Application of Regional Flood Frequency Analysis Based on L-moments in the Region of the Middle and Lower Yangtze River

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1 GIS & S n Hydrology, Water esources and Envronment, Volume, Chen et al. (eds) Applcaton of egonal Flood Frequency Analyss Based on L-moments n e egon of e Mddle and Lower Yangtze ver Chen Yuanfang Wang Qngrong Department of Hydrology and Water resources, Hoha, Unversty anjng 0098,Chna E-mal:yf.chen@jlonlne.com Sha Zhgu,Chen Janch Hydrologcal Bureau of Yangtze ver Commsson Wuhan 000,Chna; MA Fu-mng Hydrologcal Bureau of Quanzhou, Fujang, 6000,Chna Van Gelder, Peter Faculty of Cvl Engneerng and Geoscences, Delft 600 GA, The eerlands Abstract: The regonal flood frequency analyss meod based on L-moments proposed by Hoskng n 997 s appled to e flood frequency analyss of annual maxmum flood volume for fve hydrologcal statons, Ychang, Shash, Hankou, Luoshan and Datong, n e mddle and lower reaches of Yangtze rver. The meod of Hoskng s a new one for Chnese tradtonal regonal flood frequency analyss. The calculated results shows at e fve statons could be consdered as an homogenous regon for frequency analyss, so e ndex-flood meod s used to calculated desgn values for each staton, and e Wakeby dstrbuton s recommended to be populaton grow-curve (or dstrbuton),because e oer dstrbuton,.e., Pearson-III,GLO,GEV,GPA, and GL are not accepted by e Z statstc test. Key words L-moment ; egonal flood analyss; Yangtze rver; Annual maxmum flood volume; Index-flood ITODUCTIO In e flood frequency analyss especally n Chna, man focal pont of research les on e populaton dstrbuton and parameter estmaton for a sngle staton or varable, however how to use fully a regonal flood nformaton s not pad enough attenton. In e practcal flood frequency n Chna, e experence meods are usually used for utlzaton of regonal flood nformaton, for example, we adjust by eye e frequency curve(n Chna, e curve-fttng meod s used for flood frequency calculaton) n comparng w frequency curves of upper or lower statons of desgn staton. Alough t may use some regonal flood nformaton, ere s serous experence treatment and large arbtrarly. Besdes, e Pearson-III dstrbuton recommended by Mnstry of water esources [] s adopted as populaton dstrbuton n

2 most cases of flood frequency analyss n Chna. The statstc test s seldom used for verfy f t s sutable to e observed hydrologcal data whle e practcal flood frequency s done. However Hoskng et al [] developed and formed a set of regonal flood frequency approach based on L-moment rough a lot of researches on e test of consstent of a seres, dvson of regon and dentfcaton of homogeneous regon,selecton of regonal unte dstrbuton functon and ndex-flood et al. Plon and Adamowks [6] stress e mportance of e use of regonal nformaton n a flood frequency analyss, and Gngras and Adamowsk [7] have nvestgated e well performance of e L-moments meod for ese purposes. The approach has been used for precptaton frequency analyss and calculaton n whole Untes States, and e results are satsfed. Also n oer contnents (such as Australa, reported by Pearson et al [5]) e approach s successfully appled. In e utlzaton of regonal flood nformaton and select of populaton dstrbuton, e approach of Hoskng may be more reasonable and objectve comparng to present treatment n Chna. So we try to use e approach of Hoskng on regonal frequency analyss by selectng e mddle and lower reaches of Yangtze rve as a study regon. Some useful results are obtaned rough e study. DATA COLLECTIO AD TEST AALYSIS FO EACH STATIO The procedure of regonal flood frequency proposed by Hoskng et al [] s as follows Data collecton and test analyss dvson of a regon and dentfcaton of homogenous regon selecton of unte regonal populaton dstrbuton determnaton of dstrbuton functon for each staton. In s paper, e annual maxmum 0 days and 60 days flood volumes of sx statons from Ychang to Datong n e Yangtze are collected. The basc nformaton for each staton s lsted n table Table Basc nformaton of 0 and 60 days maxmum flood volume seres of sx hydrologcal statons Staton umb er Staton name Maxmum eturn Perod o of Years of observed Data (n) o of hstorc aldata (a) o of hstorcal Data n e observed data (l) Datong Hankou 5 98 Luoshan 5 98 Shash Ychang Huangzhuan g ote equvalence data years n refers to [] Equvalenc e leng(year s) n Due to e man-made actvtes nfluences,e.g, dverson and detenton of flood,e annual maxmum flood volume seres are not consstent n fact. So e annual maxmum flood volume seres of Ychang,Shash, Luoshan, Hankou, and Datong for our study are obtaned rough rver performng maematcs calculaton,not observed data.. Independent Test

