Taha B. M. J. Ouarda

A Nonstationary Extreme Value Analysis for the Assessment of Changes in Extreme Annual Wind Speed over the Gulf of St. Lawrence, Canada

Abstract Changes in the extreme annual wind speed in and around the Gulf of St. Lawrence (Canada) were investigated through a nonstationary extreme value analysis of the annual maximum 10-m wind speed obtained from the North American Regional Reanalysis (NARR) dataset as well as observed data from selected stations of Environment Canada. A generalized extreme value distribution with time-dependent location and scale parameters was used to estimate quantiles of interest as functions of time at locations where significant trend was detected. A Bayesian method, the generalized maximum likelihood approach, is implemented to estimate the parameters. The analysis yielded shape parameters very close to 0, suggesting that the distribution can be modeled using the Gumbel distribution. A similar analysis using a nonstationary Gumbel model yielded similar quantiles with narrower credibility intervals. Overall, little change was detected over the period 1979–2004. Only 7% of the investigated grids exhibited trends at...

ON SOME METHODS OF FITTING THE GENERALIZED PARETO DISTRIBUTION

The two-parameter generalized Pareto distribution (GPD) has been recommended for the frequency analysis of environmental extreme events. In the present paper, we concentrate on one form of the GPD (which we will call GPDB) which can be useful in the frequency analysis of two types of hydrological variables: (1) when the shape parameter α is positive, the distribution (denoted by GPDB-2) can be used to study phenomena such as flood flows, which are bounded from below but have a long right tail; (2) when α is negative, the resulting distribution (GPDB-3) could be used to study variables such as low flows which are bounded from both sides but with a left tail. Six versions of the generalized method of moments (GMM) for fitting GPDB are investigated. The flexibility of the GMM provides the user with the possibility of choosing a version of the method (i.e. the moment pair that is used in fitting the distribution) which assigns larger weight to the larger elements of the sample, or another version which gives more weight to the smaller elements, depending on the problem at hand. A general formula for the asymptotic variance of the T-year event XT obtained by combining any two moments of GPDB is presented and applied. It is shown that the adequate choice of the order of these two moments to fit the distribution can lead, in some cases, to a considerable reduction in the variance of the estimator of XT, in comparison with estimation by the traditional method of moments (which uses moments of order one and two). The performance indices that are used to compare the different versions of the GMM are based on root mean square error, bias, and variance—both asymptotic and observed (based on simulation)—of GPDB quantiles and parameters. It is shown that moments of order (0),−1) and (2,−1) lead to the best results when the shape parameter a is positive (GPDB − 2), and the traditional method of moments can be considered as most efficient for negative values of α (GPDB −3). The GMM with moments of order 0 and one is shown to be rather consistent and moderately satisfactory for both GPDB-2 and GPDB-3.