PHYSICAL INTERPRETATIONS OF REGIONAL VARIATIONS IN THE SCALING EXPONENTS OF FLOOD QUANTILES

The concepts of simple scaling and multiscaling provide a new theoretical framework for the study of spatial or regional flood frequency relations and their underlying physical generating mechanisms. In particular, the scaling exponents in the power law relationship between flood quantiles and drainage areas contain a 'basic signature of invariance' regarding the spatial variability of floods, and therefore suggest different hypotheses regarding their physical generating mechanisms. If regional floods obey simple scaling, then the slopes do not vary with return periods. On the other hand, if regional floods obey multiscaling, then the slopes vary with return periods in a systematic manner. This premise is expanded here by investigating the empirical variations in the scaling exponents in three states of the USA: New York, New Mexico and Utah. Distinct variations are observed in the exponents among several regions within each state. These variations provide clear empirical evidence for the presence of both simple scaling and multiscaling in regional floods. They suggest that snowmelt-generated floods exhibit simple scaling, whereas rainfall-generated floods exhibit multiscaling. Results from a simple rainfall-runoff experiment, along with the current research on the spatial scaling structure of mesoscale rainfall, are used to give additional support to these physical hypotheses underlying two different scaling structures observed in floods. In addition, the rainfall-runoff experiment suggests that the behaviour of the flood exponents in small basins is determined by basin response rather than precipitation input. This finding supports the existence of a critical drainage area, as has been reported for the Appalachia flood data in the USA, such that the spatial variability in floods in basins larger than the critical size is determined by the precipitation input, and in basins smaller than the critical size is determined by the basin response.