Determination of the Nonlinear Muskingum Model Coefficients Using Genetic Algorithm and Numerical Solution of the Continuity Equation

Transcription

1 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR) ISSN (Prn & Onlne) hp://gssrr.org/nde.php?journal=journalofbascandappled Deermnaon of he Nonlnear Muskngum Model Coeffcens Usng Genec Algorhm and Numercal Soluon of he Connuy Equaon Mohammad Shayannejad a, Nahd Akbar b, Kaveh Osad Al Askar c* a Assocae Professor, Waer Engneerng Deparmen, Isfahan Unversy Of Technology, Isfahan, Iran b MSc suden, Irrgaon and Dranage engneerng, Isfahan Unversy of Technology, Isfahan, Iran c Deparmen of Waer Engneerng, Faculy of Cvl Engneerng, Najafabad Branch, Islamc Azad Unversy, Najafabad, Isfahan, Iran a Emal: shayannejad@cc.u.ac.r b Emal: Akbar.n.9@gmal.com c Emal: Kaveh.oaa000@gmal.com Absrac The opmzaon mehod s an approprae choce for deermnng opmal parameers n he Muskngum model, n order o ncrease he speed of compuaons; coeffcens of hs model have been compued opmally wh asssance of he genec algorhm. These coeffcens were compued from he lnear Muskngum and Muskngum-Cunge models usng requred daa and he avalable relaons. In order o evaluae effcency of he procedure of opmzng coeffcens of he nonlnear Muskngum model va he genec algorhm mehod compared wh he oher wo mehods used for deermnng hese coeffcens, ouflow hydrographs were compued usng he opmal coeffcens and solvng he connuy equaons accordng o he Runge-Kua mehod order 4 and was compared wh he wo flood roung mehods from he Muskngum and Muskngum- Cunge models as well * Correspondng auhor. E-mal address: Kaveh_oaa00@yahoo.com

2 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp -4 To sudy he precson of hese hree mehods, square roo of sum of squares of dfference of dscharges compued from each of he hree mehods and observaonal dscharges obaned from he HEC-RAS RMSE sofware was used as he objecve funcon and acheved resuls ndcae more promy of he compued hydrographs from he opmzaon coeffcens n he Runge-Kua order 4 o he ouflow hydrographs obaned o he HEC-RAS sofware compared wh he wo Muskngum and Muskngum-Cunge models. Keywords: Flood roung; Muskngum model; Muskngum-Cunge model; Opmzaon; Genec algorhm; HEC-RAS sofware. Inroducon The problem of dsperson of flood wave along a rver lengh and deermnaon of flood dscharge a specfed secons and mes has numerous applcaons n reducng flood damage, desgnng of hydraulc srucures, and waer plannng. To esmae he flood wave movemen, flood roung can be used. Flood roung consss of compuaonal operaons whch predc he velocy value and he flood shape as a funcon of me a one are more pons along he waerways []. Flood roung s performed n accordance wh he procedures ha eher drecly or ndrecly are resuled from he San Venan Equaons. Flood roung operaons are dvded n o wo hydraulc and hydrologc mehods. In case flow roung s consdered as a funcon of me and locaon, along he sysem s a hydraulc or dsrbuonal roung. Hydraulc roung mehods, regardng he erms seleced from he movemen sze equaon are dvded nfo he hree caegores of knemac, dffuson and dynamc waves. On he oher hand f he waer flow s only roued as a funcon of me a a specfed locaon, s called he hydraulc or concenraed roung. In hs mehod, he flow connuy equaon, naural hydrographs and unque, dscharge and mamum surface balance of he flood are used. Usng he hydrologc mehod, alhough lackng precson of he hydraulc procedure, s very easly performed and s used wh an accepable confdence n desgnng srucures and conrollng floods []. Amongs he hydrologc flood roung mehods, he Masnum, Muskngum -Cunge, Kano and Akn mehods can be named. Muskngum mehod s one of he hydrologc mehods whch have eensve applcaons for flood roung. In hs mehod, roung parameers are deermned based on he upsream and downsream hydrograph of a flood ha has prevously accruedn he regon and by assumng he esence of a lnear relaon beween he rver sorage and oher hydraulc facors ncludng he nflow and ouflow dscharges. The lneary assumpon of he relaon beween he rver sorage and oher hydraulc facors s no eac herefore alers he mehod s precson. Anoher lmaon of hs mehod s he need o calbraon. Therefore auhores were persuaded o offer more precse and move comprehensve mehods. The Muskngum -Cunge mehod s one of such mehods n whch flood roung s performed hrough he knemac wave wh he dfference ha he knemac wave equaons have been changed o he dsperson wave wh he nfne dfference mehod. Cunge [3] showed ha he Muskngum mehod resembles he dsperson ransfer equaon and s resuls are smlar o hose of he lner knemac mehod. Through runcang he knemac wave equaon and accommodaon of he numercal dsperson wh he physcal dsperson modfed he Muskngum mehod. In hs manner, parameers of he Muskngum -Cunge mehod are compued based on physcal specfcaons of he rver. Ponce and hs colleagues [4] suded he Muskngum Cunge mehod wh wo, hree and four pon s varable parameers. Ther resuls revealed ha he wo-pon mehod does no show an approprae precson for compung he mamum dscharge and he me of s occurrence.

