^a Winand Staring Centre for Integrated Land, Soil and Water Research (SC-DLO), PO Box 125, NL-6700 AC, Wageningen, The Netherlands

^b Agricultural University of Wageningen, Department of Water Resources, Nieuwe Kanaal 11, NL-6721 MK, Wageningen, The Netherlands

The most widely used parameterization in soil hydrology, the Darcy-Richards (DR) equation, is gaining increasing importance in mesoscale and climate modelling. This is mainly due to the need to introduce plant-interactive soil water depletion and stomatal conductance parameterizations and to improve the calculation of deep percolation and runoff. Covering a grid of several hundreds of square kilometres, the DR parameterization in soil-vegetation-atmosphere-transfer schemes (SVATs) is assumed to be scale-invariant. The parameters describing the non-linear, area-average soil hydraulic functions in this scale-invariant DR-equation should be treated as calibration-parameters, which do not necessarily have a physical meaning. The saturated hydraulic conductivity is one of the soil parameters to which the models show very high sensitivity. It is shown that saturated hydraulic conductivity can be scaled in both vertical and horizontal directions for large flow domains.

In this paper, a distinction is made between effective and aggregated soil parameters. Effective parameters are defined as area-average values or distributions over a domain with a single, distinct textural soil type. They can be obtained by scaling or inverse modelling. Aggregated soil parameters represent grid-domains with several textural soil types. In soil science dimensional methods have been developed to scale up soil hydraulic characteristics. With some specific assumptions, these techniques can be extrapolated from classical field-scale problems in soil heterogeneity to larger domains, compatible with the grid-size of large scale models. Particularly promising is the estimation of effective soil hydraulic parameters from area averaging measurements through inverse modelling of the unsaturated flow.

Techniques to scale and aggregate the soil characteristics presented in this paper qualify for direct or indirect use in large scale meteorological models. One of the interesting results is the effective behaviour of the reference curve, which can be obtained from similar media scaling. If the conclusions of this paper survive further studies, a relatively simple method will become available to parameterize soil variability at large scales. The inverse technique is found to provide effective soil parameters which perform well in predicting both the area-average evaporation and the area-average soil moisture fluxes, such as subsurface runoff. This is not the case for aggregated soil parameters. Obtained from regression relationships between soil textural composition and hydraulic characteristics, these aggregated parameters predict evaporation fluxes well, but fail to predict water balance terms such as percolation and runoff. This is a serious drawback which could eventually hamper the improvement of the representation of the hydrological cycle in mesoscale atmospheric models and in GCMs.