Searching for the Holy Grail of scientific hydrology: Q_t=(S, R, Δt)A as closure

Abstract. Representative Elementary Watershed concepts provide a useful scale-independent framework for the representation of hydrological processes. The balance equations that underlie the concepts, however, require the definition of boundary flux closures that should be expected to be scale dependent. The relationship between internal state variables of an REW element and the boundary fluxes will be nonlinear, hysteretic and scale-dependent and may depend on the extremes of the heterogeneities within the REW. Because of the nonlinearities involved, simple averaging of local scale flux relationships are unlikely to produce an adequate decription of the closure problem at the REW scale. Hysteresis in the dynamic response is demonstrated for some small experimental catchments and it is suggested that at least some of this hysteresis can be represented by the use of simple transfer functions. The search for appropriate closure schemes is the second most important problem in hydrology of the 21st Century (the most important is providing the techniques to measure integrated fluxes and storages at useful scales). The closure problem is a scientific Holy Grail: worth searching for even if a general solution might ultimate prove impossible to find.