DEVELOPMENT OF FLOOD ROUTING MODELS FOR WANG RIVER BASIN

Transcription

1 DEVELOPMEN OF FLOOD ROUING MODELS FOR WANG RIVER BASIN Athara Komsai 1, Wiai Liegharersit 2, suyoshi Kiouhi 3 1 Graduate studet, Departmet of Evirometal Siee ad ehology, okyo Istitute of ehology, 4259 Nagatsuta-ho, Midori-ku, Yokohama, Japa, atkomsai@gmail.om 2 Assoiate professor, Departmet of Evirometal Egieerig, Kasetsart Uiversity, 5 Ngamwogwa Road, Chatuhak, Bagkok 19, hailad, fegwl@ku.a.th 3 Professor, Departmet of Evirometal Siee ad ehology, okyo Istitute of ehology, 4259 Nagatsuta-ho, Midori-ku, Yokohama, Japa, kiouhi.t.ab@m.titeh.a.jp Abstrat Reeived Date: Marh 31, 214 Nowadays, severe floodig frequetly ours i various parts of hailad resulted from hages i limati oditio ad lad use patters. he floodig has aused great damages to properties ad lives ad affets outry eoomy. Experiee from the most severe floodig i the orther ad etral regios of hailad i the year 211 reveals that reliable flood warig system is still laggig. For flood warig purpose, it is eessary to have a aurate flood routig system. his study is aimed at developig mathematial models for flood routig so as to provide data for flood warig. wo differet models are developed, i.e., kiemati overlad flow model ad kiemati stream flow model. he fiite elemet method with Galerki s weighted residual tehique is used i model developmet. he seod-order Ruge-Kutta method is applied to solve the set of differetial equatios obtaied from fiite elemet formulatio. he developed models are applied to simulate flows i the Wag river basi i the orther regio of hailad durig July 1 Otober 31, 211 whe severe floodig ourred i this regio. Model alibratio is made by adjustig some parameters i the models ad omparig the obtaied results with measured data reorded by RID at 5 stream flow gauge statios alog the Wag river. For orrelatio aalysis, three statistial idies are determied, these ilude oeffiiet of determiatio, R 2, Nash Sutliffe model effiiey oeffiiet, NSE, ad oeffiiet of variatio of the root mea square error, CV(RMSE). It is foud that the model results at the upstream portio of the river satisfatorily agree with the observed data, with the values of R 2 greater tha.55 ad CV(RMSE) less tha.57. For the dowstream portio of the river, there are remarkable differees betwee the model results ad the observed data. he values of R 2 are less tha.35, CV(RMSE) greater tha.76, ad the NSE values are less tha.16. his might be due to some errors i the iput data, iludig raifall patter, topography, lad use, river ross-setioal area, ad water seepage alog the river. More detailed field ivestigatio ad model alibratio are still eeded. Keywords: Fiite Elemet Method, Flood Routig, Hydrologial Model, Wag River Basi Itrodutio Rapid populatio growth ad urbaizatio i hailad i the past few deades have reated high demad of lad resoures. As a result, deforestatio has bee udertake i may parts of the outry, espeially i moutaious areas. It was reported that the whole forest area i hailad had dereased from 53.3% of the outry area i 1961 to 3.9% i 26 [1]. I additio, lad use patters have bee gradually haged. hese ativities together with some other fators iludig global warmig whih has affeted raifall ad stream flow patters i various regios [2]. Flash flood ad drought our very ofte owadays. I 211, floodig ourred i may regios of hailad for prologed period whih aused great damage to lives ad eoomy of the outry [3]. Oe fator whih aused great damage was the lakig of iformatio o flood magitude ad time of ourree [4]. So, ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.16

