On the Effective Averaging Schemes of Hydraulic Properties at the Landscape Scale

Hydraulic parameters of the vadose zone at a spatial resolution typically larger than 1 km 2 are a key input for land–atmosphere feedback schemes in soil–vegetation–atmosphere transfer (SVAT) models. Previous studies investigated the significance of first- and secondorder moments of soil hydraulic parameters on ‘‘effective’’ parameter estimation in heterogeneous soils at the landscape or remote-sensing footprint/pixel scale. In this study, we examined the impact of the skewness (third-order moment) of hydraulic parameter distributions on ‘‘effective’’ soil hydraulic parameter averaging schemes for steadystate vertical flow in heterogeneous soils in a flat landscape. The effective soil hydraulic parameter of the heterogeneous soil formation is obtained by conceptualizing the soil as an equivalent homogeneous medium. The averaging scheme requires that the effective homogeneous soil will discharge the same ensemble moisture flux across the soil surface. Using three widely used unsaturated hydraulic conductivity functions and various types of probability distribution functions to represent spatial variability for the nonlinear shape factor in the hydraulic conductivity function, we derive the effective parameter values. Numerical and field experimental results show that distribution skewness is also important in determining the upscaled effective parameters in addition to the mean and variance. Negative skewness enhances heterogeneity effects, which make the ‘‘effective’’ a parameter deviate more significantly from the arithmetic mean. In the case of negative skewness, a few small a values make the heterogeneous soil more permeable (with larger flux), which hence causes the ‘‘effective’’ heterogeneous system to deviate more from the homogeneous formation with arithmetic mean parameters. D IFFERENT HYDROLOGIC and hydroclimatic models at watershed, regional, and global scales require soil hydrologic parameters at grid scales of several hundred square meters to thousands of square kilometers. The representation of soil hydrologic processes and parameters at a scale different from the one at which observations and parameters are made is a major challenge. With measurement techniques for soil hydraulic parameters often being limited to a few square centimeters, aggregation of local parameters to the model grid–pixel scale needs careful and thorough evaluation of the preservation of ensemble behavior for the hydrologic processes at larger scales. These so-called upscaled models are characterized by effective parameters or processes, which capture the influence of the small-scale heterogeneities at the larger scale. The impact of spatial heterogeneity characterized by different statistics of the soil hydraulic parameters on ensemble hydrologic fluxes, and thus the effectiveness of various upscaled parameters should be addressed in a systematic fashion with controlled numerical experiments and followup field evaluation at the watershed, basin, region, or global scale. Evolving hydraulic property upscaling algorithms in the recent past typically aggregate a mesh of hydraulic properties defined at the measurement scale (support) into a coarser mesh with ‘‘effective/average’’ hydraulic properties that can be used in large-scale (e.g., landscape-scale, watershed-scale, basin-scale) hydroclimate modeling and SVAT schemes of general circulation models. This study focuses on the case where hydraulic parameter variability is in the horizontal plane. To simplify the analysis, the domain is assumed to be composed of homogeneous soil columns without mutual interaction, while keeping focus on the main processes of many practical field applications. For example, in meso- or regional-scale SVAT schemes used in hydroclimatic models pixel dimensions may range from several hundred square meters to several hundred