It may seem strange to end a review of modelling with an observation that future progress is very strongly linked to the acquisition of new data and to new experimental work, but that, in our opinion, is the state of the science. The recognition that hydrological science is in greater need of more and better experimentation than of more and better models (although the latter must ineluctably follow the former) has been recognized for many years ( NAS 1991; Hornberger 1993). To make progress with the issues of heterogeneity and scaling, hydrologists will have to come to terms with the need to pay closer attention to gathering appropriate, high-quality data. It is also clear that, because solutions to the modelling problems are so vexed and because questions about phenomena that occur on widely disparate time and space scales are of legitimate scientific interest, there is room for more than just one approach. ``Empirical'' studies of potential relationships among measurable catchment characteristics and the estimated parameters of some watershed model (e.g., Song and James 1992; Jakeman et al. 1992; Sefton et al. 1994) are needed as much as are small-scale studies of physics-based models.
This is not to say that most efforts should be aimed at only input-output relationships of catchments. There is much to be learned about complex flow paths within catchments, and models based on our best representation of physical processes will remain an essential part of studies designed to understand catchment processes. To be sure, there are unresolved (and perhaps some unresolvable) problems associated with the use of mathematical models of watershed responses, but these should not be misconstrued to imply that models are not useful. When unreasonable expectations are set for models, it is quite easy to be critical. For example, when regulators want to take the term ``validation'' as applied to models to mean ``proven to provide absolute truth,'' scientists must continue to rediscover that there is no solution to Hume's problem of induction ( Konikow and Bredehoeft 1992; Oreskes et al. 1994). Despite this ``limitation'' of models, they are useful; as pointed out by Konikow and Bredehoeft (1992), models can be used to critically analyze a problem, to organize our thinking, and to formulate critical experiments to test hypotheses. This optimistic view of the utility of models notwithstanding, watershed modelling in the future must continue to make inroads in the critical areas of treatment of heterogeneity and of scaling.
The work for this review was supported by National Science Foundation Grant EAR-9304794. The manuscript benefitted from the comments of the ``official'' reviewers, Roger Grayson and David Wolock. The editor, Roger Pielke, also made very useful suggestions. In addition, a number of others (Keith Beven, Robbins Church, Keith Eshleman, Ted Engman, James A. Smith, and Tony Jakeman) graciously provided comments that resulted in improvements to the manuscript. We thank all of these reviewers.
