Modelling the vertical distribution of radionuclides in soil. Part 1: the convection–dispersion equation revisited

The convective–dispersive transport and linear sorption model is discussed for the vertical migration of radionuclides in soil. An alternative procedure of solving the corresponding system of partial differential equations is presented as well as the special solution for the pulse-like fallout initial condition. Idealizations and simplifications of the model and properties of the solution are discussed. The model is fitted to a set of 528 measured radionuclide soil profiles and the resulting model parameters, apparent convection velocity v and apparent dispersion constant D, are evaluated statistically. Typical orders of magnitude of the velocities and the diffusion constants of Chernobyl-134Cs are 0.3 cm/year and 0.3 cm2/year, respectively. The mobilities of the radionuclides are ranked as 137Cs (global fallout) < 134Cs < 106Ru, 125Sb. Significant regional differences (related to different soils and geological properties below ground) of v and D exist. These analyses also indicate that v and D are not mere fitting parameters, but can be given a real physical interpretation. While in most cases, the convection–dispersion equation (CDE) model produces good descriptions for near-surface soil layers, potentially important limitations are its failure to describe “young” profiles shortly after fallout.