Aggregation of vertical flow in the vadose zone with auto- and cross-correlated hydraulic properties

Quantifying water flow across larger areas of the vadose zone has applications in water resources management and climate modeling. The nonlinearity of unsaturated flow and the variability of vadose zone parameters make it difficult, if not impossible, to accurately simulate near-surface water content and flux with large-scale models. Monte Carlo simulations of one-dimensional infiltration and evaporation were conducted with the Richards equation to simulate moisture content and flux in a heterogeneous field according to the streamtube concept. A set of 126 retention curves and saturated hydraulic conductivities from the UNSODA database was used to generate random fields of hydraulic parameters with pre-defined auto- and cross-correlation. Two stochastic parameters were used: the retention shape factor, ln mn, and either the retention scale parameter θs or ln hG or the saturated hydraulic conductivity, ln Ks. Infiltration is mostly governed by ln Ks. The evaporative flux is strongly determined by the “structural” parameter ln hG and also by the “textural” parameter ln mn. The water content in the upper part of the soil depends mostly on ln mn and somewhat on θs. Cross-correlations all resulted in clusters with consistently low or high water contents and moisture fluxes. Aggregation to obtain results at larger scales was done by a posteriori averaging of local results. This procedure is a convenient benchmark for large-scale modeling approaches. In an example of a priori aggregation, effective retention parameters were optimized to synthetic retention curves for the larger pixel scale and subsequently used in the Richards equation. The amount of infiltrated water was overestimated by up to 40%, large parts of the upper profile were erroneously predicted to be saturated. Although effective hydraulic properties have been used successfully in evaporation studies, considerable errors, which increased with pixel size, also occurred for evaporation. The stream tube modeling offers a convenient and accurate, albeit mundane, approach to elucidate the role of hydraulic properties and to obtain large-scale hydrological data.