A hierarchical approach for the regionalization of precipitation annual maxima in Canada

Abstract

Abstract. The L moments are used in the three stages of regional frequency analysis: the delineation of homogeneous regions, the identification of a regional parent distribution, and the estimation of distribution parameters. Numerical analysis is conducted on 5 min to 24 hours annual rainfall extremes from 375 precipitation gaging stations in Canada. The numerical analysis concluded that Canada could be considered as a single homogeneous region in which the L skewness and L kurtosis display no significant spatial variability. Also, on the basis of mean annual precipitation (MAP), Canada can be divided into climatologically homogeneous subregions, in which the L coefficient of variation is virtually constant. The parent distribution was identified as the general extreme value (GEV), the parameters of which depend on the MAP and storm duration. A hierarchical regional approach is proposed for fitting the identified GEV distribution, where the L skewness, L coefficient of variation, and mean are estimated on a regional, subregional, and single-site basis, respectively. Monte Carlo simulations indicate that design storms estimated by the proposed hierarchical approach are substantially more accurate than those estimated by the single-site method. The simulations also demonstrate that the proposed hierarchical approach makes the estimation of design storms at ungaged sites less dependent on the availability of precipitation data. While current procedures for estimating design storms in Canada are exclusively based on single-site frequency analysis, it has long been recognized that regional analysis techniques have the ability to significantly reduce uncertainties in quantile estimates relative to that inherent in the single-site approach [Lettenmaier et al., 1987;Pilon and Adamowski, 1992]. Regionalization procedures can further be considered equivalent to extending of the gaging network and provide planners and designers with a better alternative for the estimation of design storms at ungaged sites than currently used rainfall frequency maps. The advantages of regional frequency models and the large uncertainties involved in single-site approaches justify the need for a new regional methodology leading to more reliable design storm estimates at both short-term record sites and ungaged locations.The purpose of this paper is to develop a regional rainfall frequency approach for estimating design storms in Canada and to evaluate the accuracy of such approach relative to that of the current single-site frequency method. Linear Moment StatisticsThis study draws heavily on the linear moments or L moments [Hosking, 1990]. The L moments suffer less from the effects of sampling variability than the conventional moments, they are more robust to outliers in the data, and hence they enable more secure inferences to be made from samples about the underlying probability distribution [Royston, 1991]. The rth 31,645

Relationships between statistics of rainfall extremes and mean annual precipitation: an application for design-storm estimation in northern central Italy

“…This assumption contrasts with the findings of other studies, which show that the statistics of rainfall extremes vary systematically with location Alila, 1999;Brath et al, 2003). These studies also identified statistically significant relationships between these statistics and the mean annual precipitation (MAP), which was used as a surrogate of geographical location.…”

“…The study described in this paper investigates the applicability of the findings of and Alila (1999) in a large geographical area of northern central Italy. The analysis considers annual series of precipitation maxima for storm duration from 15 min to 1 day that were observed by a dense raingauge network.…”

“…We present a regional model that can be considered to be an extension of the index flood model as well. Similarly to what originally proposed in and Alila (1999), we assume that a homogeneous region, within which L-Cv and L-Cs are constant, is a group of climatically homogeneous sites, within which the variability of MAP is very limited.…”

“…The study investigates the applicability of the finding of and Alila (1999) in this particular context, making use of a raingauge network with a higher resolution than the networks considered in the above mentioned papers. The variability of the sample L-moment ratio (Hosking, 1990) of skewness and variation was examined against the variability of MAP.…”

“…Alila (1999) studied the Canadian raingauge network and detected analogous relationship between the L-coefficients of variation, L-Cv (for a definition of the coefficients see e.g. Hosking and Wallis, 1997).…”