to inflation model building
International Nuclear Information System (INIS)
Ramirez, Erandy; Liddle, Andrew R.
2005-01-01
While inflation gives an appealing explanation of observed cosmological data, there are a wide range of different inflation models, providing differing predictions for the initial perturbations. Typically models are motivated either by fundamental physics considerations or by simplicity. An alternative is to generate large numbers of models via a random generation process, such as the flow equations approach. The flow equations approach is known to predict a definite structure to the observational predictions. In this paper, we first demonstrate a more efficient implementation of the flow equations exploiting an analytic solution found by Liddle (2003). We then consider alternative stochastic methods of generating large numbers of inflation models, with the aim of testing whether the structures generated by the flow equations are robust. We find that while typically there remains some concentration of points in the observable plane under the different methods, there is significant variation in the predictions amongst the methods considered
Stochastic modeling of financial electricity contracts
International Nuclear Information System (INIS)
Benth, Fred Espen; Koekebakker, Steen
2008-01-01
We discuss the modeling of electricity contracts traded in many deregulated power markets. These forward/futures type contracts deliver (either physically or financially) electricity over a specified time period, and is frequently referred to as swaps since they in effect represent an exchange of fixed for floating electricity price. We propose to use the Heath-Jarrow-Morton approach to model swap prices since the notion of a spot price is not easily defined in these markets. For general stochastic dynamical models, we connect the spot price, the instantaneous-delivery forward price and the swap price, and analyze two different ways to apply the Heath-Jarrow-Morton approach to swap pricing: Either one specifies a dynamics for the non-existing instantaneous-delivery forwards and derives the implied swap dynamics, or one models directly on the swaps. The former is shown to lead to quite complicated stochastic models for the swap price, even when the forward dynamics is simple. The latter has some theoretical problems due to a no-arbitrage condition that has to be satisfied for swaps with overlapping delivery periods. To overcome this problem, a practical modeling approach is analyzed. The market is supposed only to consist of non-overlapping swaps, and these are modelled directly. A thorough empirical study is performed using data collected from Nord Pool. Our investigations demonstrate that it is possible to state reasonable models for the swap price dynamics which is analytically tractable for risk management and option pricing purposes, however, this is an area of further research. (author)
Interpolation of daily rainfall using spatiotemporal models and clustering
Militino, A. F.
2014-06-11
Accumulated daily rainfall in non-observed locations on a particular day is frequently required as input to decision-making tools in precision agriculture or for hydrological or meteorological studies. Various solutions and estimation procedures have been proposed in the literature depending on the auxiliary information and the availability of data, but most such solutions are oriented to interpolating spatial data without incorporating temporal dependence. When data are available in space and time, spatiotemporal models usually provide better solutions. Here, we analyse the performance of three spatiotemporal models fitted to the whole sampled set and to clusters within the sampled set. The data consists of daily observations collected from 87 manual rainfall gauges from 1990 to 2010 in Navarre, Spain. The accuracy and precision of the interpolated data are compared with real data from 33 automated rainfall gauges in the same region, but placed in different locations than the manual rainfall gauges. Root mean squared error by months and by year are also provided. To illustrate these models, we also map interpolated daily precipitations and standard errors on a 1km2 grid in the whole region. © 2014 Royal Meteorological Society.
Interpolation of daily rainfall using spatiotemporal models and clustering
Militino, A. F.; Ugarte, M. D.; Goicoa, T.; Genton, Marc G.
2014-01-01
Accumulated daily rainfall in non-observed locations on a particular day is frequently required as input to decision-making tools in precision agriculture or for hydrological or meteorological studies. Various solutions and estimation procedures have been proposed in the literature depending on the auxiliary information and the availability of data, but most such solutions are oriented to interpolating spatial data without incorporating temporal dependence. When data are available in space and time, spatiotemporal models usually provide better solutions. Here, we analyse the performance of three spatiotemporal models fitted to the whole sampled set and to clusters within the sampled set. The data consists of daily observations collected from 87 manual rainfall gauges from 1990 to 2010 in Navarre, Spain. The accuracy and precision of the interpolated data are compared with real data from 33 automated rainfall gauges in the same region, but placed in different locations than the manual rainfall gauges. Root mean squared error by months and by year are also provided. To illustrate these models, we also map interpolated daily precipitations and standard errors on a 1km2 grid in the whole region. © 2014 Royal Meteorological Society.
Stochastic modeling of thermal fatigue crack growth
Radu, Vasile
2015-01-01
The book describes a systematic stochastic modeling approach for assessing thermal-fatigue crack-growth in mixing tees, based on the power spectral density of temperature fluctuation at the inner pipe surface. It shows the development of a frequency-temperature response function in the framework of single-input, single-output (SISO) methodology from random noise/signal theory under sinusoidal input. The frequency response of stress intensity factor (SIF) is obtained by a polynomial fitting procedure of thermal stress profiles at various instants of time. The method, which takes into account the variability of material properties, and has been implemented in a real-world application, estimates the probabilities of failure by considering a limit state function and Monte Carlo analysis, which are based on the proposed stochastic model. Written in a comprehensive and accessible style, this book presents a new and effective method for assessing thermal fatigue crack, and it is intended as a concise and practice-or...
Hopf bifurcation of the stochastic model on business cycle
International Nuclear Information System (INIS)
Xu, J; Wang, H; Ge, G
2008-01-01
A stochastic model on business cycle was presented in thas paper. Simplifying the model through the quasi Hamiltonian theory, the Ito diffusion process was obtained. According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired. Solving the stationary FPK equation and analyzing the stationary probability density, the stochastic Hopf bifurcation was explained. The result indicated that the change of parameter awas the key factor to the appearance of the stochastic Hopf bifurcation
Double diffusivity model under stochastic forcing
Chattopadhyay, Amit K.; Aifantis, Elias C.
2017-05-01
The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into
Gires, A.; Tchiguirinskaia, I.; Schertzer, D. J.; Lovejoy, S.
2011-12-01
In large urban areas, storm water management is a challenge with enlarging impervious areas. Many cities have implemented real time control (RTC) of their urban drainage system to either reduce overflow or limit urban contamination. A basic component of RTC is hydraulic/hydrologic model. In this paper we use the multifractal framework to suggest an innovative way to test the sensitivity of such a model to the spatio-temporal variability of its rainfall input. Indeed the rainfall variability is often neglected in urban context, being considered as a non-relevant issue at the scales involve. Our results show that on the contrary the rainfall variability should be taken into account. Universal multifractals (UM) rely on the concept of multiplicative cascade and are a standard tool to analyze and simulate with a reduced number of parameters geophysical processes that are extremely variable over a wide range of scales. This study is conducted on a 3 400 ha urban area located in Seine-Saint-Denis, in the North of Paris (France). We use the operational semi-distributed model that was calibrated by the local authority (Direction Eau et Assainnissement du 93) that is in charge of urban drainage. The rainfall data comes from the C-Band radar of Trappes operated by Météo-France. The rainfall event of February 9th, 2009 was used. A stochastic ensemble approach was implemented to quantify the uncertainty on discharge associated to the rainfall variability occurring at scales smaller than 1 km x 1 km x 5 min that is usually available with C-band radar networks. An analysis of the quantiles of the simulated peak flow showed that the uncertainty exceeds 20 % for upstream links. To evaluate a potential gain from a direct use of the rainfall data available at the resolution of X-band radar, we performed similar analysis of the rainfall fields of the degraded resolution of 9 km x 9 km x 20 min. The results show a clear decrease in uncertainty when the original resolution of C
Stochastic stability and bifurcation in a macroeconomic model
International Nuclear Information System (INIS)
Li Wei; Xu Wei; Zhao Junfeng; Jin Yanfei
2007-01-01
On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis
Stochastic inverse problems: Models and metrics
International Nuclear Information System (INIS)
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-01-01
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds
Stochastic inverse problems: Models and metrics
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-03-01
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds.
modelling relationship between rainfall variability and yields
African Journals Online (AJOL)
, S. and ... factors to rice yield. Adebayo and Adebayo (1997) developed double log multiple regression model to predict rice yield in Adamawa State, Nigeria. The general form of .... the second are the crop yield/values for millet and sorghum ...
Modeling rainfall-runoff process using soft computing techniques
Kisi, Ozgur; Shiri, Jalal; Tombul, Mustafa
2013-02-01
Rainfall-runoff process was modeled for a small catchment in Turkey, using 4 years (1987-1991) of measurements of independent variables of rainfall and runoff values. The models used in the study were Artificial Neural Networks (ANNs), Adaptive Neuro-Fuzzy Inference System (ANFIS) and Gene Expression Programming (GEP) which are Artificial Intelligence (AI) approaches. The applied models were trained and tested using various combinations of the independent variables. The goodness of fit for the model was evaluated in terms of the coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), coefficient of efficiency (CE) and scatter index (SI). A comparison was also made between these models and traditional Multi Linear Regression (MLR) model. The study provides evidence that GEP (with RMSE=17.82 l/s, MAE=6.61 l/s, CE=0.72 and R2=0.978) is capable of modeling rainfall-runoff process and is a viable alternative to other applied artificial intelligence and MLR time-series methods.
Stochastic models for surface diffusion of molecules
Energy Technology Data Exchange (ETDEWEB)
Shea, Patrick, E-mail: patrick.shea@dal.ca; Kreuzer, Hans Jürgen [Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada)
2014-07-28
We derive a stochastic model for the surface diffusion of molecules, starting from the classical equations of motion for an N-atom molecule on a surface. The equation of motion becomes a generalized Langevin equation for the center of mass of the molecule, with a non-Markovian friction kernel. In the Markov approximation, a standard Langevin equation is recovered, and the effect of the molecular vibrations on the diffusion is seen to lead to an increase in the friction for center of mass motion. This effective friction has a simple form that depends on the curvature of the lowest energy diffusion path in the 3N-dimensional coordinate space. We also find that so long as the intramolecular forces are sufficiently strong, memory effects are usually not significant and the Markov approximation can be employed, resulting in a simple one-dimensional model that can account for the effect of the dynamics of the molecular vibrations on the diffusive motion.
Can Household Benefit from Stochastic Programming Models?
DEFF Research Database (Denmark)
Rasmussen, Kourosh Marjani; Madsen, Claus A.; Poulsen, Rolf
2014-01-01
The Danish mortgage market is large and sophisticated. However, most Danish mortgage banks advise private home-owners based on simple, if sensible, rules of thumb. In recent years a number of papers (from Nielsen and Poulsen in J Econ Dyn Control 28:1267–1289, 2004 over Rasmussen and Zenios in J...... Risk 10:1–18, 2007 to Pedersen et al. in Ann Oper Res, 2013) have suggested a model-based, stochastic programming approach to mortgage choice. This paper gives an empirical comparison of performance over the period 2000–2010 of the rules of thumb to the model-based strategies. While the rules of thumb.......3–0.9 %-points (depending on the borrower’s level of conservatism) compared to the rules of thumb without increasing the risk. The answer to the question in the title is thus affirmative....
Ghazavi, Reza; Moafi Rabori, Ali; Ahadnejad Reveshty, Mohsen
2016-01-01
Estimate design storm based on rainfall intensity–duration–frequency (IDF) curves is an important parameter for hydrologic planning of urban areas. The main aim of this study was to estimate rainfall intensities of Zanjan city watershed based on overall relationship of rainfall IDF curves and appropriate model of hourly rainfall estimation (Sherman method, Ghahreman and Abkhezr method). Hydrologic and hydraulic impacts of rainfall IDF curves change in flood properties was evaluated via Stormw...
An adaptive stochastic model for financial markets
International Nuclear Information System (INIS)
Hernández, Juan Antonio; Benito, Rosa Marı´a; Losada, Juan Carlos
2012-01-01
An adaptive stochastic model is introduced to simulate the behavior of real asset markets. The model adapts itself by changing its parameters automatically on the basis of the recent historical data. The basic idea underlying the model is that a random variable uniformly distributed within an interval with variable extremes can replicate the histograms of asset returns. These extremes are calculated according to the arrival of new market information. This adaptive model is applied to the daily returns of three well-known indices: Ibex35, Dow Jones and Nikkei, for three complete years. The model reproduces the histograms of the studied indices as well as their autocorrelation structures. It produces the same fat tails and the same power laws, with exactly the same exponents, as in the real indices. In addition, the model shows a great adaptation capability, anticipating the volatility evolution and showing the same volatility clusters observed in the assets. This approach provides a novel way to model asset markets with internal dynamics which changes quickly with time, making it impossible to define a fixed model to fit the empirical observations.
Stochastic modeling of consumer preferences for health care institutions.
Malhotra, N K
1983-01-01
This paper proposes a stochastic procedure for modeling consumer preferences via LOGIT analysis. First, a simple, non-technical exposition of the use of a stochastic approach in health care marketing is presented. Second, a study illustrating the application of the LOGIT model in assessing consumer preferences for hospitals is given. The paper concludes with several implications of the proposed approach.
A stochastic modeling of recurrent measles epidemic | Kassem ...
African Journals Online (AJOL)
A simple stochastic mathematical model is developed and investigated for the dynamics of measles epidemic. The model, which is a multi-dimensional diffusion process, includes susceptible individuals, latent (exposed), infected and removed individuals. Stochastic effects are assumed to arise in the process of infection of ...
Review of "Stochastic Modelling for Systems Biology" by Darren Wilkinson
Directory of Open Access Journals (Sweden)
Bullinger Eric
2006-12-01
Full Text Available Abstract "Stochastic Modelling for Systems Biology" by Darren Wilkinson introduces the peculiarities of stochastic modelling in biology. This book is particularly suited to as a textbook or for self-study, and for readers with a theoretical background.
Approximate models for broken clouds in stochastic radiative transfer theory
International Nuclear Information System (INIS)
Doicu, Adrian; Efremenko, Dmitry S.; Loyola, Diego; Trautmann, Thomas
2014-01-01
This paper presents approximate models in stochastic radiative transfer theory. The independent column approximation and its modified version with a solar source computed in a full three-dimensional atmosphere are formulated in a stochastic framework and for arbitrary cloud statistics. The nth-order stochastic models describing the independent column approximations are equivalent to the nth-order stochastic models for the original radiance fields in which the gradient vectors are neglected. Fast approximate models are further derived on the basis of zeroth-order stochastic models and the independent column approximation. The so-called “internal mixing” models assume a combination of the optical properties of the cloud and the clear sky, while the “external mixing” models assume a combination of the radiances corresponding to completely overcast and clear skies. A consistent treatment of internal and external mixing models is provided, and a new parameterization of the closure coefficient in the effective thickness approximation is given. An efficient computation of the closure coefficient for internal mixing models, using a previously derived vector stochastic model as a reference, is also presented. Equipped with appropriate look-up tables for the closure coefficient, these models can easily be integrated into operational trace gas retrieval systems that exploit absorption features in the near-IR solar spectrum. - Highlights: • Independent column approximation in a stochastic setting. • Fast internal and external mixing models for total and diffuse radiances. • Efficient optimization of internal mixing models to match reference models
Interplanetary Alfvenic fluctuations: A stochastic model
International Nuclear Information System (INIS)
Barnes, A.
1981-01-01
The strong alignment of the average directions of minimum magnetic variance and mean magnetic field in interplanetary Alfvenic fluctuations is inconsistent with the usual wave-propagation models. We investigate the concept of minimum variance for nonplanar Alfvenic fluctuations in which the field direction varies stochastically. It is found that the tendency of the minimum variance and mean field directions to be aligned may be purely a consequence of the randomness of the field direction. In particular, a well-defined direction of minimum variance does not imply that the fluctuations are necessarily planar. The fluctuation power spectrum is a power law for frequencies much higher than the inverse of the correlation time. The probability distribution of directions a randomly fluctuating field of constant magnitude is calculated. A new approach for observational studies of interplanetary fluctuations is suggested
Spatial Stochastic Point Models for Reservoir Characterization
Energy Technology Data Exchange (ETDEWEB)
Syversveen, Anne Randi
1997-12-31
The main part of this thesis discusses stochastic modelling of geology in petroleum reservoirs. A marked point model is defined for objects against a background in a two-dimensional vertical cross section of the reservoir. The model handles conditioning on observations from more than one well for each object and contains interaction between objects, and the objects have the correct length distribution when penetrated by wells. The model is developed in a Bayesian setting. The model and the simulation algorithm are demonstrated by means of an example with simulated data. The thesis also deals with object recognition in image analysis, in a Bayesian framework, and with a special type of spatial Cox processes called log-Gaussian Cox processes. In these processes, the logarithm of the intensity function is a Gaussian process. The class of log-Gaussian Cox processes provides flexible models for clustering. The distribution of such a process is completely characterized by the intensity and the pair correlation function of the Cox process. 170 refs., 37 figs., 5 tabs.
Random Modeling of Daily Rainfall and Runoff Using a Seasonal Model and Wavelet Denoising
Directory of Open Access Journals (Sweden)
Chien-ming Chou
2014-01-01
Full Text Available Instead of Fourier smoothing, this study applied wavelet denoising to acquire the smooth seasonal mean and corresponding perturbation term from daily rainfall and runoff data in traditional seasonal models, which use seasonal means for hydrological time series forecasting. The denoised rainfall and runoff time series data were regarded as the smooth seasonal mean. The probability distribution of the percentage coefficients can be obtained from calibrated daily rainfall and runoff data. For validated daily rainfall and runoff data, percentage coefficients were randomly generated according to the probability distribution and the law of linear proportion. Multiplying the generated percentage coefficient by the smooth seasonal mean resulted in the corresponding perturbation term. Random modeling of daily rainfall and runoff can be obtained by adding the perturbation term to the smooth seasonal mean. To verify the accuracy of the proposed method, daily rainfall and runoff data for the Wu-Tu watershed were analyzed. The analytical results demonstrate that wavelet denoising enhances the precision of daily rainfall and runoff modeling of the seasonal model. In addition, the wavelet denoising technique proposed in this study can obtain the smooth seasonal mean of rainfall and runoff processes and is suitable for modeling actual daily rainfall and runoff processes.
12th Workshop on Stochastic Models, Statistics and Their Applications
Rafajłowicz, Ewaryst; Szajowski, Krzysztof
2015-01-01
This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.
DEFF Research Database (Denmark)
Löwe, Roland; Mikkelsen, Peter Steen; Rasmussen, Michael R.
2013-01-01
Merging of radar rainfall data with rain gauge measurements is a common approach to overcome problems in deriving rain intensities from radar measurements. We extend an existing approach for adjustment of C-band radar data using state-space models and use the resulting rainfall intensities as input...
DEFF Research Database (Denmark)
Löwe, Roland; Mikkelsen, Peter Steen; Rasmussen, Michael R.
2012-01-01
Merging of radar rainfall data with rain gauge measurements is a common approach to overcome problems in deriving rain intensities from radar measurements. We extend an existing approach for adjustment of C-band radar data using state-space models and use the resulting rainfall intensities as input...
Stochastic modeling of sunshine number data
Energy Technology Data Exchange (ETDEWEB)
Brabec, Marek, E-mail: mbrabec@cs.cas.cz [Department of Nonlinear Modeling, Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodarenskou vezi 2, 182 07 Prague 8 (Czech Republic); Paulescu, Marius [Physics Department, West University of Timisoara, V. Parvan 4, 300223 Timisoara (Romania); Badescu, Viorel [Candida Oancea Institute, Polytechnic University of Bucharest, Spl. Independentei 313, 060042 Bucharest (Romania)
2013-11-13
In this paper, we will present a unified statistical modeling framework for estimation and forecasting sunshine number (SSN) data. Sunshine number has been proposed earlier to describe sunshine time series in qualitative terms (Theor Appl Climatol 72 (2002) 127-136) and since then, it was shown to be useful not only for theoretical purposes but also for practical considerations, e.g. those related to the development of photovoltaic energy production. Statistical modeling and prediction of SSN as a binary time series has been challenging problem, however. Our statistical model for SSN time series is based on an underlying stochastic process formulation of Markov chain type. We will show how its transition probabilities can be efficiently estimated within logistic regression framework. In fact, our logistic Markovian model can be relatively easily fitted via maximum likelihood approach. This is optimal in many respects and it also enables us to use formalized statistical inference theory to obtain not only the point estimates of transition probabilities and their functions of interest, but also related uncertainties, as well as to test of various hypotheses of practical interest, etc. It is straightforward to deal with non-homogeneous transition probabilities in this framework. Very importantly from both physical and practical points of view, logistic Markov model class allows us to test hypotheses about how SSN dependents on various external covariates (e.g. elevation angle, solar time, etc.) and about details of the dynamic model (order and functional shape of the Markov kernel, etc.). Therefore, using generalized additive model approach (GAM), we can fit and compare models of various complexity which insist on keeping physical interpretation of the statistical model and its parts. After introducing the Markovian model and general approach for identification of its parameters, we will illustrate its use and performance on high resolution SSN data from the Solar
Stochastic modeling of sunshine number data
Brabec, Marek; Paulescu, Marius; Badescu, Viorel
2013-11-01
In this paper, we will present a unified statistical modeling framework for estimation and forecasting sunshine number (SSN) data. Sunshine number has been proposed earlier to describe sunshine time series in qualitative terms (Theor Appl Climatol 72 (2002) 127-136) and since then, it was shown to be useful not only for theoretical purposes but also for practical considerations, e.g. those related to the development of photovoltaic energy production. Statistical modeling and prediction of SSN as a binary time series has been challenging problem, however. Our statistical model for SSN time series is based on an underlying stochastic process formulation of Markov chain type. We will show how its transition probabilities can be efficiently estimated within logistic regression framework. In fact, our logistic Markovian model can be relatively easily fitted via maximum likelihood approach. This is optimal in many respects and it also enables us to use formalized statistical inference theory to obtain not only the point estimates of transition probabilities and their functions of interest, but also related uncertainties, as well as to test of various hypotheses of practical interest, etc. It is straightforward to deal with non-homogeneous transition probabilities in this framework. Very importantly from both physical and practical points of view, logistic Markov model class allows us to test hypotheses about how SSN dependents on various external covariates (e.g. elevation angle, solar time, etc.) and about details of the dynamic model (order and functional shape of the Markov kernel, etc.). Therefore, using generalized additive model approach (GAM), we can fit and compare models of various complexity which insist on keeping physical interpretation of the statistical model and its parts. After introducing the Markovian model and general approach for identification of its parameters, we will illustrate its use and performance on high resolution SSN data from the Solar
Stochastic modeling of sunshine number data
International Nuclear Information System (INIS)
Brabec, Marek; Paulescu, Marius; Badescu, Viorel
2013-01-01
In this paper, we will present a unified statistical modeling framework for estimation and forecasting sunshine number (SSN) data. Sunshine number has been proposed earlier to describe sunshine time series in qualitative terms (Theor Appl Climatol 72 (2002) 127-136) and since then, it was shown to be useful not only for theoretical purposes but also for practical considerations, e.g. those related to the development of photovoltaic energy production. Statistical modeling and prediction of SSN as a binary time series has been challenging problem, however. Our statistical model for SSN time series is based on an underlying stochastic process formulation of Markov chain type. We will show how its transition probabilities can be efficiently estimated within logistic regression framework. In fact, our logistic Markovian model can be relatively easily fitted via maximum likelihood approach. This is optimal in many respects and it also enables us to use formalized statistical inference theory to obtain not only the point estimates of transition probabilities and their functions of interest, but also related uncertainties, as well as to test of various hypotheses of practical interest, etc. It is straightforward to deal with non-homogeneous transition probabilities in this framework. Very importantly from both physical and practical points of view, logistic Markov model class allows us to test hypotheses about how SSN dependents on various external covariates (e.g. elevation angle, solar time, etc.) and about details of the dynamic model (order and functional shape of the Markov kernel, etc.). Therefore, using generalized additive model approach (GAM), we can fit and compare models of various complexity which insist on keeping physical interpretation of the statistical model and its parts. After introducing the Markovian model and general approach for identification of its parameters, we will illustrate its use and performance on high resolution SSN data from the Solar
Influence of rainfall observation network on model calibration and application
Directory of Open Access Journals (Sweden)
A. Bárdossy
2008-01-01
Full Text Available The objective in this study is to investigate the influence of the spatial resolution of the rainfall input on the model calibration and application. The analysis is carried out by varying the distribution of the raingauge network. A meso-scale catchment located in southwest Germany has been selected for this study. First, the semi-distributed HBV model is calibrated with the precipitation interpolated from the available observed rainfall of the different raingauge networks. An automatic calibration method based on the combinatorial optimization algorithm simulated annealing is applied. The performance of the hydrological model is analyzed as a function of the raingauge density. Secondly, the calibrated model is validated using interpolated precipitation from the same raingauge density used for the calibration as well as interpolated precipitation based on networks of reduced and increased raingauge density. Lastly, the effect of missing rainfall data is investigated by using a multiple linear regression approach for filling in the missing measurements. The model, calibrated with the complete set of observed data, is then run in the validation period using the above described precipitation field. The simulated hydrographs obtained in the above described three sets of experiments are analyzed through the comparisons of the computed Nash-Sutcliffe coefficient and several goodness-of-fit indexes. The results show that the model using different raingauge networks might need re-calibration of the model parameters, specifically model calibrated on relatively sparse precipitation information might perform well on dense precipitation information while model calibrated on dense precipitation information fails on sparse precipitation information. Also, the model calibrated with the complete set of observed precipitation and run with incomplete observed data associated with the data estimated using multiple linear regressions, at the locations treated as
Gompertzian stochastic model with delay effect to cervical cancer growth
International Nuclear Information System (INIS)
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah
2015-01-01
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits
Gompertzian stochastic model with delay effect to cervical cancer growth
Energy Technology Data Exchange (ETDEWEB)
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor and UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2015-02-03
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.
Stochastic growth logistic model with aftereffect for batch fermentation process
Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md
2014-06-01
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.
Stochastic growth logistic model with aftereffect for batch fermentation process
International Nuclear Information System (INIS)
Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md
2014-01-01
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits
Stochastic growth logistic model with aftereffect for batch fermentation process
Energy Technology Data Exchange (ETDEWEB)
Rosli, Norhayati; Ayoubi, Tawfiqullah [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah; Rahman, Haliza Abdul [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia); Salleh, Madihah Md [Department of Biotechnology Industry, Faculty of Biosciences and Bioengineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2014-06-19
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.
Simultaneous perturbation stochastic approximation for tidal models
Altaf, M.U.
2011-05-12
The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.
Simultaneous perturbation stochastic approximation for tidal models
Altaf, M.U.; Heemink, A.W.; Verlaan, M.; Hoteit, Ibrahim
2011-01-01
The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.
A stochastic model for early placental development.
Cotter, Simon L
2014-08-01
In the human, placental structure is closely related to placental function and consequent pregnancy outcome. Studies have noted abnormal placental shape in small-for-gestational-age infants which extends to increased lifetime risk of cardiovascular disease. The origins and determinants of placental shape are incompletely understood and are difficult to study in vivo. In this paper, we model the early development of the human placenta, based on the hypothesis that this is driven by a chemoattractant effect emanating from proximal spiral arteries in the decidua. We derive and explore a two-dimensional stochastic model, and investigate the effects of loss of spiral arteries in regions near to the cord insertion on the shape of the placenta. This model demonstrates that disruption of spiral arteries can exert profound effects on placental shape, particularly if this is close to the cord insertion. Thus, placental shape reflects the underlying maternal vascular bed. Abnormal placental shape may reflect an abnormal uterine environment, predisposing to pregnancy complications. Through statistical analysis of model placentas, we are able to characterize the probability that a given placenta grew in a disrupted environment, and even able to distinguish between different disruptions.
Stochastic model of the spinning electron
International Nuclear Information System (INIS)
Simaciu, I.; Borsos, Z.
2002-01-01
In Stochastic Electrodynamics (SED) it is demonstrated that electrostatic interaction is the result of the scattering of the Classical Zero-Point Field (CZPF) background by the charged particles. In such models, the electron is modelled as a two-dimensional oscillator, which interacts with the electric component of the CZPF background. The electron with spin is not only an electric monopole but also a magnetic dipole. The interaction of the spin electron with the CZPF background is not only electric but also magnetic. We calculate the scattering cross-section of magnetic dipole in the situation when a magnetic field, variable in time B arrow = B 0 arrow sin ωt, acts over the rigid magnetic dipole given by the symmetry of the model. The cross-section of a magnetic dipole σ m must be equal to the cross-section of an electric monopole σ e . This equality between σ m and σ e cross-sections is motivated, too, by the fact that, in the model of the two-dimensional oscillator, the electric charge q e has the motion speed c. (authors)
Stochastic modelling of two-phase flows including phase change
International Nuclear Information System (INIS)
Hurisse, O.; Minier, J.P.
2011-01-01
Stochastic modelling has already been developed and applied for single-phase flows and incompressible two-phase flows. In this article, we propose an extension of this modelling approach to two-phase flows including phase change (e.g. for steam-water flows). Two aspects are emphasised: a stochastic model accounting for phase transition and a modelling constraint which arises from volume conservation. To illustrate the whole approach, some remarks are eventually proposed for two-fluid models. (authors)
Warning Model for Shallow Landslides Induced by Extreme Rainfall
Directory of Open Access Journals (Sweden)
Lien-Kwei Chien
2015-08-01
Full Text Available In this study, the geophysical properties of the landslide-prone catchment of the Gaoping River in Taiwan were investigated using zones based on landslide history in conjunction with landslide analysis using a deterministic approach based on the TRIGRS (Transient Rainfall Infiltration and Grid-based Regional Slope-Stability model. Typhoon Morakot in 2009 was selected as a simulation scenario to calibrate the combination of geophysical parameters in each zone before analyzing changes in the factor of safety (FS. Considering the amount of response time required for typhoons, suitable FS thresholds for landslide warnings are proposed for each town in the catchment area. Typhoon Fanapi of 2010 was used as a test scenario to verify the applicability of the FS as well as the efficacy of the cumulative rainfall thresholds derived in this study. Finally, the amount of response time provided by the FS thresholds in cases of yellow and red alerts was determined. All five of the landslide events reported by the Soil and Water Conservation Bureau were listed among the unstable sites identified in the proposed model, thereby demonstrating its effectiveness and accuracy in determining unstable areas and areas that require evacuation. These cumulative rainfall thresholds provide a valuable reference to guide disaster prevention authorities in the issuance of yellow and red alerts with the ability to reduce losses and save lives.
Survival Analysis of a Nonautonomous Logistic Model with Stochastic Perturbation
Directory of Open Access Journals (Sweden)
Chun Lu
2012-01-01
Full Text Available Taking white noise into account, a stochastic nonautonomous logistic model is proposed and investigated. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, stochastic permanence, and global asymptotic stability are established. Moreover, the threshold between weak persistence and extinction is obtained. Finally, we introduce some numerical simulink graphics to illustrate our main results.
