Upscaled soil-water retention using van Genuchten's function

Soils are often layered at scales smaller than the block size used in numerical and conceptual models of variably saturated flow. Consequently, the small-scale variability in water content within each block must be homogenized (upscaled). Laboratory results have shown that a linear volume average (LVA) of water content at a uniform suction is a good approximation to measured water contents in heterogeneous cores. Here, we upscale water contents using van Genuchten's function for both the local and upscaled soil-water-retention characteristics. The van Genuchten (vG) function compares favorably with LVA results, laboratory experiments under hydrostatic conditions in 3-cm cores, and numerical simulations of large-scale gravity drainage. Our method yields upscaled vG parameter values by fitting the vG curve to the LVA of water contents at various suction values. In practice, it is more efficient to compute direct averages of the local vG parameter values. Nonlinear power averages quantify a feasible range of values for each upscaled vG shape parameter; upscaled values of N are consistently less than the harmonic means, reflecting broad pore-size distributions of the upscaled soils. The vG function is useful for modeling soil-water retention at large scales, and these results provide guidance for its application.