3 For each staton, e front ten order auto-correlaton coeffcents are calculated. The front order auto-correlaton coeffcents of annual maxmum 0 days flood volume seres are lsted n table. Due to e smlar coeffcent results between annual maxmum 0 days flood volume seres and annual maxmum 60 days flood volume seres, no lst n table for e results of annual maxmum 60 days flood volume seres. From table, each staton may be consdered as ndependent. Table esults of trend and ndependent tests for 0 maxmum flood volume seres Staton name r r r u Sample leng (years, n) Datong Hankou Luoshan Shash Ychnag Huangzhuan g ote: u,u are e value of statstc of Kendall, e crtcal value u α =.96 (α=0.05). Test of Consstent The meod of Kendall s used The prncple and procedure of e tests refers to [] e data used for test s observed data(wout hstorcal data) for each staton. The test results for maxmum 0 days flood volume are lsted n table. From e table, all of e oer statons except, may be accepted as no trend or consstent at e sgnfcant level of α=0.05, but staton may be accepted as consstent at a sgnfcant level of α=0.0. The results of maxmum 60 days flood volume seres are smlar to at of 0 days.. Dscordancy measure test It s developed by Hoskng[] Its purpose s to test f ere s an outler and t s consstent n e regon concerned. The detaled meod s descrbed as follows: Suppose at ere are statons n a regon studed, and e sample L-moments ratos estmated for each staton are ( t, t, t, =, Λ, ) T Let u = [ t, t, t ] u = u A = T ( ) = u u A ( u u u u T ( )( ) u D u) Whle D = n e regon concerned for each staton s calculated, e test results may be obtaned. When D value for staton s relatve larger, t ndcates at ere s outler or a trend for staton. The crtcal value of D has a relatonshp w, refers to table.

4 Table Crtcal value D of dscordancy measure test o of Staton D From e table where e results of D value calculated from sample are lsted, The values of D for all of fve statons not staton are smaller an e crtcal value, so ey may be consdered as no trend or no outler n e regon. However, when all of sx statons are consdered as a regon togeer, e D value for staton s a lttle larger an e crtcal value of D, whch ndcates at ere exsts probably a trend or outler for Huangzhang Staton. The test results are smlar to e statstc test n.. From e curve of flood volume w tme of staton, we fnd at ts trend s not so obvous, so all of sx statons staton are fnally consdered as no trend. Table Calculated results of dscordancy measure test for 6 or 5 statons o of Statons D D D D D 5 D 6 5 Statons,not Statons, 5 Statons,not 6 Statons, * * o of Days of flood volume ote * ndcates larger an e crtcal value In summary, e hydrologcal data of all of sx statons may pass e tests of relablty,consstent and ndependent. DIVISIO OF A EGIO AD IDETIFICATIO OF HOMOGEOUS EGIO The dvson of a regon whch contans all watershed of Yangtze or even more larger area has not been done n e paper, however e test of dentfcaton of homogenous regon for mddle and lower reaches n Yangtze rver w 6 statons s carred out. The test meod and results are descrbed as follows. Assume at ere s statons n a regon concerned, for staton w sample leng n and L-moment ratos ( t, t, t, =,Λ, ).The regonal average L-moment ratos are recommended to be calculated bu e followng formulae. t = n t t n t = n t / n = nt / n / The standard devaton of L-moment rato t n a regon concerned w consderaton sample leng as a weght s calculated by followng formula 0 60