On the small-time behavior of stochastic logistic models
Directory of Open Access Journals (Sweden)
Dung Tien Nguyen
2017-09-01
Full Text Available In this paper we investigate the small-time behaviors of the solution to a stochastic logistic model. The obtained results allow us to estimate the number of individuals in the population and can be used to study stochastic prey-predator systems.
Analysis and reconstruction of stochastic coupled map lattice models
International Nuclear Information System (INIS)
Coca, Daniel; Billings, Stephen A.
2003-01-01
The Letter introduces a general stochastic coupled lattice map model together with an algorithm to estimate the nodal equations involved based only on a small set of observable variables and in the presence of stochastic perturbations. More general forms of the Frobenius-Perron and the transfer operators, which describe the evolution of densities under the action of the CML transformation, are derived
A probabilistic graphical model based stochastic input model construction
International Nuclear Information System (INIS)
Wan, Jiang; Zabaras, Nicholas
2014-01-01
Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks. However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. - Highlights: • Data-driven stochastic input models without the assumption of independence of the reduced random variables. • The problem is transformed to a Bayesian network structure learning problem. • Examples are given in flows in random media
Stochastic modeling of virus capsid assembly pathways
Schwartz, Russell
2009-03-01
Virus capsids have become a key model system for understanding self-assembly due to their high complexity, robust and efficient assembly processes, and experimental tractability. Our ability to directly examine and manipulate capsid assembly kinetics in detail nonetheless remains limited, creating a need for computer models that can infer experimentally inaccessible features of the assembly process and explore the effects of hypothetical manipulations on assembly trajectories. We have developed novel algorithms for stochastic simulation of capsid assembly [1,2] that allow us to model capsid assembly over broad parameter spaces [3]. We apply these methods to study the nature of assembly pathway control in virus capsids as well as their sensitivity to assembly conditions and possible experimental interventions. [4pt] [1] F. Jamalyaria, R. Rohlfs, and R. Schwartz. J Comp Phys 204, 100 (2005). [0pt] [2] N. Misra and R. Schwartz. J Chem Phys 129, in press (2008). [0pt] [3] B. Sweeney, T. Zhang, and R. Schwartz. Biophys J 94, 772 (2008).
Systematic parameter inference in stochastic mesoscopic modeling
Energy Technology Data Exchange (ETDEWEB)
Lei, Huan; Yang, Xiu [Pacific Northwest National Laboratory, Richland, WA 99352 (United States); Li, Zhen [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States); Karniadakis, George Em, E-mail: george_karniadakis@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)
2017-02-01
We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving dissipative particle dynamics (eDPD). The response surfaces of various target properties (viscosity, diffusivity, pressure, etc.) with respect to model parameters are constructed based on the generalized polynomial chaos (gPC) expansion using simulation results on sampling points (e.g., individual parameter sets). To alleviate the computational cost to evaluate the target properties, we employ the compressive sensing method to compute the coefficients of the dominant gPC terms given the prior knowledge that the coefficients are “sparse”. The proposed method shows comparable accuracy with the standard probabilistic collocation method (PCM) while it imposes a much weaker restriction on the number of the simulation samples especially for systems with high dimensional parametric space. Fully access to the response surfaces within the confidence range enables us to infer the optimal force parameters given the desirable values of target properties at the macroscopic scale. Moreover, it enables us to investigate the intrinsic relationship between the model parameters, identify possible degeneracies in the parameter space, and optimize the model by eliminating model redundancies. The proposed method provides an efficient alternative approach for constructing mesoscopic models by inferring model parameters to recover target properties of the physics systems (e.g., from experimental measurements), where those force field parameters and formulation cannot be derived from the microscopic level in a straight forward way.
Modelling rainfall amounts using mixed-gamma model for Kuantan district
Zakaria, Roslinazairimah; Moslim, Nor Hafizah
2017-05-01
An efficient design of flood mitigation and construction of crop growth models depend upon good understanding of the rainfall process and characteristics. Gamma distribution is usually used to model nonzero rainfall amounts. In this study, the mixed-gamma model is applied to accommodate both zero and nonzero rainfall amounts. The mixed-gamma model presented is for the independent case. The formulae of mean and variance are derived for the sum of two and three independent mixed-gamma variables, respectively. Firstly, the gamma distribution is used to model the nonzero rainfall amounts and the parameters of the distribution (shape and scale) are estimated using the maximum likelihood estimation method. Then, the mixed-gamma model is defined for both zero and nonzero rainfall amounts simultaneously. The formulae of mean and variance for the sum of two and three independent mixed-gamma variables derived are tested using the monthly rainfall amounts from rainfall stations within Kuantan district in Pahang Malaysia. Based on the Kolmogorov-Smirnov goodness of fit test, the results demonstrate that the descriptive statistics of the observed sum of rainfall amounts is not significantly different at 5% significance level from the generated sum of independent mixed-gamma variables. The methodology and formulae demonstrated can be applied to find the sum of more than three independent mixed-gamma variables.
A hierarchical stochastic model for bistable perception.
Directory of Open Access Journals (Sweden)
Stefan Albert
2017-11-01
Full Text Available Viewing of ambiguous stimuli can lead to bistable perception alternating between the possible percepts. During continuous presentation of ambiguous stimuli, percept changes occur as single events, whereas during intermittent presentation of ambiguous stimuli, percept changes occur at more or less regular intervals either as single events or bursts. Response patterns can be highly variable and have been reported to show systematic differences between patients with schizophrenia and healthy controls. Existing models of bistable perception often use detailed assumptions and large parameter sets which make parameter estimation challenging. Here we propose a parsimonious stochastic model that provides a link between empirical data analysis of the observed response patterns and detailed models of underlying neuronal processes. Firstly, we use a Hidden Markov Model (HMM for the times between percept changes, which assumes one single state in continuous presentation and a stable and an unstable state in intermittent presentation. The HMM captures the observed differences between patients with schizophrenia and healthy controls, but remains descriptive. Therefore, we secondly propose a hierarchical Brownian model (HBM, which produces similar response patterns but also provides a relation to potential underlying mechanisms. The main idea is that neuronal activity is described as an activity difference between two competing neuronal populations reflected in Brownian motions with drift. This differential activity generates switching between the two conflicting percepts and between stable and unstable states with similar mechanisms on different neuronal levels. With only a small number of parameters, the HBM can be fitted closely to a high variety of response patterns and captures group differences between healthy controls and patients with schizophrenia. At the same time, it provides a link to mechanistic models of bistable perception, linking the group
A hierarchical stochastic model for bistable perception.
Albert, Stefan; Schmack, Katharina; Sterzer, Philipp; Schneider, Gaby
2017-11-01
Viewing of ambiguous stimuli can lead to bistable perception alternating between the possible percepts. During continuous presentation of ambiguous stimuli, percept changes occur as single events, whereas during intermittent presentation of ambiguous stimuli, percept changes occur at more or less regular intervals either as single events or bursts. Response patterns can be highly variable and have been reported to show systematic differences between patients with schizophrenia and healthy controls. Existing models of bistable perception often use detailed assumptions and large parameter sets which make parameter estimation challenging. Here we propose a parsimonious stochastic model that provides a link between empirical data analysis of the observed response patterns and detailed models of underlying neuronal processes. Firstly, we use a Hidden Markov Model (HMM) for the times between percept changes, which assumes one single state in continuous presentation and a stable and an unstable state in intermittent presentation. The HMM captures the observed differences between patients with schizophrenia and healthy controls, but remains descriptive. Therefore, we secondly propose a hierarchical Brownian model (HBM), which produces similar response patterns but also provides a relation to potential underlying mechanisms. The main idea is that neuronal activity is described as an activity difference between two competing neuronal populations reflected in Brownian motions with drift. This differential activity generates switching between the two conflicting percepts and between stable and unstable states with similar mechanisms on different neuronal levels. With only a small number of parameters, the HBM can be fitted closely to a high variety of response patterns and captures group differences between healthy controls and patients with schizophrenia. At the same time, it provides a link to mechanistic models of bistable perception, linking the group differences to
Stochastic modeling of wetland-groundwater systems
Bertassello, Leonardo Enrico; Rao, P. Suresh C.; Park, Jeryang; Jawitz, James W.; Botter, Gianluca
2018-02-01
Modeling and data analyses were used in this study to examine the temporal hydrological variability in geographically isolated wetlands (GIWs), as influenced by hydrologic connectivity to shallow groundwater, wetland bathymetry, and subject to stochastic hydro-climatic forcing. We examined the general case of GIWs coupled to shallow groundwater through exfiltration or infiltration across wetland bottom. We also examined limiting case with the wetland stage as the local expression of the shallow groundwater. We derive analytical expressions for the steady-state probability density functions (pdfs) for wetland water storage and stage using few, scaled, physically-based parameters. In addition, we analyze the hydrologic crossing time properties of wetland stage, and the dependence of the mean hydroperiod on climatic and wetland morphologic attributes. Our analyses show that it is crucial to account for shallow groundwater connectivity to fully understand the hydrologic dynamics in wetlands. The application of the model to two different case studies in Florida, jointly with a detailed sensitivity analysis, allowed us to identify the main drivers of hydrologic dynamics in GIWs under different climate and morphologic conditions.
Reversibility in Quantum Models of Stochastic Processes
Gier, David; Crutchfield, James; Mahoney, John; James, Ryan
Natural phenomena such as time series of neural firing, orientation of layers in crystal stacking and successive measurements in spin-systems are inherently probabilistic. The provably minimal classical models of such stochastic processes are ɛ-machines, which consist of internal states, transition probabilities between states and output values. The topological properties of the ɛ-machine for a given process characterize the structure, memory and patterns of that process. However ɛ-machines are often not ideal because their statistical complexity (Cμ) is demonstrably greater than the excess entropy (E) of the processes they represent. Quantum models (q-machines) of the same processes can do better in that their statistical complexity (Cq) obeys the relation Cμ >= Cq >= E. q-machines can be constructed to consider longer lengths of strings, resulting in greater compression. With code-words of sufficiently long length, the statistical complexity becomes time-symmetric - a feature apparently novel to this quantum representation. This result has ramifications for compression of classical information in quantum computing and quantum communication technology.
Real Time Updating in Distributed Urban Rainfall Runoff Modelling
DEFF Research Database (Denmark)
Borup, Morten; Madsen, Henrik
that are being updated from system measurements was studied. The results showed that the fact alone that it takes time for rainfall data to travel the distance between gauges and catchments has such a big negative effect on the forecast skill of updated models, that it can justify the choice of even very...... as in a real data case study. The results confirmed that the method is indeed suitable for DUDMs and that it can be used to utilise upstream as well as downstream water level and flow observations to improve model estimates and forecasts. Due to upper and lower sensor limits many sensors in urban drainage...
Uncertainty modelling of atmospheric dispersion by stochastic ...
Indian Academy of Sciences (India)
by stochastic response surface method under aleatory ... 3Health Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India e-mail: ...... Brandimarte P 2011 Quantitative methods: An introduction for business management.
Stochastic models for predicting environmental impact in aquatic ecosystems
International Nuclear Information System (INIS)
Stewart-Oaten, A.
1986-01-01
The purpose of stochastic predictions are discussed in relation to the environmental impacts of nuclear power plants on aquatic ecosystems. One purpose is to aid in making rational decisions about whether a power plant should be built, where, and how it should be designed. The other purpose is to check on the models themselves in the light of what eventually happens. The author discusses the role or statistical decision theory in the decision-making problem. Various types of stochastic models and their problems are presented. In addition some suggestions are made for generating usable stochastic models, and checking and improving on them. 12 references
Stochastic Watershed Models for Risk Based Decision Making
Vogel, R. M.
2017-12-01
Over half a century ago, the Harvard Water Program introduced the field of operational or synthetic hydrology providing stochastic streamflow models (SSMs), which could generate ensembles of synthetic streamflow traces useful for hydrologic risk management. The application of SSMs, based on streamflow observations alone, revolutionized water resources planning activities, yet has fallen out of favor due, in part, to their inability to account for the now nearly ubiquitous anthropogenic influences on streamflow. This commentary advances the modern equivalent of SSMs, termed `stochastic watershed models' (SWMs) useful as input to nearly all modern risk based water resource decision making approaches. SWMs are deterministic watershed models implemented using stochastic meteorological series, model parameters and model errors, to generate ensembles of streamflow traces that represent the variability in possible future streamflows. SWMs combine deterministic watershed models, which are ideally suited to accounting for anthropogenic influences, with recent developments in uncertainty analysis and principles of stochastic simulation
Model selection for integrated pest management with stochasticity.
Akman, Olcay; Comar, Timothy D; Hrozencik, Daniel
2018-04-07
In Song and Xiang (2006), an integrated pest management model with periodically varying climatic conditions was introduced. In order to address a wider range of environmental effects, the authors here have embarked upon a series of studies resulting in a more flexible modeling approach. In Akman et al. (2013), the impact of randomly changing environmental conditions is examined by incorporating stochasticity into the birth pulse of the prey species. In Akman et al. (2014), the authors introduce a class of models via a mixture of two birth-pulse terms and determined conditions for the global and local asymptotic stability of the pest eradication solution. With this work, the authors unify the stochastic and mixture model components to create further flexibility in modeling the impacts of random environmental changes on an integrated pest management system. In particular, we first determine the conditions under which solutions of our deterministic mixture model are permanent. We then analyze the stochastic model to find the optimal value of the mixing parameter that minimizes the variance in the efficacy of the pesticide. Additionally, we perform a sensitivity analysis to show that the corresponding pesticide efficacy determined by this optimization technique is indeed robust. Through numerical simulations we show that permanence can be preserved in our stochastic model. Our study of the stochastic version of the model indicates that our results on the deterministic model provide informative conclusions about the behavior of the stochastic model. Copyright © 2017 Elsevier Ltd. All rights reserved.
Modeling stochasticity and robustness in gene regulatory networks.
Garg, Abhishek; Mohanram, Kartik; Di Cara, Alessandro; De Micheli, Giovanni; Xenarios, Ioannis
2009-06-15
Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations. In this article, we introduce the stochasticity in functions (SIF) model for simulating stochasticity in Boolean models of GRNs. By providing biological motivation behind the use of the SIF model and applying it to the T-helper and T-cell activation networks, we show that the SIF model provides more biologically robust results than the existing SIN model of stochasticity in GRNs. Algorithms are made available under our Boolean modeling toolbox, GenYsis. The software binaries can be downloaded from http://si2.epfl.ch/ approximately garg/genysis.html.
Directory of Open Access Journals (Sweden)
Nejc Bezak
2018-02-01
Full Text Available In the case of ungauged catchments, different procedures can be used to derive the design hydrograph and design peak discharge, which are crucial input data for the design of different hydrotechnical engineering structures, or the production of flood hazard maps. One of the possible approaches involves using a hydrological model where one can calculate the design hydrograph through the design of a rainfall event. This study investigates the impact of the design rainfall on the combined one-dimensional/two-dimensional (1D/2D hydraulic modelling results. The Glinščica Stream catchment located in Slovenia (central Europe is used as a case study. Ten different design rainfall events were compared for 10 and 100-year return periods, where we used Huff curves for the design rainfall event definition. The results indicate that the selection of the design rainfall event should be regarded as an important step, since the hydraulic modelling results for different scenarios differ significantly. In the presented experimental case study, the maximum flooded area extent was twice as large as the minimum one, and the maximum water velocity over flooded areas was more than 10 times larger than the minimum one. This can lead to the production of very different flood hazard maps, and consequently planning very different flood protection schemes.
On changes of measure in stochastic volatility models
Directory of Open Access Journals (Sweden)
Bernard Wong
2006-01-01
models. This had led many researchers to “assume the condition away,” even though the condition is not innocuous, and nonsensical results can occur if it is in fact not satisfied. We provide an applicable theorem to check the conditions for a general class of Markovian stochastic volatility models. As an example we will also provide a detailed analysis of the Stein and Stein and Heston stochastic volatility models.
Fitting PAC spectra with stochastic models: PolyPacFit
Energy Technology Data Exchange (ETDEWEB)
Zacate, M. O., E-mail: zacatem1@nku.edu [Northern Kentucky University, Department of Physics and Geology (United States); Evenson, W. E. [Utah Valley University, College of Science and Health (United States); Newhouse, R.; Collins, G. S. [Washington State University, Department of Physics and Astronomy (United States)
2010-04-15
PolyPacFit is an advanced fitting program for time-differential perturbed angular correlation (PAC) spectroscopy. It incorporates stochastic models and provides robust options for customization of fits. Notable features of the program include platform independence and support for (1) fits to stochastic models of hyperfine interactions, (2) user-defined constraints among model parameters, (3) fits to multiple spectra simultaneously, and (4) any spin nuclear probe.
Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates
Jiang, G.J.; van der Sluis, P.J.
2000-01-01
This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Directory of Open Access Journals (Sweden)
A. Valor
2013-01-01
Full Text Available The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.
Quantitative rainfall metrics for comparing volumetric rainfall retrievals to fine scale models
Collis, Scott; Tao, Wei-Kuo; Giangrande, Scott; Fridlind, Ann; Theisen, Adam; Jensen, Michael
2013-04-01
Precipitation processes play a significant role in the energy balance of convective systems for example, through latent heating and evaporative cooling. Heavy precipitation "cores" can also be a proxy for vigorous convection and vertical motions. However, comparisons between rainfall rate retrievals from volumetric remote sensors with forecast rain fields from high-resolution numerical weather prediction simulations are complicated by differences in the location and timing of storm morphological features. This presentation will outline a series of metrics for diagnosing the spatial variability and statistical properties of precipitation maps produced both from models and retrievals. We include existing metrics such as Contoured by Frequency Altitude Diagrams (Yuter and Houze 1995) and Statistical Coverage Products (May and Lane 2009) and propose new metrics based on morphology, cell and feature based statistics. Work presented focuses on observations from the ARM Southern Great Plains radar network consisting of three agile X-Band radar systems with a very dense coverage pattern and a C Band system providing site wide coverage. By combining multiple sensors resolutions of 250m2 can be achieved, allowing improved characterization of fine-scale features. Analyses compare data collected during the Midlattitude Continental Convective Clouds Experiment (MC3E) with simulations of observed systems using the NASA Unified Weather Research and Forecasting model. May, P. T., and T. P. Lane, 2009: A method for using weather radar data to test cloud resolving models. Meteorological Applications, 16, 425-425, doi:10.1002/met.150, 10.1002/met.150. Yuter, S. E., and R. A. Houze, 1995: Three-Dimensional Kinematic and Microphysical Evolution of Florida Cumulonimbus. Part II: Frequency Distributions of Vertical Velocity, Reflectivity, and Differential Reflectivity. Mon. Wea. Rev., 123, 1941-1963, doi:10.1175/1520-0493(1995)1232.0.CO;2.
Some Remarks on Stochastic Versions of the Ramsey Growth Model
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2012-01-01
Roč. 19, č. 29 (2012), s. 139-152 ISSN 1212-074X R&D Projects: GA ČR GAP402/10/1610; GA ČR GAP402/10/0956; GA ČR GAP402/11/0150 Institutional support: RVO:67985556 Keywords : Economic dynamics * Ramsey growth model with disturbance * stochastic dynamic programming * multistage stochastic programs Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2013/E/sladky-some remarks on stochastic versions of the ramsey growth model.pdf
Stochastic Modeling and Analysis of Power System with Renewable Generation
DEFF Research Database (Denmark)
Chen, Peiyuan
Unlike traditional fossil-fuel based power generation, renewable generation such as wind power relies on uncontrollable prime sources such as wind speed. Wind speed varies stochastically, which to a large extent determines the stochastic behavior of power generation from wind farms...... that such a stochastic model can be used to simulate the effect of load management on the load duration curve. As CHP units are turned on and off by regulating power, CHP generation has discrete output and thus can be modeled by a transition matrix based discrete Markov chain. As the CHP generation has a strong diurnal...
Modeling of the Monthly Rainfall-Runoff Process Through Regressions
Directory of Open Access Journals (Sweden)
Campos-Aranda Daniel Francisco
2014-10-01
Full Text Available To solve the problems associated with the assessment of water resources of a river, the modeling of the rainfall-runoff process (RRP allows the deduction of runoff missing data and to extend its record, since generally the information available on precipitation is larger. It also enables the estimation of inputs to reservoirs, when their building led to the suppression of the gauging station. The simplest mathematical model that can be set for the RRP is the linear regression or curve on a monthly basis. Such a model is described in detail and is calibrated with the simultaneous record of monthly rainfall and runoff in Ballesmi hydrometric station, which covers 35 years. Since the runoff of this station has an important contribution from the spring discharge, the record is corrected first by removing that contribution. In order to do this a procedure was developed based either on the monthly average regional runoff coefficients or on nearby and similar watershed; in this case the Tancuilín gauging station was used. Both stations belong to the Partial Hydrologic Region No. 26 (Lower Rio Panuco and are located within the state of San Luis Potosi, México. The study performed indicates that the monthly regression model, due to its conceptual approach, faithfully reproduces monthly average runoff volumes and achieves an excellent approximation in relation to the dispersion, proved by calculation of the means and standard deviations.
Stochastic models for predicting pitting corrosion damage of HLRW containers
International Nuclear Information System (INIS)
Henshall, G.A.
1991-10-01
Stochastic models for predicting aqueous pitting corrosion damage of high-level radioactive-waste containers are described. These models could be used to predict the time required for the first pit to penetrate a container and the increase in the number of breaches at later times, both of which would be useful in the repository system performance analysis. Monte Carlo implementations of the stochastic models are described, and predictions of induction time, survival probability and pit depth distributions are presented. These results suggest that the pit nucleation probability decreases with exposure time and that pit growth may be a stochastic process. The advantages and disadvantages of the stochastic approach, methods for modeling the effects of environment, and plans for future work are discussed
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Valor, A.; Caleyo, F.; Alfonso, L.; Velázquez, J. C.; Hallen, J. M.
2013-01-01
The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure ...
Stochastic Modelling of Shiroro River Stream flow Process
Musa, J. J
2013-01-01
Economists, social scientists and engineers provide insights into the drivers of anthropogenic climate change and the options for adaptation and mitigation, and yet other scientists, including geographers and biologists, study the impacts of climate change. This project concentrates mainly on the discharge from the Shiroro River. A stochastic approach is presented for modeling a time series by an Autoregressive Moving Average model (ARMA). The development and use of a stochastic stream flow m...
Stochastic higher spin six vertex model and Macdonald measures
Borodin, Alexei
2018-02-01
We prove an identity that relates the q-Laplace transform of the height function of a (higher spin inhomogeneous) stochastic six vertex model in a quadrant on one side and a multiplicative functional of a Macdonald measure on the other. The identity is used to prove the GUE Tracy-Widom asymptotics for two instances of the stochastic six vertex model via asymptotic analysis of the corresponding Schur measures.
Computational stochastic model of ions implantation
Energy Technology Data Exchange (ETDEWEB)
Zmievskaya, Galina I., E-mail: zmi@gmail.ru; Bondareva, Anna L., E-mail: bal310775@yandex.ru [M.V. Keldysh Institute of Applied Mathematics RAS, 4,Miusskaya sq., 125047 Moscow (Russian Federation); Levchenko, Tatiana V., E-mail: tatlevchenko@mail.ru [VNII Geosystem Russian Federal Center, Varshavskoye roadway, 8, Moscow (Russian Federation); Maino, Giuseppe, E-mail: giuseppe.maino@enea.it [Scuola di Lettere e BeniCulturali, University di Bologna, sede di Ravenna, via Mariani 5, 48100 Ravenna (Italy)
2015-03-10
Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.
A simple analytical infiltration model for short-duration rainfall
Wang, Kaiwen; Yang, Xiaohua; Liu, Xiaomang; Liu, Changming
2017-12-01
Many infiltration models have been proposed to simulate infiltration process. Different initial soil conditions and non-uniform initial water content can lead to infiltration simulation errors, especially for short-duration rainfall (SHR). Few infiltration models are specifically derived to eliminate the errors caused by the complex initial soil conditions. We present a simple analytical infiltration model for SHR infiltration simulation, i.e., Short-duration Infiltration Process model (SHIP model). The infiltration simulated by 5 models (i.e., SHIP (high) model, SHIP (middle) model, SHIP (low) model, Philip model and Parlange model) were compared based on numerical experiments and soil column experiments. In numerical experiments, SHIP (middle) and Parlange models had robust solutions for SHR infiltration simulation of 12 typical soils under different initial soil conditions. The absolute values of percent bias were less than 12% and the values of Nash and Sutcliffe efficiency were greater than 0.83. Additionally, in soil column experiments, infiltration rate fluctuated in a range because of non-uniform initial water content. SHIP (high) and SHIP (low) models can simulate an infiltration range, which successfully covered the fluctuation range of the observed infiltration rate. According to the robustness of solutions and the coverage of fluctuation range of infiltration rate, SHIP model can be integrated into hydrologic models to simulate SHR infiltration process and benefit the flood forecast.
Coupling Radar Rainfall to Hydrological Models for Water Abstraction Management
Asfaw, Alemayehu; Shucksmith, James; Smith, Andrea; MacDonald, Ken
2015-04-01
The impacts of climate change and growing water use are likely to put considerable pressure on water resources and the environment. In the UK, a reform to surface water abstraction policy has recently been proposed which aims to increase the efficiency of using available water resources whilst minimising impacts on the aquatic environment. Key aspects to this reform include the consideration of dynamic rather than static abstraction licensing as well as introducing water trading concepts. Dynamic licensing will permit varying levels of abstraction dependent on environmental conditions (i.e. river flow and quality). The practical implementation of an effective dynamic abstraction strategy requires suitable flow forecasting techniques to inform abstraction asset management. Potentially the predicted availability of water resources within a catchment can be coupled to predicted demand and current storage to inform a cost effective water resource management strategy which minimises environmental impacts. The aim of this work is to use a historical analysis of UK case study catchment to compare potential water resource availability using modelled dynamic abstraction scenario informed by a flow forecasting model, against observed abstraction under a conventional abstraction regime. The work also demonstrates the impacts of modelling uncertainties on the accuracy of predicted water availability over range of forecast lead times. The study utilised a conceptual rainfall-runoff model PDM - Probability-Distributed Model developed by Centre for Ecology & Hydrology - set up in the Dove River catchment (UK) using 1km2 resolution radar rainfall as inputs and 15 min resolution gauged flow data for calibration and validation. Data assimilation procedures are implemented to improve flow predictions using observed flow data. Uncertainties in the radar rainfall data used in the model are quantified using artificial statistical error model described by Gaussian distribution and
Sperber, K. R.; Palmer, T. N.
1996-11-01
The interannual variability of rainfall over the Indian subcontinent, the African Sahel, and the Nordeste region of Brazil have been evaluated in 32 models for the period 1979-88 as part of the Atmospheric Model Intercomparison Project (AMIP). The interannual variations of Nordeste rainfall are the most readily captured, owing to the intimate link with Pacific and Atlantic sea surface temperatures. The precipitation variations over India and the Sahel are less well simulated. Additionally, an Indian monsoon wind shear index was calculated for each model. Evaluation of the interannual variability of a wind shear index over the summer monsoon region indicates that the models exhibit greater fidelity in capturing the large-scale dynamic fluctuations than the regional-scale rainfall variations. A rainfall/SST teleconnection quality control was used to objectively stratify model performance. Skill scores improved for those models that qualitatively simulated the observed rainfall/El Niño- Southern Oscillation SST correlation pattern. This subset of models also had a rainfall climatology that was in better agreement with observations, indicating a link between systematic model error and the ability to simulate interannual variations.A suite of six European Centre for Medium-Range Weather Forecasts (ECMWF) AMIP runs (differing only in their initial conditions) have also been examined. As observed, all-India rainfall was enhanced in 1988 relative to 1987 in each of these realizations. All-India rainfall variability during other years showed little or no predictability, possibly due to internal chaotic dynamics associated with intraseasonal monsoon fluctuations and/or unpredictable land surface process interactions. The interannual variations of Nordeste rainfall were best represented. The State University of New York at Albany/National Center for Atmospheric Research Genesis model was run in five initial condition realizations. In this model, the Nordeste rainfall
Haberlandt, Uwe; Wallner, Markus; Radtke, Imke
2013-04-01
Derived flood frequency analysis based on continuous hydrological modelling is very demanding regarding the required length and temporal resolution of precipitation input data. Often such flood predictions are obtained using long precipitation time series from stochastic approaches or from regional climate models as input. However, the calibration of the hydrological model is usually done using short time series of observed data. This inconsistent employment of different data types for calibration and application of a hydrological model increases its uncertainty. Here, it is proposed to calibrate a hydrological model directly on probability distributions of observed peak flows using model based rainfall in line with its later application. Two examples are given to illustrate the idea. The first one deals with classical derived flood frequency analysis using input data from an hourly stochastic rainfall model. The second one concerns a climate impact analysis using hourly precipitation from a regional climate model. The results show that: (I) the same type of precipitation input data should be used for calibration and application of the hydrological model, (II) a model calibrated on extreme conditions works quite well for average conditions but not vice versa, (III) the calibration of the hydrological model using regional climate model data works as an implicit bias correction method and (IV) the best performance for flood estimation is usually obtained when model based precipitation and observed probability distribution of peak flows are used for model calibration.
Gao, S.; Fang, N. Z.
2017-12-01
A previously developed Dynamic Moving Storm (DMS) generator is a multivariate rainfall model simulating the complex nature of precipitation field: spatial variability, temporal variability, and storm movement. Previous effort by the authors has investigated the sensitivity of DMS parameters on corresponding hydrologic responses by using synthetic storms. In this study, the DMS generator has been upgraded to generate more realistic precipitation field. The dependence of hydrologic responses on rainfall features was investigated by dissecting the precipitation field into rain cells and modifying their spatio-temporal specification individually. To retrieve DMS parameters from radar rainfall data, rain cell segmentation and tracking algorithms were respectively developed and applied on high resolution radar rainfall data (1) to spatially determine the rain cells within individual radar image and (2) to temporally analyze their dynamic behavior. Statistics of DMS parameters were established by processing a long record of rainfall data (10 years) to keep the modification on real storms within the limit of regional climatology. Empirical distributions of the DMS parameters were calculated to reveal any preferential pattern and seasonality. Subsequently, the WRF-Hydro model forced by the remodeled and modified precipitation was used for hydrologic simulation. The study area was the Upper Trinity River Basin (UTRB) watershed, Texas; and two kinds of high resolution radar data i.e. the Next-Generation Radar (NEXRAD) level III Digital Hybrid Reflectivity (DHR) product and Multi-Radar Multi-Sensor (MRMS) precipitation rate product, were utilized to establish parameter statistics and to recreate/remodel historical events respectively. The results demonstrated that rainfall duration is a significant linkage between DMS parameters and their hydrologic impacts—any combination of spatiotemporal characteristics that keep rain cells longer over the catchment will produce higher
Composed particle model in stochastic electrodynamics
International Nuclear Information System (INIS)
Brunini, S.A.
