The framework of regional analysis allows superior discrimination as well as better identification of the shape of a population distribution in a hydrological frequency analysis. The aim of this study is to incorporate the better of regional concept while performing an at-site frequency analysis. The study proposes a new method in the form of sub-sampling technique with the aid of a regional distribution selection procedure to choose an appropriate probability distribution function for frequency analysis. The technique is evaluated against common distribution selection methods: a widely used goodness-of-fit method in Anderson–Darling (AD) and a popular graphical assessment tool in L-moment ratio diagram (LMRD). The performance is evaluated by applying the technique to gauged annual maximum daily precipitation data series of 24 stations located across China. It is found that the technique accomplished a better performance in discriminating among distributions which or else may not be achievable only by the AD or LMRD test. In general, all results indicate that the proposed technique can be an attractive means in discriminating as well as identifying the best distribution for at-site frequency analysis.
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Bryson MC (1974) Heavy-tailed distributions: properties and tests. Technometrics 16:61–68. https://doi.org/10.1080/00401706.1974.10489150
Cassalho F, Beskow S, de Mello CR et al (2018) At-site flood frequency analysis coupled with multiparameter probability distributions. Water Resour Manag 32:285–300. https://doi.org/10.1007/s11269-017-1810-7
Chen YD, Zhang Q, Xiao M et al (2014) Precipitation extremes in the Yangtze River basin, China: regional frequency and spatial-temporal patterns. Theor Appl Climatol 116:447–461. https://doi.org/10.1007/s00704-013-0964-3
Cunnane C (1988) Methods and merits of regional flood frequency analysis. J Hydrol 100:269–290
Cunnane C (1989) Statistical distributions for flood frequency analysis. Operational Hydrology Report (WMO), Geneva
D’Agostino RB (1986) Goodness-of-fit-techniques. CRC press
Dalrymple T (1960) Flood frequency methods. U. S. Geol. Surv.1543-A,11–51
Das S (2016) An assessment of using subsampling method in selection of a flood frequency distribution. Stoch Env Res Risk A 31:1–13. https://doi.org/10.1007/s00477-016-1318-3
Das S (2018) Goodness-of-fit tests for generalized Normal distribution for use in hydrological frequency analysis. Pure Appl Geophys. https://doi.org/10.1007/s00024-018-1877-y
Das S, Cunnane C (2012) Performance of flood frequency pooling analysis in a low CV context. Hydrol Sci J 57:433–444. https://doi.org/10.1080/02626667.2012.666635
Fowler HJ, Kilsby CG (2003) A regional frequency analysis of United Kingdom extreme rainfall from 1961 to 2000. Int J Climatol 23:1313–1334. https://doi.org/10.1002/joc.943
Heo JH, Shin H, Nam W et al (2013) Approximation of modified Anderson-Darling test statistics for extreme value distributions with unknown shape parameter. J Hydrol 499:41–49. https://doi.org/10.1016/j.jhydrol.2013.06.008
Hosking JRM (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc 52:105–124
Hosking JRM, Wallis JR (1997) Regional frequency analysis: an approach based on L-moments. Cambridge University Press
Institute of Hydrology (1999) Flood estimation handbook, vol 1-5. Institute of Hydrology, Wallingford
Jingyi Z, Hall MJ (2004) Regional flood frequency analysis for the Gan-Ming River basin in China. J Hydrol 296:98–117. https://doi.org/10.1016/j.jhydrol.2004.03.018
Kjeldsen TR, Prosdocimi I (2014) A bivariate extension of the Hosking and Wallis goodness-of-fit measure for regional distributions. Water Resour Res. https://doi.org/10.1002/2014WR015912
Kumar R, Goel NK, Chatterjee C, Nayak PC (2015) Regional flood frequency analysis using soft computing techniques. Water Resour Manag 29:1965–1978. https://doi.org/10.1007/s11269-015-0922-1
