At-site and regional modeling of extreme hydrologic events

At-site and regional estimation of extreme hydrologic events based on the partial duration series (PDS) method has been analysed. The PDS model comprises the assumptions of a Poisson distributed number of threshold exceedances and generalized Pareto distributed exceedance magnitudes, corresponding to a generalized extreme value distribution for the annual maximum series (AMS). At-site T-year event estimation in AMS and PDS has been compared using three different estimation methods, respectively, the maximum likelihood method, the method of moments, and the method of probability weighted moments. In common applications, which correspond to heavy-tailed distributions, the PDS model with the method of moments estimation is generally to be preferred. A regional index-flood method based on PDS data where the regional parameters are estimated using w eighted L-moment ratios has been introduced. The performance of the method is evaluated by comparing with atsite estimation and estimation based on the corresponding AMS index-flood method. Even in strongly heterogeneous regions, regional estimation is su perior to at-site estimation, and, compared to the AMS procedure, the regional PDS method is more robust with respect to violation of the basic homogeneity assumption of the indexflood method. Procedures to define homogeneous regions and determine regiona l parent distributions have been discussed and applied to New Zealand flood records. Flood frequency groups defined in terms of catchment characteristics appear more homogeneous with respect to L-moment ratios for PDS than AMS data. Moreover, in determination of the regional parent distribution using L-moment ratio diagrams, PDS data, in contrast to AMS data, provide an unambiguous interpretation. A regional method has been introduced that combines the index-flood model with an empirical Bayes procedure. The prior information of the PDS parameters is inferred from regional data using generalized least squares (GLS) regression that accounts for intersite dependence and regional heterogeneity. In the case of a strongly heterogeneous intersite correlation structure, the GLS procedure provides a more efficient estimate of a regional parameter as compared to the usually applied record - length-weighted average procedure. In addition, the GLS procedure offers a general framework for a reliable assessment of regional homogeneity and parameter uncertainty. A linear Bayes estimation procedure results in reasonable and simple estimates of the T-year event and the associated uncertainty at both gauged and ungauged sites.