Analytic description of the moving moisture front in soils

The fact that moisture propagates in soils at a finite speed is confirmed by natural everyday experience as well as by controlled laboratory tests. In this text, we rigorously derive analytical upper bounds for the speed of moisture front propagation under gravity for the solution to the Richards equation with compactly supported initial data. The main result is an explicit criterion describing a competition between gravity and capillarity, where the dominant effect is determined by the characteristics of the soil. If capillarity prevails, the initially wet regions remain wet for all times, while if gravity is dominant, moisture travels downward at a speed that is asymptotically bounded from below and above. As a by-product, we prove the existence and uniqueness of a solution to an initial value problem for the degenerate Richards equation on the whole space. Numerical simulations based on the proposed model confirm the theoretical predictions, with results that closely match experimental observations.