Scale: Landscape attributes and geographical information systems

The roles and limitations of geographical information systems (GISs) in scaling hydrological models over heterogeneous land surfaces are outlined. Scaling is defined here as the extension of small-scale process models, which may be directly parameterized and validated, to larger spatial extents. A process computation can be successfully scaled if this extension can be carried out with minimal bias. Much of our understanding of land surface hydrological processes as currently applied within distributed models has been derived in conjunction with 'point' or 'plot' experiments, in which spatial variations and patterns of the controlling soil, canopy and meteorological factors are not defined. In these cases, prescription of model input parameters can be accomplished by direct observation. As the spatial extent is expanded beyond these point experiments to catchment or larger watershed regions, the direct extension of the point models requires an estimation of the distribution of the model parameters and process computations over the heterogeneous land surface. If the distribution of the set of spatial variables required for a given hydrological model (e.g. surface slope, soil hydraulic conductivity) can be described by a joint density function, f(x), where x = x 1 ,x 2 ,x 3 ,... are the model variables, then a GIS may be evaluated as a tool for estimating this function. In terms of the scaling procedure, the GIS is used to replace direct measurement or sampling of f(x) as the area of simulation is increased beyond the extent over which direct sampling of the distribution is feasible. The question to be asked is whether current GISs and current available spatial data sets are sufficient to adequately estimate these density functions.