A direct analysis of flood interval probability using approximately 100-year streamflow datasets

Abstract

Series of observed flood intervals, defined as the time intervals between successive flood peaks over a threshold, were extracted directly from eleven approximately 100-year streamflow datasets from Queensland, Australia. A range of discharge thresholds were analysed that correspond to approximately 3.7 months to 6.3 year return periods. Flood interval histograms at South East Queensland gauges were consistently unimodal whereas those of the North and Central Queensland sites were often multimodal. The exponential probability distribution (pd) is often used to describe interval exceedance probabilities, but fitting utilizing the Anderson Darling statistic found little evidence that it is the most suitable. The fatigue life pd dominated sub-year return periods (<1 year), often transitioning to a log Pearson 3 pd at above-year return periods. Fatigue life pd is used in analysis of the life time to structural failure when a threshold is exceeded and this paper demonstrates its relevance also to the elapsed time between above-threshold floods. At most sites, the interval medians were substantially less than the means for sub-year return periods. Statistically the median is a better measure of central tendency of skewed distributions but the mean is generally used in practice to describe the classical concept of flood return period.Key words Flood frequency analysis; design discharges; partial series, peaks over threshold, annual series, flood interval, return period, probability distribution, nonparametric test. INTRODUCTIONStreamgauge records are statistically analyzed to provide crucial information about the probability of floods, in terms of the frequency and magnitude of peak discharges associated with individual events. Inherent within this type of analysis is the flood return period, defined as the average interval of time within which the magnitude of the event will be equalled or exceeded once (Chow 1964). In this paper, the intervening time between successive exceedances of peak discharge over a threshold is referred to as the flood interval.Flood frequency analysis is based on data pertaining to the independent flood discharge maxima during each year (the annual series) or alternatively the partial series (PS). Various procedures for PS analysis are available; a common three-step approach is described by Kuczera and Franks (2006): (a) A sample of flood peaks is obtained from the streamflow record by selecting peaks that equal or exceed a selected threshold discharge. This sample is the PS, alternatively referred to as the peaks over threshold or partial duration series. An example PS sample including discharges Xi (i=1 to n) ≥ a threshold XT is shown on Figure 1, (b) A statistical distribution relating the flood discharge peaks to exceedance probability (the probability distribution, or pd) is fitted to the sample data, and (c) The probabilities are transformed into 'annualised' return periods, based fundamentally on Equation (1).( 1) where TA (XT) is the return period (in years) of flood threshol...

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