1985-01-01
We analyse the statistical properties of the non-relativistic motion of a particle that has two constituents having finite nasses and charges. The main interaction is in contact with thermal and zero point radiation of Stochastic Electrodynamics. (M.W.O.) [pt
Directory of Open Access Journals (Sweden)
Elston Timothy C
2004-03-01
Full Text Available Abstract Background Intrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks. Results We have developed the software package Biochemical Network Stochastic Simulator (BioNetS for efficientlyand accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solvesthe appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from http://www.biospice.org. BioNetS also can be run as a stand alone package. All the required files are accessible from http://x.amath.unc.edu/BioNetS. Conclusions We have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems.
Multivariate moment closure techniques for stochastic kinetic models
International Nuclear Information System (INIS)
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-01-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs
Multivariate moment closure techniques for stochastic kinetic models
Energy Technology Data Exchange (ETDEWEB)
Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H., E-mail: m.stumpf@imperial.ac.uk [Department of Life Sciences, Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ (United Kingdom)
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Stochastic bifurcation in a model of love with colored noise
Yue, Xiaokui; Dai, Honghua; Yuan, Jianping
2015-07-01
In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.
A complementarity model for solving stochastic natural gas market equilibria
International Nuclear Information System (INIS)
Zhuang Jifang; Gabriel, Steven A.
2008-01-01
This paper presents a stochastic equilibrium model for deregulated natural gas markets. Each market participant (pipeline operators, producers, etc.) solves a stochastic optimization problem whose optimality conditions, when combined with market-clearing conditions give rise to a certain mixed complementarity problem (MiCP). The stochastic aspects are depicted by a recourse problem for each player in which the first-stage decisions relate to long-term contracts and the second-stage decisions relate to spot market activities for three seasons. Besides showing that such a market model is an instance of a MiCP, we provide theoretical results concerning long-term and spot market prices and solve the resulting MiCP for a small yet representative market. We also note an interesting observation for the value of the stochastic solution for non-optimization problems
Tsunamis: stochastic models of occurrence and generation mechanisms
Geist, Eric L.; Oglesby, David D.
2014-01-01
The devastating consequences of the 2004 Indian Ocean and 2011 Japan tsunamis have led to increased research into many different aspects of the tsunami phenomenon. In this entry, we review research related to the observed complexity and uncertainty associated with tsunami generation, propagation, and occurrence described and analyzed using a variety of stochastic methods. In each case, seismogenic tsunamis are primarily considered. Stochastic models are developed from the physical theories that govern tsunami evolution combined with empirical models fitted to seismic and tsunami observations, as well as tsunami catalogs. These stochastic methods are key to providing probabilistic forecasts and hazard assessments for tsunamis. The stochastic methods described here are similar to those described for earthquakes (Vere-Jones 2013) and volcanoes (Bebbington 2013) in this encyclopedia.
A complementarity model for solving stochastic natural gas market equilibria
International Nuclear Information System (INIS)
Jifang Zhuang; Gabriel, S.A.
2008-01-01
This paper presents a stochastic equilibrium model for deregulated natural gas markets. Each market participant (pipeline operators, producers, etc.) solves a stochastic optimization problem whose optimality conditions, when combined with market-clearing conditions give rise to a certain mixed complementarity problem (MiCP). The stochastic aspects are depicted by a recourse problem for each player in which the first-stage decisions relate to long-term contracts and the second-stage decisions relate to spot market activities for three seasons. Besides showing that such a market model is an instance of a MiCP, we provide theoretical results concerning long-term and spot market prices and solve the resulting MiCP for a small yet representative market. We also note an interesting observation for the value of the stochastic solution for non-optimization problems. (author)
Huang, Y. F.; Tsang, Y. P.
2017-12-01
Rainfall in Hawaii is characterized with high spatial and temporal variability. In the south side of Oahu, the Manoa watershed, with an area of 11 km2, has the annual maximum rainfall of 3900mm and the minimum rainfall of 1000 mm. Despite this high spatial heterogeneity, the rain gage network seems insufficiently capture this pattern. When simulating stream flow and predicting floods with hydrological models in Hawaii, the model performance is often unsatisfactory because of inadequate representation of rainfall data. Longman et al. (in prep.) have developed the spatially distributed daily rainfall across the Hawaiian Islands by applying ordinary kriging, yet these data have not been applied to hydrological models. In this study, we used the Soil and Water Assessment Tool (SWAT) model to assess the streamflow simulation by applying spatially-distributed rainfall in the Manoa watershed. We first used point daily-rainfall at Lyon Arboretum from National Center of Environmental Information (NCEI) as the uniform rainfall input. Secondly, we summarized sub-watershed mean rainfall from the daily spatial-statistical rainfall. Both rainfall data are available from 1999 to 2014. The SWAT was set up for five-year warm-up, nine-year calibration, and two-year validation. The model parameters were calibrated and validated with four U.S. Geological Survey stream gages. We compared the calibrated watershed parameters, characteristics, and assess the streamflow hydrographs from these two rainfall inputs. The differences and improvement of using spatially distributed rainfall input in SWAT were discussed. In addition to improving the model by the representation of rainfall, this study helped us having a better understanding of the watershed hydrological response in Hawaii.
Analysis of dynamic regimes in stochastically forced Kaldor model
International Nuclear Information System (INIS)
Bashkirtseva, Irina; Ryazanova, Tatyana; Ryashko, Lev
2015-01-01
We consider the business cycle Kaldor model forced by random noise. Detailed parametric analysis of deterministic system is carried out and zones of coexisting stable equilibrium and stable limit cycle are found. Noise-induced transitions between these attractors are studied using stochastic sensitivity function technique and confidence domains method. Critical values of noise intensity corresponding to noise-induced transitions “equilibrium → cycle” and “cycle → equilibrium” are estimated. Dominants in combined stochastic regimes are discussed.
A stochastic analysis for a phytoplankton-zooplankton model
International Nuclear Information System (INIS)
Ge, G; Wang, H-L; Xu, J
2008-01-01
A simple phytoplankton-zooplankton nonlinear dynamical model was proposed to study the coexistence of all the species and a Hopf bifurcation was observed. In order to study the effect of environmental robustness on this system, we have stochastically perturbed the system with respect to white noise around its positive interior equilibrium. We have observed that the system remains stochastically stable around the positive equilibrium for same parametric values in the deterministic situation
Analysis of stochastic effects in Kaldor-type business cycle discrete model
Bashkirtseva, Irina; Ryashko, Lev; Sysolyatina, Anna
2016-07-01
We study nonlinear stochastic phenomena in the discrete Kaldor model of business cycles. A numerical parametric analysis of stochastically forced attractors (equilibria, closed invariant curves, discrete cycles) of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is modeled by confidence domains. The phenomenon of noise-induced transitions ;chaos-order; is discussed.
The multivariate supOU stochastic volatility model
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole; Stelzer, Robert
Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order...... structure of the volatility, the log returns, as well as their "squares" are discussed in detail. Moreover, we give several examples in which long memory effects occur and study how the model as well as the simple Ornstein-Uhlenbeck type stochastic volatility model behave under linear transformations....... In particular, the models are shown to be preserved under invertible linear transformations. Finally, we discuss how (sup)OU stochastic volatility models can be combined with a factor modelling approach....
Stochastic line motion and stochastic flux conservation for nonideal hydromagnetic models
International Nuclear Information System (INIS)
Eyink, Gregory L.
2009-01-01
We prove that smooth solutions of nonideal (viscous and resistive) incompressible magnetohydrodynamic (MHD) equations satisfy a stochastic law of flux conservation. This property implies that the magnetic flux through a surface is equal to the average of the magnetic fluxes through an ensemble of surfaces advected backward in time by the plasma velocity perturbed with a random white noise. Our result is an analog of the well-known Alfven theorem of ideal MHD and is valid for any value of the magnetic Prandtl number. A second stochastic conservation law is shown to hold at unit Prandtl number, a random version of the generalized Kelvin theorem derived by Bekenstein and Oron for ideal MHD. These stochastic conservation laws are not only shown to be consequences of the nonideal MHD equations but are proved in fact to be equivalent to those equations. We derive similar results for two more refined hydromagnetic models, Hall MHD and the two-fluid plasma model, still assuming incompressible velocities and isotropic transport coefficients. Finally, we use these results to discuss briefly the infinite-Reynolds-number limit of hydromagnetic turbulence and to support the conjecture that flux conservation remains stochastic in that limit.
Stochastic models to simulate paratuberculosis in dairy herds
DEFF Research Database (Denmark)
Nielsen, Søren Saxmose; Weber, M.F.; Kudahl, Anne Margrethe Braad
2011-01-01
Stochastic simulation models are widely accepted as a means of assessing the impact of changes in daily management and the control of different diseases, such as paratuberculosis, in dairy herds. This paper summarises and discusses the assumptions of four stochastic simulation models and their use...... the models are somewhat different in their underlying principles and do put slightly different values on the different strategies, their overall findings are similar. Therefore, simulation models may be useful in planning paratuberculosis strategies in dairy herds, although as with all models caution...
Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations
Christensen, H. M.; Dawson, A.; Palmer, T.
2017-12-01
Stochastic parametrisations are used in weather and climate models as a physically motivated way to represent model error due to unresolved processes. Designing new stochastic schemes has been the target of much innovative research over the last decade. While a focus has been on developing physically motivated approaches, many successful stochastic parametrisation schemes are very simple, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) multiplicative scheme `Stochastically Perturbed Parametrisation Tendencies' (SPPT). The SPPT scheme improves the skill of probabilistic weather and seasonal forecasts, and so is widely used. However, little work has focused on assessing the physical basis of the SPPT scheme. We address this matter by using high-resolution model simulations to explicitly measure the `error' in the parametrised tendency that SPPT seeks to represent. The high resolution simulations are first coarse-grained to the desired forecast model resolution before they are used to produce initial conditions and forcing data needed to drive the ECMWF Single Column Model (SCM). By comparing SCM forecast tendencies with the evolution of the high resolution model, we can measure the `error' in the forecast tendencies. In this way, we provide justification for the multiplicative nature of SPPT, and for the temporal and spatial scales of the stochastic perturbations. However, we also identify issues with the SPPT scheme. It is therefore hoped these measurements will improve both holistic and process based approaches to stochastic parametrisation. Figure caption: Instantaneous snapshot of the optimal SPPT stochastic perturbation, derived by comparing high-resolution simulations with a low resolution forecast model.
Deterministic and stochastic CTMC models from Zika disease transmission
Zevika, Mona; Soewono, Edy
2018-03-01
Zika infection is one of the most important mosquito-borne diseases in the world. Zika virus (ZIKV) is transmitted by many Aedes-type mosquitoes including Aedes aegypti. Pregnant women with the Zika virus are at risk of having a fetus or infant with a congenital defect and suffering from microcephaly. Here, we formulate a Zika disease transmission model using two approaches, a deterministic model and a continuous-time Markov chain stochastic model. The basic reproduction ratio is constructed from a deterministic model. Meanwhile, the CTMC stochastic model yields an estimate of the probability of extinction and outbreaks of Zika disease. Dynamical simulations and analysis of the disease transmission are shown for the deterministic and stochastic models.
Exploring the potential of multivariate depth-damage and rainfall-damage models
DEFF Research Database (Denmark)
van Ootegem, Luc; van Herck, K.; Creten, T.
2018-01-01
In Europe, floods are among the natural catastrophes that cause the largest economic damage. This article explores the potential of two distinct types of multivariate flood damage models: ‘depth-damage’ models and ‘rainfall-damage’ models. We use survey data of 346 Flemish households that were...... victim of pluvial floods complemented with rainfall data from both rain gauges and weather radars. In the econometrical analysis, a Tobit estimation technique is used to deal with the issue of zero damage observations. The results show that in the ‘depth-damage’ models flood depth has a significant...... impact on the damage. In the ‘rainfall-damage’ models there is a significant impact of rainfall accumulation on the damage when using the gauge rainfall data as predictor, but not when using the radar rainfall data. Finally, non-hazard indicators are found to be important for explaining pluvial flood...
Stochastic model of forecasting spare parts demand
Directory of Open Access Journals (Sweden)
Ivan S. Milojević
2012-01-01
Full Text Available If demand is known for the whole planning period (complete information, then this type of demand or a supply system is deterministic. In the simplest cases, the demand per time unit is constant. If demand levels change over time following a precisely determined and pre-known principle, this type of demand is also classified as deterministic. This quality of demand is very rare. In most cases demand is the product of a process, for example TMS maintenance, whose progression cannot be predicted due to a number of factors influencing the process and causing random demand changes. In this case, a supply system must function according to the complete information and with a certain degree of uncertainty. In cases when demand may be defined by some of the laws of the probability theory, we are talking about stochastic demand and a stochastic supply system. Demand can be described by mathematical expectation, mathematical expectation and standard deviation, probability distribution or as a random process. However, there is usually a need for the most complex description, i.e. the complex random process because both intensity of demand and the probability distribution change during the observed intervals. The level of temporal (dynamic series is traditionally considered as a complex phenomenon consisting of four components: - basic tendency of phenomenon development - cyclical impact (long-term, 'ancient' - seasonal effects - random fluctuations. The basic tendency of phenomenon development means a long-term evolution of phenomena. A function that expresses the trajectory of changes of the basic tendency of a phenomenon development in the form of the equation is called a trend. Often, the trend involves time regression; i.e. the coefficients of the proposed functions are often determined by the least squares method. To roughly determine the coefficients of the proposed function, the sum of three and three-point methods are also used. After checking the
Electricity Market Stochastic Dynamic Model and Its Mean Stability Analysis
Directory of Open Access Journals (Sweden)
Zhanhui Lu
2014-01-01
Full Text Available Based on the deterministic dynamic model of electricity market proposed by Alvarado, a stochastic electricity market model, considering the random nature of demand sides, is presented in this paper on the assumption that generator cost function and consumer utility function are quadratic functions. The stochastic electricity market model is a generalization of the deterministic dynamic model. Using the theory of stochastic differential equations, stochastic process theory, and eigenvalue techniques, the determining conditions of the mean stability for this electricity market model under small Gauss type random excitation are provided and testified theoretically. That is, if the demand elasticity of suppliers is nonnegative and the demand elasticity of consumers is negative, then the stochastic electricity market model is mean stable. It implies that the stability can be judged directly by initial data without any computation. Taking deterministic electricity market data combined with small Gauss type random excitation as numerical samples to interpret random phenomena from a statistical perspective, the results indicate the conclusions above are correct, valid, and practical.
Dynamic stochastic accumulation model with application to pension savings management
Directory of Open Access Journals (Sweden)
Melicherčik Igor
2010-01-01
Full Text Available We propose a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. Stock prices are assumed to be driven by the geometric Brownian motion. Interest rates are modeled by means of the Cox-Ingersoll-Ross model. The optimal decision as a solution to the corresponding dynamic stochastic program is a function of the duration of saving, the level of savings and the short rate. Qualitative and quantitative properties of the optimal solution are analyzed. The model is tested on the funded pillar of the Slovak pension system. The results are calculated for various risk preferences of a saver.
Methods and models in mathematical biology deterministic and stochastic approaches
Müller, Johannes
2015-01-01
This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
INFERENCE AND SENSITIVITY IN STOCHASTIC WIND POWER FORECAST MODELS.
Elkantassi, Soumaya
2017-10-03
Reliable forecasting of wind power generation is crucial to optimal control of costs in generation of electricity with respect to the electricity demand. Here, we propose and analyze stochastic wind power forecast models described by parametrized stochastic differential equations, which introduce appropriate fluctuations in numerical forecast outputs. We use an approximate maximum likelihood method to infer the model parameters taking into account the time correlated sets of data. Furthermore, we study the validity and sensitivity of the parameters for each model. We applied our models to Uruguayan wind power production as determined by historical data and corresponding numerical forecasts for the period of March 1 to May 31, 2016.
Stochastic description of heterogeneities of permeability within groundwater flow models
International Nuclear Information System (INIS)
Cacas, M.C.; Lachassagne, P.; Ledoux, E.; Marsily, G. de
1991-01-01
In order to model radionuclide migration in the geosphere realistically at the field scale, the hydrogeologist needs to be able to simulate groundwater flow in heterogeneous media. Heterogeneity of the medium can be described using a stochastic approach, that affects the way in which a flow model is formulated. In this paper, we discuss the problems that we have encountered in modelling both continuous and fractured media. The stochastic approach leads to a methodology that enables local measurements of permeability to be integrated into a model which gives a good prediction of groundwater flow on a regional scale. 5 Figs.; 8 Refs
INFERENCE AND SENSITIVITY IN STOCHASTIC WIND POWER FORECAST MODELS.
Elkantassi, Soumaya; Kalligiannaki, Evangelia; Tempone, Raul
2017-01-01
Reliable forecasting of wind power generation is crucial to optimal control of costs in generation of electricity with respect to the electricity demand. Here, we propose and analyze stochastic wind power forecast models described by parametrized stochastic differential equations, which introduce appropriate fluctuations in numerical forecast outputs. We use an approximate maximum likelihood method to infer the model parameters taking into account the time correlated sets of data. Furthermore, we study the validity and sensitivity of the parameters for each model. We applied our models to Uruguayan wind power production as determined by historical data and corresponding numerical forecasts for the period of March 1 to May 31, 2016.
Duangdai, Eakkapong; Likasiri, Chulin
2017-03-01
In this work, 4 models for predicting rainfall amounts are investigated and compared using Northern Thailand's seasonal rainfall data for 1973-2008. Two models, global temperature, forest area and seasonal rainfall (TFR) and modified TFR based on a system of differential equations, give the relationships between global temperature, Northern Thailand's forest cover and seasonal rainfalls in the region. The other two models studied are time series and Autoregressive Moving Average (ARMA) models. All models are validated using the k-fold cross validation method with the resulting errors being 0.971233, 0.740891, 2.376415 and 2.430891 for time series, ARMA, TFR and modified TFR models, respectively. Under Business as Usual (BaU) scenario, seasonal rainfalls in Northern Thailand are projected through the year 2020 using all 4 models. TFR and modified TFR models are also used to further analyze how global temperature rise and government reforestation policy affect seasonal rainfalls in the region. Rainfall projections obtained via the two models are also compared with those from the International Panel on Climate Change (IPCC) under IS92a scenario. Results obtained through a mathematical model for global temperature, forest area and seasonal rainfall show that the higher the forest cover, the less fluctuation there is between rainy-season and summer rainfalls. Moreover, growth in forest cover also correlates with an increase in summer rainfalls. An investigation into the relationship between main crop productions and rainfalls in dry and rainy seasons indicates that if the rainy-season rainfall is high, that year's main-crop rice production will decrease but the second-crop rice, maize, sugarcane and soybean productions will increase in the following year.
Stochastic models of the Social Security trust funds.
Burdick, Clark; Manchester, Joyce
Each year in March, the Board of Trustees of the Social Security trust funds reports on the current and projected financial condition of the Social Security programs. Those programs, which pay monthly benefits to retired workers and their families, to the survivors of deceased workers, and to disabled workers and their families, are financed through the Old-Age, Survivors, and Disability Insurance (OASDI) Trust Funds. In their 2003 report, the Trustees present, for the first time, results from a stochastic model of the combined OASDI trust funds. Stochastic modeling is an important new tool for Social Security policy analysis and offers the promise of valuable new insights into the financial status of the OASDI trust funds and the effects of policy changes. The results presented in this article demonstrate that several stochastic models deliver broadly consistent results even though they use very different approaches and assumptions. However, they also show that the variation in trust fund outcomes differs as the approach and assumptions are varied. Which approach and assumptions are best suited for Social Security policy analysis remains an open question. Further research is needed before the promise of stochastic modeling is fully realized. For example, neither parameter uncertainty nor variability in ultimate assumption values is recognized explicitly in the analyses. Despite this caveat, stochastic modeling results are already shedding new light on the range and distribution of trust fund outcomes that might occur in the future.
Characterizing economic trends by Bayesian stochastic model specification search
DEFF Research Database (Denmark)
Grassi, Stefano; Proietti, Tommaso
We extend a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. In particular, we focus on autoregressive models with possibly time-varying intercept and slope and decide on ...
Introduction to modeling and analysis of stochastic systems
Kulkarni, V G
2011-01-01
This is an introductory-level text on stochastic modeling. It is suited for undergraduate students in engineering, operations research, statistics, mathematics, actuarial science, business management, computer science, and public policy. It employs a large number of examples to teach the students to use stochastic models of real-life systems to predict their performance, and use this analysis to design better systems. The book is devoted to the study of important classes of stochastic processes: discrete and continuous time Markov processes, Poisson processes, renewal and regenerative processes, semi-Markov processes, queueing models, and diffusion processes. The book systematically studies the short-term and the long-term behavior, cost/reward models, and first passage times. All the material is illustrated with many examples, and case studies. The book provides a concise review of probability in the appendix. The book emphasizes numerical answers to the problems. A collection of MATLAB programs to accompany...
Rainfall-runoff modeling in the Turkey River using numerical and ...
African Journals Online (AJOL)
Modeling rainfall-runoff relationships in a watershed have an important role in water resources engineering. Researchers have used numerical models for modeling rainfall-runoff ... Also, by using SPSS software, the regression equations were developed and then the best equation was selected from regression analysis.
Stochastic dynamic modeling of regular and slow earthquakes
Aso, N.; Ando, R.; Ide, S.
2017-12-01
Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal
Qualitative and Quantitative Integrated Modeling for Stochastic Simulation and Optimization
Directory of Open Access Journals (Sweden)
Xuefeng Yan
2013-01-01
Full Text Available The simulation and optimization of an actual physics system are usually constructed based on the stochastic models, which have both qualitative and quantitative characteristics inherently. Most modeling specifications and frameworks find it difficult to describe the qualitative model directly. In order to deal with the expert knowledge, uncertain reasoning, and other qualitative information, a qualitative and quantitative combined modeling specification was proposed based on a hierarchical model structure framework. The new modeling approach is based on a hierarchical model structure which includes the meta-meta model, the meta-model and the high-level model. A description logic system is defined for formal definition and verification of the new modeling specification. A stochastic defense simulation was developed to illustrate how to model the system and optimize the result. The result shows that the proposed method can describe the complex system more comprehensively, and the survival probability of the target is higher by introducing qualitative models into quantitative simulation.
Distributed parallel computing in stochastic modeling of groundwater systems.
Dong, Yanhui; Li, Guomin; Xu, Haizhen
2013-03-01
Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.
A stochastic model for intermittent search strategies
International Nuclear Information System (INIS)
Benichou, O; Coppey, M; Moreau, M; Suet, P H; Voituriez, R
2005-01-01
It is often necessary, in scientific or everyday life problems, to find a randomly hidden target. What is then the optimal strategy to reach it as rapidly as possible? In this article, we develop a stochastic theory for intermittent search behaviours, which are often observed: the searcher alternates phases of intensive search and slow motion with fast displacements. The first results of this theory have already been announced recently. Here we provide a detailed presentation of the theory, as well as the full derivation of the results. Furthermore, we explicitly discuss the minimization of the time needed to find the target
Deterministic and stochastic models for middle east respiratory syndrome (MERS)
Suryani, Dessy Rizki; Zevika, Mona; Nuraini, Nuning
2018-03-01
World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by using random variables. From the models that were built, the threshold value for deterministic models and stochastic models obtained in the same form and the probability of disease extinction can be computed by stochastic model. Simulations for both models using several of different parameters are shown, and the probability of disease extinction will be compared with several initial conditions.
Baracchini, Theo; King, Aaron A.; Bouma, Menno J.; Rodó, Xavier; Bertuzzo, Enrico; Pascual, Mercedes
2017-10-01
Seasonal patterns in cholera dynamics exhibit pronounced variability across geographical regions, showing single or multiple peaks at different times of the year. Although multiple hypotheses related to local climate variables have been proposed, an understanding of this seasonal variation remains incomplete. The historical Bengal region, which encompasses the full range of cholera's seasonality observed worldwide, provides a unique opportunity to gain insights on underlying environmental drivers. Here, we propose a mechanistic, rainfall-temperature driven, stochastic epidemiological model which explicitly accounts for the fluctuations of the aquatic reservoir, and analyze with this model the historical dataset of cholera mortality in the Bengal region. Parameters are inferred with a recently developed sequential Monte Carlo method for likelihood maximization in partially observed Markov processes. Results indicate that the hydrological regime is a major driver of the seasonal dynamics of cholera. Rainfall tends to buffer the propagation of the disease in wet regions due to the longer residence times of water in the environment and an associated dilution effect, whereas it enhances cholera resurgence in dry regions. Moreover, the dynamics of the environmental water reservoir determine whether the seasonality is unimodal or bimodal, as well as its phase relative to the monsoon. Thus, the full range of seasonal patterns can be explained based solely on the local variation of rainfall and temperature. Given the close connection between cholera seasonality and environmental conditions, a deeper understanding of the underlying mechanisms would allow the better management and planning of public health policies with respect to climate variability and climate change.
Constraining continuous rainfall simulations for derived design flood estimation
Woldemeskel, F. M.; Sharma, A.; Mehrotra, R.; Westra, S.
2016-11-01
Stochastic rainfall generation is important for a range of hydrologic and water resources applications. Stochastic rainfall can be generated using a number of models; however, preserving relevant attributes of the observed rainfall-including rainfall occurrence, variability and the magnitude of extremes-continues to be difficult. This paper develops an approach to constrain stochastically generated rainfall with an aim of preserving the intensity-durationfrequency (IFD) relationships of the observed data. Two main steps are involved. First, the generated annual maximum rainfall is corrected recursively by matching the generated intensity-frequency relationships to the target (observed) relationships. Second, the remaining (non-annual maximum) rainfall is rescaled such that the mass balance of the generated rain before and after scaling is maintained. The recursive correction is performed at selected storm durations to minimise the dependence between annual maximum values of higher and lower durations for the same year. This ensures that the resulting sequences remain true to the observed rainfall as well as represent the design extremes that may have been developed separately and are needed for compliance reasons. The method is tested on simulated 6 min rainfall series across five Australian stations with different climatic characteristics. The results suggest that the annual maximum and the IFD relationships are well reproduced after constraining the simulated rainfall. While our presentation focusses on the representation of design rainfall attributes (IFDs), the proposed approach can also be easily extended to constrain other attributes of the generated rainfall, providing an effective platform for post-processing of stochastic rainfall generators.
Projections of West African summer monsoon rainfall extremes from two CORDEX models
Akinsanola, A. A.; Zhou, Wen
2018-05-01
Global warming has a profound impact on the vulnerable environment of West Africa; hence, robust climate projection, especially of rainfall extremes, is quite important. Based on two representative concentration pathway (RCP) scenarios, projected changes in extreme summer rainfall events over West Africa were investigated using data from the Coordinated Regional Climate Downscaling Experiment models. Eight (8) extreme rainfall indices (CDD, CWD, r10mm, r20mm, PRCPTOT, R95pTOT, rx5day, and sdii) defined by the Expert Team on Climate Change Detection and Indices were used in the study. The performance of the regional climate model (RCM) simulations was validated by comparing with GPCP and TRMM observation data sets. Results show that the RCMs reasonably reproduced the observed pattern of extreme rainfall over the region and further added significant value to the driven GCMs over some grids. Compared to the baseline period 1976-2005, future changes (2070-2099) in summer rainfall extremes under the RCP4.5 and RCP8.5 scenarios show statistically significant decreasing total rainfall (PRCPTOT), while consecutive dry days and extreme rainfall events (R95pTOT) are projected to increase significantly. There are obvious indications that simple rainfall intensity (sdii) will increase in the future. This does not amount to an increase in total rainfall but suggests a likelihood of greater intensity of rainfall events. Overall, our results project that West Africa may suffer more natural disasters such as droughts and floods in the future.
The critical domain size of stochastic population models.
Reimer, Jody R; Bonsall, Michael B; Maini, Philip K
2017-02-01
Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including this variability. We study populations with distinct dispersal and sedentary stages, which have traditionally been modelled using a deterministic integrodifference equation (IDE) framework. Individual-based models (IBMs) are the most intuitive stochastic analogues to IDEs but yield few analytic insights. We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton-Watson branching processes and branching processes in random environments. These branching process models closely approximate the IBM and yield insight into the factors determining the critical domain size for a given population subject to stochasticity.
Stochastic fractional differential equations: Modeling, method and analysis
International Nuclear Information System (INIS)
Pedjeu, Jean-C.; Ladde, Gangaram S.
2012-01-01
By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.
Spatial Disaggregation of Areal Rainfall Using Two Different Artificial Neural Networks Models
Directory of Open Access Journals (Sweden)
Sungwon Kim
2015-06-01
Full Text Available The objective of this study is to develop artificial neural network (ANN models, including multilayer perceptron (MLP and Kohonen self-organizing feature map (KSOFM, for spatial disaggregation of areal rainfall in the Wi-stream catchment, an International Hydrological Program (IHP representative catchment, in South Korea. A three-layer MLP model, using three training algorithms, was used to estimate areal rainfall. The Levenberg–Marquardt training algorithm was found to be more sensitive to the number of hidden nodes than were the conjugate gradient and quickprop training algorithms using the MLP model. Results showed that the networks structures of 11-5-1 (conjugate gradient and quickprop and 11-3-1 (Levenberg-Marquardt were the best for estimating areal rainfall using the MLP model. The networks structures of 1-5-11 (conjugate gradient and quickprop and 1-3-11 (Levenberg–Marquardt, which are the inverse networks for estimating areal rainfall using the best MLP model, were identified for spatial disaggregation of areal rainfall using the MLP model. The KSOFM model was compared with the MLP model for spatial disaggregation of areal rainfall. The MLP and KSOFM models could disaggregate areal rainfall into individual point rainfall with spatial concepts.
Stochastic processes analysis in nuclear reactor using ARMA models
International Nuclear Information System (INIS)
Zavaljevski, N.
1990-01-01
The analysis of ARMA model derived from general stochastic state equations of nuclear reactor is given. The dependence of ARMA model parameters on the main physical characteristics of RB nuclear reactor in Vinca is presented. Preliminary identification results are presented, observed discrepancies between theory and experiment are explained and the possibilities of identification improvement are anticipated. (author)
Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes
DEFF Research Database (Denmark)
Starke, Jens; Reichert, Christian; Eiswirth, Markus
2007-01-01
of stochastic origin can be observed in experiments. The models include a new approach to the platinum phase transition, which allows for a unification of existing models for Pt(100) and Pt(110). The rich nonlinear dynamical behavior of the macroscopic reaction kinetics is investigated and shows good agreement...
