Advances in Water Resources, August 2012, Vol.44, pp.101-112
► New averaging approach that conserves hydraulic non-equilibrium during rapid infiltration of water. ► New indicators to describe hydraulic non-equilibrium quantitatively. ► Direct link between front morphology and hydraulic non-equilibrium. ► Insights into how structural connectivity affects hydraulic non-equilibrium. ► Shortcomings of an upscaled Richards model extended by hydraulic non-equilibrium. Water infiltration into heterogeneous, structured soil leads to hydraulic non-equilibrium across the infiltration front. That is, the water content and pressure head are not in equilibrium according to some static water retention curve. The water content increases more rapidly in more conductive regions followed by a slow relaxation towards an equilibrium state behind the front. An extreme case is preferential infiltration into macropores. Since flow paths adapt to the structural heterogeneity of the porous medium, there is a direct link between structure and non-equilibrium. The aim of our study is to develop an upscaled description of water dynamics which conserves the macroscopic effects of non-equilibrium and which can be directly linked to structural properties of the material. A critical question is how to define averaged state variables at the larger scale. We propose a novel approach based on flux-weighted averaging of pressure head, and compare its performance to alternative methods for averaging. Further, we suggest some meaningful indicators of hydraulic non-equilibrium that can be related to morphological characteristics of infiltration fronts in quantitative terms. These methods provide a sound basis to assess the impact of structural connectivity on hydraulic non-equilibrium. We demonstrate our approach using numerical case studies for infiltration into two-dimensional heterogeneous media using three different structure models with distinct differences in connectivity. Our results indicate that an increased isotropic, short-range connectivity reduces non-equilibrium, whereas anisotropic structures that are elongated in the direction of flow enforce it. We observe a good agreement between front morphology and effective hydraulic non-equilibrium. A detailed comparison of averaged state variables with results from an upscaled model that includes hydraulic non-equilibrium outlines potential improvements in the description of non-equilibrium dynamics including preferential flow in simplified, upscaled models based on Richards equation.
Transient Flow ; Upscaling ; Pressure Head Averaging ; Hydraulic Non-Equilibrium ; Preferential Flow ; Connectivity ; Engineering
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