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

Abstract

The purpose of this model is to enable implementation of the theory of linear systems control in operational management of waste and fertiliser applications onto land, so that the underlying groundwater is protected from pollution by leachate. The state-space form of the model enables use of the extensive theory and available software on stochastic linear systems. In particular, the Kalman filter is relevant to the imperfectly understood and highly variable processes of solute transport and transformation in field soils. The series of mixing cells was selected as a linear system model of one-dimensional, vertical, advective-dispersive transport, and based on cumulative soil water drainage as 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 nonequilibrium linear adsorption, are represented as lumped processes by two fractions linked by rate-limited transfer. The resident solute concentrations in the cell fractions are the states of the system. The complete model of solute transport and transformation for a uniform soil has four parameters, and can be described in MATLAB® with about ten lines of code. The software library can then be 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. A demonstration of the model is reported for ³⁵S-labelled sulphate leached from five replicated lysimeters (800 mm diameter, l100 mm depth) of an undisturbed field soil (a free-draining silt loam) under pasture receiving rainfall and irrigation, The results show satisfactory one-step-ahead forecasts with the Kalman filter for the period of record, and a forecast is given of the complete response to the solute pulse application beyond the data record.