Scaling in hydrology

Correspondence to: G. Bloschl, Institut fur Hydraulik, Gewasserkunde und Wasserwirtschaft, Technische Universitat Wien, Karrsplatz 13/223, A-1040 Wien, Austria. E-mail: bloeschl@hydro.tuwien.ac.at The term ‘scaling’, to many, is veiled in a nimbus of exciting mystery. At a basic level, part of the mystery simply comes from confusion of two connotations of the word—meaning either scale invariance (i.e. processes behaving similarly at small and large scales) or upscaling/downscaling (i.e. aggregating/disaggregating data). However, once this hurdle is surmounted, from whence does this excitement come and in what direction does it lead? If we follow the scale invariance track of enquiry, some hidden signature of hydrologic systems that can be encapsulated in beautifully simple equations is promised. The idea of self-similarity, first conceived by L. F. Richardson and expertly marketed by B. Mandelbrot, is compelling given so much visual evidence of variability at small and large scales. And, indeed, if you believe there exists a single universal relationship underlying hydrologic processes at many scales it is hard not to fly off to cloud-cuckoo land with this idea. The upscaling/downscaling track of enquiry is more practical. In hydrology, much of the recent interest began in the 1970s with the early work of A. Freeze and L. Gelhar aggregating the groundwater flow equation based on a stochastic approach, and gained additional momentum in the 1980s when it was realized that spatial heterogeneity of the land surface matters for atmospheric models. Those subdisciplines of hydrology in which the basic equations are known with some degree of confidence (e.g. groundwater flow) have a head start, but for catchment hydrology and hillslope hydrology there is still a long way to go before the derivation of an aggregate large-scale equation from first principles will be possible. It is likely that ad hoc relationships with little theoretical justification will be with us for another few years. Field hydrologists may wonder what role field observations and onsite experience have in all this, and I wonder too. Is it coincidence that most of the celebrated (and rightly so) pioneers of the scaling community never were personally involved in fieldwork, or is there a causal relationship? I believe it is the latter. Fieldwork and scaling theory, apparently, are too widely divergent for a single individual to excel in both. Or perhaps it is something else. I continue to be intrigued by the complexity of hydrological processes when in the field. The rich diversity in the spatial arrangements of flow paths and mechanisms that, to the observer, quite obviously change with scale make it difficult for me, when back in the office, to write down simple formulations that neglect most of what I know is out there. Many of the betterknown scaling relationships do neglect the important bits. For example, stochastically averaged groundwater flow equations usually assume that