A hybrid simulated annealing and gradient-based algorithm for the estimation of unsaturated soil parameters

Abstract

Simulation of water flow in the unsaturated zone requires knowledge of hydraulic conductivity and water content functions. In most applied studies these functions are described by the well-known van Genuchten constitutive model, which has five independent parameters. Model parameters are usually determined from laboratory experiments, although often these estimates are non-representative of field conditions. In recent years, the use of inverse methods in conjunction with field experiments has become a promising alternative for the accurate estimation of unsaturated soil parameters. Essentially, this procedure involves the minimization of a cost or objective function that measures the discrepancy between observed and simulated data. In the present work we estimate the van Genuchten model parameters from hypothetical drainage experiments using a hybrid optimization strategy based on simulated annealing and a quasi-Newton method. Drainage experiments are modeled by solving Richards equation with appropriate initial and boundary conditions. To obtain approximate solutions of Richards equation we use a Galerkin finite element method. The algorithm behavior and the consequences on the estimated van Genuchten model parameters using different objective functions are explored. Objective functions are constructed from two sets of data which are usually obtained on field experiments: pressure head p versus time measured at different depths and water content θ versus depth measured at different times. The proposed estimation procedure is tested using synthetically generated data. Numerical examples show that the inverse modeling of drainage experiments using a hybrid simulated annealing and gradient-based algorithm provides an excellent methodology for an efficient and accurate estimation of unsaturated soil parameters.