Selection of the best fit flood frequency distribution and parameter estimation procedure: a case study for Tasmania in Australia

Abstract

Selection of a flood frequency distribution and associated parameter estimation procedure is an important step in flood frequency analysis. This is however a difficult task due to problems in selecting the best fit distribution from a large number of candidate distributions and parameter estimation procedures available in the literature. This paper presents a case study with flood data from Tasmania in Australia, which examines four model selection criteria: Akaike Information Criterion (AIC), Akaike Information Criterion—second order variant (AICc), Bayesian Information Criterion (BIC) and a modified Anderson–Darling Criterion (ADC). It has been found from the Monte Carlo simulation that ADC is more successful in recognizing the parent distribution correctly than the AIC and BIC when the parent is a three-parameter distribution. On the other hand, AIC and BIC are better in recognizing the parent distribution correctly when the parent is a two-parameter distribution. From the seven different probability distributions examined for Tasmania, it has been found that two-parameter distributions are preferable to three-parameter ones for Tasmania, with Log Normal appears to be the best selection. The paper also evaluates three most widely used parameter estimation procedures for the Log Normal distribution: method of moments (MOM), method of maximum likelihood (MLE) and Bayesian Markov Chain Monte Carlo method (BAY). It has been found that the BAY procedure provides better parameter estimates for the Log Normal distribution, which results in flood quantile estimates with smaller bias and standard error as compared to the MOM and MLE. The findings from this study would be useful in flood frequency analyses in other Australian states and other countries in particular, when selecting an appropriate probability distribution from a number of alternatives.

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Acknowledgments

The authors would like to thank Hydro Tasmania for providing the data for this study as part of the development of regional flood frequency estimation techniques that are being undertaken for revision of Book 4 Australian Rainfall and Runoff. The authors would also like to thank Department of Climate Change and Engineers Australia for providing financial support for this research and Dr Fiona Ling, Professor George Kuczera, Associate Professor James Ball, Mr Erwin Weinmann, Dr William Weeks and Mr Mark Babister for their input to the project. Finally, the authors would like to acknowledge the comments and suggestions by three anonymous reviewers which have helped to improve the paper notably.

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Correspondence to Ataur Rahman.

Appendix

Appendix

See Tables 4 and 5.

Table 4 List of the selected stream gauging stations from Tasmania, Australia
Table 5 Summary of goodness of fit tests using the four model selection criteria

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Haddad, K., Rahman, A. Selection of the best fit flood frequency distribution and parameter estimation procedure: a case study for Tasmania in Australia. Stoch Environ Res Risk Assess 25, 415–428 (2011). https://doi.org/10.1007/s00477-010-0412-1

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Keywords

  • Flood frequency analysis
  • Monte Carlo simulation
  • Bayesian method
  • Floods
  • Tasmania