| Summary: | This research deals with the estimation of rainfalls and floods for locations at which the corresponding data are unavailable (ungauged sites). The overall study can be divided into three different parts. The first part explores the validity of the distributional similarity of the rainfall time series aggregated at different time scales. Based on the theory of multiplicative cascade process, a scale independent mathematical model has been proposed to describe the probability distributions of rainfall time series aggregated at different time scales. It has been demonstrated that the multifractal formalism can be used to estimate the probability distribution of rainfalls for a wide range of space and time scales. === The second part of the research deals with the estimation of floods at an ungauged site using regional physiographic and climatic variables. To this end, a detailed study was carried out to determine the best technique for estimating the parameters of the commonly used power-form flood regionalization model, and to identify the minimum number of physiographic and hydrometeorological variables which should be included in the model. The study was further elaborated by applying the linear and nonlinear covariance structural models. Results of a numerical example using hydrologic data from Quebec and Ontario have indicated the superior performance of the nonlinear optimization method. Further, it was found that the significant variables which should be considered in the estimation of floods, are the area of the basin, the basin slope and the total precipitation five days before the flood for Quebec, and the area of the basin, the area of forests, lakes, and marses and the slope of the main channel for Ontario. === The third part of the study proposed a new method of flood estimation based on the scaling of the statistical moments of the regional flood series with the basin area. Analysis of the physiographic and hydrologic data from Quebec and Ontario showed that the non-central moments of order from one to six are scaling with the basin area. This empirical evidence was used in defining the hydrologically similar basins (i.e., homogeneous flood regions), and in selecting a suitable regional distribution function for the estimation of flood quantiles. It was observed that the grouping of homogeneous basins as proposed in this study formed well-defined geographical regions with distinct climatic characteristics. Further, it was recommended that the selection of regional probability distribution and the corresponding parameter estimation method should be made such that the scaling properties of the flood series were preserved. The improved estimates of the statistical moments and flood quantiles for unguaged sites have indicated the superiority of the proposed approach as compared to those values given by existing methods.
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