Selection of the best fit probability distribution in rainfall frequency analysis for Qatar
Design rainfall is widely used in urban infrastructure planning and design such as culverts and urban drainage systems. In design rainfall estimation, one of the primary steps is the selection of a suitable probability distribution that fits the observed rainfall data adequately. This study examines...
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| Published in | Natural hazards (Dordrecht) Vol. 86; no. 1; pp. 281 - 296 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Springer Netherlands
01.03.2017
Springer Nature B.V |
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| Abstract | Design rainfall is widely used in urban infrastructure planning and design such as culverts and urban drainage systems. In design rainfall estimation, one of the primary steps is the selection of a suitable probability distribution that fits the observed rainfall data adequately. This study examines the selection of the best fit probability distribution in design rainfall estimation. The annual maximum (AM) rainfall data from 29 rainfall stations in Qatar are used in this study. The rainfall record lengths of these stations are in the range of 24–49 years (average of 36 years). Fourteen different distributions and three goodness-of-fit tests (Kolmogorov–Smirnov, Anderson–Darling and Chi-squared) are considered. Based on a relative scoring method, the GEV distribution is found to be the best fit distribution. Results from bootstrapping and simulation analyses show that sample estimates of skewness of the AM rainfall series are subject to a higher degree of sensitivity to data length compared with standard deviation and mean as expected. Since the rainfall quantile estimates of higher return periods are greatly influenced by skewness, a longer data length is needed in reducing the uncertainty in rainfall quantile estimates for higher return periods, which is currently unavailable in Qatar. |
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| AbstractList | Design rainfall is widely used in urban infrastructure planning and design such as culverts and urban drainage systems. In design rainfall estimation, one of the primary steps is the selection of a suitable probability distribution that fits the observed rainfall data adequately. This study examines the selection of the best fit probability distribution in design rainfall estimation. The annual maximum (AM) rainfall data from 29 rainfall stations in Qatar are used in this study. The rainfall record lengths of these stations are in the range of 24-49 years (average of 36 years). Fourteen different distributions and three goodness-of-fit tests (Kolmogorov-Smirnov, Anderson-Darling and Chi-squared) are considered. Based on a relative scoring method, the GEV distribution is found to be the best fit distribution. Results from bootstrapping and simulation analyses show that sample estimates of skewness of the AM rainfall series are subject to a higher degree of sensitivity to data length compared with standard deviation and mean as expected. Since the rainfall quantile estimates of higher return periods are greatly influenced by skewness, a longer data length is needed in reducing the uncertainty in rainfall quantile estimates for higher return periods, which is currently unavailable in Qatar. Design rainfall is widely used in urban infrastructure planning and design such as culverts and urban drainage systems. In design rainfall estimation, one of the primary steps is the selection of a suitable probability distribution that fits the observed rainfall data adequately. This study examines the selection of the best fit probability distribution in design rainfall estimation. The annual maximum (AM) rainfall data from 29 rainfall stations in Qatar are used in this study. The rainfall record lengths of these stations are in the range of 24–49 years (average of 36 years). Fourteen different distributions and three goodness-of-fit tests (Kolmogorov–Smirnov, Anderson–Darling and Chi-squared) are considered. Based on a relative scoring method, the GEV distribution is found to be the best fit distribution. Results from bootstrapping and simulation analyses show that sample estimates of skewness of the AM rainfall series are subject to a higher degree of sensitivity to data length compared with standard deviation and mean as expected. Since the rainfall quantile estimates of higher return periods are greatly influenced by skewness, a longer data length is needed in reducing the uncertainty in rainfall quantile estimates for higher return periods, which is currently unavailable in Qatar. |