5 V = n ( t t ) / n 5 Takng Kappa dstrbuton w four parameters as a populaton dstrbuton for a regon studed, and ts populaton parameters of L-moment ratos are equal to ts regonal average,.e. λ 0 = t 0 = t t 0 = t t 0 = t.whle λ0 t 0 t 0 t 0 are determned e parameters n Kappa dstrbuton functon may be calculated n terms of [].Then s sets of regonal samples may be generated by Monte-Carlo meod, where any two statons have not correlaton and sample leng for each staton s equal to e leng of observed data. For each regonal sample w statons, V = s may be calculated by formulae (),(5). Accordng to s samples results, e mean and standard devaton of V may be obtaned from e followng formulae s s µ V = V, σv = ( V µ V ) 6 s H statstc ndcatng a heterogenety measure for a regon s calculated as follows V H = σ V µ V 7 When H< e regon studed may be accepted as homogenous regon; If H en e regon concerned s probably heterogenety regon If H> en t s an heterogenety regon. Hoskng [] has used Monte-Carlo meod to verfy at H statstc has relatve hgher ablty to dentfy homogenous regon. Therefore above approach s used to de e dentfcaton of Homogeneous regon for mddle ad lower reaches of Yangtze. For smple consderaton, e generatng sample leng for each staton s equal to ts equvalence leng n.s=500.the test results are lsted n table 5. From table 5, t s easly to know at a regon w 6 statons s not accepted homogenous regon,due to very large H values(much larger an ),but for a regon w 5 statons not s accepted by homogenous regon, snce e absolute value of H s less an. So we consder at Datong,Hankou,Luoshan,Shash and Ychang as a homogenous regon for flood frequency analyss. Table 5 esults of homogeneous regon test for flood frequency analyss (H statstcs) o of Statons t t 5 Statons,not 6Statons,ncludn g 5 Statons,not 6 Statons, t V µ V σ V H Days 0 days 60 days SELECTIO OF UITE IBUTIO I A HOMOGEOUS EGIO 5

6 . prncple Suppose at ere are statons n an homogenous regon, each staton w n years data, sample L-moments ratos estmated from observed data ( t, t, t, =, Λ, ) e regonal average of L-moments ratos are t, t, t. For a gven dstrbuton called w more an or equal to parameters alough ts populaton L-moments ratos of second and rd order may take e values of regonal averages t and t ts correspondng four order populaton L-moment rato t s not often equal to t The reason s at t s estmated by sample observed, however t has a relatonshp not only w t t,but also w e dstrbuton form of gven dstrbuton. It s obvous at whle t correspondng w a gven dstrbuton -- s closer to t t ndcates at e dstrbuton selected s better fttng to e observed data. Ths s e prncple of dstrbuton selecton based on L-moment. As for t s usually no-based, t may be somewhat based whle e sample leng s short or populaton t 0. 0 Hoskng et al gave a fttng test statstc of L-moment w consderng e bas of t. Test meod Test statstc: where B Z s ( m) = ( t t ) s m= = ( t + σ t B ) / 8 s ( ) m σ = ( s ) ( t t ) sb 9 m= ( m) t egonal average four L-moment rato for m generatng sample, where e populaton s Kappa dstrbuton w four parameters, ts populaton L-moment ratos take e values of t t t respectvely for each staton has ts sample leng n and ere s no correlaton between each two statons. s The number of regonal sample generatng. The populaton dstrbutons consdered are Generalzed Logstc (GLO), Generalzed Extreme-value (GEV),Generalzed Pareto (GPA),Generalzed Lognormal (GL),Pearson-III. Whle Z.6 en e dstrbuton gven s consdered as a regonal unte dstrbuton. For e effect of dstrbuton selecton by usng above meod, Hoskng[]has used Monte-Carlo experment to do e test, e test results show at 90% populaton dstrbutons accepted are e same as at assumed, so e effect by above meod to select regonal unte populaton dstrbuton s satsfed. In e paper, e unte populaton dstrbuton selecton test results for e homogenous regon of 5 statons are lsted n table 6. Due to all Z values calculated for fve dstrbutons assumed much larger an.6 t ndcates at all fve dstrbutons can not pass above statstc test, so e Wakeby dstrbuton w 5 parameters s fnally selected as e unte regonal dstrbuton for e regon. Accordng to e analyss, t may be caused by e specal flood volume seres whch are not really observed data, but are obtaned rough rver performng maematcs calculaton. We have done e flood frequency analyss for above seres w Pearson--III as populaton, and e results are specal and seldom met, where e quantles estmated by Moment meod are much larger an at estmated by Curve-fttng and L-moment meod. 6