2 flood warig system is eeded for hailad ad it is eessary to have reliable iformatio o flood magitudes i dowstream regios, espeially i urbaized ad idustrial areas. Several flow routig ad water resoures maagemet models have bee developed i the past few deades. hese ilude HEC programs, suh as HEC-1, HEC-2, HEC-HMS, HEC-RAS, et., developed by Hydrologi Egieerig Ceter of the U.S. Army Corps of Egieers [5], Watershed Modelig System (WMS) developed by the Evirometal Modelig Researh Laboratory of Brigham Youg Uiversity [6], Soil ad Water Assessmet ool (SWA) developed by USDA Agriultural Researh Servie ad exas A & M AgriLife Researh [7], CASC2D developed by exas A & M Uiversity ad U.S. Bureau of Relamatio [8], et. Some of these models were applied to ivestigate river flow ad flood propagatio i the Chao Phraya river basi ad its mai tributaries, amely Pig, Wag, Yom ad Na rivers. hese models were developed by usig fiite differee method for umerial approximatio. Besides the fiite differee method, fiite elemet method has bee foud to be a very effetive umerial tehique for solvig partial differetial equatios. It has some advatages over the fiite differee method, espeially i aalyzig problems over ompliated domais with irregular boudaries. I the fiite elemet method, the study domai is divided ito elemets of whih several types, shapes ad sizes a be used [9]. Moreover, the proedure i fiite elemet model developmet is well defied ompared with the fiite differee method [1]. With these advatages, the fiite elemet method beomes more popular owadays. I this study, the fiite elemet method is used i developig flood routig models for the Wag river basi. he objetive of this study is to develop flood routig models for Wag river basi usig fiite elemet method. he mai purposes are to determie the appliability ad auray of the fiite elemet method i flood routig ad to obtai reliable flood foreastig models for Wag river whih a be used to determie flood magitude ad time of ourree whe heavy storms our i the river basi. he obtaied results will be beefiial to those ageies whih are resposible for flood maagemet ad warig. Method he fiite elemet method is used for model developmet. he Galerki s weighted residual tehique is employed to overt basi goverig equatios whih are i the form of partial differetial equatios to sets of first-order differetial equatios. With give iitial ad boudary oditios, these sets of differetial equatios are solved by usig the seod-order Ruge-Kutta method to obtai the values of flow rates at various odal poits idetified i the study area whih iludes watershed areas ad streams. Model Formulatio I this study, 2 types of models are developed for Wag river basi, i.e. kiemati overlad flow model for omputatio of overlad flow due to exess raifall o athmet areas of the Wag river, ad kiemati stream flow model for omputatio of flow i the Wag river. Kiemati Overlad Flow Model his model is based o the followig equatios [11]: h q x Cotiuity equatio: t x q y y i f (1) ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.17

3 S 5 3 Disharge-water depth relatioship: q h m h (2) i whih h is overlad water depth (m); q is overlad flow per uit width (m 3 /s.m); q x ad q y are overlad flow rates per uit width (m 3 /s.m) i the x- ad y-diretios, respetively; i is raifall itesity (m/s); f is rate of water loss due to ifiltratio ad evaporatio (m/s); α is oveyae fator = S / o ; S is overlad flow slope; o is a effetive roughess parameter for overlad flow; ad m is a ostat = 5/3 from Maig's equatio. he overlad flow rates q x ad q y a be expressed i terms of q as follow: o q x qos ad q y q si (3) where θ is the agle betwee flow diretio of ad the x-axis. herefore, the otiuity equatio a be writte as m Replae q by h whih a be rearraged as, we obtai h q q os si i f (4) t x y h t m m h h os si i f x y h m1 h h m h os si i f (6) t x y Providig value of raifall itesity ad the rate of water loss due to ifiltratio ad evaporatio, the fiite elemet method a be used to solve for h at various time t. Details are as follow: Let the ukow variable h is approximated by ĥ whih is a futio of water depths at odal poits idetified i the study domai as follows: ĥ i1 i whih N i is a iterpolatio futio ; matrix of N i ; H is matrix of H i (5) N i H i N H (7) H i is water depth at ode i ; N Replae h i Eq.(6) with ĥ will result i some error or residual R, i whih R ĥ mĥ t m1 ĥ ĥ os si i x y I the weighted residual method, this residual is multiplied with a weightig futio w ad itegral of their produt over the whole study domai () is set to zero. his results i the followig weighted residual equatio: he parameter α ĥ m1 ĥ m1 ĥ w m os ĥ m siĥ i f da (9) t x y ad agle θ usually vary depedig o topography ad lad f (8) is ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.18

