Soil mixing depth after atmospheric deposition. I. Model development and validation

Knowledge of a soil mixing depth, or the migration depth of various pollutants in soil, is necessary to assess the soil chemical concentration resulting from atmospheric deposition of a specific air emission source. A mathematical model has been developed that describes the depth and time behavior of the soil concentration of an inert chemical after atmospheric deposition on surfaces. The soil mixing model is based on one-dimensional diffusion theory, and analytic solutions have been derived for the cases of: (1) instantaneous surface deposition; (2) continuous surface deposition; and (3) a finite period of continuous surface deposition, followed by a deposition-free time period. Comparisons of the model with measured soil depth profiles resulting from atmospheric deposition showed good agreement for lead, cesium, and dioxins. The best-fit effective diffusion coefficients in undisturbed soils varied from 0.5 cm2 yr−1 to 2 cm2 yr−1. The soil mixing depth was found to be a strong function of the atmospheric deposition time period. Calculated soil mixing depths in undisturbed soils were 2 cm after one year, 5 cm after five years, and 10 cm after 20 years of continuous atmospheric deposition on the soil surface.