Powering stochastic reliability models by discrete event simulation
DEFF Research Database (Denmark)
Kozine, Igor; Wang, Xiaoyun
2012-01-01
it difficult to find a solution to the problem. The power of modern computers and recent developments in discrete-event simulation (DES) software enable to diminish some of the drawbacks of stochastic models. In this paper we describe the insights we have gained based on using both Markov and DES models...
Stochastic Modelling of the Diffusion Coefficient for Concrete
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
In the paper, a new stochastic modelling of the diffusion coefficient D is presented. The modelling is based on physical understanding of the diffusion process and on some recent experimental results. The diffusion coefficients D is strongly dependent on the w/c ratio and the temperature....
Stochastic models for transport in a fluidized bed
Dehling, H.G; Hoffmann, A.C; Stuut, H.W.
1999-01-01
In this paper we study stochastic models for the transport of particles in a fluidized bed reactor and compute the associated residence time distribution (RTD). Our main model is basically a diffusion process in [0;A] with reflecting/absorbing boundary conditions, modified by allowing jumps to the
Stochastic Robust Mathematical Programming Model for Power System Optimization
Energy Technology Data Exchange (ETDEWEB)
Liu, Cong; Changhyeok, Lee; Haoyong, Chen; Mehrotra, Sanjay
2016-01-01
This paper presents a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with ifferent uncertainty sets. A case study of unit commitment shows the effectiveness of the proposed model and algorithms.
AUTOMATIC CALIBRATION OF A STOCHASTIC-LAGRANGIAN TRANSPORT MODEL (SLAM)
Numerical models are a useful tool in evaluating and designing NAPL remediation systems. Traditional constitutive finite difference and finite element models are complex and expensive to apply. For this reason, this paper presents the application of a simplified stochastic-Lagran...
The sensitivity of catchment runoff models to rainfall data at different spatial scales
Directory of Open Access Journals (Sweden)
V. A. Bell
2000-01-01
Full Text Available The sensitivity of catchment runoff models to rainfall is investigated at a variety of spatial scales using data from a dense raingauge network and weather radar. These data form part of the HYREX (HYdrological Radar EXperiment dataset. They encompass records from 49 raingauges over the 135 km2 Brue catchment in south-west England together with 2 and 5 km grid-square radar data. Separate rainfall time-series for the radar and raingauge data are constructed on 2, 5 and 10 km grids, and as catchment average values, at a 15 minute time-step. The sensitivity of the catchment runoff models to these grid scales of input data is evaluated on selected convective and stratiform rainfall events. Each rainfall time-series is used to produce an ensemble of modelled hydrographs in order to investigate this sensitivity. The distributed model is shown to be sensitive to the locations of the raingauges within the catchment and hence to the spatial variability of rainfall over the catchment. Runoff sensitivity is strongest during convective rainfall when a broader spread of modelled hydrographs results, with twice the variability of that arising from stratiform rain. Sensitivity to rainfall data and model resolution is explored and, surprisingly, best performance is obtained using a lower resolution of rainfall data and model. Results from the distributed catchment model, the Simple Grid Model, are compared with those obtained from a lumped model, the PDM. Performance from the distributed model is found to be only marginally better during stratiform rain (R2 of 0.922 compared to 0.911 but significantly better during convective rain (R2 of 0.953 compared to 0.909. The improved performance from the distributed model can, in part, be accredited to the excellence of the dense raingauge network which would not be the norm for operational flood warning systems. In the final part of the paper, the effect of rainfall resolution on the performance of the 2 km distributed
Reflected stochastic differential equation models for constrained animal movement
Hanks, Ephraim M.; Johnson, Devin S.; Hooten, Mevin B.
2017-01-01
Movement for many animal species is constrained in space by barriers such as rivers, shorelines, or impassable cliffs. We develop an approach for modeling animal movement constrained in space by considering a class of constrained stochastic processes, reflected stochastic differential equations. Our approach generalizes existing methods for modeling unconstrained animal movement. We present methods for simulation and inference based on augmenting the constrained movement path with a latent unconstrained path and illustrate this augmentation with a simulation example and an analysis of telemetry data from a Steller sea lion (Eumatopias jubatus) in southeast Alaska.
Estimation of Stochastic Volatility Models by Nonparametric Filtering
DEFF Research Database (Denmark)
Kanaya, Shin; Kristensen, Dennis
2016-01-01
/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle both jumps and market microstructure noise. The resulting estimators of the stochastic volatility model will carry additional biases...... and variances due to the first-step estimation, but under regularity conditions we show that these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties...
Characterization of the Sahelian-Sudan rainfall based on observations and regional climate models
Salih, Abubakr A. M.; Elagib, Nadir Ahmed; Tjernström, Michael; Zhang, Qiong
2018-04-01
The African Sahel region is known to be highly vulnerable to climate variability and change. We analyze rainfall in the Sahelian Sudan in terms of distribution of rain-days and amounts, and examine whether regional climate models can capture these rainfall features. Three regional models namely, Regional Model (REMO), Rossby Center Atmospheric Model (RCA) and Regional Climate Model (RegCM4), are evaluated against gridded observations (Climate Research Unit, Tropical Rainfall Measuring Mission, and ERA-interim reanalysis) and rain-gauge data from six arid and semi-arid weather stations across Sahelian Sudan over the period 1989 to 2008. Most of the observed rain-days are characterized by weak (0.1-1.0 mm/day) to moderate (> 1.0-10.0 mm/day) rainfall, with average frequencies of 18.5% and 48.0% of the total annual rain-days, respectively. Although very strong rainfall events (> 30.0 mm/day) occur rarely, they account for a large fraction of the total annual rainfall (28-42% across the stations). The performance of the models varies both spatially and temporally. RegCM4 most closely reproduces the observed annual rainfall cycle, especially for the more arid locations, but all of the three models fail to capture the strong rainfall events and hence underestimate its contribution to the total annual number of rain-days and rainfall amount. However, excessive moderate rainfall compensates this underestimation in the models in an annual average sense. The present study uncovers some of the models' limitations in skillfully reproducing the observed climate over dry regions, will aid model users in recognizing the uncertainties in the model output and will help climate and hydrological modeling communities in improving models.
Multi-scenario modelling of uncertainty in stochastic chemical systems
International Nuclear Information System (INIS)
Evans, R. David; Ricardez-Sandoval, Luis A.
2014-01-01
Uncertainty analysis has not been well studied at the molecular scale, despite extensive knowledge of uncertainty in macroscale systems. The ability to predict the effect of uncertainty allows for robust control of small scale systems such as nanoreactors, surface reactions, and gene toggle switches. However, it is difficult to model uncertainty in such chemical systems as they are stochastic in nature, and require a large computational cost. To address this issue, a new model of uncertainty propagation in stochastic chemical systems, based on the Chemical Master Equation, is proposed in the present study. The uncertain solution is approximated by a composite state comprised of the averaged effect of samples from the uncertain parameter distributions. This model is then used to study the effect of uncertainty on an isomerization system and a two gene regulation network called a repressilator. The results of this model show that uncertainty in stochastic systems is dependent on both the uncertain distribution, and the system under investigation. -- Highlights: •A method to model uncertainty on stochastic systems was developed. •The method is based on the Chemical Master Equation. •Uncertainty in an isomerization reaction and a gene regulation network was modelled. •Effects were significant and dependent on the uncertain input and reaction system. •The model was computationally more efficient than Kinetic Monte Carlo
International Nuclear Information System (INIS)
Laurens, J.M.
1985-01-01
A computer code was written to model food chains in order to estimate the internal and external doses, for stochastic and non-stochastic effects, on humans (adults and infants). Results are given for 67 radionuclides, for unit concentration in water (1 Bq/L) and in atmosphere (1 Bq/m 3 )
A stochastic fractional dynamics model of space-time variability of rain
Kundu, Prasun K.; Travis, James E.
2013-09-01
varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, which allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and time scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and on the Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to fit the second moment statistics of radar data at the smaller spatiotemporal scales. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well at these scales without any further adjustment.
DEFF Research Database (Denmark)
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode
2009-01-01
are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE1 approximation......The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model...... development, J. Pharmacokinet. Pharmacodyn. 32 (February(l)) (2005) 109-141; C.W. Tornoe, R.V Overgaard, H. Agerso, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8...
Stochastic lattice model of synaptic membrane protein domains.
Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A
2017-05-01
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.
An artificial neural network model for rainfall forecasting in Bangkok, Thailand
Directory of Open Access Journals (Sweden)
N. Q. Hung
2009-08-01
Full Text Available This paper presents a new approach using an Artificial Neural Network technique to improve rainfall forecast performance. A real world case study was set up in Bangkok; 4 years of hourly data from 75 rain gauge stations in the area were used to develop the ANN model. The developed ANN model is being applied for real time rainfall forecasting and flood management in Bangkok, Thailand. Aimed at providing forecasts in a near real time schedule, different network types were tested with different kinds of input information. Preliminary tests showed that a generalized feedforward ANN model using hyperbolic tangent transfer function achieved the best generalization of rainfall. Especially, the use of a combination of meteorological parameters (relative humidity, air pressure, wet bulb temperature and cloudiness, the rainfall at the point of forecasting and rainfall at the surrounding stations, as an input data, advanced ANN model to apply with continuous data containing rainy and non-rainy period, allowed model to issue forecast at any moment. Additionally, forecasts by ANN model were compared to the convenient approach namely simple persistent method. Results show that ANN forecasts have superiority over the ones obtained by the persistent model. Rainfall forecasts for Bangkok from 1 to 3 h ahead were highly satisfactory. Sensitivity analysis indicated that the most important input parameter besides rainfall itself is the wet bulb temperature in forecasting rainfall.
Stochastic Modeling of Radioactive Material Releases
Energy Technology Data Exchange (ETDEWEB)
Andrus, Jason [Idaho National Lab. (INL), Idaho Falls, ID (United States); Pope, Chad [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-09-01
Nonreactor nuclear facilities operated under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculates the radiation dose associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA was developed using the MATLAB coding framework. The software application has a graphical user input. SODA can be installed on both Windows and Mac computers and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC, rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The work was
Stochastic Modeling of Radioactive Material Releases
International Nuclear Information System (INIS)
Andrus, Jason; Pope, Chad
2015-01-01
Nonreactor nuclear facilities operated under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculates the radiation dose associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA was developed using the MATLAB coding framework. The software application has a graphical user input. SODA can be installed on both Windows and Mac computers and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC, rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The work was
Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism
Directory of Open Access Journals (Sweden)
Jian Zhang
2017-01-01
Full Text Available A new stochastic chemostat model with two substitutable nutrients and one microorganism is proposed and investigated. Firstly, for the corresponding deterministic model, the threshold for extinction and permanence of the microorganism is obtained by analyzing the stability of the equilibria. Then, for the stochastic model, the threshold of the stochastic chemostat for extinction and permanence of the microorganism is explored. Difference of the threshold of the deterministic model and the stochastic model shows that a large stochastic disturbance can affect the persistence of the microorganism and is harmful to the cultivation of the microorganism. To illustrate this phenomenon, we give some computer simulations with different intensity of stochastic noise disturbance.
Energy Technology Data Exchange (ETDEWEB)
Alves, A.S.M., E-mail: asergi@eletronuclear.gov.br [Eletrobrás Termonuclear – Eletronuclear S.A. , Rua da Candelária 65, 7° andar, GSN.T, 20091-906 Rio de Janeiro, RJ (Brazil); Melo, P.F. Frutuoso e, E-mail: frutuoso@nuclear.ufrj.br [Graduate Program of Nuclear Engineering, COPPE, Federal University of Rio de Janeiro, Av. Horácio Macedo 2030, Bloco G, sala 206, 21941-914 Rio de Janeiro, RJ (Brazil); Passos, E.M., E-mail: epassos@eletronuclear.gov.br [Eletrobrás Termonuclear – Eletronuclear S.A. , Rua da Candelária 65, 7° andar, GSN.T, 20091-906 Rio de Janeiro, RJ (Brazil); Fontes, G.S., E-mail: gsfontes@hotmail.com [Instituto Militar de Engenharia – IME, Praça General Tibúrcio 80, 22290-270 Rio de Janeiro, RJ (Brazil)
2015-06-15
Highlights: • The water infiltration scenario is evaluated for a near surface repository. • The main objective is the determination of the critical distance of the repository. • The column liquid height in the repository is governed by an Ito stochastic equation. • Practical results are obtained for the Abadia de Goiás repository in Brazil. - Abstract: The aim of this paper is to present the stochastic and deterministic models developed for the evaluation of the critical distance of a near surface repository for the disposal of intermediate (ILW) and low level (LLW) radioactive wastes. The critical distance of a repository is defined as the distance between the repository and a well in which the water activity concentration is able to cause a radiological dose to a member of the public equal to the dose limit set by the regulatory body. The mathematical models are developed based on the Richards equation for the liquid flow in the porous media and on the solute transport equation in this medium. The release of radioactive material from the repository to the environment is considered through its base and its flow is determined by Darcy's Law. The deterministic model is obtained from the stochastic approach by neglecting the influence of the Gaussian white noise on the rainfall and the equations are solved analytically with the help of conventional calculus (non-stochastic calculus). The equations of the stochastic model are solved analytically based on the Ito stochastic calculus and numerically by using the Euler–Maruyama method. The impact on the value of the critical distance of the Abadia de Goiás repository is analyzed, taken as a study case, when the deterministic methodology is replaced by the stochastic one, considered more appropriate for modeling rainfall as a stochastic process.
Improved rainfall-runoff approach using lumped and conceptual modelling
Durán Barroso, Pablo
2016-01-01
Rainfall-runoff quantification is one of the most important tasks in both engineering and watershed management as it allows to identify, forecast and explain watershed response. The division of the rainfall depth between infiltration and runoff has a high level of complexity due to the spatial heterogeneity in real catchments and the temporal precipitation variability, which provide scale effects on the overall runoff volumes. The Natural Resources Conservation Service Curve Number (NRCS CN) ...
Müller, M. F.; Thompson, S. E.
2015-09-01
The prediction of flow duration curves (FDCs) in ungauged basins remains an important task for hydrologists given the practical relevance of FDCs for water management and infrastructure design. Predicting FDCs in ungauged basins typically requires spatial interpolation of statistical or model parameters. This task is complicated if climate becomes non-stationary, as the prediction challenge now also requires extrapolation through time. In this context, process-based models for FDCs that mechanistically link the streamflow distribution to climate and landscape factors may have an advantage over purely statistical methods to predict FDCs. This study compares a stochastic (process-based) and statistical method for FDC prediction in both stationary and non-stationary contexts, using Nepal as a case study. Under contemporary conditions, both models perform well in predicting FDCs, with Nash-Sutcliffe coefficients above 0.80 in 75 % of the tested catchments. The main drives of uncertainty differ between the models: parameter interpolation was the main source of error for the statistical model, while violations of the assumptions of the process-based model represented the main source of its error. The process-based approach performed better than the statistical approach in numerical simulations with non-stationary climate drivers. The predictions of the statistical method under non-stationary rainfall conditions were poor if (i) local runoff coefficients were not accurately determined from the gauge network, or (ii) streamflow variability was strongly affected by changes in rainfall. A Monte Carlo analysis shows that the streamflow regimes in catchments characterized by a strong wet-season runoff and a rapid, strongly non-linear hydrologic response are particularly sensitive to changes in rainfall statistics. In these cases, process-based prediction approaches are strongly favored over statistical models.
Seasonal prediction of East Asian summer rainfall using a multi-model ensemble system
Ahn, Joong-Bae; Lee, Doo-Young; Yoo, Jin‑Ho
2015-04-01
Using the retrospective forecasts of seven state-of-the-art coupled models and their multi-model ensemble (MME) for boreal summers, the prediction skills of climate models in the western tropical Pacific (WTP) and East Asian region are assessed. The prediction of summer rainfall anomalies in East Asia is difficult, while the WTP has a strong correlation between model prediction and observation. We focus on developing a new approach to further enhance the seasonal prediction skill for summer rainfall in East Asia and investigate the influence of convective activity in the WTP on East Asian summer rainfall. By analyzing the characteristics of the WTP convection, two distinct patterns associated with El Niño-Southern Oscillation developing and decaying modes are identified. Based on the multiple linear regression method, the East Asia Rainfall Index (EARI) is developed by using the interannual variability of the normalized Maritime continent-WTP Indices (MPIs), as potentially useful predictors for rainfall prediction over East Asia, obtained from the above two main patterns. For East Asian summer rainfall, the EARI has superior performance to the East Asia summer monsoon index or each MPI. Therefore, the regressed rainfall from EARI also shows a strong relationship with the observed East Asian summer rainfall pattern. In addition, we evaluate the prediction skill of the East Asia reconstructed rainfall obtained by hybrid dynamical-statistical approach using the cross-validated EARI from the individual models and their MME. The results show that the rainfalls reconstructed from simulations capture the general features of observed precipitation in East Asia quite well. This study convincingly demonstrates that rainfall prediction skill is considerably improved by using a hybrid dynamical-statistical approach compared to the dynamical forecast alone. Acknowledgements This work was carried out with the support of Rural Development Administration Cooperative Research
Directory of Open Access Journals (Sweden)
Dongqin Chen
2016-03-01
Full Text Available Due to the increase of geographical disaster in China, it is necessary to study the formation mechanism to make a preparation for the future prevention of geological disasters and effectively reduce the unnecessary financial loss and casualties. We found there is a powerful connection between heavy rainfall and landslide slope. Thus, this article takes the accumulation of gravel soil as the research material to set up indoor rainfall and landslide model test. By comparing the rules of pore water pressure and soil pressure responding to different rainfall intensity and slope angle, we discussed over the effects of rainfall intensity and slope angle on the sliding of accumulation gravelly soil.
Response spectrum analysis of a stochastic seismic model
International Nuclear Information System (INIS)
Kimura, Koji; Sakata, Masaru; Takemoto, Shinichiro.
1990-01-01
The stochastic response spectrum approach is presented for predicting the dynamic behavior of structures to earthquake excitation expressed by a random process, one of whose sample functions can be regarded as a recorded strong-motion earthquake accelerogram. The approach consists of modeling recorded ground motion by a random process and the root-mean-square response (rms) analysis of a single-degree-of-freedom system by using the moment equations method. The stochastic response spectrum is obtained as a plot of the maximum rms response versus the natural period of the system and is compared with the conventional response spectrum. (author)
Stochastic geometry, spatial statistics and random fields models and algorithms
2015-01-01
Providing a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, this volume places a special emphasis on fundamental classes of models and algorithms as well as on their applications, for example in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R, which are widely used in the mathematical community. It can be regarded as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered, with a focus on asymptotic methods.
The threshold of a stochastic SIQS epidemic model
Zhang, Xiao-Bing; Huo, Hai-Feng; Xiang, Hong; Shi, Qihong; Li, Dungang
2017-09-01
In this paper, we present the threshold of a stochastic SIQS epidemic model which determines the extinction and persistence of the disease. Furthermore, we find that noise can suppress the disease outbreak. Numerical simulations are also carried out to confirm the analytical results.
Stochasticity thresholds in the Fermi-Pasta-Ulam model
International Nuclear Information System (INIS)
Callegari, B.; Galgani, L.; Milan Univ.
1979-01-01
The authors consider the celebrated model of Fermi, Pasta and Ulam and give a numerical estimate for its thresholds of stochasticity, thus determining a critical energy as a function of the frequency of the corresponding oscillators. The results turn out to be qualitatively similar to those already obtained for a chain of particles with nearest-neighbour Lennard-Jones interaction potential. (author)
A stochastic large deformation model for computational anatomy
DEFF Research Database (Denmark)
Arnaudon, Alexis; Holm, Darryl D.; Pai, Akshay Sadananda Uppinakudru
2017-01-01
In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for incorporating random variations into the Large Deformation...
Stochasticity thresholds in the Fermi-Pasta-Ulam model
Energy Technology Data Exchange (ETDEWEB)
Callegari, B [Ferrara Univ. (Italy). Ist. di Matematica; Carotta, M C; Ferrario, C [Ferrara Univ. (Italy). Ist. di Fisica; Lo Vecchio, G [Ferrara Univ. (Italy). Ist. di Fisica; Gruppo Nazionale di Struttura della Materia, Ferrara (Italy)); Galgani, L [Milan Univ. (Italy). Ist. di Fisica; Milan Univ. (Italy). Ist. di Matematica)
1979-12-11
The authors consider the celebrated model of Fermi, Pasta and Ulam and give a numerical estimate for its thresholds of stochasticity, thus determining a critical energy as a function of the frequency of the corresponding oscillators. The results turn out to be qualitatively similar to those already obtained for a chain of particles with nearest-neighbour Lennard-Jones interaction potential.
Stochastic Online Learning in Dynamic Networks under Unknown Models
2016-08-02
The key is to develop online learning strategies at each individual node. Specifically, through local information exchange with its neighbors, each...infinitely repeated game with incomplete information and developed a dynamic pricing strategy referred to as Competitive and Cooperative Demand Learning...Stochastic Online Learning in Dynamic Networks under Unknown Models This research aims to develop fundamental theories and practical algorithms for
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
S. Peiris (Shelton); M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractIn recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility
CSL model checking of deterministic and stochastic Petri nets
Martinez Verdugo, J.M.; Haverkort, Boudewijn R.H.M.; German, R.; Heindl, A.
2006-01-01
Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process dened by DSPNs, under
Model tracking dual stochastic controller design under irregular internal noises
International Nuclear Information System (INIS)
Lee, Jong Bok; Heo, Hoon; Cho, Yun Hyun; Ji, Tae Young
2006-01-01
Although many methods about the control of irregular external noise have been introduced and implemented, it is still necessary to design a controller that will be more effective and efficient methods to exclude for various noises. Accumulation of errors due to model tracking, internal noises (thermal noise, shot noise and l/f noise) that come from elements such as resistor, diode and transistor etc. in the circuit system and numerical errors due to digital process often destabilize the system and reduce the system performance. New stochastic controller is adopted to remove those noises using conventional controller simultaneously. Design method of a model tracking dual controller is proposed to improve the stability of system while removing external and internal noises. In the study, design process of the model tracking dual stochastic controller is introduced that improves system performance and guarantees robustness under irregular internal noises which can be created internally. The model tracking dual stochastic controller utilizing F-P-K stochastic control technique developed earlier is implemented to reveal its performance via simulation
Hydrological modeling using a multi-site stochastic weather generator
Weather data is usually required at several locations over a large watershed, especially when using distributed models for hydrological simulations. In many applications, spatially correlated weather data can be provided by a multi-site stochastic weather generator which considers the spatial correl...
Optimal Tax Reduction by Depreciation : A Stochastic Model
Berg, M.; De Waegenaere, A.M.B.; Wielhouwer, J.L.
1996-01-01
This paper focuses on the choice of a depreciation method, when trying to minimize the expected value of the present value of future tax payments.In a quite general model that allows for stochastic future cash- ows and a tax structure with tax brackets, we determine the optimal choice between the
A cavitation model based on Eulerian stochastic fields
Magagnato, F.; Dumond, J.
2013-12-01
Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Stochastic models in risk theory and management accounting
Brekelmans, R.C.M.
2000-01-01
This thesis deals with stochastic models in two fields: risk theory and management accounting. Firstly, two extensions of the classical risk process are analyzed. A method is developed that computes bounds of the probability of ruin for the classical risk rocess extended with a constant interest
A stochastic model for forecast consumption in master scheduling
Weeda, P.J.; Weeda, P.J.
1994-01-01
This paper describes a stochastic model for the reduction of the initial forecast in the Master Schedule (MS) of an MRP system during progress of time by the acceptance of customer orders. Results are given for the expectation and variance of the number of yet unknown deliveries as a function of
Naufan, Ihsan; Sivakumar, Bellie; Woldemeskel, Fitsum M.; Raghavan, Srivatsan V.; Vu, Minh Tue; Liong, Shie-Yui
2018-01-01
Understanding the spatial and temporal variability of rainfall has always been a great challenge, and the impacts of climate change further complicate this issue. The present study employs the concepts of complex networks to study the spatial connections in rainfall, with emphasis on climate change and rainfall scaling. Rainfall outputs (during 1961-1990) from a regional climate model (i.e. Weather Research and Forecasting (WRF) model that downscaled the European Centre for Medium-range Weather Forecasts, ECMWF ERA-40 reanalyses) over Southeast Asia are studied, and data corresponding to eight different temporal scales (6-hr, 12-hr, daily, 2-day, 4-day, weekly, biweekly, and monthly) are analyzed. Two network-based methods are applied to examine the connections in rainfall: clustering coefficient (a measure of the network's local density) and degree distribution (a measure of the network's spread). The influence of rainfall correlation threshold (T) on spatial connections is also investigated by considering seven different threshold levels (ranging from 0.5 to 0.8). The results indicate that: (1) rainfall networks corresponding to much coarser temporal scales exhibit properties similar to that of small-world networks, regardless of the threshold; (2) rainfall networks corresponding to much finer temporal scales may be classified as either small-world networks or scale-free networks, depending upon the threshold; and (3) rainfall spatial connections exhibit a transition phase at intermediate temporal scales, especially at high thresholds. These results suggest that the most appropriate model for studying spatial connections may often be different at different temporal scales, and that a combination of small-world and scale-free network models might be more appropriate for rainfall upscaling/downscaling across all scales, in the strict sense of scale-invariance. The results also suggest that spatial connections in the studied rainfall networks in Southeast Asia are
Stochastic population oscillations in spatial predator-prey models
International Nuclear Information System (INIS)
Taeuber, Uwe C
2011-01-01
It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic models yield long-lived, but ultimately decaying erratic population oscillations, which can be understood through a resonant amplification mechanism for density fluctuations. In Monte Carlo simulations of spatial stochastic predator-prey systems, one observes striking complex spatio-temporal structures. These spreading activity fronts induce persistent correlations between predators and prey. In the presence of local particle density restrictions (finite prey carrying capacity), there exists an extinction threshold for the predator population. The accompanying continuous non-equilibrium phase transition is governed by the directed-percolation universality class. We employ field-theoretic methods based on the Doi-Peliti representation of the master equation for stochastic particle interaction models to (i) map the ensuing action in the vicinity of the absorbing state phase transition to Reggeon field theory, and (ii) to quantitatively address fluctuation-induced renormalizations of the population oscillation frequency, damping, and diffusion coefficients in the species coexistence phase.
Stochastic volatility and stochastic leverage
DEFF Research Database (Denmark)
Veraart, Almut; Veraart, Luitgard A. M.
This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...
Stochastic and simulation models of maritime intercept operations capabilities
Sato, Hiroyuki
2005-01-01
The research formulates and exercises stochastic and simulation models to assess the Maritime Intercept Operations (MIO) capabilities. The models focus on the surveillance operations of the Maritime Patrol Aircraft (MPA). The analysis using the models estimates the probability with which a terrorist vessel (Red) is detected, correctly classified, and escorted for intensive investigation and neutralization before it leaves an area of interest (AOI). The difficulty of obtaining adequate int...
Extinction threshold of a population in spatial and stochastic model
Soroka, Yevheniia; Rublyov, Bogdan
2016-01-01
In this study, spatial stochastic and logistic model (SSLM) describing dynamics of a population of a certain species was analysed. The behaviour of the extinction threshold as a function of model parameters was studied. More specifically, we studied how the critical values for the model parameters that separate the cases of extinction and persistence depend on the spatial scales of the competition and dispersal kernels. We compared the simulations and analytical results to examine if and how ...
Rainfall-runoff and hydraulic modelling integration in the Blatina River
International Nuclear Information System (INIS)
Timko, J.
2017-01-01
This paper investigates the use and integration of rainfall-runoff modelling and hydrologic modelling of Blatina river catchment. Characteristics of physical-geographical sphere and its components were created within the model, enhancing the robustness of input data for the mathematical modelling of landscape runoff. Rainfall-runoff model HEC-HMS utilised in this research allows using a wide range of methodologies to determine the movement of water in the riverbed, water losses in the basin, hydraulic and hydrological methods of transformation and base-flow. Loss and transformation of water in the basin were modeled with curve numbers method SCS-CN. The simulated hydrograph was calibrated using rainfall-runoff event from June 2009. The same event was also modelled after the deforestation of the focus area. Using hydraulic model MIKE 21, a flood of focus rainfall-runoff area was simulated under both current real and changed land cover scenarios. (authors)
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik
2009-06-01
The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.
Gridded rainfall estimation for distributed modeling in western mountainous areas
Moreda, F.; Cong, S.; Schaake, J.; Smith, M.
2006-05-01
Estimation of precipitation in mountainous areas continues to be problematic. It is well known that radar-based methods are limited due to beam blockage. In these areas, in order to run a distributed model that accounts for spatially variable precipitation, we have generated hourly gridded rainfall estimates from gauge observations. These estimates will be used as basic data sets to support the second phase of the NWS-sponsored Distributed Hydrologic Model Intercomparison Project (DMIP 2). One of the major foci of DMIP 2 is to better understand the modeling and data issues in western mountainous areas in order to provide better water resources products and services to the Nation. We derive precipitation estimates using three data sources for the period of 1987-2002: 1) hourly cooperative observer (coop) gauges, 2) daily total coop gauges and 3) SNOw pack TELemetry (SNOTEL) daily gauges. The daily values are disaggregated using the hourly gauge values and then interpolated to approximately 4km grids using an inverse-distance method. Following this, the estimates are adjusted to match monthly mean values from the Parameter-elevation Regressions on Independent Slopes Model (PRISM). Several analyses are performed to evaluate the gridded estimates for DMIP 2 experiments. These gridded inputs are used to generate mean areal precipitation (MAPX) time series for comparison to the traditional mean areal precipitation (MAP) time series derived by the NWS' California-Nevada River Forecast Center for model calibration. We use two of the DMIP 2 basins in California and Nevada: the North Fork of the American River (catchment area 885 sq. km) and the East Fork of the Carson River (catchment area 922 sq. km) as test areas. The basins are sub-divided into elevation zones. The North Fork American basin is divided into two zones above and below an elevation threshold. Likewise, the Carson River basin is subdivided in to four zones. For each zone, the analyses include: a) overall
Modelling of Multi Input Transfer Function for Rainfall Forecasting in Batu City
Directory of Open Access Journals (Sweden)
Priska Arindya Purnama
2017-11-01
Full Text Available The aim of this research is to model and forecast the rainfall in Batu City using multi input transfer function model based on air temperature, humidity, wind speed and cloud. Transfer function model is a multivariate time series model which consists of an output series (Yt sequence expected to be effected by an input series (Xt and other inputs in a group called a noise series (Nt. Multi input transfer function model obtained is (b1,s1,r1 (b2,s2,r2 (b3,s3,r3 (b4,s4,r4(pn,qn = (0,0,0 (23,0,0 (1,2,0 (0,0,0 ([5,8],2 and shows that air temperature on t-day affects rainfall on t-day, rainfall on t-day is influenced by air humidity in the previous 23 days, rainfall on t-day is affected by wind speed in the previous day , and rainfall on day t is affected by clouds on day t. The results of rainfall forecasting in Batu City with multi input transfer function model can be said to be accurate, because it produces relatively small RMSE value. The value of RMSE data forecasting training is 7.7921 while forecasting data testing is 4.2184. Multi-input transfer function model is suitable for rainfall in Batu City.