3 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp -4 On he oher hand, he hree and four pon mehod s suable. Vcor and hs colleagues [5] compared he Muskngum -Cunge model wh a dynamc wave model and found ou ha hs model enjoys suable correcness and precson. Researcher appled he Muskngum -Cunge and Muskngum mehod o flood roung n he Lqvan rver and observed ha he resuls obaned of he roued flow by he wo models show a sgnfcan dfference wh he real resuls regsered n he low sream hydromeer saon and menoned as cause of hs dfference he regon beng mounanous, presence of underground drans a he nerval beween he wo up-and low sream saons [6]. Ponce and hs colleagues [4] suded he effcency rae of he Muskngum -Cunge mehod and found ou ha hgh correspondence beween he resuls and compuaonal hydrographs and observaons ndcae hgh effcency of hs mehod amongs he flood roung mehods. Karahan and hs colleagues [7] suded he applcably of he calbraed Muskngum mehod for flood roung n he waershed basn of he Manahad rver n Inda and concluded ha hs mehod afer beng calbraed hrough approprae modfcaons, can be used for a locaon and a suaon lke ha of he Manahad waershed basn [8]. The crucal pon n solvng he nonlnear Muskngum equaons s he necessy of approprae esmaon of he hree parameers presen n hs equaon whch hghly nfluence he roung resuls and her compuaon va numercal and ral and error mehods s dffcul. So far, mach sudes have been performed on esmang he lnear and nonlnear Muskngum Coeffcens. Sephanson [9] usng he lnear plannng mehod opmzed he lnear Muskngum wave parameers. Nowadays, employmen of modern nellgen mehods for predcng and opmzaon has been consdered by he researchers. Gll and hs colleagues [8] usng he leas squares mehod (LSM) opmzed he lnear Muskngum model parameers. Resuls of he research revealed hgh precson of hs mehod compared wh he ral and error mehod. Followng hem, Tung and hs colleagues [0] based on he Hook-Gouse mehod, combned wh he lnear regresson mehods (HJCG), appled he concurren slope and he DFP mehod for opmzng hese parameers resuls of whch ndcaed ha usng he (HJCG) and (HJDFP) mehods compared wh he Gale work beer. Researcher appled he parcle se opmzaon (PSO) algorhm for esmang parameers of Muskngum nonlnear model resuls revealed ha he PSO algorhm enjoys a hgh precson for esmang parameers of he Muskngum nonlnear model []. Muhan [] showed ha all he prevous mehods do no ensure achevng an absolue opmal response and wll be snared n he rap of local opmal responses. He employed GE for esmang he model parameers and resuls showed ha esmaon va GA s beer ha he prevous mehods and does no need o a prmary esmaon close he opmal response. In hs research, for he purpose of consderably ncreasng he speed of eecung compuaons of he flood roung model n he rvers, he dea of opmzng coeffcens of he nonlnear Masngum hydrologc mehod by he asssance of he genec algorhm has been used. Regardng he fac ha deermnaon of he and k coeffcens n he Muskngum mehod va he convenonal mehods needs repeve compuaons and s very me consumng, he dea of opmzng hese coeffcens wll undoubedly lead o decreased me for eecung he compuaons. In order o evaluae effcency of he opmzaon mehod n hs research, he compued coeffcens of he Muskngum and Muskngum -Cunge lnear model for flood roung were used and rougng was performed hrough solvng he dfferenal equaons of frs order by he Fung-Kua order 4 and resuls obaned of hs mehod were compared wh ouflow hydrographs compued by he hydrologc mehods lke Muskngum and Muskngum -Cunge model n 5 flood ouflows generaed by he HEC-RAS as well. 3

