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UBC Theses and Dissertations

Mixture distributions and spatial scale effects on flood hydrology Mtiraoui, Ahmed

Abstract

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-Niño/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. An analysis of flow records from streams across British Columbia (Canada), the Gila River (Arizona, USA), and the River Tees (northern England) indicated that when floods are generated by two or more distinct hydrologic processes, the resulting flood distributions may be multimodal and may not be represented by homogeneous distributions. Analysis indicated that the T-year design flood estimated by assuming heterogeneous distributions is much more conservative than those estimated by homogeneous distributions. Monte Carlo simulations were used in this study to quantify the errors in estimating design floods that are caused by a mis-identification of distributions. A set of homogeneous and heterogeneous parametric and nonparametric distributions were compared. A series of variables were also tested, namely the return period, sample size, and combinations of several two parametric distributions. An assessment of the suitability of flood estimation techniques was made based on the effect of these conditions on the accuracy of the estimates. It was found that for high L-skewness (L-Cs) and a heavytailed probability density function, both of which are characteristics of flood mixtures in arid and semi arid climates of Arizona, the Wakeby and two-component log-normal (TCLN) distributions consistently perform well compared to the nonparametric (NP), Gumbel (EV1) and log-Pearson type III (LP3) distributions. For characteristics of flood mixtures representative of the humid climates of British Columbia, where the heterogeneity results in a flood frequency distribution with smaller value of L-skewness (L-Cs) and a bimodal probability density function, the Gumbel (EV1) and nonparametric (NP) distributions perform better than the other distributions. 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 quantiledrainage 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 Lcoefficient 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. A regional linear moment analysis of annual maximum daily flows in streams in British Columbia, California, Colorado, and the Walnut Gulch Experimental Watershed are used to demonstrate that these assumptions of scale invariance of flood statistics are invalid. This is because flood statistics depend not only on physiography and climatic conditions, but also to a large extent on the size of the catchment. Scale dependence of flood statistics hampers the estimation of peak flows, in particular for small (< 100 km² ) ungauged watersheds.

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