The most direct method of design flood estimation is at-site flood frequency analysis, which relies on a relatively long period of recorded streamflow data at a given site. Selection of an appropriate probability distribution and associated parameter estimation procedure is of prime importance in at-site flood frequency analysis. The choice of the probability distribution for a given application is generally made arbitrarily as there is no sound physical basis to justify the selection. In this study, an attempt is made to investigate the suitability of as many as fifteen different probability distributions and three parameter estimation methods based on a large Australian annual maximum flood data set. A total of four goodness-of-fit tests are adopted, i.e., the Akaike information criterion, the Bayesian information criterion, Anderson-Darling test, and Kolmogorov-Smirnov test, to identify the best-fit probability distributions. Furthermore, the L-moments ratio diagram is used to make a visual assessment of the alternative distributions. It has been found that a single distribution cannot be specified as the best-fit distribution for all the Australian states as it was recommended in the Australian rainfall and runoff 1987. The log-Pearson 3, generalized extreme value, and generalized Pareto distributions have been identified as the top three best-fit distributions. It is thus recommended that these three distributions should be compared as a minimum in practical applications when making the final selection of the best-fit probability distribution in a given application in Australia.

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Abstract:Parametric method of flood frequency analysis (FFA) involves fitting of a probability distribution to the observed flood data at the site of interest. When record length at a given site is relatively longer and flood data exhibits skewness, a distribution having more than three parameters is often used in FFA such as log-Pearson type 3 distribution. This paper examines the suitability of a five-parameter Wakeby distribution for the annual maximum flood data in eastern Australia. We adopt a Monte Carlo simulation technique to select an appropriate plotting position formula and to derive a probability plot correlation coefficient (PPCC) test statistic for Wakeby distribution. The Weibull plotting position formula has been found to be the most appropriate for the Wakeby distribution. Regression equations for the PPCC tests statistics associated with the Wakeby distribution for different levels of significance have been derived. Furthermore, a power study to estimate the rejection rate associated with the derived PPCC test statistics has been undertaken. Finally, an application using annual maximum flood series data from 91 catchments in eastern Australia has been presented. Results show that the developed regression equations can be used with a high degree of confidence to test whether the Wakeby distribution fits the annual maximum flood series data at a given station. The methodology developed in this paper can be adapted to other probability distributions and to other study areas.

Regional flood frequency analysis (RFFA) is often used in hydrology to estimate flood quantiles when there is a limitation of at-site recorded flood data. One of the commonly used RFFA methods is the index flood method, which is based on the assumptions that a region satisfies criterion of simple scaling and it can be treated homogeneous. Another RFFA method is quantile regression technique where prediction equations are developed for flood quantiles of interest as function of catchment characteristics. In this paper, the scaling property of regional floods in New South Wales (NSW) State in Australia is investigated. The results indicate that the annual maximum floods in NSW satisfy a simple scaling assumption. The application of a heterogeneity test, however, reveals that NSW flood data set does not satisfy the criteria for a homogeneous region. Finally, a set of prediction equations are developed for NSW using quantile regression technique; an independent test shows that these equations can provide reasonably accurate design flood estimates with a median relative error of about 27%.

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