4 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp -4.. Hydrologc roung based on he connuy equaon.. The Muskngum model One of he flood roung mehods was frs appled n 938 by Mc Cary and he group of engneers of he USA army n connecon wh he flood conrol plans a he Muskngum Rver basn n Oho Sae and was nroduced. Hydrologc flood roung n he rvers can be performed va varous mehods amongs whch he Muskngum and Muskngum -Cunge mehods are worh menonng. Ths mehod s a lnear roung mehod n he rvers whch due o scarcy of requred parameers has been always consdered by he hydrology engneers. Ths mehod s based on he connuy equaon: ds d = I( ) O( ) () n whch S sands for waer sorage volume of he rver, I s dscharge of he nflow flood, and O s dscharge of he ouflow flood. In he lnear Muskngum model, waer sorage n dvded no wo caegores of prsmac sorage ko and he wedge sorage k(i-o). Wh he assumpon ha he sorage volume s a lnears funcon of he nflow and ouflow flood, n wo emporal seps and he lnear sorage equaon can be appled as follows: [ I ( O ] S = k ) () Through wrng he form of fne dfference equaons and, and her combnaon and fnally her smplfcaon we arrve o he followng equaon based on whch roung can be done. Oc = C0I CI C O (3) C 0 = k k k (4) C = k k k (5) C = k k k k (6) In he even of nflow and ouflow daa beng unavalable, k desgnaes he rver ravers me, and s an undeermned coeffcen whch ndcaes mporance degree of I and O. Mnmum value of s zero and should no be less han k or more mamum value s 0.5 and on he average changes beween 0. and 0.4. han k. such condons are consdered for he purpose of prevenng coeffcens o become negave and for avodng numercal nsably so ha hydrograph of he flood ouflow can be compued. The mos mporan 4

5 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp -4 sage of compuaons s deermnaon of and k coeffcens ha n case of nflow and ouflow hydrographs of a flood ncden a he channel or rver nerval beng avalable, he can be esmaed. One of hese mehods s he old ral and error graphcal mehod developed by Mc Cary (938) for he Muskngum lnear model. Sages for deermnaon of and k coeffcens n he Muskngum model hrough he ral and error graphcal mehods are as follows:. Suable values for and k coeffcens of he Muskngum model are seleced and hen he [I (-)O] value s compued consderng values of he and k coeffcens.. In each emporal perod, (I-O) values of observaonal nflow ouflow hydrographs beng he real sorage are compued. Snce of we subrac he nflow and ouflow hydrographs, sorage modfcaons a varous obaned he relaon of whch wll be: are S = ( I O) d 0 (7) 3. Now, for each, havng S (real sorage) and I(-)O n a sysem of coordnae aes draw he I(-)O, wll be observed ha he curve obaned from connecng varous loop pons wll be found ha s he value seleced for has no been correc once agan we selec anoher value for and he same scenaro s repeaed. I wll be consdered ha n case s appropraely seleced, he loop becomes narrower and wll resemble a lne. 4. The nverse lne slope (loop) wll be he k value A crucal and fundamenal ssue n he Muskngum mehod n ha he and k parameers have no physcal meanng and hey can be compued only n he even of nflow and ouflow hydrographs of a flood ncden beng avalable..3. The Muskngum Cunge model Ths problem has been solved n he Muskngum-Cunge mehod where he and k parameers are epressed accordng o he physcal properes of he channel nerval: k = c k = dq da (8) Q = Bck s0 (9) 5

