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United States Department of Agriculture

Agricultural Research Service

Title: Upscaling Schemes and Relationships for the Gardner and van Genuchten Hydraulic Functions for Heterogeneous Soils)

item Zhu, Jianting
item Young, Michael
item Van Genuchten, Martinus

Submitted to: Vadose Zone Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 9/20/2006
Publication Date: 2/27/2007
Publication URL:
Citation: Zhu, J., Young, M.H., Van Genuchten, M.T. 2007. Upscaling Schemes and Relationships for the Gardner and van Genuchten Hydraulic Functions for Heterogeneous Soils. Vadose Zone Journal. Vol. 6:186-195

Interpretive Summary: Subsurface water flow and pollutant transport studies, as well studies of regional and global climate, require estimates of the physical properties of the unsaturated or vadose zone between the soil surface and the groundwater table. Especially important are the water retention (water holding) and hydraulic conductivity (or permeability) functions which determine the water content and the rate and direction at which water and dissolved contaminants move in the unsaturated zone. Unfortunately, these hydraulic properties are generally measured at relatively small (local) scales. Major questions exist about how to best average (or upscale) the hydraulic properties from the local scale within a heterogeneous soil volume to obtain effective properties at the larger (field or watershed) scales. The main objective of this study was to find optimal ways of upscaling the local-scale properties to an equivalent homogeneous system at the larger scale with roughly the same hydraulic properties. A statistical upscaling scheme was derived based on two important criteria: predicting the same water flux across the soil surface and keeping the same soil surface moisture content. These two quantities are important in that they are key input for soil-plant-atmosphere models in terms of partitioning upward and downward fluxes at the land surface. The upscaling scheme was tested successfully using 84 field-measured hydraulic parameter data sets 84 from a site in the Mojave Desert. Results are important when trying to predict water flow and contaminant transport processes in natural field soils that are generally very heterogeneous (e.g., layered or spatially variable in many other ways).

Technical Abstract: Upscaled soil hydraulic properties are needed for many large-scale hydrologic applications such as regional and global climate studies and investigations of land-atmosphere interactions. Many larger scale subsurface flow and contaminant transport studies also require upscaled hydraulic property estimates. The objectives of this study were to develop a methodology for upscaling hydraulic property functions using a p-norm approach, to examine how p-norm values differ for two commonly used soil hydraulic property models (the Gardner and van Genuchten functions), and to investigate the relative sensitivities of p-norms and the effective hydraulic parameters to the degree of soil heterogeneity (expressed in terms of variances and auto-correlation lengths of the hydraulic parameters) and other environmental conditions. The p-norm approach expresses upscaling schemes such that it reduces their sensitivity to uncertainties (heterogeneities) in site conditions. The upscaling schemes are obtained as the result of two new criteria proposed to upscale soil hydraulic properties in this study - one preserving the ensemble vertical moisture flux across the land-atmosphere boundary, and a second preserving the ensemble soil surface moisture content. The effective soil hydraulic parameters of a heterogeneous soil formation are then derived by conceptualizing the formation as an equivalent homogeneous medium that satisfies the upscaling criteria. Upscaling relationships between the Gardner and van Genuchten models can then also be established for steady-state vertical flow using the statistical structures of the hydraulic parameters of these two models as estimated from field measurements. The upscaling scheme is demonstrated using hydraulic property data collected at 84 locations across a site in the Mojave Desert. Our results show that the p-norms generally vary less in magnitude than the effective parameters when the variances of the hydraulic parameters increase. We also show that, in general, p-norm values are better defined for the van Genuchten model than the Gardner model. Hydraulic parameter auto correlations, as defined by correlation lengths, were found to have little impact in relating the upscaling schemes (p-norm values) for the two hydraulic property models, but correlation between the hydraulic parameters within the hydraulic property models can significantly affect p-norm relationships.

Last Modified: 8/24/2016
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