Trend of the water content profile in a homogeneous soil layer from analytical solutions

The linearized one-dimensional Richards equation is solved analytically in a horizontal, homogeneous soil layer of finite thickness. The obtained solution is the soil water content at any required time and depth in the layer. Any discrete soil water content profile (e.g. experimentally measured) can be assumed as initial condition; the boundary conditions are two arbitrary functions representing the time evolution of the soil volumetric water content. Both initial and boundary conditions are approximated by means of a suitable number of step functions; therefore the solution presented will be hereafter called Step Function Solution (SFS). Making use of the variables separation method and of the superposition principle, the general solution is obtained by the sum of two solutions: one is derived for null boundary conditions and an arbitrary initial condition; the other is derived for a null initial condition and two arbitrary boundary conditions. The instantaneous fluxes at the top and at the bottom of the layer are calculated. From the time integration of these instantaneous fluxes the cumulative ones and the water gained by the soil layer in a specified time interval are obtained. These hydrological fields are relevant parameters for many studies. The stationary solution and the value of the corresponding flux are also calculated. Finally, the SFS is compared with two analytical solutions and two experimental sets of soil volumetric water content data. The finite thickness domain has been studied to represent a more realistic scheme of the surface soil with respect to the half space domain (Menziani et al., 2007). The comparison of the two sets of solutions (finite-thickness layer and half space schemes) with experimental data can help to decide when the depth of a layer can be assumed as infinite.