Challenges With Effective Representations Of Heterogeneity In Soil Hydrology Based On Local Water Content Measurements

The description of soil water movement at the field scale requires soil hydraulic material properties. These cannot be measured directly and exhibit an intrinsic multiscale heterogeneity. The estimation of soil hydraulic properties through inverse modeling or data assimilation requires measurements of the state of the system. However, these measurements are typically scarce and do not resolve soil heterogeneity leading to effective material properties with limited predictive capabilities. In a synthetic study at the scale of soil profiles, we explore the possibility to estimate an effective reduced one-dimensional representation based on only four local water content measurements in a vertical profile located in one- and two-dimensional heterogeneous media. We allow the effective material properties to deviate locally to consider the impact of the small-scale heterogeneity on the water content measurements. In the synthetic experiments, the estimated reduced one-dimensional representations predict soil water content and fluxes sufficiently well but can fail to predict the accurate timing and magnitude of infiltration fronts. Cumulative fluxes below the water content measurements were predicted correctly even on short time scales, if evaporation was estimated accurately. However, this proved to be challenging if the local evaporation fluxes above the measurement profile deviated strongly from the average evaporation fluxes of the heterogeneous medium. The one-dimensional estimation leads to soil hydraulic parameters describing effective material properties that differ from the true material properties to compensate the missing representation of heterogeneity and two-dimensional flow.