6 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp -4 In he above equaons, Q sands for he reference dscharge, B s wdh of he upper level of waer relevan o he base dscharge, and so s he longudnal lengh of he channel s lengh of he channel and ck s he wave ransfer. Procedure s so arranged ha a frs he medum dscharge s seleced as he base dscharge. Selecon of he medum dscharge as he reference dscharge s done hrough he ral and error mehod. In he ne sep, usng he Munng relaon, value of he normal deph s commued. Followng deermnng he normal deph, hydraulc parameers of he flow such as hydraulc deph (D), and upper wdh of he flow (T) a each secon can be deermned. C0, C, C coeffcens are also compued usng he 4 o 6 equaons and fnally ouflow dscharge can be compued va equaon Numercal soluon of he connuy equaon usng he Runge-Kua mehod order 4. Alhough he lnear form of he Muskngum model has a broad applcaon for flow roung however, n he majory of rvers, here governs a nonlnear relaon beween he dscharge and he sorage. Ths ssue s a move for employmen of he Muskngum lnear model o appear napproprae o a grea degree and can brng abou sgnfcan errors n predcng he flow suaon. Gll and hs colleagues [8] suggesed he relaon of he Muskngum nonlnear model a he emporal sep and n he form of equaon 0: [ I ( O ] m S = k ) [ I O ] m S = k ( ) (0) () In he Muskngum nonlnear model, he m parameer has been added as power o he equaon, whch enables he model o beer model he nonlnear relaon beween he cumulave sorage and he flow. Consderng he equaon, ouflow dscharge can be obaned n he emporal sep from he relaon. O S m = I k () In combnaon wh he connuy equaon we have: ds d m S = k I (3) Relaon 5 s a dfferenal equaon of frs order ha can be solved va varous mehods of whch s he Runge- Kua order 4 as follows: S 6 ( K K K K ) = S 3 4 (4) 6

7 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp -4 In he above sad relaon k o k4 are values of he Runge-kua order 4 coeffcens whch are obaned of he followng relaons: = m I k S K (5) = m I I k K S K (6) = 3 m I I k K S K (7) = 3 4 m I k K S K (8) Therefore for deermnng he ouflow hydrograph, he followng seps should be aken. Sep one: Compuaon of S based on relaon 0 and n echange for O and I. Sep wo: Calculaon of S from he relaon4. Sep hree: Calculaon of O based on relaon. Therefore, hrough hs procedure n he even of values of he parameers, k and m beng known, he hydrograph can be deermned. Snce he ouflow hydrograph has been compued by he HEC-RAS sofware, unknowns of he Muskngum nonlnear model n he above relaons wll be he coeffcens of hs model whch, for each developed ouflow hydrograph of he sofware whch bear parcular geomerc and hydraulc specfcaons, opmal coeffcens of he nonlnear Muskngum model are obaned. As was poned, he genec algorhm (GA) s an approprae choce oo deermnaon of opmal parameers n he Muskngum nonlnear model. Resuls of comparson of hs mehod wh oher mehods of esmang nonlnear parameers of he Muskngum model. Lke opmzaon n ecel sofware has shown ha he genec algorhm mehod s sensbly superor o hese mehods. Therefore, he genec algorhm was used o deermne opmal coeffcens of he Muskngum nonlnear model. Such sages were performed usng programmng n MATLAB sofware.. Deermnaon of he Muskngum nonlnear model coeffcens va he genec algorhm Regardng mporance of opmzaon n he feld of engneerng scences and oher dscplnes, durng he recen years much aemp has been n hs regard and numerous mehods have been employed and n deermnng he Muskngum model parameers oo opmzaon has been used. X, k and m parameers hrough 7