SR 97. Alternative models project. Stochastic continuum modelling of Aberg
International Nuclear Information System (INIS)
Widen, H.; Walker, D.
1999-08-01
As part of studies into the siting of a deep repository for nuclear waste, Swedish Nuclear Fuel and Waste Management Company (SKB) has commissioned the Alternative Models Project (AMP). The AMP is a comparison of three alternative modelling approaches to bedrock performance assessment for a single hypothetical repository, arbitrarily named Aberg. The Aberg repository will adopt input parameters from the Aespoe Hard Rock Laboratory in southern Sweden. The models are restricted to an explicit domain, boundary conditions and canister location to facilitate the comparison. The boundary conditions are based on the regional groundwater model provided in digital format. This study is the application of HYDRASTAR, a stochastic continuum groundwater flow and transport-modelling program. The study uses 34 realisations of 945 canister locations in the hypothetical repository to evaluate the uncertainty of the advective travel time, canister flux (Darcy velocity at a canister) and F-ratio. Several comparisons of variability are constructed between individual canister locations and individual realisations. For the ensemble of all realisations with all canister locations, the study found a median travel time of 27 years, a median canister flux of 7.1 x 10 -4 m/yr and a median F-ratio of 3.3 x 10 5 yr/m. The overall pattern of regional flow is preserved in the site-scale model, as is reflected in flow paths and exit locations. The site-scale model slightly over-predicts the boundary fluxes from the single realisation of the regional model. The explicitly prescribed domain was seen to be slightly restrictive, with 6% of the stream tubes failing to exit the upper surface of the model. Sensitivity analysis and calibration are suggested as possible extensions of the modelling study
DEFF Research Database (Denmark)
Thorndahl, Søren; Poulsen, Troels Sander; Bøvith, Thomas
2012-01-01
Forecast based flow prediction in drainage systems can be used to implement real time control of drainage systems. This study compares two different types of rainfall forecasts – a radar rainfall extrapolation based nowcast model and a numerical weather prediction model. The models are applied...... performance of the system is found using the radar nowcast for the short leadtimes and weather model for larger lead times....
Application of Stochastic Partial Differential Equations to Reservoir Property Modelling
Potsepaev, R.
2010-09-06
Existing algorithms of geostatistics for stochastic modelling of reservoir parameters require a mapping (the \\'uvt-transform\\') into the parametric space and reconstruction of a stratigraphic co-ordinate system. The parametric space can be considered to represent a pre-deformed and pre-faulted depositional environment. Existing approximations of this mapping in many cases cause significant distortions to the correlation distances. In this work we propose a coordinate free approach for modelling stochastic textures through the application of stochastic partial differential equations. By avoiding the construction of a uvt-transform and stratigraphic coordinates, one can generate realizations directly in the physical space in the presence of deformations and faults. In particular the solution of the modified Helmholtz equation driven by Gaussian white noise is a zero mean Gaussian stationary random field with exponential correlation function (in 3-D). This equation can be used to generate realizations in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.
DEFF Research Database (Denmark)
Duun-Henriksen, Anne Katrine; Schmidt, S.; Nørgaard, K.
2013-01-01
extension incorporating exercise effects on insulin and glucose dynamics. Our model is constructed as a stochastic state space model consisting of a set of stochastic differential equations (SDEs). In a stochastic state space model, the residual error is split into random measurement error...
Assessment of Runoff Contributing Catchment Areas in Rainfall Runoff Modelling
DEFF Research Database (Denmark)
Thorndahl, Søren Liedtke; Johansen, C.; Schaarup-Jensen, Kjeld
2005-01-01
to determine with significant precision the hydrological reduction factor is implemented to account all hydrological losses except the initial loss. This paper presents an inconsistency between calculations of the hydrological reduction factor, based on measurements of rainfall and runoff, and till now...... recommended literary values for residential areas. It is proven by comparing rainfall-runoff measurements from four different residential catchments that the literary values of the hydrological reduction factor are over-estimated for this type of catchments. In addition, different catchment descriptions...
A dependence modelling study of extreme rainfall in Madeira Island
Gouveia-Reis, Délia; Guerreiro Lopes, Luiz; Mendonça, Sandra
2016-08-01
The dependence between variables plays a central role in multivariate extremes. In this paper, spatial dependence of Madeira Island's rainfall data is addressed within an extreme value copula approach through an analysis of maximum annual data. The impact of altitude, slope orientation, distance between rain gauge stations and distance from the stations to the sea are investigated for two different periods of time. The results obtained highlight the influence of the island's complex topography on the spatial distribution of extreme rainfall in Madeira Island.
Do we really use rainfall observations consistent with reality in hydrological modelling?
Ciampalini, Rossano; Follain, Stéphane; Raclot, Damien; Crabit, Armand; Pastor, Amandine; Moussa, Roger; Le Bissonnais, Yves
2017-04-01
Spatial and temporal patterns in rainfall control how water reaches soil surface and interacts with soil properties (i.e., soil wetting, infiltration, saturation). Once a hydrological event is defined by a rainfall with its spatiotemporal variability and by some environmental parameters such as soil properties (including land use, topographic and anthropic features), the evidence shows that each parameter variation produces different, specific outputs (e.g., runoff, flooding etc.). In this study, we focus on the effect of rainfall patterns because, due to the difficulty to dispose of detailed data, their influence in modelling is frequently underestimated or neglected. A rainfall event affects a catchment non uniformly, it is spatially localized and its pattern moves in space and time. The way and the time how the water reaches the soil and saturates it respect to the geometry of the catchment deeply influences soil saturation, runoff, and then sediment delivery. This research, approaching a hypothetical, simple case, aims to stimulate the debate on the reliability of the rainfall quality used in hydrological / soil erosion modelling. We test on a small catchment of the south of France (Roujan, Languedoc Roussillon) the influence of rainfall variability with the use of a HD hybrid hydrological - soil erosion model, combining a cinematic wave with the St. Venant equation and a simplified "bucket" conceptual model for ground water, able to quantify the effect of different spatiotemporal patterns of a very-high-definition synthetic rainfall. Results indicate that rainfall spatiotemporal patterns are crucial simulating an erosive event: differences between spatially uniform rainfalls, as frequently adopted in simulations, and some hypothetical rainfall patterns here applied, reveal that the outcome of a simulated event can be highly underestimated.
Predicting population extinction or disease outbreaks with stochastic models
Directory of Open Access Journals (Sweden)
Linda J. S. Allen
2017-01-01
Full Text Available Models of exponential growth, logistic growth and epidemics are common applications in undergraduate differential equation courses. The corresponding stochastic models are not part of these courses, although when population sizes are small their behaviour is often more realistic and distinctly different from deterministic models. For example, the randomness associated with births and deaths may lead to population extinction even in an exponentially growing population. Some background in continuous-time Markov chains and applications to populations, epidemics and cancer are presented with a goal to introduce this topic into the undergraduate mathematics curriculum that will encourage further investigation into problems on conservation, infectious diseases and cancer therapy. MATLAB programs for graphing sample paths of stochastic models are provided in the Appendix.
Quantitative Sociodynamics Stochastic Methods and Models of Social Interaction Processes
Helbing, Dirk
2010-01-01
This new edition of Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioral changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics and mathematics, but they have very often proven their explanatory power in chemistry, biology, economics and the social sciences as well. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces important concepts from nonlinear dynamics (e.g. synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches, a fundamental dynamic model is obtained, which opens new perspectives in the social sciences. It includes many established models a...
Quantitative sociodynamics stochastic methods and models of social interaction processes
Helbing, Dirk
1995-01-01
Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioural changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics but they have very often proved their explanatory power in chemistry, biology, economics and the social sciences. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces the most important concepts from nonlinear dynamics (synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches a very fundamental dynamic model is obtained which seems to open new perspectives in the social sciences. It includes many established models as special cases, e.g. the log...
Stochastic Differential Equation-Based Flexible Software Reliability Growth Model
Directory of Open Access Journals (Sweden)
P. K. Kapur
2009-01-01
Full Text Available Several software reliability growth models (SRGMs have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.
Development of stochastic indicator models of lithology, Yucca Mountain, Nevada
International Nuclear Information System (INIS)
Rautman, C.A.; Robey, T.H.
1994-01-01
Indicator geostatistical techniques have been used to produce a number of fully three-dimensional stochastic simulations of large-scale lithologic categories at the Yucca Mountain site. Each realization reproduces the available drill hole data used to condition the simulation. Information is propagated away from each point of observation in accordance with a mathematical model of spatial continuity inferred through soft data taken from published geologic cross sections. Variations among the simulated models collectively represent uncertainty in the lithology at unsampled locations. These stochastic models succeed in capturing many major features of welded-nonwelded lithologic framework of Yucca Mountain. However, contacts between welded and nonwelded rock types for individual simulations appear more complex than suggested by field observation, and a number of probable numerical artifacts exist in these models. Many of the apparent discrepancies between the simulated models and the general geology of Yucca Mountain represent characterization uncertainty, and can be traced to the sparse site data used to condition the simulations. Several vertical stratigraphic columns have been extracted from the three-dimensional stochastic models for use in simplified total-system performance assessment exercises. Simple, manual adjustments are required to eliminate the more obvious simulation artifacts and to impose a secondary set of deterministic geologic features on the overall stratigraphic framework provided by the indictor models
Prediction of early summer rainfall over South China by a physical-empirical model
Yim, So-Young; Wang, Bin; Xing, Wen
2014-10-01
In early summer (May-June, MJ) the strongest rainfall belt of the northern hemisphere occurs over the East Asian (EA) subtropical front. During this period the South China (SC) rainfall reaches its annual peak and represents the maximum rainfall variability over EA. Hence we establish an SC rainfall index, which is the MJ mean precipitation averaged over 72 stations over SC (south of 28°N and east of 110°E) and represents superbly the leading empirical orthogonal function mode of MJ precipitation variability over EA. In order to predict SC rainfall, we established a physical-empirical model. Analysis of 34-year observations (1979-2012) reveals three physically consequential predictors. A plentiful SC rainfall is preceded in the previous winter by (a) a dipole sea surface temperature (SST) tendency in the Indo-Pacific warm pool, (b) a tripolar SST tendency in North Atlantic Ocean, and (c) a warming tendency in northern Asia. These precursors foreshadow enhanced Philippine Sea subtropical High and Okhotsk High in early summer, which are controlling factors for enhanced subtropical frontal rainfall. The physical empirical model built on these predictors achieves a cross-validated forecast correlation skill of 0.75 for 1979-2012. Surprisingly, this skill is substantially higher than four-dynamical models' ensemble prediction for 1979-2010 period (0.15). The results here suggest that the low prediction skill of current dynamical models is largely due to models' deficiency and the dynamical prediction has large room to improve.
A Statistical Model for Seasonal Rainfall Forecasting over the ...
African Journals Online (AJOL)
In a preliminary step, in order to identify the most influential rainfall predictor, a correlation matrix and step-wise regression of 10 predictors with different lags were analysed. The influence of the southern Indian Ocean Sea Surface Temperature was identified as the most influential predictor for the highland of Eritrea.
assessment of neural networks performance in modeling rainfall ...
African Journals Online (AJOL)
Sholagberu
neural network architecture for precipitation prediction of Myanmar, World Academy of. Science, Engineering and Technology, 48, pp. 130 – 134. Kumarasiri, A.D. and Sonnadara, D.U.J. (2006). Rainfall forecasting: an artificial neural network approach, Proceedings of the Technical Sessions,. 22, pp. 1-13 Institute of Physics ...
STOCHASTIC MODELING OF INFLATION IN NIGERIA
African Journals Online (AJOL)
2006-04-04
Apr 4, 2006 ... In this paper, we adopt a time series approach in modeling inflation in ... KEYWORDS: Buys-Ballot table; Quadratic trend; Seasonal multiplicative model, ..... Basic Statistics for Business and Economics, 2nd ed, Irwin, USA.
Stochastic long term modelling of a drainage system with estimation of return period uncertainty
DEFF Research Database (Denmark)
Thorndahl, Søren
2009-01-01
Long term prediction of maximum water levels and combined sewer overflow (CSO) in drainage systems are associated with large uncertainties. Especially on rainfall inputs, parameters, and assessment of return periods. This paper proposes a Monte Carlo based methodology for stochastic prediction of...
Stochastic population dynamic models as probability networks
M.E. and D.C. Lee. Borsuk
2009-01-01
The dynamics of a population and its response to environmental change depend on the balance of birth, death and age-at-maturity, and there have been many attempts to mathematically model populations based on these characteristics. Historically, most of these models were deterministic, meaning that the results were strictly determined by the equations of the model and...
Stochastic programming framework for Lithuanian pension payout modelling
Directory of Open Access Journals (Sweden)
Audrius Kabašinskas
2014-12-01
Full Text Available The paper provides a scientific approach to the problem of selecting a pension fund by taking into account some specific characteristics of the Lithuanian Republic (LR pension accumulation system. The decision making model, which can be used to plan a long-term pension accrual of the Lithuanian Republic (LR citizens, in an optimal way is presented. This model focuses on factors that influence the sustainability of the pension system selection under macroeconomic, social and demographic uncertainty. The model is formalized as a single stage stochastic optimization problem where the long-term optimal strategy can be obtained based on the possible scenarios generated for a particular participant. Stochastic programming methods allow including the pension fund rebalancing moment and direction of investment, and taking into account possible changes of personal income, changes of society and the global financial market. The collection of methods used to generate scenario trees was found useful to solve strategic planning problems.
Stochastic resonance in a generalized Von Foerster population growth model
Energy Technology Data Exchange (ETDEWEB)
Lumi, N.; Mankin, R. [Institute of Mathematics and Natural Sciences, Tallinn University, 25 Narva Road, 10120 Tallinn (Estonia)
2014-11-12
The stochastic dynamics of a population growth model, similar to the Von Foerster model for human population, is studied. The influence of fluctuating environment on the carrying capacity is modeled as a multiplicative dichotomous noise. It is established that an interplay between nonlinearity and environmental fluctuations can cause single unidirectional discontinuous transitions of the mean population size versus the noise amplitude, i.e., an increase of noise amplitude can induce a jump from a state with a moderate number of individuals to that with a very large number, while by decreasing the noise amplitude an opposite transition cannot be effected. An analytical expression of the mean escape time for such transitions is found. Particularly, it is shown that the mean transition time exhibits a strong minimum at intermediate values of noise correlation time, i.e., the phenomenon of stochastic resonance occurs. Applications of the results in ecology are also discussed.
Directory of Open Access Journals (Sweden)
Mauro Rossi
2017-12-01
Full Text Available Landslides can be triggered by intense or prolonged rainfall. Rain gauge measurements are commonly used to predict landslides even if satellite rainfall estimates are available. Recent research focuses on the comparison of satellite estimates and gauge measurements. The rain gauge data from the Italian network (collected in the system database “Verifica Rischio Frana”, VRF are compared with the National Aeronautics and Space Administration (NASA Tropical Rainfall Measuring Mission (TRMM products. For the purpose, we couple point gauge and satellite rainfall estimates at individual grid cells, evaluating the correlation between gauge and satellite data in different morpho-climatological conditions. We then analyze the statistical distributions of both rainfall data types and the rainfall events derived from them. Results show that satellite data underestimates ground data, with the largest differences in mountainous areas. Power-law models, are more appropriate to correlate gauge and satellite data. The gauge and satellite-based products exhibit different statistical distributions and the rainfall events derived from them differ. In conclusion, satellite rainfall cannot be directly compared with ground data, requiring local investigation to account for specific morpho-climatological settings. Results suggest that satellite data can be used for forecasting landslides, only performing a local scaling between satellite and ground data.
Stochastic modeling of central apnea events in preterm infants
International Nuclear Information System (INIS)
Clark, Matthew T; Lake, Douglas E; Randall Moorman, J; Delos, John B; Lee, Hoshik; Fairchild, Karen D; Kattwinkel, John
2016-01-01
A near-ubiquitous pathology in very low birth weight infants is neonatal apnea, breathing pauses with slowing of the heart and falling blood oxygen. Events of substantial duration occasionally occur after an infant is discharged from the neonatal intensive care unit (NICU). It is not known whether apneas result from a predictable process or from a stochastic process, but the observation that they occur in seemingly random clusters justifies the use of stochastic models. We use a hidden-Markov model to analyze the distribution of durations of apneas and the distribution of times between apneas. The model suggests the presence of four breathing states, ranging from very stable (with an average lifetime of 12 h) to very unstable (with an average lifetime of 10 s). Although the states themselves are not visible, the mathematical analysis gives estimates of the transition rates among these states. We have obtained these transition rates, and shown how they change with post-menstrual age; as expected, the residence time in the more stable breathing states increases with age. We also extrapolated the model to predict the frequency of very prolonged apnea during the first year of life. This paradigm—stochastic modeling of cardiorespiratory control in neonatal infants to estimate risk for severe clinical events—may be a first step toward personalized risk assessment for life threatening apnea events after NICU discharge. (paper)
A data driven nonlinear stochastic model for blood glucose dynamics.
Zhang, Yan; Holt, Tim A; Khovanova, Natalia
2016-03-01
The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.
Spatial stochastic regression modelling of urban land use
International Nuclear Information System (INIS)
Arshad, S H M; Jaafar, J; Abiden, M Z Z; Latif, Z A; Rasam, A R A
2014-01-01
Urbanization is very closely linked to industrialization, commercialization or overall economic growth and development. This results in innumerable benefits of the quantity and quality of the urban environment and lifestyle but on the other hand contributes to unbounded development, urban sprawl, overcrowding and decreasing standard of living. Regulation and observation of urban development activities is crucial. The understanding of urban systems that promotes urban growth are also essential for the purpose of policy making, formulating development strategies as well as development plan preparation. This study aims to compare two different stochastic regression modeling techniques for spatial structure models of urban growth in the same specific study area. Both techniques will utilize the same datasets and their results will be analyzed. The work starts by producing an urban growth model by using stochastic regression modeling techniques namely the Ordinary Least Square (OLS) and Geographically Weighted Regression (GWR). The two techniques are compared to and it is found that, GWR seems to be a more significant stochastic regression model compared to OLS, it gives a smaller AICc (Akaike's Information Corrected Criterion) value and its output is more spatially explainable
Stochastic modeling of central apnea events in preterm infants.
Clark, Matthew T; Delos, John B; Lake, Douglas E; Lee, Hoshik; Fairchild, Karen D; Kattwinkel, John; Moorman, J Randall
2016-04-01
A near-ubiquitous pathology in very low birth weight infants is neonatal apnea, breathing pauses with slowing of the heart and falling blood oxygen. Events of substantial duration occasionally occur after an infant is discharged from the neonatal intensive care unit (NICU). It is not known whether apneas result from a predictable process or from a stochastic process, but the observation that they occur in seemingly random clusters justifies the use of stochastic models. We use a hidden-Markov model to analyze the distribution of durations of apneas and the distribution of times between apneas. The model suggests the presence of four breathing states, ranging from very stable (with an average lifetime of 12 h) to very unstable (with an average lifetime of 10 s). Although the states themselves are not visible, the mathematical analysis gives estimates of the transition rates among these states. We have obtained these transition rates, and shown how they change with post-menstrual age; as expected, the residence time in the more stable breathing states increases with age. We also extrapolated the model to predict the frequency of very prolonged apnea during the first year of life. This paradigm-stochastic modeling of cardiorespiratory control in neonatal infants to estimate risk for severe clinical events-may be a first step toward personalized risk assessment for life threatening apnea events after NICU discharge.
Ensemble averaging and stacking of ARIMA and GSTAR model for rainfall forecasting
Anggraeni, D.; Kurnia, I. F.; Hadi, A. F.
2018-04-01
Unpredictable rainfall changes can affect human activities, such as in agriculture, aviation, shipping which depend on weather forecasts. Therefore, we need forecasting tools with high accuracy in predicting the rainfall in the future. This research focus on local forcasting of the rainfall at Jember in 2005 until 2016, from 77 rainfall stations. The rainfall here was not only related to the occurrence of the previous of its stations, but also related to others, it’s called the spatial effect. The aim of this research is to apply the GSTAR model, to determine whether there are some correlations of spatial effect between one to another stations. The GSTAR model is an expansion of the space-time model that combines the time-related effects, the locations (stations) in a time series effects, and also the location it self. The GSTAR model will also be compared to the ARIMA model that completely ignores the independent variables. The forcested value of the ARIMA and of the GSTAR models then being combined using the ensemble forecasting technique. The averaging and stacking method of ensemble forecasting method here provide us the best model with higher acuracy model that has the smaller RMSE (Root Mean Square Error) value. Finally, with the best model we can offer a better local rainfall forecasting in Jember for the future.
Performance modeling, stochastic networks, and statistical multiplexing
Mazumdar, Ravi R
2013-01-01
This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of introducing an appropriate mathematical framework for modeling and analysis as well as understanding the phenomenon of statistical multiplexing. The models, techniques, and results presented form the core of traffic engineering methods used to design, control and allocate resources in communication networks.The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the importan
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
Directory of Open Access Journals (Sweden)
Shelton Peiris
2017-12-01
Full Text Available This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV components in order to develop the General Long Memory SV (GLMSV model. We examine the corresponding statistical properties of this model, discuss the spectral likelihood estimation and investigate the finite sample properties via Monte Carlo experiments. We provide empirical evidence by applying the GLMSV model to three exchange rate return series and conjecture that the results of out-of-sample forecasts adequately confirm the use of GLMSV model in certain financial applications.
Stochastic quantization of a topological quantum mechanical model
International Nuclear Information System (INIS)
Antunes, Sergio; Krein, Gastao; Menezes, Gabriel; Svaiter, Nami Fux
2011-01-01
Full text: Stochastic quantization of complex actions has been extensively studied in the literature. In these models, a Markovian Langevin equation is used in order to study the quantization of such systems. In such papers, the advantages of the Markovian stochastic quantization method were explored and exposed. However, many drawbacks of the method were also pointed out, such as instability of the simulations with absence of convergence and sometimes convergence to the wrong limit. Indeed, although several alternative methods have been proposed to deal with interesting physical systems where the action is complex, these approaches do not suggest any general way of solving the particular difficulties that arise in each situation. Here, we wish to make contributions to the program of stochastic quantization of theories with imaginary action by investigating the consequences of a non-Markovian stochastic quantization in a particular situation, namely a quantum mechanical topological action. We analyze the Markovian stochastic quantization for a topological quantum mechanical action which is analog to a Maxwell-Chern-Simons action in the Weyl gauge. Afterwards we consider a Langevin equation with memory kernel and Einstein's relations with colored noise. We show that convergence towards equilibrium is achieved in both regimes. We also sketch a simple numerical analysis to investigate the possible advantages of non-Markovian procedure over the usual Markovian quantization. Both retarded Green's function for the diffusion problem are considered in such analysis. We show that, although the results indicated that the effect of memory kernel, as usually expected, is to delay the convergence to equilibrium, non-Markovian systems imply a faster decay compared to Markovian ones as well as smoother convergence to equilibrium. (author)
Introduction to stochastic models in biology
DEFF Research Database (Denmark)
Ditlevsen, Susanne; Samson, Adeline
2013-01-01
This chapter is concerned with continuous time processes, which are often modeled as a system of ordinary differential equations (ODEs). These models assume that the observed dynamics are driven exclusively by internal, deterministic mechanisms. However, real biological systems will always be exp...
Time-Weighted Balanced Stochastic Model Reduction
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Shaker, Hamid Reza
2011-01-01
A new relative error model reduction technique for linear time invariant (LTI) systems is proposed in this paper. Both continuous and discrete time systems can be reduced within this framework. The proposed model reduction method is mainly based upon time-weighted balanced truncation and a recently...
Stochastic modelling in design of mechanical properties of nanometals
International Nuclear Information System (INIS)
Tengen, T.B.; Wejrzanowski, T.; Iwankiewicz, R.; Kurzydlowski, K.J.
2010-01-01
Polycrystalline nanometals are being fabricated through different processing routes and conditions. The consequence is that nanometals having the same mean grain size may have different grain size dispersion and, hence, may have different material properties. This has often led to conflicting reports from both theoretical and experimental findings about the evolutions of the mechanical properties of nanomaterials. The present paper employs stochastic model to study the impact of microstructure evolution during grain growth on the mechanical properties of polycrystalline nanometals. The stochastic model for grain growth and the stochastic model for changes in mechanical properties of nanomaterials are proposed. The model for the mechanical properties developed is tested on aluminium samples.Many salient features of the mechanical properties of the aluminium samples are revealed. The results show that the different mechanisms of grain growth impart different nature of response to the material mechanical properties. The conventional, homologous and anomalous temperature dependences of the yield stress have also been revealed to be due to different nature of interactions of the microstructures during evolution.
Bayesian inference for hybrid discrete-continuous stochastic kinetic models
International Nuclear Information System (INIS)
Sherlock, Chris; Golightly, Andrew; Gillespie, Colin S
2014-01-01
We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process (MJP), computational cost can be prohibitive for networks of realistic size and complexity. In this paper, we consider an inference scheme based on a novel hybrid simulator that classifies reactions as either ‘fast’ or ‘slow’ with fast reactions evolving as a continuous Markov process whilst the remaining slow reaction occurrences are modelled through a MJP with time-dependent hazards. A linear noise approximation (LNA) of fast reaction dynamics is employed and slow reaction events are captured by exploiting the ability to solve the stochastic differential equation driving the LNA. This simulation procedure is used as a proposal mechanism inside a particle MCMC scheme, thus allowing Bayesian inference for the model parameters. We apply the scheme to a simple application and compare the output with an existing hybrid approach and also a scheme for performing inference for the underlying discrete stochastic model. (paper)
TIME-DEPENDENT STOCHASTIC ACCELERATION MODEL FOR FERMI BUBBLES
Energy Technology Data Exchange (ETDEWEB)
Sasaki, Kento; Asano, Katsuaki; Terasawa, Toshio, E-mail: kentos@icrr.u-tokyo.ac.jp, E-mail: asanok@icrr.u-tokyo.ac.jp, E-mail: terasawa@icrr.u-tokyo.ac.jp [Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8582 (Japan)
2015-12-01
We study stochastic acceleration models for the Fermi bubbles. Turbulence is excited just behind the shock front via Kelvin–Helmholtz, Rayleigh–Taylor, or Richtmyer–Meshkov instabilities, and plasma particles are continuously accelerated by the interaction with the turbulence. The turbulence gradually decays as it goes away from the shock fronts. Adopting a phenomenological model for the stochastic acceleration, we explicitly solve the temporal evolution of the particle energy distribution in the turbulence. Our results show that the spatial distribution of high-energy particles is different from those for a steady solution. We also show that the contribution of electrons that escaped from the acceleration regions significantly softens the photon spectrum. The photon spectrum and surface brightness profile are reproduced by our models. If the escape efficiency is very high, the radio flux from the escaped low-energy electrons can be comparable to that of the WMAP haze. We also demonstrate hadronic models with the stochastic acceleration, but they are unlikely in the viewpoint of the energy budget.
Stochastic models of solute transport in highly heterogeneous geologic media
Energy Technology Data Exchange (ETDEWEB)
Semenov, V.N.; Korotkin, I.A.; Pruess, K.; Goloviznin, V.M.; Sorokovikova, O.S.
2009-09-15
A stochastic model of anomalous diffusion was developed in which transport occurs by random motion of Brownian particles, described by distribution functions of random displacements with heavy (power-law) tails. One variant of an effective algorithm for random function generation with a power-law asymptotic and arbitrary factor of asymmetry is proposed that is based on the Gnedenko-Levy limit theorem and makes it possible to reproduce all known Levy {alpha}-stable fractal processes. A two-dimensional stochastic random walk algorithm has been developed that approximates anomalous diffusion with streamline-dependent and space-dependent parameters. The motivation for introducing such a type of dispersion model is the observed fact that tracers in natural aquifers spread at different super-Fickian rates in different directions. For this and other important cases, stochastic random walk models are the only known way to solve the so-called multiscaling fractional order diffusion equation with space-dependent parameters. Some comparisons of model results and field experiments are presented.
A Stochastic Operational Planning Model for Smart Power Systems
Directory of Open Access Journals (Sweden)
Sh. Jadid
2014-12-01
Full Text Available Smart Grids are result of utilizing novel technologies such as distributed energy resources, and communication technologies in power system to compensate some of its defects. Various power resources provide some benefits for operation domain however, power system operator should use a powerful methodology to manage them. Renewable resources and load add uncertainty to the problem. So, independent system operator should use a stochastic method to manage them. A Stochastic unit commitment is presented in this paper to schedule various power resources such as distributed generation units, conventional thermal generation units, wind and PV farms, and demand response resources. Demand response resources, interruptible loads, distributed generation units, and conventional thermal generation units are used to provide required reserve for compensating stochastic nature of various resources and loads. In the presented model, resources connected to distribution network can participate in wholesale market through aggregators. Moreover, a novel three-program model which can be used by aggregators is presented in this article. Loads and distributed generation can contract with aggregators by these programs. A three-bus test system and the IEEE RTS are used to illustrate usefulness of the presented model. The results show that ISO can manage the system effectively by using this model
Understanding onsets of rainfall in Southern Africa using temporal probabilistic modelling
CSIR Research Space (South Africa)
Cheruiyot, D
2010-12-01
Full Text Available This research investigates an alternative approach to automatically evolve the hidden temporal distribution of onset of rainfall directly from multivariate time series (MTS) data in the absence of domain experts. Temporal probabilistic modelling...
