State–space mixing cell model of unsteady solute transport in unsaturated soil

Abstract

This state–space model enables application of stochastic linear systems theory to solute transport in soil. A series of mixing cells models one-dimensional, vertical, advective–dispersive transport. Cumulative soil water drainage is the index variable for application to unsteady flow in unsaturated soil. For each cell, solute transfer between mobile and immobile soil water, as well as equilibrium and non-equilibrium linear adsorption, are represented as lumped processes by two fractions linked by rate-limited transfer. Plant uptake of solutes is treated as an unknown disturbance. For a uniform soil, the model has four parameters and can be described in MATLAB ® with about 10 lines of code. This software library is used to produce the discrete form of the model, which is unconditionally stable for any drainage interval, as well as to implement state estimation and control algorithms. The model is demonstrated with breakthrough curve data of 15N, Br −, and 35S leached from an undisturbed field soil under pasture receiving rainfall and irrigation. Process knowledge is combined with estimates of measurement and process uncertainty, by means of the Kalman filter, to forecast the response of 35S to the solute pulse application, beyond the available data record.