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–Moré 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 terms 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)(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.