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A study on selection of probability distributions for at-site flood frequency analysis in Australia

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Abstract

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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References

  • Akaike H (1973) Information theory and an extension of the maximum likelihood principle, In: Petrov BN and Csaki F (eds) Acad. Kiado′, Budapest Second International Symposium on Information Theory, p 267–281

  • Baldassarre GD, Laio F, Montanari A (2009) Design flood estimation using model selection criteria. Phys Chem Earth 34(10–12):606–611

    Google Scholar 

  • Bates BC, Rahman A, Mein RG, Weinmann PE (1998) Climatic and physical factors that influence the homogeneity of regional floods in south-eastern Australia. Water Resour Res 34(12):3369–3381

    Article  Google Scholar 

  • Bickel PJ, Docksum KA (1977) Mathematical Statistics: Basic ideas and selected topics. Holden-day, San Francisco

    Google Scholar 

  • Bobėe B, Cavidas G, Ashkar F, Bernier J, Rasmussen P (1993) Towards a systematic approach to comparing distributions used in flood frequency analysis. J Hydrol 142:121–136

    Article  Google Scholar 

  • Bureau of Meteorology (BOM) (2012) State of the climate report. Australian Bureau of Meteorology, Melbourne

    Google Scholar 

  • Conway KM (1970) Flood frequency analysis of some NSW coastal rivers. Thesis (M. Eng. Sc.), University of New South Wales, Australia

  • Cunnane C (1985) Factors affecting choice of distribution for flood series. Hydrol Sci J 30:25–36

    Article  Google Scholar 

  • Cunnane C (1989) Statistical distributions for flood frequency analysis, Operational hydrological Report No. 5/33, World Meteorological Organization (WMO), Geneva, Switzerland

  • Grubbs FE, Beck G (1972) Extension of sample sizes and percentage points for significance tests of outlying observations. Technometrics 4(14):847–853

    Article  Google Scholar 

  • Haddad K, Rahman A (2008) Investigation on at-site flood frequency analysis in south-east Australia. IEM J Inst Eng Malays 69(3):59–64

    Google Scholar 

  • Haddad K, Rahman A (2010) Selection of the best fit flood frequency distribution and parameter estimation procedure: a case study for Tasmania in Australia. Stoch Env Res Risk Assess 25:415–428

    Article  Google Scholar 

  • Haddad K, Rahman A, Kuczera G (2011) Comparison of ordinary and generalised least squares regression models in regional flood frequency analysis: a case study for New South Wales. Aust J Water Resour 15(2):59–70

    Google Scholar 

  • Haddad K, Rahman A (2012) Regional flood frequency analysis in eastern Australia: Bayesian GLS regression-based methods within fixed region and ROI framework—quantile regression versus parameter regression technique. J Hydrol 430–431(2012):142–161

    Article  Google Scholar 

  • Haddad K, Zaman M, Rahman A (2010a) Regionalisation of skew for flood frequency analysis: a case study for eastern NSW. Aust J Water Resour 14(1):33–41

    Google Scholar 

  • Haddad K, Rahman A, Weinmann PE, Kuczera G, Ball JE (2010b) Streamflow data preparation for regional flood frequency analysis: lessons from south-east Australia. Aust J Water Resour 14(1):17–32

    Google Scholar 

  • Haddad K, Rahman A, Stedinger JR (2012) Regional Flood Frequency Analysis using Bayesian Generalized Least Squares: a Comparison between Quantile and Parameter Regression Techniques. Hydrol Process 25(1):14. doi:10.1002/hyp.8189

    Google Scholar 

  • Haddad K, Rahman A, Zaman M, Shrestha S (2013) Applicability of Monte Carlo cross validation technique for model development and validation in hydrologic regression analysis using ordinary and generalised least squares regression. J Hydrol 482:119–128

    Article  Google Scholar 

  • Hosking JRM (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J Roy Stat Soc B 52(105):124

    Google Scholar 

  • Hosking JR, Wallis JR (1997) Regional frequency analysis: an approach based on L-moments. Cambridge University Press, Cambridge, UK, p 224

  • Institution of Engineers Australia (I.E. Aust.) (1987) Australian rainfall and runoff: a guide to flood estimation ARR (1987) In: Pilgrim HD (ed) The Institute of Engineers Australia, Canberra (Version 3)

  • Interagency Advisory Committee on Water Data (IAWCD) (1982) Guidelines for determining flood flow frequency: bulletin 17-B. Hydrol. Subcomm., Washington, DC, March 1982, p 28

  • Ishak EH, Rahman A, Westra S, Sharma A, Kuczera G (2010) Preliminary analysis of trends in Australian flood data. In: World Environmental and Water Resources Congress 2010, American Society of Civil Engineers (ASCE), 16–20 May 2010, Providence, Rhode Island, USA, p 120–124

  • Ishak E, Haddad K, Zaman M, Rahman A (2011) Scaling property of regional floods in New South Wales Australia. Nat Hazards 58:1155–1167

    Article  Google Scholar 

  • Ishak E, Rahman A, Westra S, Sharma A, Kuczera G (2013) Evaluating the non-stationarity of Australian annual maximum flood. J Hydrol 494:134–145

