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

Stochastic Environmental Research and Risk Assessment

Volumn 25, Issue 3, 2011, Pages 415-428

  Haddad, Khaled ^a   Rahman, Ataur ^a  

^a UNIVERSITY OF WESTERN SYDNEY   (Australia)

Author keywords

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

Indexed keywords

AKAIKE INFORMATION CRITERION; ANDERSONS; AUSTRALIA; BAYESIAN INFORMATION CRITERION; BAYESIAN MARKOV CHAIN MONTE CARLO; BAYESIAN METHODS; BEST FIT; ESTIMATION PROCEDURES; FLOOD FREQUENCY ANALYSIS; FLOOD FREQUENCY DISTRIBUTIONS; FLOOD QUANTILES; LOG-NORMAL; LOG-NORMAL DISTRIBUTION; METHOD OF MAXIMUM LIKELIHOOD; MODEL SELECTION CRITERIA; MONTE CARLO SIMULATION; PARAMETER DISTRIBUTIONS; PARAMETER ESTIMATE; SECOND ORDERS; SELECTION OF THE BEST; STANDARD ERRORS; TASMANIA;

BAYESIAN NETWORKS; COMPUTER SIMULATION; FLOOD CONTROL; FLOODS; FREQUENCY ESTIMATION; IMAGE SEGMENTATION; MARKOV PROCESSES; MAXIMUM LIKELIHOOD ESTIMATION; METAL ANALYSIS; METHOD OF MOMENTS; NORMAL DISTRIBUTION; PARAMETER ESTIMATION; PROBABILITY; STATISTICAL TESTS;

MONTE CARLO METHODS;

BAYESIAN ANALYSIS; COMPUTER SIMULATION; FLOOD FREQUENCY; FREQUENCY ANALYSIS; MARKOV CHAIN; MAXIMUM LIKELIHOOD ANALYSIS; MONTE CARLO ANALYSIS; NUMERICAL MODEL; PARAMETERIZATION; POWER LAW DISTRIBUTION; PROBABILITY DENSITY FUNCTION;

AUSTRALIA; TASMANIA;

EID: 79952008639     PISSN: 14363240     EISSN: 14363259     Source Type: Journal    
DOI: 10.1007/s00477-010-0412-1     Document Type: Article

References (53)