4 use of the area. I this study, the values α.osθ ad α.siθ are expressed i terms of the values at odal poits usig the same iterpolatio futio. Let α x = α.osθ ad α y = α.siθ be expressed i terms of their odal values as follow: x.os N i xi N α x ad.si i1 yi N α y (1) y N i i1 Substitute ĥ, os ad si expressed i terms of their odal values i Eq.(9), we obtai: w m1 N H N H mn α N H da t wmn α x y x m1 N H N H i f da I Galerki's method, the iterpolatio futio Ni i 1, 2,..., are used as the weightig futio w. So, we obtai a set of weighted residual equatios, whih a be writte i the matrix form as follows: y (11) (12) NN H da t mnn α x m1 N N H H da N y x + mnn α N H H da inda fnda y m1 whih a be writte i more ompat form as: dh M dt M h M i M f (13) i whih M = NN da (14) N x M h = mnn α N H H da M i = M f = x mnn α y N m1 H m1 N y H da (15) in da (16) fn da (17) I fiite elemet method, the study domai is divided ito a umber of elemets ad itegral over the whole study domai is equal to the sum of itegrals over these elemets [1]. I this study, a liear triagular elemet is used for the kiemati overlad flow model. he Ruge-Kutta method [12] is used to solve this set of first-order ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.19

5 differetial equatios. Oe the water depth at eah odal poit disharge per uit width at ode i, q i, a be omputed from: H i is kow, the m Si 5 3 qi ihi Hi (18) oi Whe the overlad flow rate per uit width q i at a odal poit loated o the stream bak is obtaied, the lateral iflow per uit legth of stream q a be determied from q q os os si si (19) i i whih θ is the agle betwee groud slope diretio ad the x axis ad β is the agle betwee river flow diretio ad the x axis as show i Figure 1. β θ A x axis river q i q taget to a river at poit A Kiemati Stream Flow Model Figure 1. Overlad flow q i ad lateral iflow q For stream haels, the basi equatios for kiemati routig are [11]: Cotiuity equatio: Disharge-area relatioship: A Q q q t x Q A m o (2) (21) i whih Q is stream flow rate (m 3 /s); A is ross-setioal area (m 2 ); q is lateral iflow (m 3 /s.m); q o is rate of water loss due to evaporatio ad seepage (m 3 /s.m);, m are kiemati wave parameters of whih the values deped o hael shape. or Replae Q i Eq.(19) by m A, we obtai: A A t x m q q o (22) A m 1 A m m A A q qo (23) t x x Providig value of lateral iflow ad seepage ad other model paramters, the ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.2

6 fiite elemet method a be used to solve for A at various distae x ad time t. Details are as follow: Let the ukow variable A is approximated by a futio of ross-setioal areas at odal poits idetified i the study domai as follows: i whih matrix of  i1 N i A i N A (24) N i is a iterpolatio futio; A i is ross-setioal area at ode i; N is N ; A is matrix of i A i Replae A i Eq.(22) with  will result i some error or residual R as follows: R  m  t m 1 A  x I weighted residual method, this residual is multiplied with a weightig futio w ad itegral of the produt over the whole study domai () is set to zero, whih results i the followig weighted residual equatio: m x q q o (25)  m 1  m w m   q qo dx (26) t x x he parameter usually varies with distae alog the hael. I this study, it is expressed i terms of the odal values usig the same iterpolatio futio as Â, that is Substitute  ad obtai: w i N α (27) N i i1 i Eq.(25) by the expressios i Eqs.(23) ad (26), we N A t m N N α A m N A N m 1 x α N A x q q o dx I Galerki's method, the iterpolatio futio Ni i 1, 2,...,is used as the weightig futio w. So, we obtai a set of weighted residual equatios, whih a be writte i the matrix form as follows: A m 1 NN dx m NN α N A t N N x whih a be writte i more ompat form as: N x Adx m N A α dx q Ndx q Ndx o (28) (29) ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.21