    Article  Google Scholar 

  • Kopittke RA, Stewart BJ, Tickle KS (1976) Frequency analysis of flood data in Queensland. In: Hydrological Symposium, Institution of Engineers Australia, National Conference, Publication No. 76/2, 20:24

  • Kuczera G (1999) Comprehensive at-site flood frequency analysis using Monte Carlo Bayesian inference. Water Resour Res 35(5):1551–1557

    Article  Google Scholar 

  • Laio F (2004) Cramer-von Mises and Anderson-Darling goodness of fit tests for extreme value distributions with unknown parameters. Water Resour Res 40:W09308. doi:10.1029/2004WR003204

    Article  Google Scholar 

  • Laio F, Di Baldassarre G, Montanari A (2009) Model selection techniques for the frequency analysis of hydrological extremes. Water Resour Res 45:W07416. doi:10.1029/2007/WR006666

    Article  Google Scholar 

  • McMahon TA, Srikanthan R (1981) Log Pearson III distribution is it applicable to flood frequency analysis of Australian streams? J Hydrol 52(139):147

    Google Scholar 

  • Merz B, Thieken AH (2009) Flood risk curves and uncertainty bounds. Nat Hazards 51:437–458

    Article  Google Scholar 

  • Merz R, Bloschil G, Humer G (2008) National flood discharge mapping in Austria. Nat Hazards 46:53–72

    Article  Google Scholar 

  • Meshgi A, Khalili D (2009a) Comprehensive evaluation of regional flood frequency analysis by L-abd LH-moments. 1. A re-visit to regional homogeneity. Stoch Environ Res Risk Assess 23:119–135. doi:10.1007/s00477-007-0201-7

    Article  Google Scholar 

  • Meshgi A, Khalili D (2009b) Comprehensive evaluation of regional flood frequency analysis by L-abd LH-moments. II. Devewlopment of LH-moments parameters for the generalized Pareto and generalizedlogistic distributions. Stoch Environ Res Risk Asses 23:137–152. doi:10.1007/s00477-007-0201-7

    Article  Google Scholar 

  • Nathan RJ and Weinmann PE (1991) Application of at-site and regional flood frequency analyses. In: Proceedings International Hydrology Water Resources Symposium, Perth, 2–4 October, 769:774

  • Onoz B, Bayazit M (1995) Best-fit distribution of largest available flood samples. J Hydrol 167(195):204

    Google Scholar 

  • Rahman A, Weinmann PE, Mein RG (1999). At-site flood frequency analysis: LP3-product moment, GEV-L moment and GEV-LH moment procedures compared. In: Proceeding Hydrology and Water Resource Symposium, Brisbane, 6–8 July, 2, 715–720

  • Rahman A, Haddad K, Zaman M, Kuczera G, Weinmann PE, Weeks W (2012). Regional flood estimation in Australia: an overview of the study for the upgrade of ‘Australian Rainfall and Runoff’, Hydrology and Water Resources Symposium, Engineers Australia, 19–22 November, Sydney, Australia, 1441–1448

  • Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(461):464. doi:10.1214/aos/1176344136

    Google Scholar 

  • Srikanthan R, McMahon TA (1981) Log Pearson III distribution—effect of dependence, distribution parameters and sample size on peak annual flood estimates. J Hydrol 52(1/2):149–159

    Article  Google Scholar 

  • Strupczewski WG, Singh VP, Weglarczyk S (2002) Asymptotic bias of estimation methods caused by the assumption of false probability distributions. J Hydrol 258:122–148

    Article  Google Scholar 

  • Vogel RM, McMahon TA, Chiew FHS (1993) Flood flow frequency model selection in Australia. J Hydrol 146(421):449

    Google Scholar 

  • Zaman M, Rahman A, Haddad K (2012) Regional flood frequency analysis in arid regions: a case study for Australia. J Hydrol 475:74–83

    Article  Google Scholar 

Download references

Acknowledgments

The data used in this study have been obtained from Project 5, Regional Flood Methods for Australia, in relation to the upgrade of Australian Rainfall and Runoff. The authors would like to acknowledge Professor George Kuczera, Assoc Prof James Ball, Professor Ashish Sharma, Mr Erwin Weinmann, Mr Mark Babister, and Dr William Weeks for their input to the project and two anonymous reviewers whose comments have helped to improve the paper significantly.

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Authors and Affiliations

  1. School of Computing, Engineering and Mathematics, University of Western Sydney, Sydney, NSW, Australia

    Ayesha S. Rahman, Ataur Rahman, Mohammad A. Zaman & Khaled Haddad

  2. Faculty of Engineering, University Putra Malaysia, Serdang, Malaysia

    Amimul Ahsan

  3. Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Melbourne, VIC, Australia

    Monzur Imteaz

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  1. Ayesha S. Rahman
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  2. Ataur Rahman
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  3. Mohammad A. Zaman
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  4. Khaled Haddad
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  5. Amimul Ahsan
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  6. Monzur Imteaz
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Correspondence to Ataur Rahman.

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Rahman, A.S., Rahman, A., Zaman, M.A. et al. A study on selection of probability distributions for at-site flood frequency analysis in Australia. Nat Hazards 69, 1803–1813 (2013). https://doi.org/10.1007/s11069-013-0775-y

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