| Author | Mamoon, Abdullah Al Rahman, Ataur |
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| Cites_doi | 10.1016/0022-1694(93)90008-W 10.1007/s11069-016-2576-6 10.1146/annurev.es.04.110173.000325 10.1214/aos/1176343282 10.1007/978-1-4899-4541-9 10.1137/1021092 10.1007/s00704-008-0044-2 10.1016/j.jhydrol.2015.04.043 10.1007/s00477-013-0774-2 10.1016/j.jhydrol.2012.12.005 10.2166/wst.2002.0028 10.1016/j.jhydrol.2015.11.052 10.1016/j.ijsbe.2014.07.001 10.1007/s12517-015-1999-9 10.1007/s00477-010-0412-1 10.1002/2015WR017663 10.1080/02626669909492266 10.1016/0022-1694(84)90008-8 |
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| References | TungYWongCAssessment of design rainfall uncertainty for hydrologic engineering applications in Hong KongStoch Environ Res Risk Assess20142858359210.1007/s00477-013-0774-2 QiWZhangCFuGZhouHImprecise probabilistic estimation of design floods with epistemic uncertaintiesWater Resour Res201610.1002/2015WR017663 BatanounyKHEcology and Flora of Qatar1981QatarUniversity of Qatar PhienHNAjirajahTJApplications of the log-Pearson type-3 distributions in hydrologyJ Hydrol19847335937210.1016/0022-1694(84)90008-8 ZalinaMDDesaMNMNguyenV-T-VKassimAHMSelecting a probability distribution for extreme rainfall series in MalaysiaWater Sci Technol2002452636810.2166/wst.2002.0028 EfronBBootstrap methods: another look at the jackknifeAnn Stat197931189124210.1214/aos/1176343282 KwakuSSDukeOCharacterization and frequency analysis of one day annual maximum and two to five consecutive days maximum rainfall of Accra, Ghana, ARPN J Eng Appl Sci2007252731 OlofintoyeOOSuleBFSalamiAWPhienHNAjirajahTJBest–fit probability distribution model for peak daily rainfall of selected cities in NigeriaN Y Sci J200923312 Tao DQ, Nguyen VT, Bourque A (2002). On selection of probability distributions for representing extreme precipitations in Southern Quebec. In: Annual conference of the Canadian Society for Civil Engineering, 5–8th June, p 1–8 SharmaMASinghJBUse of probability distribution in rainfall analysisN Y Sci J2010394049 OgunlelaAOStochastic analysis of rainfall events in Ilorin,NigeriaJ Agric Res Dev200113950 LeeCApplication of rainfall frequency analysis on studying rainfall distribution characteristics of Chia-nan plain in Southern TaiwanJ Crop Environ Bioinform200523138 Wan ZinWJemainAAIbrahimKThe best fitting distribution of annual maximum rainfall in Peninsular Malaysia based on methods of L-moment and LQ-momentTheor Appl Climatol20089633734410.1007/s00704-008-0044-2 SubyaniAMAl-AmriNSIDF curves and daily rainfall generation for Al-Madinah city, western Saudi ArabiaArab J Geosci201510.1007/s12517-015-1999-9 MamoonAAJeorgensenNERahmanAQasemHDerivation of new design rainfall in Qatar using L-moments based index frequency approachInt J Sustain Built Environ2014311111810.1016/j.ijsbe.2014.07.001 BobeeBCavidasGAshkarFBernierJRasmussenPTowards a systematic approach to comparing distributions used in flood frequency analysisJ Hydrol199314212113610.1016/0022-1694(93)90008-W Noy-MeirIDesert ecosystems: environment and producersAnnu Rev Ecol Syst19734255110.1146/annurev.es.04.110173.000325 SenZEljadidAGRainfall distribution functions for libya and rainfall predictionHydrol Sci J19994566568010.1080/02626669909492266 MamoonAARahmanARainfall in Qatar: is it changing?Nat Hazards201610.1007/s11069-016-2576-6 FadhilahYZalinaMDNguyenV-T-VSuhailaSZulkifliYFitting the best fit distribution for the hourly rainfall amount in the Wilayah PersekutuanJ Teknol200746C4958 ZhangCChuJFuGSobols sensitivity analysis for a distributed hydrological model of Yichun River BasinChina J Hydrol20134801–4586810.1016/j.jhydrol.2012.12.005 HaddadKJohnsonFRahmanAKuczeraGGreenJComparing three methods to form regions for design rainfall statistics: two case studies in AustraliaJ Hydrol2015527627610.1016/j.jhydrol.2015.04.043 QiWZhangCFuGZhouHQuantifying dynamic sensitivity of optimization algorithm parameters to improve hydrological model calibrationJ Hydrol201653321322310.1016/j.jhydrol.2015.11.052 Cunnane, C. 