Partial duration series in the annual domain

Abstract

Flood frequency analysis has been an important tool to estimate design floods which are essential for flood protection and management. Series of maximum annual flows MAF have been the preferred choice to collect the needed sample of high flow events for parameter estimation of the identified statistical models. However, MAF series can be short as it is restricted to the available years of record, and ignores significant high flow events, as it selects the highest for each year. Partial duration series of high flows (PDF) consist of high flows above a pre-defined threshold, and it will include all significant high events above this threshold. Moreover, PDF series can be much longer than the MAF series, as more than one event can be selected per year. Two major concerns are usually connected to the PDF series: the first is the value for the threshold which will affect the size of the series, and the second is the transformation of return periods corresponding to design floods from the PDF domain to the annual domain. A new formula has been derived to transform the return periods from the PDF domain to the annual domain, and results of this new formula have been compared to the commonly used one in the literature. The new formula, which is based on the binomial process, only requires the independence of the flood events, and produces more realistic and reliable values compared to the one available in the literature, which assumes a Poisson distribution for floods above the threshold. Hourly flow series for the Leith (46 years) and the Tokomairiro (21 years, will be referred to as Toko) Rivers in Otago, NZ have been collected from the Otago Regional Council in Dunedin. Independent flood events above several thresholds for both rivers have been identified, along with the maximum annual flows. The cumulative distribution function (CDF) of the PDF series was compared to the CDF of the MAF series for both rivers and has shown the improvement due to smoother and more consistent CDF, which will impact on the ability of any statistical model to simulate these series. Several competitive statistical models, including the Gumbel, GEV and the GP models have been fitted and tested to the MAF series and PDF series (with different sizes) of the Leith and Toko Rivers. The GP model outperformed other models, and thus it was the choice for this study. Model application and testing have shown that fitting the GP model to the PDF series outperformed the MAF series, and resulted in much more reliable model for the simulation of the flood events of these rivers. Testing criteria was based on comparison of the historical and modelled (produced by the model) CDF and histograms, in addition to Kolmogorov Smirnov goodness of fit test, Chi² goodness of fit test and Filliben correlation coefficient. In general, increasing the number of flood events in the PDF series improved the goodness of fit for the fitted GP model for the Toko River, but was limited to an arrival rate (λ) of 4 for the Leith high flows. Thus, a thorough testing for several arrival rates, corresponding to different thresholds, should be carried out for the choice of the best threshold for the PDF series. Study of the impact of the size of the PDF series (bigger λ ) on design floods indicated that, in general, their values will increase with increasing λ. However, the optimum value for λ does not have to be the highest, as was the case for the Leith River.