Kyselý J, Gaál L, Picek J (2011) Comparison of regional and at-site approaches to modelling probabilities of heavy precipitation. Int J Climatol 31:1457–1472. https://doi.org/10.1002/joc.2182
Laio F (2004) Cramer-von Mises and Anderson-Darling goodness of fit tests for extreme value distributions with unknown parameters. Water Resour Res 40:1–10. https://doi.org/10.1029/2004WR003204
Laio F, Di Baldassarre G, Montanari A (2009) Model selection techniques for the frequency analysis of hydrological extremes. Water Resour Res 45:1–11. https://doi.org/10.1029/2007WR006666
Liang Y, Liu S, Guo Y, Hua H (2017) L-moment-based regional frequency analysis of annual extreme precipitation and its uncertainty analysis. Water Resour Manag 31:3899–3919. https://doi.org/10.1007/s11269-017-1715-5
Mohanty MP, Sherly MA, Karmakar S, Ghosh S (2018) Regionalized design rainfall estimation: an appraisal of inundation mapping for flood management under data-scarce situations. Water Resour Manag 32:4725–4746. https://doi.org/10.1007/s11269-018-2080-8
Norbiato D, Borga M, Sangati M, Zanon F (2007) Regional frequency analysis of extreme precipitation in the eastern Italian Alps and the august 29, 2003 flash flood. J Hydrol 345:149–166. https://doi.org/10.1016/j.jhydrol.2007.07.009
Önöz B, Bayazit M (1995) Best-fit distributions of largest available flood samples. J Hydrol 167:195–208. https://doi.org/10.1016/0022-1694(94)02633-M
Peel MC, Wang QJ, Vogel RM, McMAHON T a. (2001) The utility of L-moment ratio diagrams for selecting a regional probability distribution. Hydrol Sci J 46:147–155. https://doi.org/10.1080/02626660109492806
Politis DN, Romano JP, Wolf M (1999) Subsampling. Springer, New York
Stephens M (1986) Tests based on EDF statistics. In: D’Agostino RB, Stephens MA (eds) Goodness-of-fit techniques. Marcel Dekker, Inc., New York
Sun H, Wang G, Li X et al (2017) Regional frequency analysis of observed sub-daily rainfall maxima over eastern China. Adv Atmos Sci 34:209–225. https://doi.org/10.1007/s00376-016-6086-y
Viglione A, Laio F, Claps P (2007) A comparison of homogeneity tests for regional frequency analysis. Water Resour Res. https://doi.org/10.1029/2006WR005095
Vogel RM, Fennessey NM (1993) L moment diagrams should replace product moment diagrams. Water Resour Res 29:1745–1752
Vogel RM, Thomas WO Jr, Mcmahon TA (1993) Flood-flow frequency model selection in southwestern United States. J Water Resour Plan Manag 119:353–366
Wallis JR, Schaefer MG, Barker BL, Taylor GH (2007) Regional precipitation-frequency analysis and spatial mapping for 24-hour and 2-hour durations for Washington state. Hydrol Earth Syst Sci 11:415–442. https://doi.org/10.5194/hess-11-415-2007
Wang D, Hutson AD (2013) Joint confidence region estimation of L-moment ratios with an extension to right censored data. J Appl Stat 40:368–379. https://doi.org/10.1080/02664763.2012.744386
Wu YC, Liou JJ, Su YF, Cheng KS (2012) Establishing acceptance regions for L-moments based goodness-of-fit tests for the Pearson type III distribution. Stoch Env Res Risk A 26:873–885. https://doi.org/10.1007/s00477-011-0519-z
Yang T, Shao Q, Hao Z-C et al (2010) Regional frequency analysis and spatio-temporal pattern characterization of rainfall extremes in the Pearl River Basin, China. J Hydrol 380:386–405. https://doi.org/10.1016/j.jhydrol.2009.11.013
Zaman MA, Rahman A, Haddad K (2012) Regional flood frequency analysis in arid regions: a case study for Australia. J Hydrol 475:74–83. https://doi.org/10.1016/j.jhydrol.2012.08.054
The research was funded by the Nanjing University of Information Science and Technology (NUIST) in the form of a grant (Grant no. 2243141501015). Comments and suggestions from two anonymous reviewers are gratefully acknowledged.
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Das, S. Assessing the Regional Concept with Sub-Sampling Approach to Identify Probability Distribution for at-Site Hydrological Frequency Analysis. Water Resour Manage 34, 803–817 (2020). https://doi.org/10.1007/s11269-019-02475-6
- Goodness-of-fit test
- At-site frequency analysis
- Regional analysis