8 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp -4 convenonal procedures requre repeaed and very me consumng compuaons. Employmen of opmzaon mehods ncludng algorhm lead o reduce of compuaons and ncreased precson. Amongs nellgen algorhms, he genec search mehod he dea of whch has been adaped from he sysem of naural evoluon of lvng creaures (gene and chromosome), as he modern mehod of opmzng nonlnear models, s very approprae and has frequen eses applcaon [8]. 3. Genec algorhm Genec algorhm ess and eamnes he algorhms developed based on he meanng of naural srucures and her naural genecs. Ths mehod has wde applcaons n engneerng ssues such as opmzaon of he flow nework n he ppes, consruconal srucures, deermnaon of culure opmzed model, deermnaon of flow dscharge of compose secons, calbraon of ran-run off and underground waers. [8, 4]. Also hese mehods have been wdely appled n hydraulc models. The opmzaon process n genec nvesgaon s such performed ha a frs, a prmary populaon s creaed and hen s mulpled, bears muaon and genec echange s performed on hs populaon. Frsly some responses whn he lm of modfcaon of parameers are esmaed and hrough converng hese numbers o zero and one chans, values of objecve funcon n leu of hs response value are obaned. In hs research, k and m parameers of he Muskngum nonlnear model wll be opmzed. The modfcaon lm for s beween 0 and 0.5. For k however, no lm has been defned. Then usng he roang wheel (roulee) mehod, he chans for whch he objecve funcon s mnmzed reman and he res are omed. Followng selecon of Chans and hrough choosng he probably percenage of he approprae combnaon, loc of he funcon of chans are seleced for echange of nformaon. In he manner ha a pon of he daa chan s seleced and hereafer all he ne zero and ones from hs pon wll be echanged n wo combnng chans. Also hrough selecon of approprae percen for he muaon probably, locus or loc of he responses chan are seleced and he numbers whn hese loc are changed from zero o one and vce versa. Then once agan he objecve funcon for he new populaon s compued and hs rend s so much repeaed ha all he responses are dreced oward he opmal pon. Ths response (chromosome) s nroduced as he bes esmaon for parameers of he flow dscharge a any me. In hs research for comparng he mehods for deermnaon of he Muskngum coeffcens, from he HEC-RAS sofware, we aemped o creae observaonal hydrographs of 5 suggesed floods and he Muskngum coeffcens wh requred daa n each mehod were deermned and as a resul, flood roung va he hree Muskngum, Muskngum-Cunge, and Runge-Kua order 4 were performed. The objecve funcon for evaluaon of opmal, k and m parameers n he nonlnear Muskngum model, mnmzaon of sum of squares of he remanders beween observaonal and roued ouflows SSQ has been consdered. The objecve funcon oo, can be compared wh he relaon 9. SSQ = n ( O c O m ) = (9) Also, for more precse sudy of he hydrographs compued of he mehods suded n hs research, he facor of square roo of dfference of sum of squares of dscharge, compued from he RMSE observed for he occurrence me was used. 8

