Parameter estimation in flow through partially saturated porous materials

A class of numerical simulators were developed and critically evaluated to be incorporated as the solver of a forward problem in the framework of an inverse modeling strategy. The strategy couples a mass-lumped Galerkin linear finite element solution of the mixed form Richards equation with an experimental time-space series and the Osborne-More revised form of the Levenberg-Marquardt algorithm; to retrieve hydraulic parameters of a partially saturated porous medium. The numerical Simulator shows excellent agreement with a reference solution, obtained on a dense grid and infinitesimal time step, in tern-is of fluid pressure head, fluid content, and fluid volumetric flux density and perfectly conserves the global mass. An adaptive algorithm was implemented to estimate sensitivity matrix in the inverse algorithm. A multi-criterion stopping rule was developed and successfully implemented to end the inverse code at the solution. The result of the optimization was compared with a large-scale in-situ soil moisture space-time series, measured during the course of a drainage experiment, and excellent agreements were found. Analysis of the parameter response surfaces and hyper-space plots, closeness of the gradient of the penalty function at minimum to zero, and positive definiteness of the approximation for the Hessian at the solution (eigs(H) > 0) indicate that the obtained solution is a strong local minimum. A state-of-the-art sensitivity analysis carried out to quantify sensitivity of the state variable with respect to uncertainty and changes in different model parameters. (C) 2008 Elsevier Inc. All rights reserved.