Design flood calculation for ungauged small basins in China

Transcription

1 236 Preicions in Ungauge Basins: PUB Kick-off (Proceeings of he PUB Kick-off meeing hel in Brasilia, November 2002). IAHS Publ. 309, Design floo calculaion for ungauge small basins in China YUANFANG CHEN, GUOXIN CHEN, ZENGCHUAN DONG & SHENGHUA GU 2, SHUJIAN LI College of Hyrology an Waer Resources, Hohai Universiy, Nanjing, 20024, China 2 General Hyrological Saion of Shanghai, Shanghai, , China Absrac The wo main mehos for calculaing he esign floo in ungauge waershes are inrouce in his aer. The Raional Meho, which is wiely use in China, is escribe. Is esign sorm formula form an arameer esimaion meho, he erivaion rocess for he esign eak floo, Q, Raional Formulae, an a case suy in Jiangxi rovince, are inrouce an escribe in eail. A brief inroucion o he secon meho, he Eirical Formula Meho, is rovie. Keywors esign floo calculaion; ungauge basin; Raional Formula; Eirical Formula; case suy INTRODUCTION In China, many reservoirs have been consruce an ohers have ye o be consruce. The saisics of he Miniser of Waer Resources show ha a oal of abou reservoirs were consruce in he as 50 years, of which 360 are very large; he majoriy of he reservoirs are mile- an small-size ones. The siuaion is ha here is usually no aa for ischarge an reciiaion in mos of he small basins in China, esecially for he years from 960 o 970. I is herefore necessary for us o ay more aenion o he esign floo calculaion for ungauge small basins. A lo of suies an analyses show ha here are hree feaures o he esign floo calculaion for small reservoirs in China: (a) he meho shoul be suiable for basins wihou floo an reciiaion aa; (b) he meho shoul be sile, since he number of reservoirs is so grea, an esigners for esign floo calculaion are usually no well secialize; (c) he main focus is usually he esign floo eak, no he esign floo hyrograh. Four mehos (Zhang Daojiang, 2002) are use o calculae he esign floo in ungauge small basins in China: he Chinese Raional Formula Meho; he Eirical Formula Meho; use of he Nash insananeous uni hyrograh o o some regionalizaion work; he so-calle invesigaion of hisorical floos meho. As a conribuion o he IAHS PUB meeing, he firs wo, he mos wiely use mehos, are inrouce. Coyrigh 2007 IAHS Press

2 Design floo calculaion for ungauge small basins in China 237 CHINESE RATIONAL FORMULA METHOD The esign sorm formula, he erivaion of he Q raional formulae an a case suy are escribe. Design sorm formula The esign formula has he form: - n x = s, a = s () where x is he esign sorm in uraion hours wih an exceeence robabiliy (mm); a is he esign sorm ensiy in uraion hours wih exceeence robabiliy (mm h - ); is sorm uraion (usually 24 hours); S is x wih = hour; n is he sorm arameer, o be eermine by he regionalizaion meho, n = The arameer n is eermine as follows: In a large region incluing he ungauge basins, he firs se is o calculae he n value for basins wih observe reciiaion aa in he region, hen o eermine he n value by he regionalizaion meho for ungauge basins (by aking he mean value of n, or by ivision of sub-regional values of n, or use of an isogram of n). In racice, n may be obaine by reaing u he relevan rovincial an naional hyrological hanbooks which collec ogeher he regionalizaion resuls of rovincial or naional ranges. The eerminaion of n in a basin wih observe aa is shown in Fig.. In Fig., he x-axis is log(), is sorm uraion; he y-axis is log(a ), an n is he negaive sloe of he curve. In some cases, he sloes when h an h are ifferen, so n is usually ivie ino wo values, i.e. n = n 2, when h, n = n when h. For he eerminaion of S, he following formula is use: S = X 24 /24 -n (2) Fig. Deerminaion of n in a basin wih observe aa.

3 238 Chen Yuanfang e al. where X 24 is eermine by he regionalizaion meho. There are usually wo ways: by using he isogram of he mean an Cv of he annual maximum 24 hour reciiaion; Cs/Cv has an isogram in naional an rovincial ranges; by using he annual maximum aily reciiaion aa, x24 = k x, where k is a coefficien ha is larger han. Derivaion of Q by he Raional Meho There are four ses o eriving he Q Raional formulae: (a) he consrucion of he esign sorm rocess; (b) runoff generaion ime c an amoun of runoff (hr) calculaion formulae; (c) eirical calculaion formula of basin concenraion ime τ; () Q formula erivaion by he raional rincile. Design sorm rocess The esign sorm rocess curve consruce is inicae in Fig. 2 where he y-axis sans for he insananeous reciiaion ensiy ( i ), an he x- axis is accumulae ime of reciiaion (x).. Fig. 2 Design sorm rocess curve. There are four feaures o he curve of esign sorm rocess: when x ens o he cenre, x 0,i(x0) (he insananeous reciiaion ensiy) is infinie; i is a symmerical curve wih a cenre x 0 ; he shae area A is equal o x = s n ; here is no exlici formulaion.