FLASH-FLOOD MODELLING WITH ARTIFICIAL NEURAL NETWORKS USING RADAR RAINFALL ESTIMATES
Directory of Open Access Journals (Sweden)
Dinu Cristian
2017-09-01
Full Text Available The use of artificial neural networks (ANNs in modelling the hydrological processes has become a common approach in the last two decades, among side the traditional methods. In regard to the rainfall-runoff modelling, in both traditional and ANN models the use of ground rainfall measurements is prevalent, which can be challenging in areas with low rain gauging station density, especially in catchments where strong focused rainfall can generate flash-floods. The weather radar technology can prove to be a solution for such areas by providing rain estimates with good time and space resolution. This paper presents a comparison between different ANN setups using as input both ground and radar observations for modelling the rainfall-runoff process for Bahluet catchment, with focus on a flash-flood observed in the catchment.
Tropospheric biennial oscillation and south Asian summer monsoon rainfall in a coupled model
Konda, Gopinadh; Chowdary, J. S.; Srinivas, G.; Gnanaseelan, C.; Parekh, Anant; Attada, Raju; Rama Krishna, S. S. V. S.
2018-06-01
In this study Tropospheric Biennial Oscillation (TBO) and south Asian summer monsoon rainfall are examined in the National Centers for Environmental Prediction (NCEP) Climate Forecast System (CFSv2) hindcast. High correlation between the observations and model TBO index suggests that the model is able to capture most of the TBO years. Spatial patterns of rainfall anomalies associated with positive TBO over the south Asian region are better represented in the model as in the observations. However, the model predicted rainfall anomaly patterns associated with negative TBO years are improper and magnitudes are underestimated compared to the observations. It is noted that positive (negative) TBO is associated with La Niña (El Niño) like Sea surface temperature (SST) anomalies in the model. This leads to the fact that model TBO is El Niño-Southern Oscillation (ENSO) driven, while in the observations Indian Ocean Dipole (IOD) also plays a role in the negative TBO phase. Detailed analysis suggests that the negative TBO rainfall anomaly pattern in the model is highly influenced by improper teleconnections allied to IOD. Unlike in the observations, rainfall anomalies over the south Asian region are anti-correlated with IOD index in CFSv2. Further, summer monsoon rainfall over south Asian region is highly correlated with IOD western pole than eastern pole in CFSv2 in contrast to the observations. Altogether, the present study highlights the importance of improving Indian Ocean SST teleconnections to south Asian summer rainfall in the model by enhancing the predictability of TBO. This in turn would improve monsoon rainfall prediction skill of the model.
Tropospheric biennial oscillation and south Asian summer monsoon rainfall in a coupled model
Konda, Gopinadh; Chowdary, Jasti S.; Srinivas, G; Gnanaseelan, C; Parekh, Anant; Attada, Raju; Rama Krishna, S S V S
2018-01-01
In this study Tropospheric Biennial Oscillation (TBO) and south Asian summer monsoon rainfall are examined in the National Centers for Environmental Prediction (NCEP) Climate Forecast System (CFSv2) hindcast. High correlation between the observations and model TBO index suggests that the model is able to capture most of the TBO years. Spatial patterns of rainfall anomalies associated with positive TBO over the south Asian region are better represented in the model as in the observations. However, the model predicted rainfall anomaly patterns associated with negative TBO years are improper and magnitudes are underestimated compared to the observations. It is noted that positive (negative) TBO is associated with La Niña (El Niño) like Sea surface temperature (SST) anomalies in the model. This leads to the fact that model TBO is El Niño-Southern Oscillation (ENSO) driven, while in the observations Indian Ocean Dipole (IOD) also plays a role in the negative TBO phase. Detailed analysis suggests that the negative TBO rainfall anomaly pattern in the model is highly influenced by improper teleconnections allied to IOD. Unlike in the observations, rainfall anomalies over the south Asian region are anti-correlated with IOD index in CFSv2. Further, summer monsoon rainfall over south Asian region is highly correlated with IOD western pole than eastern pole in CFSv2 in contrast to the observations. Altogether, the present study highlights the importance of improving Indian Ocean SST teleconnections to south Asian summer rainfall in the model by enhancing the predictability of TBO. This in turn would improve monsoon rainfall prediction skill of the model.
Tropospheric biennial oscillation and south Asian summer monsoon rainfall in a coupled model
Konda, Gopinadh
2018-05-22
In this study Tropospheric Biennial Oscillation (TBO) and south Asian summer monsoon rainfall are examined in the National Centers for Environmental Prediction (NCEP) Climate Forecast System (CFSv2) hindcast. High correlation between the observations and model TBO index suggests that the model is able to capture most of the TBO years. Spatial patterns of rainfall anomalies associated with positive TBO over the south Asian region are better represented in the model as in the observations. However, the model predicted rainfall anomaly patterns associated with negative TBO years are improper and magnitudes are underestimated compared to the observations. It is noted that positive (negative) TBO is associated with La Niña (El Niño) like Sea surface temperature (SST) anomalies in the model. This leads to the fact that model TBO is El Niño-Southern Oscillation (ENSO) driven, while in the observations Indian Ocean Dipole (IOD) also plays a role in the negative TBO phase. Detailed analysis suggests that the negative TBO rainfall anomaly pattern in the model is highly influenced by improper teleconnections allied to IOD. Unlike in the observations, rainfall anomalies over the south Asian region are anti-correlated with IOD index in CFSv2. Further, summer monsoon rainfall over south Asian region is highly correlated with IOD western pole than eastern pole in CFSv2 in contrast to the observations. Altogether, the present study highlights the importance of improving Indian Ocean SST teleconnections to south Asian summer rainfall in the model by enhancing the predictability of TBO. This in turn would improve monsoon rainfall prediction skill of the model.
Stochastic population and epidemic models persistence and extinction
Allen, Linda J S
2015-01-01
This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MATLAB programs for simulating stochastic sample paths are provided in an Appendix. These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in the Department of Mathematics and Statistics ...
Modeling and stochastic analysis of dynamic mechanisms of the perception
Pisarchik, A.; Bashkirtseva, I.; Ryashko, L.
2017-10-01
Modern studies in physiology and cognitive neuroscience consider a noise as an important constructive factor of the brain functionality. Under the adequate noise, the brain can rapidly access different ordered states, and provide decision-making by preventing deadlocks. Bistable dynamic models are often used for the study of the underlying mechanisms of the visual perception. In the present paper, we consider a bistable energy model subject to both additive and parametric noise. Using the catastrophe theory formalism and stochastic sensitivity functions technique, we analyze a response of the equilibria to noise, and study noise-induced transitions between equilibria. We demonstrate and analyse the effect of hysteresis squeezing when the intensity of noise is increased. Stochastic bifurcations connected with the suppression of oscillations by parametric noises are discussed.
Stochastic modeling of reinforced concrete structures exposed to chloride attack
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Frier, Christian
2004-01-01
For many reinforced concrete structures corrosion of reinforcement is an important problem since it can result in expensive maintenance and repair actions. Further, a significant reduction of the load-bearing capacity can occur. One mode of corrosion initiation is that the chloride content around...... concentration and reinforcement cover depth are modeled by stochastic fields. The paper contains a description of the parameters to be included in a stochastic model and a proposal for the information needed to obtain values for the parameters in order to be able to perform reliability investigations....... The distribution of the time to initiation of corrosion is estimated by simulation. As an example a bridge pier in a marine environment is considered....
Stochastic Modeling of Reinforced Concrete Structures Exposed to Chloride Attack
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Frier, Christian
2003-01-01
For many reinforced concrete structures corrosion of reinforcement is an important problem since it can result in expensive maintenance and repair actions. Further, a significant reduction of the load-bearing capacity can occur. One mode of corrosion initiation is that the chloride content around...... concentration and reinforcement cover depth are modeled by stochastic fields. The paper contains a description of the parameters to be included in a stochastic model and a proposal for the information needed to obtain values for the parameters in order to be ab le to perform reliability investigations....... The distribution of the time to initiation of corrosion is estimated by simulation. As an example a bridge pier in a marine environment is considered....
Stochastic Model for Population Exposed to Low Level Risk
International Nuclear Information System (INIS)
Merkle, J.M.
1996-01-01
In this paper the stochastic model for population size, i.e. calculation of the number of deaths due to lethal stochastic health effects caused by the exposure to low level ionising radiation is presented. The model is defined for subpopulation with parameter (a, b) being fixed. Using the corresponding density function, it is possible to find all the quantities of interest by averaging over whole possible values for (a, l). All processes ar at first defined for one radionuclide, exposure pathway and the health effect under consideration. The results obtained in this paper are the basic quantities in the risk assessment, loss of life expectancy etc. The results presented in this paper are also applicable to the other sources of low level risk, not only the radiation risk
Stochastic modeling of the hypothalamic pulse generator activity.
Camproux, A C; Thalabard, J C; Thomas, G
1994-11-01
Luteinizing hormone (LH) is released by the pituitary in discrete pulses. In the monkey, the appearance of LH pulses in the plasma is invariably associated with sharp increases (i.e, volleys) in the frequency of the hypothalamic pulse generator electrical activity, so that continuous monitoring of this activity by telemetry provides a unique means to study the temporal structure of the mechanism generating the pulses. To assess whether the times of occurrence and durations of previous volleys exert significant influence on the timing of the next volley, we used a class of periodic counting process models that specify the stochastic intensity of the process as the product of two factors: 1) a periodic baseline intensity and 2) a stochastic regression function with covariates representing the influence of the past. This approach allows the characterization of circadian modulation and memory range of the process underlying hypothalamic pulse generator activity, as illustrated by fitting the model to experimental data from two ovariectomized rhesus monkeys.
On a Versatile Stochastic Growth Model
Directory of Open Access Journals (Sweden)
Samiur Arif
2012-06-01
Full Text Available Growth phenomena are ubiquitous and pervasive not only in biology and the medical sciences, but also in economics, marketing and the computer and social sciences. We introduce a three-parameter version of the classic pure-birth process growth model when suitably instantiated, can be used to model growth phenomena in many seemingly unrelated application domains. We point out that the model is computationally attractive since it admits of conceptually simple, closed form solutions for the time-dependent probabilities.
An extension of clarke's model with stochastic amplitude flip processes
Hoel, Hakon
2014-07-01
Stochastic modeling is an essential tool for studying statistical properties of wireless channels. In multipath fading channel (MFC) models, the signal reception is modeled by a sum of wave path contributions, and Clarke\\'s model is an important example of such which has been widely accepted in many wireless applications. However, since Clarke\\'s model is temporally deterministic, Feng and Field noted that it does not model real wireless channels with time-varying randomness well. Here, we extend Clarke\\'s model to a novel time-varying stochastic MFC model with scatterers randomly flipping on and off. Statistical properties of the MFC model are analyzed and shown to fit well with real signal measurements, and a limit Gaussian process is derived from the model when the number of active wave paths tends to infinity. A second focus of this work is a comparison study of the error and computational cost of generating signal realizations from the MFC model and from its limit Gaussian process. By rigorous analysis and numerical studies, we show that in many settings, signal realizations are generated more efficiently by Gaussian process algorithms than by the MFC model\\'s algorithm. Numerical examples that strengthen these observations are also presented. © 2014 IEEE.
Stochastic Models of Molecule Formation on Dust
Charnley, Steven; Wirstroem, Eva
2011-01-01
We will present new theoretical models for the formation of molecules on dust. The growth of ice mantles and their layered structure is accounted for and compared directly to observations through simulation of the expected ice absorption spectra
Deterministic geologic processes and stochastic modeling
International Nuclear Information System (INIS)
Rautman, C.A.; Flint, A.L.
1992-01-01
This paper reports that recent outcrop sampling at Yucca Mountain, Nevada, has produced significant new information regarding the distribution of physical properties at the site of a potential high-level nuclear waste repository. consideration of the spatial variability indicates that her are a number of widespread deterministic geologic features at the site that have important implications for numerical modeling of such performance aspects as ground water flow and radionuclide transport. Because the geologic processes responsible for formation of Yucca Mountain are relatively well understood and operate on a more-or-less regional scale, understanding of these processes can be used in modeling the physical properties and performance of the site. Information reflecting these deterministic geologic processes may be incorporated into the modeling program explicitly using geostatistical concepts such as soft information, or implicitly, through the adoption of a particular approach to modeling
Stochastic Multiscale Modeling of Polycrystalline Materials
2013-01-01
The single-grid strategy is adopted. The crystal visco-plastic constitutive model proposed in [7] along with a Voce type hardening model described...in [97] is used with γ̇0 = 1s−1 and m = 0.1. The parameters in the Voce type hardening law are selected according to [97]: κ0 = 47.0MPa, κ1 = 86.0MPa
Weather model performance on extreme rainfall events simulation's over Western Iberian Peninsula
Pereira, S. C.; Carvalho, A. C.; Ferreira, J.; Nunes, J. P.; Kaiser, J. J.; Rocha, A.
2012-08-01
This study evaluates the performance of the WRF-ARW numerical weather model in simulating the spatial and temporal patterns of an extreme rainfall period over a complex orographic region in north-central Portugal. The analysis was performed for the December month of 2009, during the Portugal Mainland rainy season. The heavy rainfall to extreme heavy rainfall periods were due to several low surface pressure's systems associated with frontal surfaces. The total amount of precipitation for December exceeded, in average, the climatological mean for the 1971-2000 time period in +89 mm, varying from 190 mm (south part of the country) to 1175 mm (north part of the country). Three model runs were conducted to assess possible improvements in model performance: (1) the WRF-ARW is forced with the initial fields from a global domain model (RunRef); (2) data assimilation for a specific location (RunObsN) is included; (3) nudging is used to adjust the analysis field (RunGridN). Model performance was evaluated against an observed hourly precipitation dataset of 15 rainfall stations using several statistical parameters. The WRF-ARW model reproduced well the temporal rainfall patterns but tended to overestimate precipitation amounts. The RunGridN simulation provided the best results but model performance of the other two runs was good too, so that the selected extreme rainfall episode was successfully reproduced.
Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction
Smelyanskiy, V. N.; Luchinsky, D. G.; Stefanovska, A.; McClintock, P. V.
2005-03-01
We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.
Stochastic Model Predictive Control with Applications in Smart Energy Systems
DEFF Research Database (Denmark)
Sokoler, Leo Emil; Edlund, Kristian; Mølbak, Tommy
2012-01-01
to cover more than 50% of the total consumption by 2050. Energy systems based on significant amounts of renewable energy sources are subject to uncertainties. To accommodate the need for model predictive control (MPC) of such systems, the effect of the stochastic effects on the constraints must...... study, we consider a system consisting of fuel-fired thermal power plants, wind farms and electric vehicles....
Stochastic model of Rayleigh-Taylor turbulent mixing
International Nuclear Information System (INIS)
Abarzhi, S.I.; Cadjan, M.; Fedotov, S.
2007-01-01
We propose a stochastic model to describe the random character of the dissipation process in Rayleigh-Taylor turbulent mixing. The parameter alpha, used conventionally to characterize the mixing growth-rate, is not a universal constant and is very sensitive to the statistical properties of the dissipation. The ratio between the rates of momentum loss and momentum gain is the statistic invariant and a robust parameter to diagnose with or without turbulent diffusion accounted for
Dynamic analysis of a stochastic delayed rumor propagation model
Jia, Fangju; Lv, Guangying; Wang, Shuangfeng; Zou, Guang-an
2018-02-01
The rapid development of the Internet, especially the emergence of the social networks, has led rumor propagation into a new media era. In this paper, we are concerned with a stochastic delayed rumor propagation model. Firstly, we obtain the existence of the global solution. Secondly, sufficient conditions for extinction of the rumor are established. Lastly, the boundedness of solution is proved and some simulations are given to verify our results.
Neural network modelling of rainfall interception in four different forest stands
Ibrahim Yurtseven; Mustafa Zengin
2013-01-01
The objective of this study is to reveal whether it is possible to predict rainfall, throughfall and stemflow in forest ecosystems with less effort, using several measurements of rainfall interception (hereafter interception) and an artificial neural network based linear regression model (ANN model). To this end, the Kerpe Research Forest in the province of Kocaeli, which houses stands of mixed deciduous-broadleaf forest (Castanea sativa Mill., Fagus orientalis Lipsky, Quercus spp.), black pi...
Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes
DEFF Research Database (Denmark)
Starke, Jens; Reichert, Christian; Eiswirth, Markus
2007-01-01
Three levels of modeling, microscopic, mesoscopic and macroscopic are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. It can......, such that in contrast to the microscopic model the spatial resolution is reduced. The derivation of deterministic limit equations is in correspondence with the successful description of experiments under low-pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena...
Five challenges for stochastic epidemic models involving global transmission
Directory of Open Access Journals (Sweden)
Tom Britton
2015-03-01
Full Text Available The most basic stochastic epidemic models are those involving global transmission, meaning that infection rates depend only on the type and state of the individuals involved, and not on their location in the population. Simple as they are, there are still several open problems for such models. For example, when will such an epidemic go extinct and with what probability (questions depending on the population being fixed, changing or growing? How can a model be defined explaining the sometimes observed scenario of frequent mid-sized epidemic outbreaks? How can evolution of the infectious agent transmission rates be modelled and fitted to data in a robust way?
Extinction in neutrally stable stochastic Lotka-Volterra models
Dobrinevski, Alexander; Frey, Erwin
2012-05-01
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.
On a Stochastic Model in Insurance
Indian Academy of Sciences (India)
Insurance mathematics today is considered a part of applied probability theory. Main objectives are modelling of claims that arrive in an insurance business, and decide how premiums are to be charged to avoid ruin of the insurance company. GENERAL I ARTICLE various results and the heuristics can be appreciated.
Merging bottom-up and top-down precipitation products using a stochastic error model
Maggioni, Viviana; Massari, Christian; Brocca, Luca; Ciabatta, Luca
2017-04-01
Accurate quantitative precipitation estimation is of great importance for water resources management, agricultural planning, and forecasting and monitoring of natural hazards such as flash floods and landslides. In situ observations are limited around the Earth, especially in remote areas (e.g., complex terrain, dense vegetation), but currently available satellite precipitation products are able to provide global precipitation estimates with an accuracy that depends upon many factors (e.g., type of storms, temporal sampling, season etc…). Recently, Brocca et al. (2014) have proposed an alternative approach (i.e., SM2RAIN) that allows to estimate rainfall from space by using satellite soil moisture observations. In contrast with classical satellite precipitation products which sense the cloud properties to retrieve the instantaneous precipitation, this new bottom-up approach makes use of two consecutive soil moisture measurements for obtaining an estimate of the fallen precipitation within the interval between two satellite passes. As a result, the nature of the measurement is different and complementary to the one of classical precipitation products and could provide a different valid perspective to improve current satellite rainfall estimates via appropriate integration between the products (i.e., SM2RAIN plus a classical satellite rainfall product). However, whether SM2RAIN is able or not to improve the performance of any state-of-the-art satellite rainfall product is much dependent upon an adequate quantification and characterization of the relative errors of the products. In this study, the stochastic rainfall error model SREM2D (Hossain et al. 2006) is used for characterizing the retrieval error of both SM2RAIN and a state-of-the-art satellite precipitation product (i.e., 3B42RT). The error characterization serves for an optimal integration between SM2RAIN and 3B42RT for enhancing the capability of the resulting integrated product (i.e. SM2RAIN+3B42RT) in
Stochastic Modelling of Wireless Energy Transfer
Veilleux, Shaun; Almaghasilah, Ahmed; Abedi, Ali; Wilkerson, DeLisa
2017-01-01
This study investigates the efficiency of a new method of powering remote sensors by the means of wireless energy transfer. The increased use of sensors for data collection comes with the inherent cost of supplying power from sources such as power cables or batteries. Wireless energy transfer technology eliminates the need for power cables or periodic battery replacement. The time and cost of setting up or expanding a sensor network will be reduced while allowing sensors to be placed in areas where running power cables or battery replacement is not feasible. This paper models wireless channels for power and data separately. Smart scheduling for the data channel is proposed to avoid transmitting data on a noisy channel where the probability of data loss is high to improve power efficiency. Analytical models have been developed and verified using simulations.
Stochastic modeling of a serial killer.
Simkin, M V; Roychowdhury, V P
2014-08-21
We analyze the time pattern of the activity of a serial killer, who during 12 years had murdered 53 people. The plot of the cumulative number of murders as a function of time is of "Devil's staircase" type. The distribution of the intervals between murders (step length) follows a power law with the exponent of 1.4. We propose a model according to which the serial killer commits murders when neuronal excitation in his brain exceeds certain threshold. We model this neural activity as a branching process, which in turn is approximated by a random walk. As the distribution of the random walk return times is a power law with the exponent 1.5, the distribution of the inter-murder intervals is thus explained. We illustrate analytical results by numerical simulation. Time pattern activity data from two other serial killers further substantiate our analysis. Copyright © 2014 Elsevier Ltd. All rights reserved.
Akinsanola, A. A.; Ajayi, V. O.; Adejare, A. T.; Adeyeri, O. E.; Gbode, I. E.; Ogunjobi, K. O.; Nikulin, G.; Abolude, A. T.
2018-04-01
This study presents evaluation of the ability of Rossby Centre Regional Climate Model (RCA4) driven by nine global circulation models (GCMs), to skilfully reproduce the key features of rainfall climatology over West Africa for the period of 1980-2005. The seasonal climatology and annual cycle of the RCA4 simulations were assessed over three homogenous subregions of West Africa (Guinea coast, Savannah, and Sahel) and evaluated using observed precipitation data from the Global Precipitation Climatology Project (GPCP). Furthermore, the model output was evaluated using a wide range of statistical measures. The interseasonal and interannual variability of the RCA4 were further assessed over the subregions and the whole of the West Africa domain. Results indicate that the RCA4 captures the spatial and interseasonal rainfall pattern adequately but exhibits a weak performance over the Guinea coast. Findings from the interannual rainfall variability indicate that the model performance is better over the larger West Africa domain than the subregions. The largest difference across the RCA4 simulated annual rainfall was found in the Sahel. Result from the Mann-Kendall test showed no significant trend for the 1980-2005 period in annual rainfall either in GPCP observation data or in the model simulations over West Africa. In many aspects, the RCA4 simulation driven by the HadGEM2-ES perform best over the region. The use of the multimodel ensemble mean has resulted to the improved representation of rainfall characteristics over the study domain.
Neural network connectivity and response latency modelled by stochastic processes
DEFF Research Database (Denmark)
Tamborrino, Massimiliano
is connected to thousands of other neurons. The rst question is: how to model neural networks through stochastic processes? A multivariate Ornstein-Uhlenbeck process, obtained as a diffusion approximation of a jump process, is the proposed answer. Obviously, dependencies between neurons imply dependencies......Stochastic processes and their rst passage times have been widely used to describe the membrane potential dynamics of single neurons and to reproduce neuronal spikes, respectively.However, cerebral cortex in human brains is estimated to contain 10-20 billions of neurons and each of them...... between their spike times. Therefore, the second question is: how to detect neural network connectivity from simultaneously recorded spike trains? Answering this question corresponds to investigate the joint distribution of sequences of rst passage times. A non-parametric method based on copulas...
Environmental versus demographic variability in stochastic predator–prey models
International Nuclear Information System (INIS)
Dobramysl, U; Täuber, U C
2013-01-01
In contrast to the neutral population cycles of the deterministic mean-field Lotka–Volterra rate equations, including spatial structure and stochastic noise in models for predator–prey interactions yields complex spatio-temporal structures associated with long-lived erratic population oscillations. Environmental variability in the form of quenched spatial randomness in the predation rates results in more localized activity patches. Our previous study showed that population fluctuations in rare favorable regions in turn cause a remarkable increase in the asymptotic densities of both predators and prey. Very intriguing features are found when variable interaction rates are affixed to individual particles rather than lattice sites. Stochastic dynamics with demographic variability in conjunction with inheritable predation efficiencies generate non-trivial time evolution for the predation rate distributions, yet with overall essentially neutral optimization. (paper)
Classical and quantum stochastic models of resistive and memristive circuits
Gough, John E.; Zhang, Guofeng
2017-07-01
The purpose of this paper is to examine stochastic Markovian models for circuits in phase space for which the drift term is equivalent to the standard circuit equations. In particular, we include dissipative components corresponding to both a resistor and a memristor in series. We obtain a dilation of the problem which is canonical in the sense that the underlying Poisson bracket structure is preserved under the stochastic flow. We do this first of all for standard Wiener noise but also treat the problem using a new concept of symplectic noise, where the Poisson structure is extended to the noise as well as the circuit variables, and in particular where we have canonically conjugate noises. Finally, we construct a dilation which describes the quantum mechanical analogue.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
Energy Technology Data Exchange (ETDEWEB)
Dobay, M. P. D., E-mail: maria.pamela.david@physik.uni-muenchen.de; Alberola, A. Piera; Mendoza, E. R.; Raedler, J. O., E-mail: joachim.raedler@physik.uni-muenchen.de [Ludwig-Maximilians University, Faculty of Physics, Center for NanoScience (Germany)
2012-03-15
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
International Nuclear Information System (INIS)
Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.
2012-01-01
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.
2012-03-01
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Kang, Suchul; Im, Eun-Soon; Eltahir, Elfatih A. B.
2018-03-01
In this study, future changes in rainfall due to global climate change are investigated over the western Maritime Continent based on dynamically downscaled climate projections using the MIT Regional Climate Model (MRCM) with 12 km horizontal resolution. A total of nine 30-year regional climate projections driven by multi-GCMs projections (CCSM4, MPI-ESM-MR and ACCESS1.0) under multi-scenarios of greenhouse gases emissions (Historical: 1976-2005, RCP4.5 and RCP8.5: 2071-2100) from phase 5 of the Coupled Model Inter-comparison Project (CMIP5) are analyzed. Focusing on dynamically downscaled rainfall fields, the associated systematic biases originating from GCM and MRCM are removed based on observations using Parametric Quantile Mapping method in order to enhance the reliability of future projections. The MRCM simulations with bias correction capture the spatial patterns of seasonal rainfall as well as the frequency distribution of daily rainfall. Based on projected rainfall changes under both RCP4.5 and RCP8.5 scenarios, the ensemble of MRCM simulations project a significant decrease in rainfall over the western Maritime Continent during the inter-monsoon periods while the change in rainfall is not relevant during wet season. The main mechanism behind the simulated decrease in rainfall is rooted in asymmetries of the projected changes in seasonal dynamics of the meridional circulation along different latitudes. The sinking motion, which is marginally positioned in the reference simulation, is enhanced and expanded under global climate change, particularly in RCP8.5 scenario during boreal fall season. The projected enhancement of rainfall seasonality over the western Maritime Continent suggests increased risk of water stress for natural ecosystems as well as man-made water resources reservoirs.
Uncertainty quantification and stochastic modeling with Matlab
Souza de Cursi, Eduardo
2015-01-01
Uncertainty Quantification (UQ) is a relatively new research area which describes the methods and approaches used to supply quantitative descriptions of the effects of uncertainty, variability and errors in simulation problems and models. It is rapidly becoming a field of increasing importance, with many real-world applications within statistics, mathematics, probability and engineering, but also within the natural sciences. Literature on the topic has up until now been largely based on polynomial chaos, which raises difficulties when considering different types of approximation and does no
Stochastic Parametrisations and Regime Behaviour of Atmospheric Models
Arnold, Hannah; Moroz, Irene; Palmer, Tim
2013-04-01
The presence of regimes is a characteristic of non-linear, chaotic systems (Lorenz, 2006). In the atmosphere, regimes emerge as familiar circulation patterns such as the El-Nino Southern Oscillation (ENSO), the North Atlantic Oscillation (NAO) and Scandinavian Blocking events. In recent years there has been much interest in the problem of identifying and studying atmospheric regimes (Solomon et al, 2007). In particular, how do these regimes respond to an external forcing such as anthropogenic greenhouse gas emissions? The importance of regimes in observed trends over the past 50-100 years indicates that in order to predict anthropogenic climate change, our climate models must be able to represent accurately natural circulation regimes, their statistics and variability. It is well established that representing model uncertainty as well as initial condition uncertainty is important for reliable weather forecasts (Palmer, 2001). In particular, stochastic parametrisation schemes have been shown to improve the skill of weather forecast models (e.g. Berner et al., 2009; Frenkel et al., 2012; Palmer et al., 2009). It is possible that including stochastic physics as a representation of model uncertainty could also be beneficial in climate modelling, enabling the simulator to explore larger regions of the climate attractor including other flow regimes. An alternative representation of model uncertainty is a perturbed parameter scheme, whereby physical parameters in subgrid parametrisation schemes are perturbed about their optimal value. Perturbing parameters gives a greater control over the ensemble than multi-model or multiparametrisation ensembles, and has been used as a representation of model uncertainty in climate prediction (Stainforth et al., 2005; Rougier et al., 2009). We investigate the effect of including representations of model uncertainty on the regime behaviour of a simulator. A simple chaotic model of the atmosphere, the Lorenz '96 system, is used to study
On the abelianity of the stochastic sandpile model
Nunzi, François
2016-01-01
We consider a stochastic variant of the Abelian Sandpile Model (ASM) on a finite graph, introduced by Chan, Marckert and Selig. Even though it is a more general model, some nice properties still hold. We show that on a certain probability space, even if we lose the group structure due to topplings not being deterministic, some operators still commute. As a corollary, we show that the stationary distribution still does not depend on how sand grains are added onto the graph in our model, answer...
Test models for improving filtering with model errors through stochastic parameter estimation
International Nuclear Information System (INIS)
Gershgorin, B.; Harlim, J.; Majda, A.J.
2010-01-01
The filtering skill for turbulent signals from nature is often limited by model errors created by utilizing an imperfect model for filtering. Updating the parameters in the imperfect model through stochastic parameter estimation is one way to increase filtering skill and model performance. Here a suite of stringent test models for filtering with stochastic parameter estimation is developed based on the Stochastic Parameterization Extended Kalman Filter (SPEKF). These new SPEKF-algorithms systematically correct both multiplicative and additive biases and involve exact formulas for propagating the mean and covariance including the parameters in the test model. A comprehensive study is presented of robust parameter regimes for increasing filtering skill through stochastic parameter estimation for turbulent signals as the observation time and observation noise are varied and even when the forcing is incorrectly specified. The results here provide useful guidelines for filtering turbulent signals in more complex systems with significant model errors.
Event-based rainfall-runoff modelling of the Kelantan River Basin
Basarudin, Z.; Adnan, N. A.; Latif, A. R. A.; Tahir, W.; Syafiqah, N.
