Free-form estimation of the unsaturated soil hydraulic properties by inverse modeling using global optimization

[1] Inverse modeling is a powerful technique for identifying the hydraulic properties of unsaturated porous media. However, the selection of an appropriate parameterization of the soil water retention and hydraulic conductivity function remains a challenge. In this article, we present an improved algorithm for estimating these two relationships without assigning an a priori shape to them. The approach uses cubic Hermite interpolation and a global optimization strategy. A multilevel routine identifies the adequate number of degrees of freedom by balancing model performance, the statistical interaction of the estimated model parameters, and their number. A first-order uncertainty analysis provides a quantitative measure of how well the soil hydraulic properties can be identified in different ranges of pressure head. This offers great potential for designing optimal experimental procedures for identifying the hydraulic properties of porous media. We demonstrate the effectiveness of the algorithm for the evaluation of multistep outflow experiments by investigating synthetic data sets and real measurements. The free-form approach yields optimal model parameters that show only moderate correlation, indicating well-posed inverse problems. Since parameterization errors are almost completely avoided, the algorithm is well suited to identifying other error sources in unsaturated flow problems, e. g., limitations in the applicability of the Richards equation or problems caused by spatial heterogeneity.