Direct Hydraulic Parameter and Function Estimation for Diverse Soil Types Under Infiltration and Evaporation

Abstract

A new computationally efficient direct method is applied to estimating unsaturated hydraulic properties during steady-state infiltration and evaporation at soil surface. For different soil types with homogeneous and layered heterogeneity, soil hydraulic parameters and unsaturated conductivities are estimated. Unlike the traditional indirect inversion method, the direct method does not require forward simulations to assess the measurement-to-model fit; thus, the knowledge of model boundary conditions (BC) is not required. Instead, the method employs a set of local approximate solutions to impose continuity of pressure head and soil water fluxes throughout the inversion domain, while measurements act to condition these solutions. Given sufficient measurements, it yields a well-posed system of nonlinear equations that can be solved with optimization in a single step and is thus computationally efficient. For both Gardner’s and van Genuchten’s soil water models, unsaturated hydraulic conductivities and pressure heads (including the unknown BC) can be accurately recovered. When increasing measurement errors are imposed, inversion becomes less accurate, but the solution is stable, i.e., estimation errors remain bounded. Moreover, when the unsaturated conductivity model is known, inversion can recover its parameters; if it is unknown, inversion can recover a nonparametric, piecewise continuous function to which soil parameters can be obtained via fitting. Overall, inversion accuracy of the direct method is influenced by (1) measurement density and errors; (2) rate of infiltration or evaporation; (3) variation of the unsaturated conductivity; (4) flow direction; (5) the number of soil layers.