An investigation into the physical causes of scaling and heterogeneity of regional flood frequency

Peak discharge data from catchments in the central Appalachian region of eastern United States suggest that the coefficient of variation of annual flood peaks, CV[Q], is not constant, as implied by the index flood method but Varies with catchment size in a complex manner [Smith, 1992]. Gupta et al. [1994] have interpreted the data as indicating that for catchments smaller than a critical threshold size, CV[Q] increases with increasing catchment size, while for larger catchments CV[Q] decreases with catchment size. Our analysis of the same discharge data suggests further that the spatial heterogeneity of these flood frequency characteristics, for example, mean annual flood, E[Q], and coefficient of variation, CV[Q], between catchments in the region is also not constant but varies systematically with catchment size. The spatial heterogeneity of E[Q] appears to decrease with catchment size, while heterogeneity of CV[Q] appears to mirror the observed scaling behavior of CV[Q]. These observations have been made based on statistical analysis of empirical flood data without being underpinned by a physical theory to explain them. In this paper, motivated by these observations and by the need for a physical theory of regional flood frequency, we develop a simple derived flood frequency model. On the basis of insights provided by the model, we relate the increase of CV[Q] with catchment size for small catchments (smaller than a threshold size) to the scaling behavior of the ratio of storm duration to catchment response time. On the other hand, we connect the decrease of CV[Q] with catchment size for larger catchments to the spatial scaling of rainfall (excess) intensity. Our simple model also permits us to separate the relative contributions of catchment routing response and rainfall intensity to the scaling behavior of E[Q]. Our results also lead us to hypothesize that the heterogeneity of CV[Q] between catchments is primarily due to the heterogeneity of catchment response time, while the heterogeneity of E[Q] is primarily due to the heterogeneity of runoff generation processes.