Modeling one‐dimensional infiltration into very dry soils: 1. Model development and evaluation

Abstract

With the increasing economic growth in the arid regions of the West, and with the growing need for waste disposal and storage, the ability to efficiently model water flow and pollutant transport through unsaturated soils is becoming more important. One of the more difficult water flow problems to model, from a numerical point of view, is infiltration into very dry soils. The presence of very steep pressure gradients combined with the large field scales leads to algorithms that are very CPU intensive. Here we develop a water content based algorithm that is suitable for modeling one‐dimensional unsaturated water flow into layered soils. We show that this algorithm is a numerical approximation of a general form of Richards equation. We compare the computational efficiency of this algorithm with that of two pressure head based finite difference water flow algorithms for several test problems. We find that the mass balance errors for the noniterative water content formulation are of the order of machine round off error for most applications. We also find that for soils with fairly wet initial conditions ( h ≈ −100 cm H 2 O) the water content formulation requires approximately the same CPU time as the faster of the two pressure head formulations. For very dry soils ( h =−1000 to −50,000 cm H 2 O) the CPU time required for the water content formulation is not a function of the initial water content of the soil, whereas the CPU time required for the pressure head formulation strongly increases with decreasing initial water content. Because of this lack of sensitivity to initial conditions, the water content based algorithm is from 1 to 3 orders of magnitude faster than the pressure head based algorithms when applied to infiltration into very dry soils. The water content algorithm is not suitable for combined saturated‐unsaturated or near‐saturated flow that may be present because of local heterogeneities in the soil. In addition, the water content algorithm cannot handle positive pressure upper boundary conditions such as those associated with ponded surface water.