7 i whih M l d A M dt M l = a M b M q M qo (3) NN dx (31) M a = m NN α N A M b = NN m 1 N Adx x (32) m N A α dx x (33) M q = q N dx (34) M qo = q o N dx (34) I the fiite elemet method, the study domai is divided ito a umber of elemets ad itegral over the whole study domai is equal to the sum of itegrals over these elemets. I this study, a liear oe-dimesioal elemet is used for the kiemati stream flow model. he Ruge-Kutta method [12] is the used to solve this set of first-order differetial equatios. Oe the ross-setioal area at eah odal poit A is kow, the disharge at ode i, Q i, a be omputed from: i Q i i i m A (35) Model Appliatio Study Area he Wag river is oe mai tributary of the Chao Phraya river whih is the most sigifiat water resoure of hailad. he Wag river basi lies i the orthsouth diretio, loated betwee latitudes 16 5 N. ad 19 3 N. ad logitudes E. ad E. (Figure 2). he total athmet area overs about 1,791 km 2. he Wag river origiates i Phi Pa Nam moutai rage i Chiag Rai provie ad flows southwards passig Lampag ad ak provies before joiig the Pig river i Ba ak distrit, ak provie. he total legth of the Wag river is approximately 46 km. he Wag river basi is surrouded by moutai rages alog the easter ad wester boudaries. opography of the basi is haraterized by arrow plais ad valleys i the orther part ad flood plais i the souther part [13]. Climate i the Wag river basi is iflueed by Northeast ad Southwest mosoos together with typhoos, mosoo troughs ad depressios from South Chia Sea. he mea mothly temperature varies from 22.2 ºC to 29.7 ºC. he mea mothly raifall varies from 4.9 mm to mm with a aual average of 1,173.9 mm. he mea mothly evaporatio varies from 9.3 mm to mm with a aual average of 1,497.3 mm. he mea mothly relative humidity varies from 53.% to 82.7% with a aual average of 72.7% [14]. ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.22

8 Data Colletio Seodary data from various oered ageies are used i model appliatio ad verifiatio. hese ageies ilude Royal Irrigatio Departmet (RID) for stream flow data, hai Meteorologial Departmet (MD) for limati data, Lad Developmet Departmet (LDD) for soil data, ad Royal hai Survey Departmet (RSD) for topographi ad lad use data. A total of 13 raifall statios ad 5 ruoff statios o the mai river were used i this study. Loatios of these raifall ad stream flow gauge statios are show i Figure 3. Chiag Mai Lam Phu Phrae Lam Pag Uttaradit 25 5 km Computatio Figure 2. Wag river basi At first, the kiemati overlad flow model is applied to eah sub-basi. he area is divided ito a umber of triagular elemets. he overlad flow rates at odal poits alog the streams i eah sub-basi at eah time step are omputed from the model ad the the lateral iflows per uit legth of the tributary streams i the sub-basi are determied. he iitial overlad water depth at eah odal poit is set to zero. Also, water depths at all ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.23

9 odal poits loated alog the upper boudary of eah sub-basi, whih is maily o the moutaious area, are set to zero at eah time step. Size of time step is seleted by trial ad error so as to obtai stable results. he time step of 3 seods is fially used i this study. Next, the kiemati stream flow model is applied to all streams i eah subbasi. Eah stream is divided ito a umber of oe-dimesioal elemets. he results of lateral flow omputatio obtaied from the overlad flow model are used as iput data to the kiemati stream flow model. Flow rates i the tributary streams at eah time step are omputed first. Raifall Gauge Statio Code (1) 1613 (2) (3) 1642 (4) 1652 (5) 1672 (6) 1682 (7) 1612 (8) (9) (1) (11) 1633 (12) 1633 Ruoff Gauge Statio Figure 3. Loatio of ruoff statios ad raifall statios he, flow rates i the mai streams are omputed usig the results of lateral disharges obtaied from the overlad flow model ad the results of stream flows from the oeted tributary streams as iput data. For a tributary stream, the iitial values of stream flow at all odal poits are set to zero, so as the value at the upstream ed at eah time step. For the mai Wag river, data o river flow ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.24

