Regional analyses of precipitation annual maxima in Washington State

Abstract

Regional analyses of precipitation data were conducted using an index flood type methodology and probability weighted moments parameter estimates for the generalized extreme value distribution.Annual maximum series data were collected at 115 stations for durations of 2 and 6 hours and at 315 stations for the 24-hour duration. Because the climate in Washington State varies from arid to rain forest, the issues of homogeneity and region definition posed major problems. Those problems were circumvented by considering the state to be a heterogeneous superregion. Climatologically homogenous subregions within the superregion were defined in terms of mean annual precipitation (MAP) rather than geographic location. The subregional values of the coefficients of variation Cv and skew -y were found to vary systematically with MAP across the superregion. This allowed the superregional values of Cv and -y to be expressed as continuous variables instead of conventional fixed values and eliminated the boundary problems normally associated with subregion definition. The values of Cv and -y for the superregion were found to be largest for arid areas and shorter durations. Smaller values of Cv and -y were associated with humid and rain forest environments. All subregional solutions were within, or near, the extreme value type II family.Given these considerations, two of the major study elements identified in the original program were related to extreme storm characteristics. One study element was the probabilistic examination of the temporal and spatial characteristics of extreme storms. That study has been completed and is described in a separate report . Another study element was the development of methodologies to provide at-site precipitation magnitude-frequency information. Particular emphasis was placed on obtaining reasonable estimates of extreme events with annual exceedance probabilities of the order of 10 -2 to 10 -4. Regional analysis techniques were selected to meet this objective, and they are the subject of this paper. STUDY OVERVIEW Regional analyses techniques have been shown to offer the ability to reduce significantly the uncertainties in quantileestimation of extreme events relative to that inherent in conventional at-site frequency analysis [Wallis, 1980, 1982; Hosking and Wallis, 1988]. The utility of the solutions obtained from any regional analysis ultimately depends upon the relative success achieved in evaluating/addressing three issues: the selection and verification of homogeneous re-119 120 SCHAEFER: PRECIPITATION MAXIMA IN WASHINGTON STATE 124 49 + LEGEND 0 NON RECORDING GAGE ß RECORDING GAGE ß BOTH GAGE TYPES 2 .s REGION DESIGNATION 123 122 121 120 119 118 0 O• (• 0 0 ß 4 oeO g ß o 0 0.4-I o o.2z o o.ou) -0.2 -0.4 0 ß ß ß ß ß ß ß ß ß ß ß ß ' ß ß ß ß ß ' 24 HR DATA ß ß ß ee e ß ß ß ß ß

Divergence criteria in extreme rainfall series frequency analyses

“…Schaefer, 1990). As can be seen in Figs 4(a), 5(a) and 5(b), all the three relationships of pwm 0 , pwm 1 , and pwm 2 against tr exhibit rather smooth forms with low scatter around the regression lines in log-log plots.…”

“…However, from the literature it is clear that the four distributions analysed here, Gumbel, GEV, LN3 and LP3, are indeed among those commonly used for frequency analyses of ERS (e.g. Table II on page A6.7 of Cunnane, 1989; and also Daud et al, 2002;Porras & Porras, 2001;Schaefer, 1990;Smithers & Schulze, 2001;Slimani & Lebel, 1987;SWW, 1990). In order to give an impression of the pdfs based on the 54-element recorded sample series at Florya, the histograms of these four distributions for 5-min and 24-h ERS, along with the pdfs, are plotted in Fig.…”

“…Frequency curves of any ERS are often shown on Gumbel graph paper (e.g. Koutsoyiannis et al, 1998;Schaefer, 1990). The abscissa of a Gumbel graph background is the Gumbel reduced variate, u, which is defined as:…”

Comparison of regional and at‐site approaches to modelling probabilities of heavy precipitation

“…Weights are assigned to data from individual sites in a pooling group according to a dissimilarity measure, and all (weighted) data are employed in the estimation of model parameters and high quantiles at a given site. Most studies that made use of the ROI method (or, in a broader sense, pooling methodologies) dealt with hydrological data (high flows) while applications into precipitation data have been rare (Schaefer, 1990;Di Baldassare et al, 2006;Gaál et al, 2008).…”

Regional Frequency Analysis of Annual Maximum Rainfall in Monsoon Region of Pakistan using L-moments

“…Early examples are Bilham (1936) for regional analysis of extreme rainfall in England and Wales, Ayoade (1976) for regional analysis of daily precipitation in Nigeria. Schaefer (1990), following the index flood methodology of Dalrymple (1960), found the extreme value II distribution to be the best distribution for annual precipitation data in Washington State. Cannarozzo et al (1995) made a regional frequency analysis for Sicilian region using two-component extreme value distribution for annual maximum rainfall of various durations.…”