Mixture distributions and spatial scale effects on flood hydrology

Knowledge of the magnitude and frequency of floods on rivers is necessary for a variety of practical applications, including the design of hydraulic structures such as bridges and culverts, and floodplain management through land-use allocation and flood-protection measures. Design floods estimated by fitted distributions are prone to errors associated with (i) mis-specification of the parent distribution at a single site and (ii) the estimation of flood statistics in regional analysis.; The first part of this thesis deals with the mis-specification of the parent distribution, that is, the model governing the population from which the observed sample of data is supposedly drawn. Usually, traditional flood frequency analysis involves the assumption of homogeneity of the flood distribution. However, floods are often generated by heterogeneous distributions composed of a mixture of two or more populations. Differences between the populations may be due to a number of factors, including seasonal variations in the flood producing mechanisms, changes in weather patterns due to low frequency climate shifts and/or El-NiNo/La-Nina oscillations, changes in channel routing due to the dominance of within channel or floodplain flow, and basin variability resulting from changes in antecedent soil moisture. We demonstrated that in many cases not recognizing these physical processes in conventional flood frequency analysis is the main reason why many frequency distributions do not provide an acceptable fit to flood data.; The second part of this thesis provides new insights that serve to improve scientific understanding and professional practice in addressing regional flood hydrology problems. Currently employed peak flow regionalisation procedures inherently make assumptions of scale invariance. One assumption is that the scaling exponent of the flood quantile-drainage area power relationship is independent of catchment size. A second assumption is that the index flood method is valid such that growth factors between flood quantiles are independent of catchment size (scale). A third assumption inherent in many regional flood models is the constancy in the L-coefficient of variation (L-Cv) and the L-coefficient of skewness (L-Cs) over homogeneous geographical regions. This study focuses on the spatial scaling patterns of linear moment flood statistics, and offers plausible explanations 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. (Abstract shortened by UMI.)...