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Estimation of a Critical Spatial Discretization Limit for Solving Richards' Equation at Large Scales

^a UFZ Helmholtz Center for Environmental Research, Dep. of Soil Physics, Theodor-Lieser-Strasse 4, Halle 06120, Germany
^b Institute for Parallel and Distributed Systems, Univ. of Stuttgart, Universitätsstrasse 38, 70569 Stuttgart, Germany

Correspondence: ^* Corresponding author (hans-joerg.vogel{at}ufz.de).

Received for publication 19 December 2006. Water dynamics in soil at spatial scales larger than the representative elementary volume (REV) of the porous structure are typically described by Richards' equation, which relates the flux law of Buckingham–Darcy to the mass balance of soil water. It is based on the soil water retention characteristics and the hydraulic conductivity function as constitutive material properties. In hydrological modeling, Richards' equation is also used at large scales up to hundreds of meters. Increasing the scale is typically accompanied by increasing the spatial discretization scale for the numerical solution of the problem. However, due to the underlying assumption of local equilibrium between water content and water potential, there is an upper limit of spatial discretization above which the solution is expected to be biased. We present a simple approach to estimate this limit, which depends on the shape of the soil hydraulic functions and the local gradient of total water potential. It is in the range between millimeters and decimeters.

Abbreviations: REV, representative elementary volume