2014-02-01
Flood is one of the most common natural disasters in Malaysia. According to hydrologists there are many causes that contribute to flood events. The two most dominant factors are the meteorology factor (i.e climate change) and change in land use. These two factors contributed to floods in recent decade especially in the monsoonal catchment such as Malaysia. This paper intends to quantify the influence of rainfall during extreme rainfall events on the hydrological model in the Kelantan River catchment. Therefore, two dynamic inputs were used in the study: rainfall and river discharge. The extreme flood events in 2008 and 2004 were compared based on rainfall data for both years. The events were modeled via a semi-distributed HEC-HMS hydrological model. Land use change was not incorporated in the study because the study only tries to quantify rainfall changes during these two events to simulate the discharge and runoff value. Therefore, the land use data representing the year 2004 were used as inputs in the 2008 runoff model. The study managed to demonstrate that rainfall change has a significant impact to determine the peak discharge and runoff depth for the study area.
Event-based rainfall-runoff modelling of the Kelantan River Basin
International Nuclear Information System (INIS)
Basarudin, Z; Adnan, N A; Latif, A R A; Syafiqah, N; Tahir, W
2014-01-01
Flood is one of the most common natural disasters in Malaysia. According to hydrologists there are many causes that contribute to flood events. The two most dominant factors are the meteorology factor (i.e climate change) and change in land use. These two factors contributed to floods in recent decade especially in the monsoonal catchment such as Malaysia. This paper intends to quantify the influence of rainfall during extreme rainfall events on the hydrological model in the Kelantan River catchment. Therefore, two dynamic inputs were used in the study: rainfall and river discharge. The extreme flood events in 2008 and 2004 were compared based on rainfall data for both years. The events were modeled via a semi-distributed HEC-HMS hydrological model. Land use change was not incorporated in the study because the study only tries to quantify rainfall changes during these two events to simulate the discharge and runoff value. Therefore, the land use data representing the year 2004 were used as inputs in the 2008 runoff model. The study managed to demonstrate that rainfall change has a significant impact to determine the peak discharge and runoff depth for the study area
Atencia, A.; Llasat, M. C.; Garrote, L.; Mediero, L.
2010-10-01
The performance of distributed hydrological models depends on the resolution, both spatial and temporal, of the rainfall surface data introduced. The estimation of quantitative precipitation from meteorological radar or satellite can improve hydrological model results, thanks to an indirect estimation at higher spatial and temporal resolution. In this work, composed radar data from a network of three C-band radars, with 6-minutal temporal and 2 × 2 km2 spatial resolution, provided by the Catalan Meteorological Service, is used to feed the RIBS distributed hydrological model. A Window Probability Matching Method (gage-adjustment method) is applied to four cases of heavy rainfall to improve the observed rainfall sub-estimation in both convective and stratiform Z/R relations used over Catalonia. Once the rainfall field has been adequately obtained, an advection correction, based on cross-correlation between two consecutive images, was introduced to get several time resolutions from 1 min to 30 min. Each different resolution is treated as an independent event, resulting in a probable range of input rainfall data. This ensemble of rainfall data is used, together with other sources of uncertainty, such as the initial basin state or the accuracy of discharge measurements, to calibrate the RIBS model using probabilistic methodology. A sensitivity analysis of time resolutions was implemented by comparing the various results with real values from stream-flow measurement stations.
Matziaris, Vasileios; Marshall, Alec; Yu, Hai-Sui
2015-04-01
Rainfall-induced landslides are very common natural disasters which cause damage to properties and infrastructure and may result in the loss of human lives. These phenomena often take place in unsaturated soil slopes and are triggered by the saturation of the soil profile, due to rain infiltration, which leads to a loss of shear strength. The aim of this study is to determine rainfall thresholds for the initiation of landslides under different initial conditions. Model tests of rainfall-induced landslides are conducted in the Nottingham Centre for Geomechanics 50g-T geotechnical centrifuge. Initially unsaturated plane-strain slope models made with fine silica sand are prepared at varying densities at 1g and accommodated within a climatic chamber which provides controlled environmental conditions. During the centrifuge flight at 60g, rainfall events of varying intensity and duration are applied to the slope models causing the initiation of slope failure. The impact of soil state properties and rainfall characteristics on the landslide initiation process are discussed. The variation of pore water pressures within the slope before, during and after simulated rainfall events is recorded using miniature pore pressure transducers buried in the soil model. Slope deformation is determined by using a high-speed camera and digital image analysis techniques.
Real Time Updating in Distributed Urban Rainfall Runoff Modelling
Borup, Morten; Mikkelsen, Peter Steen; Grum, Morten; Madsen, Henrik
2014-01-01
When it rains on urban areas the rainfall runoff is transported out of the city via the drainage system. Frequently, the drainage system cannot handle all the rain water, which results in problems like flooding or overflows into natural water bodies. To reduce these problems the systems are equipped with basins and automated structures that allow for a large degree of control of the systems, but in order to do this optimally it is required to know what is happening throughout the system. For ...
Two new algorithms to combine kriging with stochastic modelling
Venema, Victor; Lindau, Ralf; Varnai, Tamas; Simmer, Clemens
2010-05-01
Two main groups of statistical methods used in the Earth sciences are geostatistics and stochastic modelling. Geostatistical methods, such as various kriging algorithms, aim at estimating the mean value for every point as well as possible. In case of sparse measurements, such fields have less variability at small scales and a narrower distribution as the true field. This can lead to biases if a nonlinear process is simulated driven by such a kriged field. Stochastic modelling aims at reproducing the statistical structure of the data in space and time. One of the stochastic modelling methods, the so-called surrogate data approach, replicates the value distribution and power spectrum of a certain data set. While stochastic methods reproduce the statistical properties of the data, the location of the measurement is not considered. This requires the use of so-called constrained stochastic models. Because radiative transfer through clouds is a highly nonlinear process, it is essential to model the distribution (e.g. of optical depth, extinction, liquid water content or liquid water path) accurately. In addition, the correlations within the cloud field are important, especially because of horizontal photon transport. This explains the success of surrogate cloud fields for use in 3D radiative transfer studies. Up to now, however, we could only achieve good results for the radiative properties averaged over the field, but not for a radiation measurement located at a certain position. Therefore we have developed a new algorithm that combines the accuracy of stochastic (surrogate) modelling with the positioning capabilities of kriging. In this way, we can automatically profit from the large geostatistical literature and software. This algorithm is similar to the standard iterative amplitude adjusted Fourier transform (IAAFT) algorithm, but has an additional iterative step in which the surrogate field is nudged towards the kriged field. The nudging strength is gradually
Modification of a rainfall-runoff model for distributed modeling in a GIS and its validation
Nyabeze, W. R.
A rainfall-runoff model, which can be inter-faced with a Geographical Information System (GIS) to integrate definition, measurement, calculating parameter values for spatial features, presents considerable advantages. The modification of the GWBasic Wits Rainfall-Runoff Erosion Model (GWBRafler) to enable parameter value estimation in a GIS (GISRafler) is presented in this paper. Algorithms are applied to estimate parameter values reducing the number of input parameters and the effort to populate them. The use of a GIS makes the relationship between parameter estimates and cover characteristics more evident. This paper has been produced as part of research to generalize the GWBRafler on a spatially distributed basis. Modular data structures are assumed and parameter values are weighted relative to the module area and centroid properties. Modifications to the GWBRafler enable better estimation of low flows, which are typical in drought conditions.
STOCHASTIC MODEL OF THE SPIN DISTRIBUTION OF DARK MATTER HALOS
Energy Technology Data Exchange (ETDEWEB)
Kim, Juhan [Center for Advanced Computation, Korea Institute for Advanced Study, Heogiro 85, Seoul 130-722 (Korea, Republic of); Choi, Yun-Young [Department of Astronomy and Space Science, Kyung Hee University, Gyeonggi 446-701 (Korea, Republic of); Kim, Sungsoo S.; Lee, Jeong-Eun [School of Space Research, Kyung Hee University, Gyeonggi 446-701 (Korea, Republic of)
2015-09-15
We employ a stochastic approach to probing the origin of the log-normal distributions of halo spin in N-body simulations. After analyzing spin evolution in halo merging trees, it was found that a spin change can be characterized by a stochastic random walk of angular momentum. Also, spin distributions generated by random walks are fairly consistent with those directly obtained from N-body simulations. We derived a stochastic differential equation from a widely used spin definition and measured the probability distributions of the derived angular momentum change from a massive set of halo merging trees. The roles of major merging and accretion are also statistically analyzed in evolving spin distributions. Several factors (local environment, halo mass, merging mass ratio, and redshift) are found to influence the angular momentum change. The spin distributions generated in the mean-field or void regions tend to shift slightly to a higher spin value compared with simulated spin distributions, which seems to be caused by the correlated random walks. We verified the assumption of randomness in the angular momentum change observed in the N-body simulation and detected several degrees of correlation between walks, which may provide a clue for the discrepancies between the simulated and generated spin distributions in the voids. However, the generated spin distributions in the group and cluster regions successfully match the simulated spin distribution. We also demonstrated that the log-normality of the spin distribution is a natural consequence of the stochastic differential equation of the halo spin, which is well described by the Geometric Brownian Motion model.
On the deterministic and stochastic use of hydrologic models
Farmer, William H.; Vogel, Richard M.
2016-01-01
Environmental simulation models, such as precipitation-runoff watershed models, are increasingly used in a deterministic manner for environmental and water resources design, planning, and management. In operational hydrology, simulated responses are now routinely used to plan, design, and manage a very wide class of water resource systems. However, all such models are calibrated to existing data sets and retain some residual error. This residual, typically unknown in practice, is often ignored, implicitly trusting simulated responses as if they are deterministic quantities. In general, ignoring the residuals will result in simulated responses with distributional properties that do not mimic those of the observed responses. This discrepancy has major implications for the operational use of environmental simulation models as is shown here. Both a simple linear model and a distributed-parameter precipitation-runoff model are used to document the expected bias in the distributional properties of simulated responses when the residuals are ignored. The systematic reintroduction of residuals into simulated responses in a manner that produces stochastic output is shown to improve the distributional properties of the simulated responses. Every effort should be made to understand the distributional behavior of simulation residuals and to use environmental simulation models in a stochastic manner.
Global Warming Induced Changes in Rainfall Characteristics in IPCC AR5 Models
Lau, William K. M.; Wu, Jenny, H.-T.; Kim, Kyu-Myong
2012-01-01
Changes in rainfall characteristic induced by global warming are examined from outputs of IPCC AR5 models. Different scenarios of climate warming including a high emissions scenario (RCP 8.5), a medium mitigation scenario (RCP 4.5), and 1% per year CO2 increase are compared to 20th century simulations (historical). Results show that even though the spatial distribution of monthly rainfall anomalies vary greatly among models, the ensemble mean from a sizable sample (about 10) of AR5 models show a robust signal attributable to GHG warming featuring a shift in the global rainfall probability distribution function (PDF) with significant increase (>100%) in very heavy rain, reduction (10-20% ) in moderate rain and increase in light to very light rains. Changes in extreme rainfall as a function of seasons and latitudes are also examined, and are similar to the non-seasonal stratified data, but with more specific spatial dependence. These results are consistent from TRMM and GPCP rainfall observations suggesting that extreme rainfall events are occurring more frequently with wet areas getting wetter and dry-area-getting drier in a GHG induced warmer climate.
Optimizing ZigBee Security using Stochastic Model Checking
DEFF Research Database (Denmark)
Yuksel, Ender; Nielson, Hanne Riis; Nielson, Flemming
, we identify an important gap in the specification on key updates, and present a methodology for determining optimal key update policies and security parameters. We exploit the stochastic model checking approach using the probabilistic model checker PRISM, and assess the security needs for realistic......ZigBee is a fairly new but promising wireless sensor network standard that offers the advantages of simple and low resource communication. Nevertheless, security is of great concern to ZigBee, and enhancements are prescribed in the latest ZigBee specication: ZigBee-2007. In this technical report...
Green function simulation of Hamiltonian lattice models with stochastic reconfiguration
International Nuclear Information System (INIS)
Beccaria, M.
2000-01-01
We apply a recently proposed Green function Monte Carlo procedure to the study of Hamiltonian lattice gauge theories. This class of algorithms computes quantum vacuum expectation values by averaging over a set of suitable weighted random walkers. By means of a procedure called stochastic reconfiguration the long standing problem of keeping fixed the walker population without a priori knowledge of the ground state is completely solved. In the U(1) 2 model, which we choose as our theoretical laboratory, we evaluate the mean plaquette and the vacuum energy per plaquette. We find good agreement with previous works using model-dependent guiding functions for the random walkers. (orig.)
Stochastic series expansion simulation of the t -V model
Wang, Lei; Liu, Ye-Hua; Troyer, Matthias
2016-04-01
We present an algorithm for the efficient simulation of the half-filled spinless t -V model on bipartite lattices, which combines the stochastic series expansion method with determinantal quantum Monte Carlo techniques widely used in fermionic simulations. The algorithm scales linearly in the inverse temperature, cubically with the system size, and is free from the time-discretization error. We use it to map out the finite-temperature phase diagram of the spinless t -V model on the honeycomb lattice and observe a suppression of the critical temperature of the charge-density-wave phase in the vicinity of a fermionic quantum critical point.
ARMA modelling of neutron stochastic processes with large measurement noise
International Nuclear Information System (INIS)
Zavaljevski, N.; Kostic, Lj.; Pesic, M.
1994-01-01
An autoregressive moving average (ARMA) model of the neutron fluctuations with large measurement noise is derived from langevin stochastic equations and validated using time series data obtained during prompt neutron decay constant measurements at the zero power reactor RB in Vinca. Model parameters are estimated using the maximum likelihood (ML) off-line algorithm and an adaptive pole estimation algorithm based on the recursive prediction error method (RPE). The results show that subcriticality can be determined from real data with high measurement noise using much shorter statistical sample than in standard methods. (author)
Dynamic analysis of a stochastic rumor propagation model
Jia, Fangju; Lv, Guangying
2018-01-01
The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. In this paper, we are concerned with a stochastic rumor propagation model. Sufficient conditions for extinction and persistence in the mean of the rumor are established. The threshold between persistence in the mean and extinction of the rumor is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system.
Minimalistic models of the vertical distribution of roots under stochastic hydrological forcing
Laio, Francesco
2014-05-01
The assessment of the vertical root profile can be useful for multiple purposes: the partition of water fluxes between evaporation and transpiration, the evaluation of root soil reinforcement for bioengineering applications, the influence of roots on biogeochemical and microbial processes in the soil, etc. In water-controlled ecosystems the shape of the root profile is mainly determined by the soil moisture availability at different depths. The long term soil water balance in the root zone can be assessed by modeling the stochastic incoming and outgoing water fluxes, influenced by the stochastic rainfall pulses and/or by the water table fluctuations. Through an ecohydrological analysis one obtains that in water-controlled ecosystems the vertical root distribution is a decreasing function with depth, whose parameters depend on pedologic and climatic factors. The model can be extended to suitably account for the influence of the water table fluctuations, when the water table is shallow enough to exert an influence on root development, in which case the vertical root distribution tends to assume a non-monotonic form. In order to evaluate the validity of the ecohydrological estimation of the root profile we have tested it on a case study in the north of Tuscany (Italy). We have analyzed data from 17 landslide-prone sites: in each of these sites we have assessed the pedologic and climatic descriptors necessary to apply the model, and we have measured the mean rooting depth. The results show a quite good matching between observed and modeled mean root depths. The merit of this minimalistic approach to the modeling of the vertical root distribution relies on the fact that it allows a quantitative estimation of the main features of the vertical root distribution without resorting to time- and money-demanding measuring surveys.
A stochastic phase-field model determined from molecular dynamics
von Schwerin, Erik; Szepessy, Anders
2010-01-01
The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modelling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitatively correct result of dendritic side branching. This work presents a method to determine stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has three steps: (1) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (2) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics (that is Brownian or over damped Langevin dynamics); and (3) numerical computation of the coarse-grained model functions. The coarse-grained model approximates Gibbs ensemble averages of the atomistic phase-field, by choosing coarse-grained drift and diffusion functions that minimize the approximation error of observables in this ensemble average. © EDP Sciences, SMAI, 2010.
A stochastic phase-field model determined from molecular dynamics
von Schwerin, Erik
2010-03-17
The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modelling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitatively correct result of dendritic side branching. This work presents a method to determine stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has three steps: (1) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (2) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics (that is Brownian or over damped Langevin dynamics); and (3) numerical computation of the coarse-grained model functions. The coarse-grained model approximates Gibbs ensemble averages of the atomistic phase-field, by choosing coarse-grained drift and diffusion functions that minimize the approximation error of observables in this ensemble average. © EDP Sciences, SMAI, 2010.
Stochastic modeling for river pollution of Sungai Perlis
Energy Technology Data Exchange (ETDEWEB)
Yunus, Nurul Izzaty Mohd.; Rahman, Haliza Abd. [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia,81310 Johor Bahru, Johor (Malaysia); Bahar, Arifah [UTM-Centre of Industrial and Applied Mathematics (UTM-CIAM) Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2015-02-03
River pollution has been recognized as a contributor to a wide range of health problems and disorders in human. It can pose health dangers to humans who come into contact with it, either directly or indirectly. Therefore, it is most important to measure the concentration of Biochemical Oxygen Demand (BOD) as a water quality parameter since the parameter has long been the basic means for determining the degree of water pollution in rivers. In this study, BOD is used as a parameter to estimate the water quality at Sungai Perlis. It has been observed that Sungai Perlis is polluted due to lack of management and improper use of resources. Therefore, it is of importance to model the Sungai Perlis water quality in order to describe and predict the water quality systems. The BOD concentration secondary data set is used which was extracted from the Drainage and Irrigation Department Perlis State website. The first order differential equation from Streeter – Phelps model was utilized as a deterministic model. Then, the model was developed into a stochastic model. Results from this study shows that the stochastic model is more adequate to describe and predict the BOD concentration and the water quality systems in Sungai Perlis by having smaller value of mean squared error (MSE)
Stochastic modeling for river pollution of Sungai Perlis
International Nuclear Information System (INIS)
Yunus, Nurul Izzaty Mohd.; Rahman, Haliza Abd.; Bahar, Arifah
2015-01-01
River pollution has been recognized as a contributor to a wide range of health problems and disorders in human. It can pose health dangers to humans who come into contact with it, either directly or indirectly. Therefore, it is most important to measure the concentration of Biochemical Oxygen Demand (BOD) as a water quality parameter since the parameter has long been the basic means for determining the degree of water pollution in rivers. In this study, BOD is used as a parameter to estimate the water quality at Sungai Perlis. It has been observed that Sungai Perlis is polluted due to lack of management and improper use of resources. Therefore, it is of importance to model the Sungai Perlis water quality in order to describe and predict the water quality systems. The BOD concentration secondary data set is used which was extracted from the Drainage and Irrigation Department Perlis State website. The first order differential equation from Streeter – Phelps model was utilized as a deterministic model. Then, the model was developed into a stochastic model. Results from this study shows that the stochastic model is more adequate to describe and predict the BOD concentration and the water quality systems in Sungai Perlis by having smaller value of mean squared error (MSE)
Calibration of a stochastic health evolution model using NHIS data
Gupta, Aparna; Li, Zhisheng
2011-10-01
This paper presents and calibrates an individual's stochastic health evolution model. In this health evolution model, the uncertainty of health incidents is described by a stochastic process with a finite number of possible outcomes. We construct a comprehensive health status index (HSI) to describe an individual's health status, as well as a health risk factor system (RFS) to classify individuals into different risk groups. Based on the maximum likelihood estimation (MLE) method and the method of nonlinear least squares fitting, model calibration is formulated in terms of two mixed-integer nonlinear optimization problems. Using the National Health Interview Survey (NHIS) data, the model is calibrated for specific risk groups. Longitudinal data from the Health and Retirement Study (HRS) is used to validate the calibrated model, which displays good validation properties. The end goal of this paper is to provide a model and methodology, whose output can serve as a crucial component of decision support for strategic planning of health related financing and risk management.
Stochastic modelling of avascular tumour growth and therapy
International Nuclear Information System (INIS)
Sahoo, S; Sahoo, A; Shearer, S F C
2011-01-01
In this paper, a generalized stochastic model for the growth of avascular tumours is presented. This model captures the dynamical evolution of avascular tumour cell subpopulations by incorporating Gaussian white noise into the growth rate of the mitotic function. This work generalizes the deterministic model proposed by Sherratt and Chaplain (2001 J. Math. Biol. 43 291) where they formulated a tumour model in an in vivo setting, in terms of continuum densities of proliferating, quiescent and necrotic cells. Detailed simulations of our model show that the inclusion of Gaussian noise in the original model of Sherratt and Chaplain substantially distorts the overall structure of the density profiles in addition to reducing the speed of tumour growth. Within this stochastic carcinogenesis framework the action of therapy is also investigated by replacing Gaussian white noise with a therapy term. We compare a constant therapy protocol with a logarithmic time-dependent protocol. Our results predict that a logarithmic therapy is more effective than the constant therapy protocol.
Spatio-temporal modelling of rainfall in the Murray-Darling Basin
Nowak, Gen; Welsh, A. H.; O'Neill, T. J.; Feng, Lingbing
2018-02-01
The Murray-Darling Basin (MDB) is a large geographical region in southeastern Australia that contains many rivers and creeks, including Australia's three longest rivers, the Murray, the Murrumbidgee and the Darling. Understanding rainfall patterns in the MDB is very important due to the significant impact major events such as droughts and floods have on agricultural and resource productivity. We propose a model for modelling a set of monthly rainfall data obtained from stations in the MDB and for producing predictions in both the spatial and temporal dimensions. The model is a hierarchical spatio-temporal model fitted to geographical data that utilises both deterministic and data-derived components. Specifically, rainfall data at a given location are modelled as a linear combination of these deterministic and data-derived components. A key advantage of the model is that it is fitted in a step-by-step fashion, enabling appropriate empirical choices to be made at each step.
A stochastic surplus production model in continuous time
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Berg, Casper Willestofte
2017-01-01
surplus production model in continuous time (SPiCT), which in addition to stock dynamics also models the dynamics of the fisheries. This enables error in the catch process to be reflected in the uncertainty of estimated model parameters and management quantities. Benefits of the continuous-time state......Surplus production modelling has a long history as a method for managing data-limited fish stocks. Recent advancements have cast surplus production models as state-space models that separate random variability of stock dynamics from error in observed indices of biomass. We present a stochastic......-space model formulation include the ability to provide estimates of exploitable biomass and fishing mortality at any point in time from data sampled at arbitrary and possibly irregular intervals. We show in a simulation that the ability to analyse subannual data can increase the effective sample size...
Williams, C.; Kniveton, D.; Layberry, R.
2009-04-01
It is increasingly accepted that any possible climate change will not only have an influence on mean climate but may also significantly alter climatic variability. A change in the distribution and magnitude of extreme rainfall events (associated with changing variability), such as droughts or flooding, may have a far greater impact on human and natural systems than a changing mean. This issue is of particular importance for environmentally vulnerable regions such as southern Africa. The subcontinent is considered especially vulnerable to and ill-equipped (in terms of adaptation) for extreme events, due to a number of factors including extensive poverty, famine, disease and political instability. Rainfall variability is a function of scale, so high spatial and temporal resolution data are preferred to identify extreme events and accurately predict future variability. In this research, satellite-derived rainfall data are used as a basis for undertaking model experiments using a state-of-the-art climate model, run at both high and low spatial resolution. Once the model's ability to reproduce extremes has been assessed, idealised regions of sea surface temperature (SST) anomalies are used to force the model, with the overall aim of investigating the ways in which SST anomalies influence rainfall extremes over southern Africa. In this paper, a brief overview is given of the authors' research to date, pertaining to southern African rainfall. This covers (i) a description of present-day rainfall variability over southern Africa; (ii) a comparison of model simulated daily rainfall with the satellite-derived dataset; (iii) results from sensitivity testing of the model's domain size; and (iv) results from the idealised SST experiments.
Wang, Jie; Chen, Li; Yu, Zhongbo
2018-02-01
Rainfall infiltration on hillslopes is an important issue in hydrology, which is related to many environmental problems, such as flood, soil erosion, and nutrient and contaminant transport. This study aimed to improve the quantification of infiltration on hillslopes under both steady and unsteady rainfalls. Starting from Darcy's law, an analytical integral infiltrability equation was derived for hillslope infiltration by use of the flux-concentration relation. Based on this equation, a simple scaling relation linking the infiltration times on hillslopes and horizontal planes was obtained which is applicable for both small and large times and can be used to simplify the solution procedure of hillslope infiltration. The infiltrability equation also improved the estimation of ponding time for infiltration under rainfall conditions. For infiltration after ponding, the time compression approximation (TCA) was applied together with the infiltrability equation. To improve the computational efficiency, the analytical integral infiltrability equation was approximated with a two-term power-like function by nonlinear regression. Procedures of applying this approach to both steady and unsteady rainfall conditions were proposed. To evaluate the performance of the new approach, it was compared with the Green-Ampt model for sloping surfaces by Chen and Young (2006) and Richards' equation. The proposed model outperformed the sloping Green-Ampt, and both ponding time and infiltration predictions agreed well with the solutions of Richards' equation for various soil textures, slope angles, initial water contents, and rainfall intensities for both steady and unsteady rainfalls.
Areal rainfall estimation using moving cars - computer experiments including hydrological modeling
Rabiei, Ehsan; Haberlandt, Uwe; Sester, Monika; Fitzner, Daniel; Wallner, Markus
2016-09-01
The need for high temporal and spatial resolution precipitation data for hydrological analyses has been discussed in several studies. Although rain gauges provide valuable information, a very dense rain gauge network is costly. As a result, several new ideas have emerged to help estimating areal rainfall with higher temporal and spatial resolution. Rabiei et al. (2013) observed that moving cars, called RainCars (RCs), can potentially be a new source of data for measuring rain rate. The optical sensors used in that study are designed for operating the windscreen wipers and showed promising results for rainfall measurement purposes. Their measurement accuracy has been quantified in laboratory experiments. Considering explicitly those errors, the main objective of this study is to investigate the benefit of using RCs for estimating areal rainfall. For that, computer experiments are carried out, where radar rainfall is considered as the reference and the other sources of data, i.e., RCs and rain gauges, are extracted from radar data. Comparing the quality of areal rainfall estimation by RCs with rain gauges and reference data helps to investigate the benefit of the RCs. The value of this additional source of data is not only assessed for areal rainfall estimation performance but also for use in hydrological modeling. Considering measurement errors derived from laboratory experiments, the result shows that the RCs provide useful additional information for areal rainfall estimation as well as for hydrological modeling. Moreover, by testing larger uncertainties for RCs, they observed to be useful up to a certain level for areal rainfall estimation and discharge simulation.
Modelling of extreme minimum rainfall using generalised extreme value distribution for Zimbabwe
Directory of Open Access Journals (Sweden)
Delson Chikobvu
2015-09-01
Full Text Available We modelled the mean annual rainfall for data recorded in Zimbabwe from 1901 to 2009. Extreme value theory was used to estimate the probabilities of meteorological droughts. Droughts can be viewed as extreme events which go beyond and/or below normal rainfall occurrences, such as exceptionally low mean annual rainfall. The duality between the distribution of the minima and maxima was exploited and used to fit the generalised extreme value distribution (GEVD to the data and hence find probabilities of extreme low levels of mean annual rainfall. The augmented Dickey Fuller test confirmed that rainfall data were stationary, while the normal quantile-quantile plot indicated that rainfall data deviated from the normality assumption at both ends of the tails of the distribution. The maximum likelihood estimation method and the Bayesian approach were used to find the parameters of the GEVD. The Kolmogorov-Smirnov and Anderson-Darling goodnessof- fit tests showed that the Weibull class of distributions was a good fit to the minima mean annual rainfall using the maximum likelihood estimation method. The mean return period estimate of a meteorological drought using the threshold value of mean annual rainfall of 473 mm was 8 years. This implies that if in the year there is a meteorological drought then another drought of the same intensity or greater is expected after 8 years. It is expected that the use of Bayesian inference may better quantify the level of uncertainty associated with the GEVD parameter estimates than with the maximum likelihood estimation method. The Markov chain Monte Carlo algorithm for the GEVD was applied to construct the model parameter estimates using the Bayesian approach. These findings are significant because results based on non-informative priors (Bayesian method and the maximum likelihood method approach are expected to be similar.
Davini, Paolo; von Hardenberg, Jost; Corti, Susanna; Christensen, Hannah M.; Juricke, Stephan; Subramanian, Aneesh; Watson, Peter A. G.; Weisheimer, Antje; Palmer, Tim N.
2017-03-01
The Climate SPHINX (Stochastic Physics HIgh resolutioN eXperiments) project is a comprehensive set of ensemble simulations aimed at evaluating the sensitivity of present and future climate to model resolution and stochastic parameterisation. The EC-Earth Earth system model is used to explore the impact of stochastic physics in a large ensemble of 30-year climate integrations at five different atmospheric horizontal resolutions (from 125 up to 16 km). The project includes more than 120 simulations in both a historical scenario (1979-2008) and a climate change projection (2039-2068), together with coupled transient runs (1850-2100). A total of 20.4 million core hours have been used, made available from a single year grant from PRACE (the Partnership for Advanced Computing in Europe), and close to 1.5 PB of output data have been produced on SuperMUC IBM Petascale System at the Leibniz Supercomputing Centre (LRZ) in Garching, Germany. About 140 TB of post-processed data are stored on the CINECA supercomputing centre archives and are freely accessible to the community thanks to an EUDAT data pilot project. This paper presents the technical and scientific set-up of the experiments, including the details on the forcing used for the simulations performed, defining the SPHINX v1.0 protocol. In addition, an overview of preliminary results is given. An improvement in the simulation of Euro-Atlantic atmospheric blocking following resolution increase is observed. It is also shown that including stochastic parameterisation in the low-resolution runs helps to improve some aspects of the tropical climate - specifically the Madden-Julian Oscillation and the tropical rainfall variability. These findings show the importance of representing the impact of small-scale processes on the large-scale climate variability either explicitly (with high-resolution simulations) or stochastically (in low-resolution simulations).
Modelling biochemical reaction systems by stochastic differential equations with reflection.
Niu, Yuanling; Burrage, Kevin; Chen, Luonan
2016-05-07
In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.
Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB.
Ullah, M; Schmidt, H; Cho, K H; Wolkenhauer, O
2006-03-01
The analysis of complex biochemical networks is conducted in two popular conceptual frameworks for modelling. The deterministic approach requires the solution of ordinary differential equations (ODEs, reaction rate equations) with concentrations as continuous state variables. The stochastic approach involves the simulation of differential-difference equations (chemical master equations, CMEs) with probabilities as variables. This is to generate counts of molecules for chemical species as realisations of random variables drawn from the probability distribution described by the CMEs. Although there are numerous tools available, many of them free, the modelling and simulation environment MATLAB is widely used in the physical and engineering sciences. We describe a collection of MATLAB functions to construct and solve ODEs for deterministic simulation and to implement realisations of CMEs for stochastic simulation using advanced MATLAB coding (Release 14). The program was successfully applied to pathway models from the literature for both cases. The results were compared to implementations using alternative tools for dynamic modelling and simulation of biochemical networks. The aim is to provide a concise set of MATLAB functions that encourage the experimentation with systems biology models. All the script files are available from www.sbi.uni-rostock.de/ publications_matlab-paper.html.
