Abstract
Abstract This study presents a depth–duration–frequency (DDF) model, which is applied to the annual maxima of sub-hourly rainfall totals of selected stations in England and Wales. The proposed DDF model follows from the standard assumption that the block maxima are generalised extreme value (GEV) distributed. The model structure is based on empirical features of the observed data and the assumption that, for each site, the distribution of the rainfall maxima of all durations can be characterised by common lower bound and skewness parameters. Some basic relationships between the location and scale parameters of the GEV distributions are enforced to ensure that frequency estimates for different durations are consistent. The derived DDF curves give a good fit to the observed data. The rainfall depths estimated by the proposed model are then compared with the standard DDF models used in the United Kingdom. The proposed model performs well for the shorter return periods for which reliable estimates of the rainfall frequency can be obtained from the observed data, while the standard methods show more variable results. Although the standard methods used no or little sub-hourly data in their calibration, they give fairly reliable estimates for the estimated rainfall depths overall.
Highlights
Estimates of the magnitude of rainfall events of a given duration with an expected annual exceedance probability p, are an important component of current methods of flood frequency estimation, used in the design and assessment of flood defence schemes, bridges and reservoir spillways, as well as urban drainage systems
The proposed unified generalised extreme value (GEV) model requires the estimation of a total of six parameters (a, b, c, g, ‘, κ), a relatively parsimonious model which, given some constraints in the location function, allows for consistent frequency estimates for different durations
The proposed model builds on the standard assumption that block maxima follow a GEV distribution: the properties of the GEV distribution are exploited to construct a unified model which is fitted to the data of different duration simultaneously
Summary
Estimates of the magnitude of rainfall events of a given duration with an expected annual exceedance probability p, are an important component of current methods of flood frequency estimation, used in the design and assessment of flood defence schemes, bridges and reservoir spillways, as well as urban drainage systems. The performance of the unified GEV, FSR and FEH99 models for short-duration rainfall frequency estimation are compared in the section Comparisons of the unified GEV results to current methods.
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