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The effects of scale and storm severity on the linearity of watershed response revealed through the regional L-moment analysis of annual peak flows Cathcart, Jaime Grant

Abstract

Natural basins rarely demonstrate linear response patterns across a large range of spatial scales and storm severities, yet assumptions of linearity, both explicit and implicit, are common to most peak flow estimating techniques. The extent to which these assumptions are valid is one of the most intriguing and challenging questions facing hydrologists today. This thesis presents the results of an effort to shed some light on the darkness of our understanding of this issue. The study represents the first time that the relationship between storm severity and the linearity of peak flow response has been considered on a regional basis, in contrast with the more conventional approach of investigating linearity through the use of deterministic models of single watersheds. An effort is made to introduce some understanding of causative physical processes into the frequency analysis of extremes, thereby distinguishing the work from the common approach of applying mathematically rigorous but physically sterile curve-fitting exercises. The study focuses on the spatial scaling patterns of linear moment flood statistics, and plausible explanations are offered for observed regional scaling trends in terms of the various precipitation and runoff mechanisms that dominate at different scales and in different climates. The characteristics of these mechanisms are then linked back to the effects that variations in L-moment ratio statistics have on flood quantile estimates, and most importantly, the tail behaviour of flood frequency distributions. The research program mainly utilizes historical records of USGS peak flow values for Oregon State, but USGS equations for other states, as well as hourly streamflow and precipitation data from the Carnation Creek Watershed on the west coast of Vancouver Island, British Columbia, are also analyzed. The findings indicate that the primary flood statistics, namely the mean, L-coefficient of variation, L-skewness and L-kurtosis, generally demonstrate different degrees of spatial scaling linearity at small and large scales, with contrasting patterns for humid and arid regions. Furthermore, these variations in spatial scaling linearity are shown to translate into differences in the scaling patterns of return period quantiles, thereby demonstrating differences in storm linearity at different spatial scales. This in turn equates to differences in the tail behaviours of flood frequency distributions at different scales. The observed variations in linearity are attributed to the differing relative roles played by various moisture input and runoff generation mechanisms at different scales and under different climate regimes. To the author's knowledge, this work presents an original attempt to physically explain the tail behaviour of flood frequency curves. The results cast doubt on the validity of many commonly applied flood frequency analysis concepts, techniques and models, such as the delineation of geographically defined hydrologic regions, the statistical testing of hydrologic homogeneity, the mapping of flood statistics, the use of regional flood frequency distributions and the application of the index flood method across a broad range of spatial scales. Furthermore, the findings raise concerns about the common practice of applying rainfall-runoff concepts and models, such as the unit hydrograph approach, popular time of concentration equations and the Rational Method, without serious consideration of the significance of basin size or climate type.

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