Sampling from stochastic reservoir models constrained by production data
Energy Technology Data Exchange (ETDEWEB)
Hegstad, Bjoern Kaare
1997-12-31
When a petroleum reservoir is evaluated, it is important to forecast future production of oil and gas and to assess forecast uncertainty. This is done by defining a stochastic model for the reservoir characteristics, generating realizations from this model and applying a fluid flow simulator to the realizations. The reservoir characteristics define the geometry of the reservoir, initial saturation, petrophysical properties etc. This thesis discusses how to generate realizations constrained by production data, that is to say, the realizations should reproduce the observed production history of the petroleum reservoir within the uncertainty of these data. The topics discussed are: (1) Theoretical framework, (2) History matching, forecasting and forecasting uncertainty, (3) A three-dimensional test case, (4) Modelling transmissibility multipliers by Markov random fields, (5) Up scaling, (6) The link between model parameters, well observations and production history in a simple test case, (7) Sampling the posterior using optimization in a hierarchical model, (8) A comparison of Rejection Sampling and Metropolis-Hastings algorithm, (9) Stochastic simulation and conditioning by annealing in reservoir description, and (10) Uncertainty assessment in history matching and forecasting. 139 refs., 85 figs., 1 tab.
DEFF Research Database (Denmark)
Panagos, Panos; Ballabio, Cristiano; Borrelli, Pasquale
2015-01-01
Rainfall is one the main drivers of soil erosion. The erosive force of rainfall is expressed as rainfall erosivity. Rainfall erosivity considers the rainfall amount and intensity, and is most commonly expressed as the Rfactor in the USLE model and its revised version, RUSLE. At national...... and continental levels, the scarce availability of data obliges soil erosion modellers to estimate this factor based on rainfall data with only low temporal resolution (daily, monthly, annual averages). The purpose of this study is to assess rainfall erosivity in Europe in the form of the RUSLE R-factor, based...
Nonstationary modeling of a long record of rainfall and temperature over Rome
Villarini, Gabriele; Smith, James A.; Napolitano, Francesco
2010-10-01
A long record (1862-2004) of seasonal rainfall and temperature from the Rome observatory of Collegio Romano are modeled in a nonstationary framework by means of the Generalized Additive Models in Location, Scale and Shape (GAMLSS). Modeling analyses are used to characterize nonstationarities in rainfall and related climate variables. It is shown that the GAMLSS models are able to represent the magnitude and spread in the seasonal time series with parameters which are a smooth function of time. Covariate analyses highlight the role of seasonal and interannual variability of large-scale climate forcing, as reflected in three teleconnection indexes (Atlantic Multidecadal Oscillation, North Atlantic Oscillation, and Mediterranean Index), for modeling seasonal rainfall and temperature over Rome. In particular, the North Atlantic Oscillation is a significant predictor during the winter, while the Mediterranean Index is a significant predictor for almost all seasons.
Simulation of the Indian summer monsoon onset-phase rainfall using a regional model
Srinivas, C. V.
2015-09-11
This study examines the ability of the Advanced Research WRF (ARW) regional model to simulate Indian summer monsoon (ISM) rainfall climatology in different climate zones during the monsoon onset phase in the decade 2000–2009. The initial and boundary conditions for ARW are provided from the NCEP/NCAR Reanalysis Project (NNRP) global reanalysis. Seasonal onset-phase rainfall is compared with corresponding values from 0.25° IMD (India Meteorological Department) rainfall and NNRP precipitation data over seven climate zones (perhumid, humid, dry/moist, subhumid, dry/moist, semiarid and arid) of India to see whether dynamical downscaling using a regional model yields advantages over just using large-scale model predictions. Results show that the model could simulate the onset phase in terms of progression and distribution of rainfall in most zones (except over the northeast) with good correlations and low error metrics. The observed mean onset dates and their variability over different zones are well reproduced by the regional model over most climate zones. It has been found that the ARW performed similarly to the reanalysis in most zones and improves the onset time by 1 to 3 days in zones 4 and 7, in which the NNRP shows a delayed onset compared to the actual IMD onset times. The variations in the onset-phase rainfall during the below-normal onset (June negative) and above-normal onset (June positive) phases are well simulated. The slight underestimation of onset-phase rainfall in the northeast zone could be due to failure in resolving the wide extent of topographic variations and the associated multiscale interactions in that zone. Spatial comparisons showed improvement of pentad rainfall in both space and quantity in ARW simulations over NNRP data, as evident from a wider eastward distribution of pentad rainfall over the Western Ghats, central and eastern India, as in IMD observations. While NNRP under-represented the high pentad rainfall over northeast, east and
Simulation of the Indian summer monsoon onset-phase rainfall using a regional model
Directory of Open Access Journals (Sweden)
C. V. Srinivas
2015-09-01
Full Text Available This study examines the ability of the Advanced Research WRF (ARW regional model to simulate Indian summer monsoon (ISM rainfall climatology in different climate zones during the monsoon onset phase in the decade 2000–2009. The initial and boundary conditions for ARW are provided from the NCEP/NCAR Reanalysis Project (NNRP global reanalysis. Seasonal onset-phase rainfall is compared with corresponding values from 0.25° IMD (India Meteorological Department rainfall and NNRP precipitation data over seven climate zones (perhumid, humid, dry/moist, subhumid, dry/moist, semiarid and arid of India to see whether dynamical downscaling using a regional model yields advantages over just using large-scale model predictions. Results show that the model could simulate the onset phase in terms of progression and distribution of rainfall in most zones (except over the northeast with good correlations and low error metrics. The observed mean onset dates and their variability over different zones are well reproduced by the regional model over most climate zones. It has been found that the ARW performed similarly to the reanalysis in most zones and improves the onset time by 1 to 3 days in zones 4 and 7, in which the NNRP shows a delayed onset compared to the actual IMD onset times. The variations in the onset-phase rainfall during the below-normal onset (June negative and above-normal onset (June positive phases are well simulated. The slight underestimation of onset-phase rainfall in the northeast zone could be due to failure in resolving the wide extent of topographic variations and the associated multiscale interactions in that zone. Spatial comparisons showed improvement of pentad rainfall in both space and quantity in ARW simulations over NNRP data, as evident from a wider eastward distribution of pentad rainfall over the Western Ghats, central and eastern India, as in IMD observations. While NNRP under-represented the high pentad rainfall over
A geomorphology-based ANFIS model for multi-station modeling of rainfall-runoff process
Nourani, Vahid; Komasi, Mehdi
2013-05-01
This paper demonstrates the potential use of Artificial Intelligence (AI) techniques for predicting daily runoff at multiple gauging stations. Uncertainty and complexity of the rainfall-runoff process due to its variability in space and time in one hand and lack of historical data on the other hand, cause difficulties in the spatiotemporal modeling of the process. In this paper, an Integrated Geomorphological Adaptive Neuro-Fuzzy Inference System (IGANFIS) model conjugated with C-means clustering algorithm was used for rainfall-runoff modeling at multiple stations of the Eel River watershed, California. The proposed model could be used for predicting runoff in the stations with lack of data or any sub-basin within the watershed because of employing the spatial and temporal variables of the sub-basins as the model inputs. This ability of the integrated model for spatiotemporal modeling of the process was examined through the cross validation technique for a station. In this way, different ANFIS structures were trained using Sugeno algorithm in order to estimate daily discharge values at different stations. In order to improve the model efficiency, the input data were then classified into some clusters by the means of fuzzy C-means (FCMs) method. The goodness-of-fit measures support the gainful use of the IGANFIS and FCM methods in spatiotemporal modeling of hydrological processes.
Directory of Open Access Journals (Sweden)
B. Salahi
2017-01-01
Full Text Available Introduction: Rainfall has the highest variability at time and place scale. Rainfall fluctuation in different geographical areas reveals the necessity of investigating this climate element and suitable models to forecast the rate of precipitation for regional planning. Ardabil province has always faced rainfall fluctuations and shortage of water supply. Precipitation is one of the most important features of the environment. The amount of precipitation over time and in different places is subject to large fluctuations which may be periodical. Studies show that, due to the certain complexities of rainfall, the models which used to predict future values will also need greater accuracy and less error. Among the forecasting models, Arima has more applications and it has replaced with other models. Materials and Methods: In this research, through order 2 Autoregrressive, Winters, and Arima models, monthly rainfalls of Ardabil synoptic station (representing Ardabil province for a 31-year period (1977-2007 were investigated. To assess the presence or absence of significant changes in mean precipitation of Ardabil synoptic station, rainfall of this station was divided into two periods: 1977-1993 and 1994-2010. T-test was used to statistically examine the difference between the two periods. After adjusting the data, descriptive statistics were applied. In order to model the total monthly precipitation of Ardabil synoptic station, Winters, Autoregressive, and Arima models were used. Among different models, the best options were chosen to predict the time series including the mean absolute deviation (MAD, the mean squared errors (MSE, root mean square errors (RMSE and mean absolute percentage errors (MAPE. In order to select the best model among the available options under investigation, the predicted value of the deviation of the actual value was utilized for the months of 2006-2010. Results and Discussion: Statistical characteristics of the total monthly
A Family of Poisson Processes for Use in Stochastic Models of Precipitation
Penland, C.
2013-12-01
Both modified Poisson processes and compound Poisson processes can be relevant to stochastic parameterization of precipitation. This presentation compares the dynamical properties of these systems and discusses the physical situations in which each might be appropriate. If the parameters describing either class of systems originate in hydrodynamics, then proper consideration of stochastic calculus is required during numerical implementation of the parameterization. It is shown here that an improper numerical treatment can have severe implications for estimating rainfall distributions, particularly in the tails of the distributions and, thus, on the frequency of extreme events.
Evapotranspiration Estimates for a Stochastic Soil-Moisture Model
Chaleeraktrakoon, Chavalit; Somsakun, Somrit
2009-03-01
Potential evapotranspiration is information that is necessary for applying a widely used stochastic model of soil moisture (I. Rodriguez Iturbe, A. Porporato, L. Ridolfi, V. Isham and D. R. Cox, Probabilistic modelling of water balance at a point: The role of climate, soil and vegetation, Proc. Roy. Soc. London A455 (1999) 3789-3805). An objective of the present paper is thus to find a proper estimate of the evapotranspiration for the stochastic model. This estimate is obtained by comparing the calculated soil-moisture distribution resulting from various techniques, such as Thornthwaite, Makkink, Jensen-Haise, FAO Modified Penman, and Blaney-Criddle, with an observed one. The comparison results using five sequences of daily soil-moisture for a dry season from November 2003 to April 2004 (Udornthani Province, Thailand) have indicated that all methods can be used if the weather information required is available. This is because their soil-moisture distributions are alike. In addition, the model is shown to have its ability in approximately describing the phenomenon at a weekly or biweekly time scale which is desirable for agricultural engineering applications.
Clustering network layers with the strata multilayer stochastic block model.
Stanley, Natalie; Shai, Saray; Taylor, Dane; Mucha, Peter J
2016-01-01
Multilayer networks are a useful data structure for simultaneously capturing multiple types of relationships between a set of nodes. In such networks, each relational definition gives rise to a layer. While each layer provides its own set of information, community structure across layers can be collectively utilized to discover and quantify underlying relational patterns between nodes. To concisely extract information from a multilayer network, we propose to identify and combine sets of layers with meaningful similarities in community structure. In this paper, we describe the "strata multilayer stochastic block model" (sMLSBM), a probabilistic model for multilayer community structure. The central extension of the model is that there exist groups of layers, called "strata", which are defined such that all layers in a given stratum have community structure described by a common stochastic block model (SBM). That is, layers in a stratum exhibit similar node-to-community assignments and SBM probability parameters. Fitting the sMLSBM to a multilayer network provides a joint clustering that yields node-to-community and layer-to-stratum assignments, which cooperatively aid one another during inference. We describe an algorithm for separating layers into their appropriate strata and an inference technique for estimating the SBM parameters for each stratum. We demonstrate our method using synthetic networks and a multilayer network inferred from data collected in the Human Microbiome Project.
Directory of Open Access Journals (Sweden)
Xiaona Leng
2017-06-01
Full Text Available Abstract This paper proposes a new nonlinear stochastic SIVS epidemic model with double epidemic hypothesis and Lévy jumps. The main purpose of this paper is to investigate the threshold dynamics of the stochastic SIVS epidemic model. By using the technique of a series of stochastic inequalities, we obtain sufficient conditions for the persistence in mean and extinction of the stochastic system and the threshold which governs the extinction and the spread of the epidemic diseases. Finally, this paper describes the results of numerical simulations investigating the dynamical effects of stochastic disturbance. Our results significantly improve and generalize the corresponding results in recent literatures. The developed theoretical methods and stochastic inequalities technique can be used to investigate the high-dimensional nonlinear stochastic differential systems.
Stochastic radiative transfer model for mixture of discontinuous vegetation canopies
International Nuclear Information System (INIS)
Shabanov, Nikolay V.; Huang, D.; Knjazikhin, Y.; Dickinson, R.E.; Myneni, Ranga B.
2007-01-01
Modeling of the radiation regime of a mixture of vegetation species is a fundamental problem of the Earth's land remote sensing and climate applications. The major existing approaches, including the linear mixture model and the turbid medium (TM) mixture radiative transfer model, provide only an approximate solution to this problem. In this study, we developed the stochastic mixture radiative transfer (SMRT) model, a mathematically exact tool to evaluate radiation regime in a natural canopy with spatially varying optical properties, that is, canopy, which exhibits a structured mixture of vegetation species and gaps. The model solves for the radiation quantities, direct input to the remote sensing/climate applications: mean radiation fluxes over whole mixture and over individual species. The canopy structure is parameterized in the SMRT model in terms of two stochastic moments: the probability of finding species and the conditional pair-correlation of species. The second moment is responsible for the 3D radiation effects, namely, radiation streaming through gaps without interaction with vegetation and variation of the radiation fluxes between different species. We performed analytical and numerical analysis of the radiation effects, simulated with the SMRT model for the three cases of canopy structure: (a) non-ordered mixture of species and gaps (TM); (b) ordered mixture of species without gaps; and (c) ordered mixture of species with gaps. The analysis indicates that the variation of radiation fluxes between different species is proportional to the variation of species optical properties (leaf albedo, density of foliage, etc.) Gaps introduce significant disturbance to the radiation regime in the canopy as their optical properties constitute major contrast to those of any vegetation species. The SMRT model resolves deficiencies of the major existing mixture models: ignorance of species radiation coupling via multiple scattering of photons (the linear mixture model
Stochastic Modelling and Optimization of Complex Infrastructure Systems
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
In this paper it is shown that recent progress in stochastic modelling and optimization in combination with advanced computer systems has now made it possible to improve the design and the maintenance strategies for infrastructure systems. The paper concentrates on highway networks and single large...... bridges. united states has perhaps the largest highway networks in the world with more than 0.5 million highway bridges; see Chase, S.B. 1999. About 40% of these bridges are considered deficient and more than $50 billion is estimated needed to correct the deficiencies; see Roberts, J.E. 2001...
Elementary amplitudes from full QCD and the stochastic vacuum model
International Nuclear Information System (INIS)
Martini, A.F.; Menon, M.J.
2002-01-01
In a previous work, making use of the gluon gauge-invariant two-point correlation function determined from lattice QCD in the quenched approximation and the stochastic vacuum model, we determined the elementary (parton-parton) scattering amplitude in the momentum transfer space. In this communication we compute the elementary amplitude from new lattice QCD calculations that include the effects of dynamical fermions (full QCD). The main conclusion is that the inclusion of dynamical fermions leads to a normalized elementary amplitude that decreases more quickly with the momentum transfer than that in the quenched approximation. (author)
Investment timing decisions in a stochastic duopoly model
Energy Technology Data Exchange (ETDEWEB)
Marseguerra, Giovanni [Istituto di Econometria e CRANEC, Universita Cattolica del Sacro Cuore di Milan (Italy)]. E-mail: giovanni.marseguerra@unicatt.it; Cortelezzi, Flavia [Dipartimento di Diritto ed Economia delle Persone e delle Imprese, Universita dell' Insubria (Italy)]. E-mail: flavia.cortelezzi@uninsubria.it; Dominioni, Armando [CORE-Catholique de Louvain la Neuve (Belgium)]. E-mail: dominioni@core.ucl.ac.be
2006-08-15
We investigate the role of strategic considerations on the optimal timing of investment when firms compete for a new market (e.g., the provision of an innovative product) under demand uncertainty. Within a continuous time model of stochastic oligopoly, we show that strategic considerations are likely to be of limited impact when the new product is radically innovative whilst the fear of a rival's entry may deeply affect firms' decisions whenever innovation is to some extent limited. The welfare analysis shows surprisingly that the desirability of the different market structures considered does not depend on the fixed entry cost.
Investment timing decisions in a stochastic duopoly model
International Nuclear Information System (INIS)
Marseguerra, Giovanni; Cortelezzi, Flavia; Dominioni, Armando
2006-01-01
We investigate the role of strategic considerations on the optimal timing of investment when firms compete for a new market (e.g., the provision of an innovative product) under demand uncertainty. Within a continuous time model of stochastic oligopoly, we show that strategic considerations are likely to be of limited impact when the new product is radically innovative whilst the fear of a rival's entry may deeply affect firms' decisions whenever innovation is to some extent limited. The welfare analysis shows surprisingly that the desirability of the different market structures considered does not depend on the fixed entry cost
A spatial and nonstationary model for the frequency of extreme rainfall events
DEFF Research Database (Denmark)
Gregersen, Ida Bülow; Madsen, Henrik; Rosbjerg, Dan
2013-01-01
of extreme rainfall events, a statistical model is tested for this purpose. The model is built on the theory of generalized linear models and uses Poisson regression solved by generalized estimation equations. Spatial and temporal explanatory variables can be included simultaneously, and their relative...
Daily rainfall-runoff modelling by neural networks in semi-arid zone ...
African Journals Online (AJOL)
This research work will allow checking efficiency of formal neural networks for flows' modelling of wadi Ouahrane's basin from rainfall-runoff relation which is non-linear. Two models of neural networks were optimized through supervised learning and compared in order to achieve this goal, the first model with input rain, and ...
Watterson, I. G.
2010-05-01
Rainfall in southeastern Australia has declined in recent years, particularly during austral autumn over the state of Victoria. A recent study suggests that sea surface temperature (SST) variations in both the Indonesian Throughflow (ITF) region and in a meridional dipole in the central Indian Ocean have influenced Victorian late autumn rainfall since 1950. However, it remains unclear to what extent SSTs in these and other regions force such a teleconnection. Analysis of a 1080 year simulation by the climate model CSIRO Mk3.5 shows that the model Victorian rainfall is correlated rather realistically with SSTs but that part of the above relationships is due to the model ENSO. Furthermore, the remote patterns of pressure, rainfall, and land temperature greatly diminish when the data are lagged by 1 month, suggesting that the true forcing by the persisting SSTs is weak. In a series of simulations of the atmospheric Mk3.5 with idealized SST anomalies, raised SSTs to the east of Indonesia lower the simulated Australian rainfall, while those to the west raise it. A positive ITF anomaly lowers pressure over Australia, but with little effect on Victorian rainfall. The meridional dipole and SSTs to the west and southeast of Australia have little direct effect on southeastern Australia in the model. The results suggest that tropical SSTs predominate as an influence on Victorian rainfall. However, the SST indices appear to explain only a fraction of the observed trend, which in the case of decadal means remains within the range of unforced variability simulated by Mk3.5.
Prediction of Meiyu rainfall in Taiwan by multi-lead physical-empirical models
Yim, So-Young; Wang, Bin; Xing, Wen; Lu, Mong-Ming
2015-06-01
Taiwan is located at the dividing point of the tropical and subtropical monsoons over East Asia. Taiwan has double rainy seasons, the Meiyu in May-June and the Typhoon rains in August-September. To predict the amount of Meiyu rainfall is of profound importance to disaster preparedness and water resource management. The seasonal forecast of May-June Meiyu rainfall has been a challenge to current dynamical models and the factors controlling Taiwan Meiyu variability has eluded climate scientists for decades. Here we investigate the physical processes that are possibly important for leading to significant fluctuation of the Taiwan Meiyu rainfall. Based on this understanding, we develop a physical-empirical model to predict Taiwan Meiyu rainfall at a lead time of 0- (end of April), 1-, and 2-month, respectively. Three physically consequential and complementary predictors are used: (1) a contrasting sea surface temperature (SST) tendency in the Indo-Pacific warm pool, (2) the tripolar SST tendency in North Atlantic that is associated with North Atlantic Oscillation, and (3) a surface warming tendency in northeast Asia. These precursors foreshadow an enhanced Philippine Sea anticyclonic anomalies and the anomalous cyclone near the southeastern China in the ensuing summer, which together favor increasing Taiwan Meiyu rainfall. Note that the identified precursors at various lead-times represent essentially the same physical processes, suggesting the robustness of the predictors. The physical empirical model made by these predictors is capable of capturing the Taiwan rainfall variability with a significant cross-validated temporal correlation coefficient skill of 0.75, 0.64, and 0.61 for 1979-2012 at the 0-, 1-, and 2-month lead time, respectively. The physical-empirical model concept used here can be extended to summer monsoon rainfall prediction over the Southeast Asia and other regions.
STOCHASTIC MODELING OF COMPRESSIVE STRENGTH OF PHOSPHORUS SLAG CONTENT CEMENT
Directory of Open Access Journals (Sweden)
Ali Allahverdi
2016-07-01
Full Text Available One of the common methods for quick determination of compressive strength as one of the most important properties for assessment of cement quality is to apply various modeling approaches. This study is aimed at finding a model for estimating the compressive strength of phosphorus slag content cements. For this purpose, the compressive strengths of chemically activated high phosphorus slag content cement prepared from phosphorus slag (80 wt.%, Portland cement (14 wt.% and a compound chemical activator containing sodium sulfate and anhydrite (6 wt.% were measured at various Blaine finenesses and curing times. Based on the obtained results, a primary stochastic model in terms of curing time and Blaine fineness has been developed. Then, another different dataset was used to incorporate composition variable including weight fractions of phosphorus slag, cement, and activator in the model. This model can be effectively used to predict the compressive strength of phosphorus slag content cements at various Blaine finenesses, curing times, and compositions.
Algorithmic detectability threshold of the stochastic block model
Kawamoto, Tatsuro
2018-03-01
The assumption that the values of model parameters are known or correctly learned, i.e., the Nishimori condition, is one of the requirements for the detectability analysis of the stochastic block model in statistical inference. In practice, however, there is no example demonstrating that we can know the model parameters beforehand, and there is no guarantee that the model parameters can be learned accurately. In this study, we consider the expectation-maximization (EM) algorithm with belief propagation (BP) and derive its algorithmic detectability threshold. Our analysis is not restricted to the community structure but includes general modular structures. Because the algorithm cannot always learn the planted model parameters correctly, the algorithmic detectability threshold is qualitatively different from the one with the Nishimori condition.
A stochastic pocket model for aluminum agglomeration in solid propellants
Energy Technology Data Exchange (ETDEWEB)
Gallier, Stany [SNPE Materiaux Energetiques, Vert le Petit (France)
2009-04-15
A new model is derived to estimate the size and fraction of aluminum agglomerates at the surface of a burning propellant. The basic idea relies on well-known pocket models in which aluminum is supposed to aggregate and melt within pocket volumes imposed by largest oxidizer particles. The proposed model essentially relaxes simple assumptions of previous pocket models on propellant structure by accounting for an actual microstructure obtained by packing. The use of statistical tools from stochastic geometry enables to determine a statistical pocket size volume and hence agglomerate diameter and agglomeration fraction. Application to several AP/Al propellants gives encouraging results that are shown to be superior to former pocket models. (Abstract Copyright [2009], Wiley Periodicals, Inc.)
Stochastic Modeling and Performance Analysis of Multimedia SoCs
DEFF Research Database (Denmark)
Raman, Balaji; Nouri, Ayoub; Gangadharan, Deepak
2013-01-01
solutions where each modeling technique has both the above mentioned characteristics. We present a probabilistic analytical framework and a statistical model checking approach to design system-on-chips for low-cost multimedia systems. We apply the modeling techniques to size the output buffer in a video......Reliability and flexibility are among the key required features of a framework used to model a system. Existing approaches to design resource-constrained, soft-real time systems either provide guarantees for output quality or account for loss in the system, but not both. We propose two independent...... decoder. The results shows that, for our stochastic design metric, the analytical framework upper bounds (and relatively accurate) compare to the statistical model checking technique. Also, we observed significant reduction in resource usage (such as output buffer size) with tolerable loss in output...
A Simple, Realistic Stochastic Model of Gastric Emptying.
Directory of Open Access Journals (Sweden)
Jiraphat Yokrattanasak
Full Text Available Several models of Gastric Emptying (GE have been employed in the past to represent the rate of delivery of stomach contents to the duodenum and jejunum. These models have all used a deterministic form (algebraic equations or ordinary differential equations, considering GE as a continuous, smooth process in time. However, GE is known to occur as a sequence of spurts, irregular both in size and in timing. Hence, we formulate a simple stochastic process model, able to represent the irregular decrements of gastric contents after a meal. The model is calibrated on existing literature data and provides consistent predictions of the observed variability in the emptying trajectories. This approach may be useful in metabolic modeling, since it describes well and explains the apparently heterogeneous GE experimental results in situations where common gastric mechanics across subjects would be expected.
Brownian motion model with stochastic parameters for asset prices
Ching, Soo Huei; Hin, Pooi Ah
2013-09-01
The Brownian motion model may not be a completely realistic model for asset prices because in real asset prices the drift μ and volatility σ may change over time. Presently we consider a model in which the parameter x = (μ,σ) is such that its value x (t + Δt) at a short time Δt ahead of the present time t depends on the value of the asset price at time t + Δt as well as the present parameter value x(t) and m-1 other parameter values before time t via a conditional distribution. The Malaysian stock prices are used to compare the performance of the Brownian motion model with fixed parameter with that of the model with stochastic parameter.
Mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory
Constable, George W. A.; McKane, Alan J.
2017-08-01
The relationship between the M -species stochastic Lotka-Volterra competition (SLVC) model and the M -allele Moran model of population genetics is explored via timescale separation arguments. When selection for species is weak and the population size is large but finite, precise conditions are determined for the stochastic dynamics of the SLVC model to be mappable to the neutral Moran model, the Moran model with frequency-independent selection, and the Moran model with frequency-dependent selection (equivalently a game-theoretic formulation of the Moran model). We demonstrate how these mappings can be used to calculate extinction probabilities and the times until a species' extinction in the SLVC model.
Development of the Stochastic Lung Model for Asthma
International Nuclear Information System (INIS)
Dobos, E.; Borbely-Kiss, I.; Kertesz, Zs.; Balashazy, I.
2005-01-01
Complete text of publication follows. The Stochastic Lung Model is a state-of-the-art tool for the investigation of the health impact of atmospheric aerosols. This model has already been tested and applied to calculate the deposition fractions of aerosols in different regions of the human respiratory tract. The health effects of inhaled aerosols may strongly depend on the distribution of deposition within the respiratory tract. In the current study three Asthma Models have been incorporated into the Stochastic Lung Deposition Code. A common new feature of these models is that the breathing cycle may be asymmetric. It means that the inspiration time, the expiration time and the two breath hold times are independent. And the code can simulate the mucus blockage, too. The main characteristics of the models are the followings: a) ASTHMA MODEL I: One input bronchial asthma factor is applied for the whole tracheobronchial region. The code multiplies all tracheobroncial diameters with this single value. b) ASTHMA MODEL II: Bronchial asthma factors have to be given for each bronchial generation as input data (21 values). The program multiplies the diameter of bronchi with these factors. c) ASTHMA MODEL III: Here, only the range of bronchial asthma factors are presented as input data and the code selects randomly the exact factors in pre-described airway generations. In this case the stochastic character appears in the Asthma Model, as well. As an example, Figure 1 shows the deposition fractions in the tracheobronchial and acinar regions of the human lung in the case of healthy and asthmatic adults at sitting breathing conditions as a function of particle size computed by Asthma Model I where the bronchial asthma factor was 30%. These models have been tested and compared for different types of asthma at various breathing conditions and in a wide range of particle sizes. The distribution of deposition in the characteristic regions of the respiratory tract have been computed
Alternative Approaches to Technical Efficiency Estimation in the Stochastic Frontier Model
Acquah, H. de-Graft; Onumah, E. E.
2014-01-01
Estimating the stochastic frontier model and calculating technical efficiency of decision making units are of great importance in applied production economic works. This paper estimates technical efficiency from the stochastic frontier model using Jondrow, and Battese and Coelli approaches. In order to compare alternative methods, simulated data with sample sizes of 60 and 200 are generated from stochastic frontier model commonly applied to agricultural firms. Simulated data is employed to co...
Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA
Energy Technology Data Exchange (ETDEWEB)
Thimmisetty, Charanraj A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Zhao, Wenju [Florida State Univ., Tallahassee, FL (United States). Dept. of Scientific Computing; Chen, Xiao [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Tong, Charles H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; White, Joshua A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Atmospheric, Earth and Energy Division
2017-10-18
Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.
Integrating Artificial Neural Networks into the VIC Model for Rainfall-Runoff Modeling
Directory of Open Access Journals (Sweden)
Changqing Meng
2016-09-01
Full Text Available A hybrid rainfall-runoff model was developed in this study by integrating the variable infiltration capacity (VIC model with artificial neural networks (ANNs. In the proposed model, the prediction interval of the ANN replaces separate, individual simulation (i.e., single simulation. The spatial heterogeneity of horizontal resolution, subgrid-scale features and their influence on the streamflow can be assessed according to the VIC model. In the routing module, instead of a simple linear superposition of the streamflow generated from each subbasin, ANNs facilitate nonlinear mappings of the streamflow produced from each subbasin into the total streamflow at the basin outlet. A total of three subbasins were delineated and calibrated independently via the VIC model; daily runoff errors were simulated for each subbasin, then corrected by an ANN bias-correction model. The initial streamflow and corrected runoff from the simulation for individual subbasins serve as inputs to the ANN routing model. The feasibility of this proposed method was confirmed according to the performance of its application to a case study on rainfall-runoff prediction in the Jinshajiang River Basin, the headwater area of the Yangtze River.