9 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp -4 RMSE = n ( Oc Om ) = n (0) Procedure used for compung hs parameer s as follows: In whch Oc sands for he compued dscharge, Om s he observaonal dscharge of he HEC-RAS sofware and n s he number of observed and compuaonal par dscharges of each model. The SSQ and RMSE parameers for resuls of each of he hree roung mehods are presened n ables o 3. In order o conrol he resuls obaned from he prevous comparson and denfyng he probable msake or error facors, he observaonal and compuaonal values for each flood have been compared separaely. 4. Resuls and concluson Sandard errors and opmzed coeffcens of he Muskngum nonlnear model obaned of he genec algorhm mehod, along wh he coeffcens obaned of he Muskngum lnear hydrologc models and Muskngum Cunge models are presened n he ables o 3. Table : The comparson beween non-lnear Muskngum model error and opmzaon coeffcen n Runge- Kua 4h. Sandard error for esmaed Flood Flood Flood 3 Flood 4 Flood 5 parameers SSQ (m 3 /s) RMSE (m 3 /s) K (hours) m Table : The comparson beween lnear Muskngum-Cunge model coeffcen and error value Sandard error for esmaed Flood Flood Flood 3 Flood 4 Flood 5 parameers SSQ (m3/s) RMSE (m3/s) K (hours)

10 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp -4 Table 3: The comparson beween lnear Muskngum model coeffcen and error value Sandard error for esmaed Flood Flood Flood 3 Flood 4 Flood 5 parameers SSQ (m3/s) RMSE (m3/s) K (hours) Regardng he mehods used for deermnng coeffcens of he Muskngum model, n he graphcal mehod, due o he ral and error mehod, precson of hs mehod s low and values of he Muskngum coeffcens have been appromae herefore hese compued values n he sandard error as well, has been more compared wh oher suded mehods. Also he Muskngum-Cunge model for deermnng he Muskngum coeffcens requres daa on cross secons, longudnal sop of he rver, roughness coeffcen of he rver bed, and also he physcal specfcaons of he rver ncludng lengh of he rver, upper wdh of he flow, and he weed permeer whch s very comple and me consumng. Compared wh hese wo mehods, he genec algorhm n spe of he long me requred for opmzng he consdered parameers, doesn need collecon of a lo of comple daa and only hrough avalably of nflow and ouflow hydrographs and wrng he nended program n MATLAB, opmzes coeffcens of he Muskngum nonlnear model. In order o deermne precson of he hree developed models and he Muskngum and he Muskngum-Cunge models n esmang values of he peak dscharge and me of occurrence, compuaon error percenage of each parameer relave o observaonal values was deermned and s resuls are presened n he followng dagrams. In hese dagrams, he facor of dscharge error percen or he peak me compued from he all hree mehods were compared wh he real value n he observed hydrograph of ha ncden and s dsperson relave o lne zero has been obaned. In sudyng he resuls of RMSE and SSQ error values reveals ha he Runge-Kua order 4 roung regardng he mnmum error value n he fve occurred flood, compared wh he wo Muskngum and Muskngum-Cunge mehods, has compued he ouflow hydrograph closer o he values of he observaonal ouflow hydrographs obaned of he HEC-RAS sofware. In he sudy of resuls relevan o he facor of error percen for esmaon of he peak dscharge, and value of hs parameer n wo Runge-Kuaorder 4 and he Muskngum-Cunge model and for each of he floods a negave number has been acheved. Ths means ha boh wo mehods have always esmaed he peak dscharge value less han he real value. In he Muskngum model however, he peak dscharge error percenage has been obaned as posve for mos of he floods whch n hs model, always he peak dscharge value has been esmaed o be more han he real value. In comparson, dagrams relevan o dsperson around he zero lne for he peak dscharge error percenage facor, n he overall dsperson for he Runge-Kua order 4 mehod and he Muskngum Cunge model s less and hus, hese wo mehods have compued he peak dscharge value wh more precson. In he dagrams relevan o dsperson around he zero lne for he facor of peak dscharge occurrence me error percenage, s seen ha he Muskngum-Cunge model n hree of he fve floods have correcly compued he peak dscharge occurrence me (regardng he zero error percenage for hree cases of he floods). Also, n he Range-Kua order 4 mehod resuls have been esmaed very close o esmaons of peak dscharge me by he Muskngum Cunge model. In he 0

11 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp -4 Muskngum model however, mes for he peak dscharge have been esmaed less ha he real me. Therefore, he Muskngum-Cunge and he Runge-Kua order 4 models are more precse for esmang he peak dscharge me esmaon. Fgure : The dsrbuon around 0 lne for peak of flow error percenage. Fgure : The dsrbuon around 0 lne for peak of flow error percenage. Fgure 3: The dsrbuon around 0 lne for peak of flow error percenage.

