Capillary tension head variance, mean soil moisture content, and effective specific soil moisture capacity of transient unsaturated flow in stratified soils

Abstract

The capillary tension head variance, the mean soil moisture content, and the effective specific soil moisture capacity are evaluated in the case of transient unsaturated flow in stratified soils using a three‐dimensional stochastic approach. The large difference in the correlation scales in stratified soils simplifies the related stochastic equations, allowing for analytical evaluations and derivation of generic expressions. Simplified asymptotic expressions, valid at particular ranges of the soil property and the mean flow characteristics, are also derived. Examples applying the theoretical results to two real soils are presented. It was found that the capillary tension head variance, the mean soil moisture content, and the effective specific soil moisture capacity show a large‐scale hysteresis which is due to spatial variability of the local hydraulic soil properties rather than to hysteresis in the local parameters. A companion paper shows that the effective hydraulic conductivities also show hysteresis produced by spatial soil variability. Such large‐scale hysteresis is mathematically, physically, and intuitively plausible. This may suggest that the hysteresis observed in laboratory or field experiments is, at least partly, due to soil variability rather than pore scale effects. This could be anticipated since spatial variability is the rule rather than the exception and it exists even in small‐scale experiments.