¹³⁷Cs is an artificial radionuclide with a half-life of 30.12 years which released into the environment as a result of atmospheric testing of thermo-nuclear weapons primarily during the period of 1950s-1970s with the maximum rate of ¹³⁷Cs fallout from atmosphere in 1963. ¹³⁷Cs fallout is strongly and rapidly adsorbed by fine particles in the surface horizons of the soil, when it falls down on the ground mostly with precipitation. Its subsequent redistribution is associated with movements of the soil or sediment particles, The ¹³⁷Cs nuclide tracing technique has been used for assessment of soil losses for both undisturbed and cultivated soils. For undisturbed soils, a simple profile-shape model was developed in 1990 to describe the ¹³⁷Cs depth distribution in profile, where the maximum ¹³⁷Cs occurs in the surface horizon and it exponentially decrease with depth. The model implied that the total ¹³⁷Cs fallout amount deposited on the earth surface in 1963 and the ¹³⁷Cs profile shape has not changed with time. The model has been widely used for assessment of soil losses on undisturbed land. However, temporal variations of ¹³⁷Cs depth distribution in undisturbed soils after its deposition on the ground due to diffusion and migration processes are not considered in the previous simple profile-shape model. Thus, the soil losses are overestimated by the model. A simplified diffusion process model is developed to describe the post redistribution of ¹³⁷Cs fallout in an undisturbed soil profile under the same assumption that the total ¹³⁷Cs fallout amount deposited on the earth surface in 1963 as the previous simple profile-distribution model in this paper. The change of ¹³⁷Cs depth distribution due to diffusion processes in an undisturbed soil profile with time after its deposition on the ground can be generally described as following: ¹³⁷Cs concentration in the surface horizons decreases with time while ¹³⁷Cs distribution depth increases with time. However, the ¹³⁷Cs concentration still always decreases exponentially with depth and the maximum ¹³⁷Cs concentration occurs in the surface horizon of the profile. Although the ¹³⁷Cs inventory at an eroded site is less than the reference value, the soil profile has same ¹³⁷Cs depth distribution shape as the profile at the reference site if the two profiles have same uniform soil textures. The soil losses related to different ¹³⁷Cs loss proportions of the reference inventory at the Kaixian site of the Three Gorge Region, China, are estimated by the two models. As to 20% -60% of ¹³⁷Cs loss proportions of the reference inventory, the annual soil loss depths estimated by the new simplified diffusion process model are only 21.9%~28.4% of the values estimated by the simple profile shape model.

Keywords: ¹³⁷Cs redistribution; undisturbed soil; simplified diffusion process model.