Inverse modeling of dynamic nonequilibrium in water flow with an effective approach

Observations of water flow in unsaturated soils often show "dynamic effects,'' indicated by nonequilibrium between water contents and water potential, a phenomenon that cannot be modeled with the Richards equation. The objective of this article is to formulate an effective process description of dynamic nonequilibrium flow in variably saturated soil which is both flexible enough to match experimental observations and as parsimonious as possible to allow unique parameter estimation by inverse modeling. In the conceptual model, water content is partitioned into two fractions. Water in one fraction is in equilibrium with the pressure head, whereas water in the second fraction is in nonequilibrium, described by the kinetic equilibration approach of Ross and Smettem (2000). Between the two fractions an instantaneous equilibration of the pressure head is assumed. The new model, termed the dual-fraction nonequilibrium model, requires only one additional parameter compared to the nonequilibrium approach of Ross and Smettem. We tested the model with experimental data from multistep outflow experiments conducted on two soils and compared it to the Richards equation, the nonequilibrium model of Ross and Smettem, and the dual-porosity model of Philip (1968). The experimental data were evaluated by inverse modeling using a robust Markov chain Monte Carlo sampler. The results show that the proposed model is superior to the Richards equation and the Ross and Smettem model in describing dynamic nonequilibrium effects occurring in multistep outflow experiments. The three popular model selection criteria (Akaike information criterion, Bayesian information criterion, and deviance information criterion) all favored the new model because of its smaller number of parameters.