1. 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): 3369-3382.
2. Bernier J (1967) Sur la thėorie du renouvellement et son application en hydrologie. Electricitė de France, Hyd 67(10): 32 (in French).
3. Bickel PJ, Docksum KA (1977) Mathematical statistics: basic ideas and selected topics. Holden-day, San Francisco.
4. 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.
5. Burham KP, Anderson DR (2002) Model selection and multi model inference, 2nd edn. Springer, New York.
6. Calenda G, Mancini CP, Volpi E (2009) Selection of the probabilistic model of extreme floods: the case of the River Tiber in Rome. J Hydrol 27: 1-11.
7. Casella G, George EI (1992) Explaining the Gibbs sampler. Am Stat Assoc 46(3): 167-174.
8. Chebana F, Ouarda TBMJ (2008) Depth and homogeneity in regional flood frequency analysis. Water Resour Res 44: W11422. doi: 10. 1029/2007WR006771.
9. Cunanne C (1973) A particular comparison of annual maxima and partial duration series methods of flood frequency prediction. J Hydrol 18: 257-271.
10. Cunnane C (1989) Statistical distributions for flood frequency analysis. WMO No. 718, WMP, Geneva.
11. Di Baldassarre G, Laio F, Montanari A (2008) Design flood estimation using model selection criteria. Phys Chem Earth. doi: 10/1016/j. pce. 2008. 10. 066.
12. Fernandes W, Naghettini M, Loschi R (2010) A Bayesian approach for estimating extreme flood probabilities with upper-bounded distribution functions. Stoch Environ Res Risk A 24. doi: 10. 1007/s00477-010-0365-4.
13. Geman S, Geman D (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 6: 721-741.
14. Grubbs FE, Beck G (1972) Extension of sample sizes and percentage points for significance tests of outlying observations. Technometrics 4(14): 847-853.
15. Haddad K, Rahman A (2008) Investigation on at-site flood frequency analysis in south-east Australia. J Inst Eng Malays 69(3): 59-64.
16. Hastings WK (1970) Monte Carlo sampling methods using markov chains and their applications. Biometrika 57: 97-109.
17. Hosking JRM (1990) L-moments analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc Ser B Methodol 52(2): 105-124.
18. Hosking JR, Wallis JR (1993) Some statistics useful in regional frequency analysis. Water Resour Res 29(2): 271-281.
19. Hosking JR, Wallis JR (1997) Regional frequency analysis: an approach based on L-moments. Cambridge University Press, Cambridge.
20. Institution of Engineers Australia (IE Aust) (1987, 2001) In: Pilgrim DH (ed) Australian Rainfall and Runoff: a guide to flood estimation, vol. 1. I. E. Aust. Canberra.
21. Kendall MG (1970) Rank correlation methods, 4th edn. Griffen, London.
22. Kuczera G (1982) Combining site-specific and regional information: an empirical Bayes approach. Water Resour Res 18(2): 306-314.
23. Kuczera G (1983a) A Bayesian surrogate for regional skew in flood frequency analysis. Water Resour Res 1919(3): 821-832.
24. Kuczera G (1983b) Effect of sampling uncertainity and spatial correlation on an empirical Bayes procedure for combining site and regional information. J Hydrol 65: 373-398.
25. Kuczera G (1999) Comprehensive at-site flood frequency analysis using Monte Carlo Bayesian inference. Water Resour Res 35(5): 1551-1557.
26. Kuczera G, Parent E (1998) Monte Carlo assessment of parameter uncertainty in conceptual catchment models: the Metropolis algorithm. J Hydro 211(1-4): 69-85.
27. 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.
28. 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.
29. Lim YH, Lye LM (2003) Regional flood estimation for ungauged basins in Sarawak, Malaysia. Hydrol Sci J 48(1): 79-94.
30. Madsen H, Rasmussen PF, Rosbjerg D (1997) Comparison of annual maximum series and partial duration series methods for modeling extreme hydrological events 1: at-site modeling. Water Resour Res 33(4): 747-757.
31. Markiewicz I, Strupczewski WG, Kochanek K, Singh V (2006) Discussion of Non-stationary pooled flood frequency analysis. J Hydrol 276: 210-223.
32. Martins ES, Stedinger JR (2000) Generalized maximum likelihood GEV quantile estimators for hydrologic data. Water Resour Res 36(3): 737-744.
33. McGilchrist CA, Woodyer KD (1975) Note on a distribution free CUSUM technique. Technometrics 17(3): 321-325.
34. 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 A 23: 119-135. doi: 10. 1007/s00477-007-0201-7.
35. Meshgi A, Khalili D (2009b) Comprehensive evaluation of regional flood frequency analysis by L-abd LH-moments. II. Development of LH-moments parameters for the generalized Pareto and generalised logistic distributions. Stoch Environ Res Risk A 23: 137-152. doi: 10. 1007/s00477-007-0201-7.
36. Metropolis N, Rosenbluth AW, Teller AH, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Phys 21: 1087-1092.
37. Micevski T, Kuczera G (2008) A general and practical Bayesian procedure for regional and at-site flood frequency analysis. In: Proceedings of water down under, Adelaide, Australia.
38. Mitosek HT, Strupczewski WG, Singh VP (2006) Three procedures for selection of annual flood peak distribution. J Hydrol 323: 57-73.
39. Natural Environment Research Council (NERC) (1975). Flood studies report. NERC, London.
40. Onoz B, Bayazit M (1995) Best-fit distribution of largest available flood samples. J Hydrol 167: 195-204. doi: 10. 1016/0022-1694(94)02633-M.
41. Reis R Jr, Stedinger R (2005) Bayesian MCMC flood frequency analysis with historical information. J Hydrol 313: 97-116.
42. Ribatet R, Sauquet E, Michel-Grėsillon J, Ouarda TBMJ (2007) A regional Bayesian POT model for flood frequency analysis. Stoch Environ Res Risk A 21: 327-339. doi: 10. 1007/s00477-006-0068-z.
43. Rosbjerg D, Madsen H (2008) Uncertainty measures of regional flood frequency estimators. J Hydrol 167(1-4): 209-224.
44. 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.
45. Stedinger JR (1980) Fitting lognormal distributions to hydrologic data. Water Resour Res 16(3): 481-490.
46. Stedinger JR, Vogel RM, Foufoula-Georgiou E (1992) Frequency analysis of extreme events. In: Maidment DR (ed) Handbook of hydrology. McGraw-Hill, New York.
47. Strupczewski WG, Singh VP, Feluch W (2001) Non-stationarity approach to at-site flood frequency modeling: I. Maximum likelihood estimation. J Hydrol 248: 123-142. doi: 10. 1016/S0022-1694(01)00397-3.
48. 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. doi: 10. 1016/S0022-1694(01)00563-7.
49. Vogel RM, McMahon TA, Chiew FHS (1993) Flood flow frequency model selection in Australia. J Hydrol 146: 421-449.
50. Wang QJ (1997) LH moments for statistical analysis of extreme events. Water Resour Res 33(12): 2841-2848.
51. Wood EF, Rodriguez-Iturbe I (1975) Bayesian inference and decision making for extreme hydrological events. Water Resour Res 11(4): 533-542.
52. Yang T, Yu Xu C, Xi Shao Q, Chen X (2010) Regional flood frequency and spatial pattern analysis in the Pearl River Delta region using L-moments approach. Environ Res Risk A 24: 165-182. doi: 10. 1007/s00477-009-0308-0.
53. Zucchini W (2000) An introduction to model selection. J Math Psychol 44: 41-61.