Natural soils exhibit considerable spatial heterogeneity in both the horizontal and vertical directions, and at all distance scales from the pore to the continent, to a degree that it is difficult to capture this variability in routine measurements.45,46 This large variation in soil properties, infiltration, and soil moisture over relatively small areas makes it difficult to transfer the understanding of processes developed at a point to catchment scales. Many hydrological models assume that a single spatially representative average soil property can be used to characterize catchment (or even larger) scale processes. It is clear from the nonlinear character of soil water processes [Eq. 94)] that catchment average infiltration cannot be computed based on catchment average soil properties. It is also clear that the physical meaning of a soil property, say porosity, is relative to the volume over which it is averaged.47 However, there is a need to understand and reduce this complexity for the purposes of prediction and management. Several approaches, including dividing the catchment into hydrologi-cally similar subareas,48 various statistical approaches,49 and scaling and similarity theory50,51 have made headway toward an understanding of infiltration and soil moisture spatial variability, but are not being widely used in practical applications.
One of the most important recent findings in this regard is the scale invariance of soil water behavior. If a heterogenous field is the union of homogenous spatial domains, each with associated characteristic length scales, then heterogeneity simplifies into the spatial variability of these length scales, while the functional relationships that describe soil water movement (i.e., the Richards equation) remain uniform across spatial scales.52 This new understanding of the underlying symmetry of the Richards equation may help to facilitate a workable scale invariant analytical soil water dynamical model.
Finally, there is a continuing need for the observation of soil properties, soil moisture, and infiltration processes at multiple scales to facilitate understanding and prediction of these complex and socially significant processes. It is likely that remote sensing of soil moisture and other land surface factors will be instrumental in this respect.
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