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Water resources investigation report 99–4232 SS Kwaku (2687_CR13) 2007; 2 AO Ogunlela (2687_CR19) 2001; 1 Y Fadhilah (2687_CR7) 2007; 46 W Qi (2687_CR23) 2016 AA Mamoon (2687_CR15) 2016 K Haddad (2687_CR11) 2015; 527 C Zhang (2687_CR33) 2013; 480 AA Mamoon (2687_CR16) 2014; 3 W Qi (2687_CR22) 2016; 533 HN Phien (2687_CR21) 1984; 73 AM Subyani (2687_CR27) 2015 2687_CR29 2687_CR28 B Efron (2687_CR4) 1979; 3 Y Tung (2687_CR30) 2014; 28 2687_CR8 2687_CR3 OO Olofintoye (2687_CR20) 2009; 2 B Efron (2687_CR6) 1993 W Wan Zin (2687_CR31) 2008; 96 K Haddad (2687_CR9) 2010 B Bobee (2687_CR2) 1993; 142 MD Zalina (2687_CR32) 2002; 45 F Johnson (2687_CR12) 2012 B Efron (2687_CR5) 1979; 21 I Noy-Meir (2687_CR18) 1973; 4 C Lee (2687_CR14) 2005; 2 KH Batanouny (2687_CR1) 1981 Z Sen (2687_CR24) 1999; 4 MA Sharma (2687_CR25) 2010; 3 |
| References_xml | – reference: MamoonAARahmanARainfall in Qatar: is it changing?Nat Hazards201610.1007/s11069-016-2576-6 – reference: MamoonAAJeorgensenNERahmanAQasemHDerivation of new design rainfall in Qatar using L-moments based index frequency approachInt J Sustain Built Environ2014311111810.1016/j.ijsbe.2014.07.001 – reference: HaddadKRahmanASelection of the best fit flood frequency distribution and parameter estimation procedure: a case study for Tasmania in AustraliaStoch Environ Res Risk Assess201010.1007/s00477-010-0412-1 – reference: EfronBBootstrap methods: another look at the jackknifeAnn Stat197931189124210.1214/aos/1176343282 – reference: OlofintoyeOOSuleBFSalamiAWPhienHNAjirajahTJBest–fit probability distribution model for peak daily rainfall of selected cities in NigeriaN Y Sci J200923312 – reference: TungYWongCAssessment of design rainfall uncertainty for hydrologic engineering applications in Hong KongStoch Environ Res Risk Assess20142858359210.1007/s00477-013-0774-2 – reference: JohnsonFHaddadKRahmanAGreenJApplication of Bayesian GLSR to estimate sub-daily rainfall parameters for the IDF revision project, hydrology and water resources symposium, 19–22 Nov 20122012SydneyAustralia – reference: Wan ZinWJemainAAIbrahimKThe best fitting distribution of annual maximum rainfall in Peninsular Malaysia based on methods of L-moment and LQ-momentTheor Appl Climatol20089633734410.1007/s00704-008-0044-2 – reference: OgunlelaAOStochastic analysis of rainfall events in Ilorin,NigeriaJ Agric Res Dev200113950 – reference: EfronBTibshiraniRAn introduction to the bootstrap1993Boca RatonChapman & Hall/CRC10.1007/978-1-4899-4541-9 – reference: Noy-MeirIDesert ecosystems: environment and producersAnnu Rev Ecol Syst19734255110.1146/annurev.es.04.110173.000325 – reference: SenZEljadidAGRainfall distribution functions for libya and rainfall predictionHydrol Sci J19994566568010.1080/02626669909492266 – reference: Tortorelli RL, Alan R, Asquith WH (1999). Depth-duration frequency of precipitation for Oklahoma, US geological survey. Water resources investigation report 99–4232 – reference: EfronBComputers and theory of statistics: thinking the unthinkableSIAM Rev19792146048010.1137/1021092 – reference: BatanounyKHEcology and Flora of Qatar1981QatarUniversity of Qatar – reference: SharmaMASinghJBUse of probability distribution in rainfall analysisN Y Sci J2010394049 – reference: ZhangCChuJFuGSobols sensitivity analysis for a distributed hydrological model of Yichun River BasinChina J Hydrol20134801–4586810.1016/j.jhydrol.2012.12.005 – reference: Cunnane, C. (1989). Statistical distributions for flood frequency analysis. Operational hydrological report, No. 5/33, World Meteorological Organization (WMO), Geneva. – reference: Green J, Xuereb K, Johnson F, Moore G. (2012). The revised intensity–frequency–duration (IFD) design rainfall estimates for Australia—an overview. 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| Title | Selection of the best fit probability distribution in rainfall frequency analysis for Qatar |
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