An Efficient Method for Inverse Modeling of Soil Evaporation: Rationale and Numerical Example

An initial–boundary value problem for the one-dimensional nonlinear parabolic second-order partial differential equation that describes water movement in soil is considered. The inverse problem is to restore a boundary condition (evaporation) based on the comparison of modeled values of soil moisture at various points with some prescribed values. A criterion of the proximity of the selected evaporation to its true value is the mean-square deviation of the prescribed values of soil moisture at various points from the simulated soil moisture values corresponding to the selected evaporation. A numerical solution of a discretized optimization problem is investigated. The cases of accurate and inaccurate data are considered. The results of the numerical experiments are analyzed.