Analytical equation for rapid estimation of pesticide leaching risk accounting for nonlinear sorption with bulk soil biodegradation

Abstract

Mathematical models are used extensively to estimate soil pesticide leaching in regulatory risk assessments and are often solved numerically, which can obscure simple insights. We developed an analytical solution that highlights the role of the ratio of sorption to degradation in compound leaching, denoted as the sorption-extinction (S_e) coefficient. We extend the classic analytical work of Jury to derive a steady-state solution for pesticide concentrations as a function of soil depth considering nonlinear sorption. We consider degradation in the soil water and solid phases and transport driven by advection, diffusion, and dispersion. Nonlinear sorption was handled using the mathematical technique of asymptotic expansions. We compared the steady-state analytic solution with extended duration simulations of the European regulatory numerical model PEARL for all FOCUS scenarios (i.e., nine European regions). The analytic solution was consistent with the long-term PEARL results across most FOCUS scenarios, and the results show that for a fixed S_e coefficient, similar mean pesticide concentrations at the regulatory leaching depth (1 m) are obtained despite varying the sorption and degradation by an order of magnitude. This indicates that the S_e coefficient is a dominant component of mean leaching behavior rather than degradation or sorption alone. However, as the absolute value of degradation and sorption decreases, variability of the pesticide concentration increases. While we demonstrate the approach using the FOCUS scenarios weather and soil data, this method can be applied as a rapid and time-efficient predictive tool for any region with either highly or more scarcely parameterized soil/weather data.