Constrained identification of the aggregated mixing zone model of solute transport in soil

Abstract

The Aggregated Mixing Zone (AMZ) concept has been used in previous research to model solute transport processes in soils. Dispersive and convective flow mechanisms are represented as a linear systems network of mixing elements and flow delays, which can be expressed in terms of an autoregressive moving-average (ARMA) transfer function model. Use of semi-automatic ARMA model identification algorithms sometimes result in physically unrealistic process parameter values, and indeterminate structure in the associated AMZ model description. The research reported in this paper demonstrates how both problems were overcome by introducing physically-based prior restrictions on the AMZ model before transformation to a constrained ARMA structure. The identification procedure was applied by supervised use of the Simple Refined Instrumental-Variable (SRIV) algorithm in MICROCAPTAIN software, to breakthrough curve (BTC) data from four lysimeter experiments. The resulting ARMA models of each BTC were sometimes of high order but with an implicit small number of parameters. The ARMA transfer function model facilitates exploration of process hypotheses according to dynamic behaviour, and also provides a linear systems model suitable for incorporation into control algorithms for environmental management.