10 reorded by RID o July 1, 211 are used to iterpolate iitial flow at eah ode idetified i the Wag river. Model Calibratio Flow rates i the mai streams are ompared with the measured data obtaied from the RID. Some parameters i the models, whih ilude the rate of water loss due to ifiltratio ad evaporatio f, effetive roughess parameter for overlad flow o, ad the rate of water loss due to evaporatio ad seepage q o, are adjusted so that the results from the models agree with the measured data. Results ad Disussios he model parameters at 5 ruoff statios are used for the overlad flow ad hael flow omputatio. After applyig these parameters together with the raifall data i the model, the simulatio results are ompared with the observed data at 5 ruoff statios as show i Figures 4-8. For orrelatio aalysis, three statistial idies are determied, these ilude oeffiiet of determiatio, R 2, Nash Sutliffe model effiiey oeffiiet, NSE, ad oeffiiet of variatio of the root mea square error, CV(RMSE). he obtaied results are summarized i able 1. It is foud that the values of R 2 ad NSE at statios W.1A ad W.5A are higher tha.7 ad the values of CV(RMSE) are less tha.5, idiatig that the simulatio results are good fitted with the observed data. So, the simulatio results at these two statios are aeptable. For statios W.1C, the values of R 2 ad CV(RMSE) are moderate, but the value of NSE is rather low, idiatig that there are remarkable differees betwee the simulatio results ad the observed data. For statios W.6A ad W.4A, the values of R 2 ad NSE are rather low, while the values of CV(RMSE) are rather high, idiatig that there are sigifiat differees betwee the simulatio results ad the observed data. he results obtaied from this study show that at some statios the differee betwee the model results ad the measured data a be otied. hese are due to some fators, iludig: 1) there are oly few rai gauge statios i the study area, so the raifall data applied to eah elemet i the watershed might be differet from the real raifall patters; 2) topography of the upstream watershed is moutaious with steep slope, so, it is rather diffiult to determie the slope of the area i eah elemet from the available topographi maps; 3) lad use maps of the study area are ot up-to-date; ad 4) data o ross-setioal areas of various streams are available at some setios oly, so iterpolatio has bee used ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.25

11 35 W.1A Disharge (m 3 /s) Raifall Observed Simulated Raifall (mm/d) Jul. 1 Aug. 1 Sep. 1 Ot. 31 Ot. Figure 4. Simulated ad observed flood hydrograph at ruoff statio W.1A 8 7 W.1C 4 Disharge (m 3 /s) Raifall Observed Simulated Raifall (mm/d) 32 1 Jul. 1 Aug. 1 Sep. 1 Ot. 31 Ot. Figure 5. Simulated ad observed flood hydrograph at ruoff statio W.1C ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.26

12 12 15 W.5A 4 Disharge (m 3 /s) Raifall Observed Simulated Raifall (mm/d) Jul. 1 Aug. 1 Sep. 1 Ot. 31 Ot. Figure 6. Simulated ad observed flood hydrograph at ruoff statio W.5A W.6A 4 Disharge (m 3 /s) Raifall Observed Simulated Raifall (mm/d) 36 1 Jul. 1 Aug. 1 Sep. 1 Ot. 31 Ot. Figure 7. Simulated ad observed flood hydrograph at ruoff statio W.6A ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.27

