Regional frequency analysis of extreme rainfalls V-T-V. Nguyen*, T-D. Nguyen* and F. Ashkar** *Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6 **Department of Mathematics, University of Moncton, Moncton, New Brunswick, Canada E1A 3E9 Abstract This study proposes two alternative methods for estimating the distribution of extreme rainfalls for sites where rainfall data are available (gaged sites) and for locations without data (ungaged sites). The first method deals with the estimation of short-duration rainfall extremes from available rainfall data for longer durations using the “scale-invariance” concept to account for the relationship between statistical properties of extreme rainfall processes for different time scales. The second method is concerned with the estimation of extreme rainfalls for ungaged sites. This method relies on a new definition of homogeneous sites. Results of the numerical application using data from a network of 10 recording rain gauges in Quebec (Canada) indicate that the proposed methods are able to provide extreme rainfall estimates that are comparable with those based on observed at-site rainfall data. Keywords Extreme rainfalls; frequency analysis; generalized extreme value distribution; regionalization; scale invariance; statistical modelling Introduction Rainfall frequency analyses are commonly used for the design of various hydraulic struc- tures. More specifically, rainfall frequency analysis studies are necessary for the develop- ment of a “design storm”; that is, a rainfall temporal pattern used in the design of a hydraulic structure. The objective of rainfall frequency analyses is to estimate the amount of rainfall falling at a given point or over a given area for a specified duration and return period. For a site for which sufficient rainfall data are available (a gaged site), a frequency analysis can be performed. The precipitation data used for frequency analysis are typically available in the form of annual maximum series (AMS) (or converted to this form using continuous records of hourly or daily rainfall data). These series contain the largest rainfall in each complete year of record. An alternative data format for rainfall frequency studies is “partial duration series” (PDS) (also referred to as peaks over threshold data) which consist of all large precipitation amounts above certain thresholds selected for different durations. Arguments in favor of either of these techniques are well described in the literature (National Research Council of Canada, 1989; Stedinger et al., 1993). Due to its simpler structure, the AMS-based method is more popular in practice. Several probability models have been developed to describe the distribution of extreme rainfalls at a single site (Wilks, 1993). Unfortunately, these models are accurate only for the specific time frame associated with the data used. Hence, it was argued that the usefulness of a model should lie in its potential ability to adequately describe the rainfall process at time scales that are not included in the building of its mathematical structure. It has necessi- tated the need for formulating models whose mathematical structure will follow the main statistical features of the past history through a continuum of levels of aggregation. This formulation implies that the suggested model should statistically and simultaneously match various properties of the rainfall process at different levels of aggregation, whether or not these properties are included in the model. The most important practical implication of such models is that, from a higher aggregation model we could infer the statistical Water Science and Technology Vol 45 No 2 pp 75–81 © IWA Publishing 2002 75 Downloaded from http://iwaponline.com/wst/article-pdf/45/2/75/425130/75.pdf by guest on 04 December 2023