7 Table 6 esults of dstrbuton selecton test based on L-moment Dstrbuto 0 days flood volume 60 days flood volume ns t t Z t t Z GLO GEV GL GPA P-III DETEMIATIO OF IBUTIO FUCTIO FO EACH STATIO The dstrbuton functon of each staton by ndex flood meod s ndcated as follows: X ( p) = u q( p) (0 p, =,, Λ, ) where µ ndex flood actually takes sample mean value of each staton, X (p) dstrbuton functon for staton. q(p)--dmensonless dstrbuton functon b regonalzaton,.e. a grow curve w mean. The quantles of maxmum 0 days and 60 days flood volume are lsted n table 7. Table 7 Estmated results of desgn values of maxmum flood volume for dfferent statons Staton quantles Datong Hankou Luoshan Ychang X P X P X P X P ote P =0.0 P =0.0 P = P =0 6 COCLUSIO The regonal flood frequency meod proposed by Hoskng s frst used n e desgn flood calculaton n mddle and lower reaches of Yangtze rver. Ths study s valuable for open up new dea for hydrologsts especally for Chnese hydrologsts, and t may also help us to obtan more relable desgn results for mddle and lower reaches of Yangtze rver. We hope at e furer applcaton of above regonalzaton meod based on L-moment wll be used n a wder regon, and studyng varables may not only be flood peak or volume, but also precptaton, water levels, and oer hydrologcal quanttes. EFEECES Mnstry of Water esources, Desgn flood calculaton norm for hydraulc and hydropower engneerng [M],Chnese Water esources Publshng House,99 Hoskng J..M. Walls J.. egonal Frequency Analyss An approach Based on 7

8 L-moment(M).London Cambrdge Unversty Press,997,~80 Chen Y.F. Sha Z.G. et al, Study on L-Moment Estmaton Meod for P-III Dstrbuton W Hstorcal Flood,J. Hoha Unversty,, 7-78 Yang Weqng, Gu Lang Tme seres analyss and Dynamc data modelng[m], Bejng Bejng Insttute of Industry Press, Pearson, C.P., McKerchar, A.I., and Woods,.A., 99. egonal flood frequency analyss of Western Australan data usng L-moments. Internatonal Hydrology and Water esources Symposum 99 Part. v n 9 pt. p 6-6. Plon, P.J., and Adamowsk, K., 99. The value of regonal nformaton to flood frequency analyss usng e meod of L-moments, Can. J. Cv. Eng., 9, 7-7. Gngras, D., and Adamowsk, K., 99. Performance of L-moments and nonparametrc flood frequency analyss. Canadan Journal of Cvl Engneerng. v n 5 Oct 99. p