4 Design floo calculaion for ungauge small basins in China 239 In fac, he same frequency meho for all uraions is use o obain he esign sorm rocess. I means ha he maximal sorm value for all uraions in he sorm rocess curve is equal o he esign sorm value. Runoff generaion ime c an runoff hr calculaion For siliciy, he loss rae of reciiaion is consiere as a consan μ. Accoring o he analysis, he relaionshi beween insananeous reciiaion ensiy i an sorm uraion is as follows: x ( s ) n i( ) = = = ( n) s (3) Le i() = μ, in his case, is equal o c. c ( n) s = μ n The amoun of runoff generaing hr of esign sorm uring c (4) hr = s c μ c = s c ( n) s c c = ns c (5) Calculaion of basin concenraion ime, τ Using he eirical formula roose by Chinese hyrologiss: τ = / 3 / L /( mj Q ) (6) where L is river lengh (km); J is average longiuinal graien; m is he concenraion arameer; an Q is he esign eak ischarge (m 3 s - ). Q formula erivaion by he raional meho The General Raional formulae of Q has wo cases, c τ an c τ (Fig. 3). For c τ, hen: Q hτ = 0.278( aτ μ) F = F (7) τ For c τ, hen: Q hr = F (8) τ The raional formulae roose by Chinese hyrologiss use combinaions of equaions (), (5), (6), (7) an (8). For c τ, hen: Q n = 0.278( s τ μ F m )

5 240 Chen Yuanfang e al. (a) (b) Fig. 3 Design sorm rocess in cases of c τ an c τ. 3 / 4 an τ = L /( mj / Q ),The former air of equaions are calle equaions (a). For c τ, hen: ns c Qm = 0.278( ) F τ 3 4 an τ = L /( mj / Q / ). These wo equaions are calle equaions (b) In orer o solve he above equaions, one nees o know he following seven arameers: F, L, J, n, S, μ an m. The recommene roceure for solving equaions(a)(b) is as follows: Deermine he above seven arameer values. Assume c τ, hen use he iagram meho (Fig. 4) o solve equaions (a), when Q is solve, use equaion(4) o calculae c value. If c τ, i inicaes ha he above assuion is correc. So he Q calculae is he resul exece, or else urn o solve anoher se of equaions (b) Fig. 4 Diagram meho o calculae Q for raional formulae.

6 Design floo calculaion for ungauge small basins in China 24 CASE STUDY A small reservoir is o be consruce in Jiangxi rovince, China. Calculaion of he esign eak ischarge wih he reurn erio of 00 years by he raional meho is require. The roceure of Q calculaion is as follows: Deerminaion of basins arameers F, L an J Using o oograhic ma, i is easy o measure F an L. For he basin suie, F = 04 km 2, L = 26 km, J = Deerminaion of sorm arameers n, S In erms of he hyrological hanbook of Jiangxi rovince, n 2 is The arameers of annual maximal aily reciiaion are: x = 5mm, Cv = 0.42, Cs = 3.5Cv x =.x s 24 = x 24,, 24 n 2 = 84.8mm / h Deerminaion of μ an m Accoring o hyrological hanbook, he value of μ is 3.0 mm h -, an m = 0.7. Use iagram meho o solve raional equaions Assume c τ, so Q an τ can be eermine by solving he following wo equaions: Q = τ 50. τ = 4 Q Table Relaionshi of Q an τ. Q = f(τ) τ = f(q ) τ Q Q τ From he Fig. 3, Q = 50 m 3 s -, an τ = 0.55 h. Check c an τ. ( n s n 2) c = = = 57h 3.0 μ since τ = 0.55 h < c = 57h, he above assuion is correc. So he esign eak ischarge Q = 50 m 3 s - ( = %). 0.

7 242 Chen Yuanfang e al. OTHER Q CALCULATION METHODS FOR SMALL UNGAUGED BASINS The Eirical formula meho is briefly escribe below. For oher Q calculaion mehos for small ungauge basins, lease refer o oher references. Single facor formula Q = C F n where C is he corehensive coefficien, n is an eirical inex ha is relae o basin area. Mulile facors formulae Q = Ch 24 F n Q = Ch α 24f γ F n in which f is equal o F/L 2 ; h 24 is he esign annual maximal excess rain for 24 hours (mm); α, γ an n are inexes; an C reresens corehensive coefficiens. CONCLUSION I is very ioran o research he esign floo for ungauge small basins. Some sile mehos incluing he raional formula an eirical formula have been eveloe an are racise in China. These may also be use in basins ousie of China, bu i is sill necessary o o some work in orer o moify hem because here are some assuions which are no suiable o real cases. REFERENCE Zhang Daojiang, Ye Shouze e al. (2002) Engineering Hyrology. China Waer Conservancy an Hyroower Publishing House, Beijing, China.