A linear cascade model for predicting transport of dissolved agrochemicals by surface runoff

A cascade-based model is used to predict the dissolved chemical concentration profile at the effluent of a field. The source of chemicals is the soil surface layer, from which the chemicals are transferred to the surface runoff and transported to the field outlet. The model applies a cascade of perfectly mixed cells analogous to an equivalent surface runoff water and soil surface layer. Each cell is made of two interconnected units, where the upper unit represents the runoff water and the lower unit represents the soil bulk. Chemical transfer between the two units is controlled by the convective mass-transfer process through the laminar boundary layer of the surface runoff flow. The cells are interconnected through their upper units by runoff water flow. The lower unit applies a perfectly mixed reactor analog to an equivalent and homogeneous soil layer of uniform concentration near the soil surface, called the effective depth of transfer (EDT). The expression for the concentration within the EDT is simplified and agrees well with the soil surface concentration as determined by an analytical solution of the one-dimensional diffusion equation for the limiting case of no infiltration. The number of cells in the cascade is a measure of the extent of axial mixing in runoff flow where the limiting cases are: (1) a perfectly mixed system represented by one cell, and (2) a zero-mixing system (plug flow) represented by a cascade made of an infinite number of cells. The distribution of chemical concentrations for these two extreme cases and for other flows with varying degrees of mixing are presented.