Water dynamics in a gradually nonhomogeneous soil described by the linearized Richards equation

In order to investigate the influence of the soil vertical nonhomogeneity on the dynamics of the water in the upper soil layer, an analytical solution of the linearized Richards equation was derived. Here the hydraulic conductivity Ks at saturation is
assumed to decrease exponentially with depth, in accordance with field data reported in the literature and collected during our surveys in mountain catchments. Gardner’s constitutive laws were assumed for the hydraulic conductivity and water retention
characteristics K(s) and Y(s). The resulting one-dimensional Richards equation is linear, and its coefficients decrease exponentially with depth. An analytical solution was found
by using the method of Laplace transform and compared with some test cases both analytically and numerically. The soil water content profile exhibits a maximum at one point in the domain. Moreover, it accounts for a different behavior in the water dynamics, depending on the prevailing role of diffusive effects, related to the soil water retention, or of the transport effects, related to the hydraulic conductivity profile.