Estimability Analysis for Optimization of Hysteretic Soil Hydraulic Parameters Using Data of a Field Irrigation Experiment

To improve the quality of parameter optimization, estimability analysis has been proposed as the first step before inverse modeling. When using field data of irrigation experiments for the determination of soil hydraulic parameters, wetting and drying processes may complicate optimization. The objectives of this study were to compare estimability analysis and inverse optimization of the soil hydraulic parameters in the models with and without considering hysteresis of the soil water retention function. Soil water pressure head data of a field irrigation experiment were used. The one-dimensional vertical water movement in variably saturated soil was described with the Richards equation using the HYDRUS-1D code. Estimability of the unimodal van Genuchten–Mualem hydraulic model parameters as well as of the hysteretic parameter model of Parker and Lenhard was classified according to a sensitivity coefficient matrix. The matrix was obtained by sequentially calculating effects of initial parameter variations on changes in the simulated pressure head values. Optimization was carried out by means of the Levenberg-Marquardt method implemented in the HYDRUS-1D code. The parameters \(\alpha , K_{s}, \theta _{s}\) , and \(n\) in the nonhysteretic model were found sensitive and parameter \(\theta _{s}\) strongly correlated with parameter \(n\) . When assuming hysteresis, the estimability was decreased with soil depth for \(K_{s}\) and \(\alpha ^{d}\) , and increased for \(\theta _{s}\) and n. Among the shape parameters, \(\alpha ^{w}\) was the most estimable. The hysteretic model could approximate the pressure heads in the soil by considering parameters from wetting and drying periods separately as initial estimates. The inverse optimization could be carried out more efficiently with most estimable parameters. Despite the remaining weaknesses of the local optimization algorithm and the inflexibility of the unimodal van Genuchten model, the results suggested that estimability analysis could be considered as a guidance to better define the optimization scenarios and then improved the determination of soil hydraulic parameters.