Multiple Non-linear Reservoirs to Model Water Balance Components in Sandy Soils

Abstract

In the hydrologic literature, to model water flow in unsaturated soils, the Richards equation is usually applied, allowing the main components of the hydrologic cycle, as rainfall partitioning into surface runoff and infiltration, to be determined. The Richards equation is highly nonlinear, making very challenging to derive analytical solutions. Recently, for constant rainfall intensity, under the simplified hypothesis of gravity-driven infiltration, and by assuming a capacitance framework, a simplified solution of the Richards equation that considers the Brooks and Corey hydraulic conductivity function was suggested. By maintaining the assumption that the infiltration process is dominated by gravity, the objective of this paper is to relax the capacitance sketch applied to only one reservoir, by replicating the internal water content travel times through the discretization of the soil profile into multiple tanks connected in series. First, the previous analysis is briefly summarized, which is useful for the further development. Then, for a fixed soil pore connectivity index (c = 0.5), which could be assumed for sandy soils, the same approach is extended to multiple non-linear reservoirs to model water balance components, achieving more reliable conditions. The presented approach could be not affected by uncertainty, since it is simply hydraulic, provided the hypotheses c = 0.5 and the assumption of a gravity-driven infiltration are satisfied. The suggested solution was compared with that derived by the Richards equation (via Hydrus-1D), where the gravity-driven hypothesis is relaxed, the effect of the number of reservoirs was analyzed, and applications for both constant and time-variable rainfall intensity were performed.