We have focused above on contributions to watershed modelling over the past four years with particular emphasis on the uses of new sources of information that have become readily available. Does this mean that the major problems facing those interested in computing the hydrological responses of catchments have been solved, at least for the most part? Not at all! Although we envision ever more widespread use of distributed data as they become available and believe that these indeed will lead to improvements in models, very serious problems remain. The most serious problems relative to the establishment of a truly accurate, useful, and tenable theory of catchment functioning as embodied in mathematical models are those of 1) the identifiability of model parameters, either through a measurement program or through solution of an ill-conditioned inverse problem, and 2) the incorporation of relatively small-scale heterogeneity into models applied at relatively larger scales. The difficulties posed for the science by these problems have been expounded elsewhere (e.g., Beven 1993b; Loague 1990; Grayson et al. 1992) and will not be repeated here.
The limitations inherent in using data on catchment ``inputs'' (i.e., measurements of precipitation, temperature, wind speed, humidity, etc.) and on catchment ``outputs'' (i.e., streamflow) to estimate the parameters in rainfall-runoff models have been appreciated for some time (e.g., see Clarke 1973). Although progress has been made on improvement of methods for finding ``optimal'' parameter sets (e.g., Duan et al. 1992), there is a fundamental limitation on how many parameters can be estimated, a limitation set by the amount of information in a rainfall-runoff record ( Jakeman and Hornberger 1993). It also has been pointed out that parameters in many hydrological models are dependent on the climate during the calibration period ( Gan and Burges 1990a,b). Because of these limitations, a heavy burden must be borne by models that seek to use parameter-rich, physics-based descriptions of catchment response---a way to measure the parameters independently of input-output data must be found.
This need for independent, spatially distributed data is one of the primary stimuli in the development of index-based modelling methods that we focus on in this review. The availability of DTM data, for example, makes it possible to take into account one of the most important physical drivers (gravity) for water flow through a catchment in an area of relatively high relief. Furthermore, the issue of how use of different scales (directly related to grid spacing in this case) affects results can be addressed by subsampling the most refined data that one has available ( Zhang and Montgomery 1994). Despite some of the advances that have been made along these lines, the issue of how to parameterize physical processes in a computer code that solves a set of equations intended to represent physical processes over some finite part of a catchment, a part that itself is heterogeneous with respect to processes being modelled, is a major challenge for hydrologists. This issue is sometimes called the sub-grid-scale variability problem.
Smith et al. (1994) suggest that a failure to account for heterogeneity may be a major contributing cause to the ``failure'' of some models. They point out that ground-water hydrologists, rather than ``give up'' in the face of heterogeneities at various scales, have made much progress in developing approaches for characterizing heterogeneity in geological formations and for incorporating the appropriate characteristics into (stochastic) models. This in fact may be a goal toward which catchment hydrologists may aspire in the future. As Beven (1994) has pointed out, however, to employ such stochastic approaches, we will need to know the structure of the heterogeneities important at the catchment scale (e.g., preferential flow paths on and below the ground surface). As yet, we are far from any measurement techniques that even hold the promise of revealing such structure.
Successful approaches for incorporating heterogeneity into catchment models to date have emphasized the use of distribution functions. The distribution function approach for catchment modelling has been with us for some time (e.g., see Moore and Clarke 1981). The method has been, and continues to be, one of the cornerstones for investigating appropriate interfaces between land-surface hydrological models and atmospheric circulation models (e.g., Entekhabi and Eagleson 1989; Avisar 1992; Wood et al. 1992). As powerful as these approaches have been for modelling the land-surface interactions with the atmosphere, they fail to consider explicitly ``lateral'' hydrological flows; that is, they have focused on one dimension, the vertical. A major goal in catchment hydrology is to model these ``lateral'' interactions. Famiglietti et al. (1992) and Famiglietti and Wood (1994a,b) have pioneered the application of the distribution-function approach incorporating lateral interactions. They employ a distribution-function version of TOPMODEL as a first step toward the development of macroscale equations that preserve sub-grid-scale variability. Famiglietti (1992) thoroughly investigated this approach, exploring theoretical issues and demonstrating its value in application to the FIFE project.
The difficulties in accounting for heterogeneities in general, and preferred flow paths in particular, in catchment models are compounded when chemical response, in addition to purely flow response, of catchments is considered. The basic identifiability problems mentioned above are present ( Kleissen et al. 1990), and these reflect parameters associated with geochemical reactions in a heterogeneous system as well as the flow parameters. There is a clear need for an interactive evolution of hybrid hydrological-hydrochemical modelling in close conjunction with field observations (e.g., Christophersen and Neal 1990; see also Hooper, this issue).