12 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp -4 Fgure 4: The dsrbuon around 0 lne for peak of flow error percenage. Fgure 5: The dsrbuon around 0 lne for peak of flow error percenage. Fgure 6: The dsrbuon around 0 lne for peak of flow error percenage.

13 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp Concluson In hs research effcency and precson of he hree genec algorhm, Muskngum and Muskngum Cunge mehods for deermnaon of he Muskngum model coeffcens of all he hree mehods wh soluon of he relevan equaons, and flood roung usng hese coeffcens n all hese hree mehods, were nvesgaed. Parameers relevan o comparson of resuls obaned of roung of fve floods due o promy of he compued values o he observaonal values from he HEC-RAS sofware wh he genec algorhm opmzaon mehods relave o he oher wo mehods ndcae hgh precson of hs mehod whch s close o ha of he HEC-RAS sofware for flood roung. Also he genec algorhm and he Muskngum-Cunge model enjoy a hgh poenal for deermnng he value and me of occurrence of he peak dscharge. The advanage of he genec algorhm however, n comparson wh he Muskngum Cunge model s s easy and rapd applcaon of he Maskngum nonlnear model opmzed coeffcens over he genec algorhm n flood roung by he Runge-Kua order 4 and also s lack of need o use ral and error appromaon mehods and collecon of much daa from he rver lke he Muskngum and he Muskngum-Cunge models, herefore, employmen of hs mehod for flood roung s recommended. References [] Luo J, Xe J." "Parameer Esmaon for Nonlnear Muskngum Model Based on Immune Clonal Selecon Algorhm". Journal of Hydrology Engneerng. 00; 5(0), [] Hoon Km J, Woo Geem Z, Km ES. "Parameer Esmaon of he Nonlnear Muskngum Model Usng Harmony Search". Journal of he Amercan Waer Resources Assocaon. 00; 37(5):3 38 [3] Cunge JA. "On he subjec of he flood propagaon compuaon mehod (Muskngum mehod)". Journal of Hydraulc Research, IAHR. 969; 7(): [4] Ponce VM, Laha AK, Scheyhm C." Analycal verfcaon of Muskngum-Cunge roung". Journal of Hydrology.996; 76: [5] Vcor M. Ponce T. Alolph L. "Modellng Looped Rang n Muskngum-Cunge Roung". Journal of Hydrologc Engneerng. 00; 6(): 9-4. [6] Geem ZW. "Issues n opmal parameer esmaon for he nonlnear Muskngum flood roung model". Engneerng Opmzaon. 04; 46(3): [7] Karahan H, Gurarslan G, Geem Z. "Parameer Esmaon of he Nonlnear Muskngum Flood-Roung Model Usng a Hybrd Harmony Search Algorhm". Joural of Hydrolology Engneerng. 03; 8(3), [8] Gll MA. "Flood Roung by Muskngum Mehod". Journal of Hydrology. 978; 36, [9] Sephenson D. "Drec opmzaon of Muskngum roung coeffcens". Journal of Hydrology. 979;4 :

14 Inernaonal Journal of Scences: Basc and Appled Research (IJSBAR)(05) Volume, No, pp -4 [0] Tung YK. "Rver Flood Roung by Nonlnear Muskngum Mehod". Hydraulc Engneerng ASCE. 985; (): [] Hone JC, Lang CC. "Applyng Parcle Swarm Opmzaon o Parameer Esmaon of he Nonlnear Muskngum Model". Hydrologc Engneerng. ASCE. 009: [] Mohan S. "Parameer Esmaon of Nonlnear Muskngum Models Usng Genec Algorhm". Journal of Hydraulc Engneerng (ASCE). 997; 3(),