The first part of the research deals with the estimation of extreme rainfalls for locations where rainfall records are sufficiently available (gaged sites); the second part is concerned with cases where rainfall data are limited (partially-gaged sites); and finally the third part involves the most complex situation where rainfall data are unavailable (ungaged sites).; For gaged sites, two methods were developed for estimating the annual extreme (AE) rainfalls based on the simple scaling behaviour of the first three non-central moments (NCMs) of the AE rainfall processes and using the Generalized Extreme Value (GEV) distribution as the parent distribution. The first estimation method was called one-moment (OM) method since it only relied on the first-order NCM of AE rainfall series in the computation of the rainfall quantiles, while the second method was called three-moment (TM) procedure since it used all first three NCMs of AE rainfalls in the estimation of the quantiles.; For partially-gaged and ungaged sites, a new approach to defining rainfall homogeneous regions has been proposed based on the similarity of rainfall occurrences at different raingage stations. In addition, a Principal Component Analysis technique was used to assess the similarity of raingages and to delineate homogeneous regions.; On the basis of the proposed method for identifying rainfall homogeneous regions, two new methods (PG-1 and PG-2) were developed for estimating annual maximum (AM) rainfalls at partially gauged sites. These methods were also based on the scaling properties of AM rainfall series for different durations.; For ungaged sites, three methods (UG-1, UG-2, and NR) were proposed for estimating AM rainfalls. Method UG-1 was based on the NCMs of AM rainfalls at an ungaged site that were computed by direct interpolation of the corresponding NCM values from the gaged sites within the same homogeneous region. Method UG-2 used the pooled data set from all gaged sites in the homogeneous region for this computation. On the other hand, the NR method estimated the NCMs of AM rainfalls for an ungaged site using the regional regression between the first three NCMs and the number of rainfall occurrence (NR) values that were interpolated from the NR values of the gaged sites.; Finally, to assess the uncertainty of extreme rainfall estimates, two new methods (CI-1 and CI-2) were developed for computing the confidence limits (CLs) based on these estimated values. The proposed methods were based on the bootstrap technique and the scaling properties of the NCMs of extreme rainfall series. (Abstract shortened by UMI.)
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