Model of the long-term transfer of radionuclides in forests
This report describes a model of the long-term behaviour in temperate and boreal forests of radionuclides entering the ecosystem with subsurface water. The model can be applied for most radionuclides that are of relevance in safety assessment of repositories for high-level radioactive waste. The model can be used for estimating radionuclide concentrations in soil, trees, understorey plants, mushrooms and forest mammals. A recommended (nominal) value and an interval of variation are provided for each model parameter and a classification of parameters by the degree of confidence in the values is given. Model testing against existing empirical data showing satisfactory results is also presented. Forests can play an important role in the spatial and temporal distribution of radionuclides in the environment. Despite of this, forest ecosystems have not been addressed in previous safety assessments. This can be explained by the fact that a suitable model of the long-term transfer of a wide range of radionuclides in forests has not been readily available. The objective of this work was to develop a forest model applicable for a wide range of radionuclides of relevance for high level radioactive waste management (Am-241, Cl-36, Cs-135, I-129, Ni-59, Np-237, Pu-239, Ra-226, Sr-90, Tc-99, Th-232, U-238) that can potentially enter the ecosystem with contaminated groundwater. The model assumes that biomass growth, precipitation and evapo-transpiration drive the radionuclide cycling in the system by influencing the uptake of radionuclides by vegetation and their export from the system via runoff. The mathematical model of radionuclide transfer consists of a system of ordinary differential describing the mass balance in different forest compartments, taking into account the fluxes in and out from the compartment and the radionuclides decay. The fluxes between compartments are calculated by multiplying a transfer coefficient (TC) by the radionuclide inventory in the compartment. The model assumes that the fluxes of radionuclides are driven by fluxes of water and nutrients and hence the TCs are expressed as function of ecological parameters, such as biomass growth, and evapotranspiration. The following radionuclide fluxes are included in the model: flux from soil to tree wood via root uptake, flux from soil to tree leaves via root uptake, flux from soil to understorey (plants and mushrooms) via root (mycelia) uptake, flux from tree leaves to litter by leaves fall, flux from tree wood to litter by wood fall, flux from understorey plants to litter by plant senescence, flux from litter to soil following litter decomposition. In the report alternative approaches to describe the transfer from soil to plants are presented. In the simpler approach, applicable when soil to plant concentration ratios (CR) are available for the radionuclide or its stable analogue, the root uptake rates are calculated by multiplying the concentration in the plant, obtained with the help of the CR, by the biomass production. A second approach is based on the assumption that some elements are taken-up passively with the transpiration flux. For them, the total flux from soil to plants can be expressed as a function of the transpiration rate and the radionuclide concentration in the pore water. The CRs from soil to understorey plants as well as the CRs from soil to tree leaves and tree wood were estimated by performing probabilistic simulations. It was assumed that roots have the same permeability for radionuclides and water. It should be taken into account, that the literature data used in the comparison were obtained at different sites and using different methods. A better agreement could be achieved if the model parameters and the empirical data of CRs are obtained for the same site. In some cases the differences might abide more fundamental reasons, for instance that the implicit assumption of linear proportionality of the radionuclide uptake rates to the transpiration rate and the radionuclide concentration in the soil solution might not hold. For these radionuclides, and in particular for analogues of plant macronutrients, an alternative approach was implemented based on the assumption that their uptake by plants is modulated by the plant uptake of the nutrient. This means that the radionuclide and its corresponding analogue nutrient are taken up by plants in an identical manner via the same carrier molecules. Assuming that only ions in the soil solution near the roots, where the radionuclide concentrations are much lower than analogue concentrations, are available for transition into the roots, the transition of radionuclides from soil to plants can be represented as an independent Poisson process. In this case, the uptake rate of the radionuclide will be proportional to the uptake rate of the analogue nutrient and the concentration of the radionuclide in the soil solution near the roots and inversely proportional to the analogue concentration in the soil solution near the roots. Transfer factors to forest wild animals are lacking for many of the relevant radionuclides. Hence, an alternative approach was introduced which uses an allometric equation relating the radionuclide concentration in the animal diet to the radionuclide concentration in the animal body. In order to test the model, predictions of the transfer factor (TF) from soil to herbivores (expressed in Bq/kg fresh weight per Bq/kg dry weight) were compared with empirical values found in the literature. For Caesium and Strontium the predicted TFs were within the range of empirical observations. The model predictions were slightly higher for Radium and Uranium and slightly lower for Thorium. However, it should be noted that the intervals given for these three elements are based on few empirical data.