13 Disharge (m 3 /s) W.4A Raifall Observed Simulated Raifall (mm/d) 36 1 Jul. 1 Aug. 1 Sep. 1 Ot. 31 Ot. Figure 8. Simulated ad observed flood hydrograph at ruoff statio W.4A able 1. Compariso of Correlatio Parameters used i Model Verifiatio Proess Idex Statio W.1A W.1C W.5A W.6A W.4A R NSE CV(RMSE) for estimatig the value of ross-setioal area at eah ode idetified i the model; 5) it is rather diffiult to estimate the rate of water loss due to evaporatio ad seepage (q o ) i the stream flow model. Error i assumig the values of q o i various elemets i the simulated model will lead to error i stream flow rates omputed from the model. Colusios I this study, mathematial equatios expressig overlad flow ad stream flow are used as basis equatios i developig two-dimesioal overlad flow model ad oe-dimesioal stream flow model. he fiite elemet method with Galerki s weighted residual tehique is used i model formulatio. he seod-order Ruge-Kutta method is applied to solve the set of differetial equatios obtaied from fiite elemet formulatio. he developed models are applied to the Wag river basi i the orther regio of hailad durig July 1 - Otober 31, 211 whe severe floodig ourred i this river basi. I omparig the model results with the observed river flow data of RID at 5 gaugig ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.28

14 statios i the Wag river, it is foud that the model results at the upstream portio of the river (the upper 3 statios) satisfatorily agree with the observed data, with the values of R 2 greater tha.55 ad CV(RMSE) less tha.57, though the NSE value at statio W.1C is rather low. For the dowstream portio of the river, there are remarkable differees betwee the model results ad the observed data. he values of R 2 are less tha.35, CV(RMSE) greater tha.76, ad the NSE values are less tha.16. his might be due to some errors i the iput data, iludig raifall patter, topography, lad use, river rosssetioal area, ad water seepage alog the river. More detailed field ivestigatio ad model alibratio are still eeded. Akowledgmets he authors gratefully appreiate fiaial support from Kasetsart Uiversity ad the Natioal Researh Couil of hailad (NRC) ad the Japa Siee Promotio Soiety (JSPS). hey are grateful to the Royal Irrigatio Departmet, the hai Meteorologial Departmet, the Lad Developmet Departmet, ad the Royal hai Survey Departmet for providig useful data for this study. Referees [1] Royal Forestry Departmet, Aual Report, Miistry of Natural Resoures ad Eviromet, Bagkok, hailad, 27. [2] S. Kure, ad. ebakari, Hydrologial impat of regioal limate hage i the Chao Phraya River Basi, hailad, Hydrologial Researh Letters, 212. [3] NESDB, DWR, RID, ad JICA, Flood Maagemet Pla for the Chao Phraya River Basi, 213. [4] W. Liegharersit, Fators whih aused serious floodig i hailad i 211, ASEAN Egieerig Cooperative Leture, Saga Uiversity, Japa, 212. [5] Software - Hydrologi Egieerig Ceter U.S. Army Corps of Egieers, Available: [Aessed: Sep, 214] [6] Watershed Modelig System Hydrologi & Hydrauli Software, Available: [Aessed: Sep, 214] [7] SWA Soil ad Water Assessmet ool, Available: [Aessed: Sep, 214] [8] CASC2D: Hydrologi Modellig, Available: wms_overview/wms_overview.html. [Aessed: Sep, 214] [9] R.D. Cook, D.S. Malkus, ad M.E. Plesha, Coepts ad Appliatios of Fiite Elemet Aalysis, Joh Wiley & Sos, New York, [1] O.C. Ziekiewiz, ad R.L. aylor, he Fiite Elemet Method, 5 th Ed., Butterworth- Heiema, Oxford, 2. [11] P.B. Bediet, ad W.C. Huber, Hydrology ad Floodplai Aalysis, 3 rd Editio. Pretie Hall, I. NJ., 22. [12] M.C. Potter, ad J. Goldberg, Mathematial Methods, Pretie Hall Iteratioal, I., Lodo, [13] Global Water Partership Southeast Asia - GWP-SEA oolbox - Wag River Basi, hailad, Available: [Aessed: July, 214] [14] Hydrology ad Water Maagemet Ceter for Upper Norther hailad - RID, Available: [Aessed: July, 214] ASEAN Egieerig Joural Part C, Vol 4 No 1 (EvE Speial Issue), ISSN p.29