Estimation of Hydrochemical Unsaturated Soil Parameters Using a Multivariational Objective Analysis

Abstract

Numerical experiment involving both moisture and solute transport predictions is performed to estimate the hydrochemical characteristics of unsaturated porous soil. The moisture and solute transport in the soil are described by the flow and advection–dispersion transport equations. These transport equations are solved by the spectral element method, which is based on Legendre–Gauss–Lobatto quadrature rule and the fully implicit time scheme using the modified Picard iterative procedure constructed with the standard chord slope approximation. The estimation of hydraulic and solute transport parameters has been conducted using the Levenberg–Marquardt method. The goals of the inverse problem were to develop soil hydrochemical characteristics estimation strategies based on combined two of the following functional cost measurements: moisture content, pressure head, hydraulic conductivity, cumulative outflow, and solute concentration. The performance of the inverse algorithm was evaluated using the coefficient of determination, the root-mean-square error, and the relative error analysis which provide an optimal scheme for parameters estimation. The spectral element method was shown to provide good results with negligible error when compared to analytical values. The obtained results indicate excellent agreement of the method for estimating hydraulic and transport parameters with negligible relative error when compared estimated parameters and true values. The choice and the order of combination of objective functions affect crucially the inverse solution especially in case of large hydrochemical parameters estimates.