Simulation model for the management of groundwater in the Yun-Lin basin

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1 INTRODUCTION Improvmnts of Mthods of Long Trm Prdiction of Variations in Groundwatr Rsourcs and Rgims Du to Human Activity (Procdings of th Extr Symposium, July 1982). IAHS Publ. no Simulation modl for th managmnt of groundwatr in th Yun-Lin basin YII-SOONG TSAO Agricultural Enginring Dpt., National Taiwan Univrsity, Taipi, Taiwan ABSTRACT Du to ovr-rlianc and ovr-pumping of groundwatr in th Yun-Lin Basin, ill-ffcts such as sawatr intrusion, land subsidnc, lowring of groundwatr lvl, and dtrioration of groundwatr quality ar found to b in xistnc and bcoming mor srious vry yar. A finit-lmnt modl, using Galrkin's wighting rsidual mthod, was st up to simulat th problm. It is found that all ill-ffcts can b controlld by modifying th pumping pattrn alon without matrially rducing th volum of xtraction. Th Yun-Lin ara is a vry important cntr of agricultural production in Taiwan. Th soil in this ara is famous for its frtility and th limitations on agricultural production thrfor li solly on th supply of irrigation watr. Howvr, th supply of surfac watr is incapabl of mting th irrigation dmand du to th xtrmly changabl natur of discharg in th strams, togthr with a larg amount of sdimnt which maks th building of any storag rsrvoir impossibl. Thrfor, a larg shar of th irrigation watr has to b drivd from groundwatr, spcially during th dry sason; this has ld to an ovr-rlianc on groundwatr supply. In total thr ar mor than 6508 dp wlls in opration in th ara, not counting th shallow wlls and thos for domstic uss. Du to ovr-pumping, som of th rsulting ill ffcts hav bn in xistnc for yars and ar continuing to bcom vn mor srious. Such ffcts ar as follows: (1) Th dclin of groundwatr lvls: th watr lvl in th whol basin is dclining stadily and mor than 250 km^ now hav a groundwatr lvl blow th sa surfac. (2) Th dclin of yild from wlls: th yilds of most wlls ar dclining and som hav bn abandond for this rason, whil othr wlls hav had to chang pumps or b dpnd. (3) In th coastal ara, sa watr intrusion progrsss stadily with incrasing damag. (4) Thr ar srious cass of land subsidnc in this ara. In som locations, subsidnc as grat as 1.5m has bn found, rducing th ffctivnss of flood control dyks and causing many drainag problms. 333

2 334 Yii-Soong Tsao (5) Th dtrioration of groundwatr quality is also vry srious in this ara and its caus can b tracd back to ovrpumping. Th widsprad distribution of black-foot disas, which is a cancrous disas, is undoubtdly closly rlatd to th arsnic and fluorid in som groundwatr. In rcnt studis, it is also suspctd that thr is som corrlation btwn contaminatd groundwatr and lung cancr and pancras cancr. In ordr to chck ths ill-ffcts, th govrnmnt gav instructions in 1975 that no nw wll was to b drilld in th four townships (Kou-Hu, Szu-Hu, Shui-Lin and Pi-Kong). In th mantim, mathmatical modls wr to b stablishd for th groundwatr in Yun-Lin Basin so as to find managmnt solutions (both practical and thortical) for th groundwatr problms in this important basin. Th whol projct was carrid out as an intrnational cooprativ rsarch projct btwn th National Scinc Foundation of USA and th National Scinc Council of ROC. Th Amrican rsarchrs, Robrt Willis and P.L-F. Liu dvlopd a probabilistic mthodology for th analysis of paramtr and hydrologi uncrtainty in rgional groundwatr systms so as to assss th rliability and fasibility of groundwatr rsourcs managmnt undr conditions of hydrologi risks. Simultanously, th writr and local rsarchrs utilizd Galrkin's wighting rsidual mthod of th finit-lmnt modl to simulat and analys groundwatr rcharg and withdrawal in th Yun-Lin ara so as to stablish a propr managmnt policy and to liminat all th abovmntiond ill-ffcts. GENERAL DESCRIPTION OF THE BASIN Th Yun-Lin ara is locatd in th midwst of Taiwan mainly in th southrn part of th alluvial fan of th Cho-shui Rivr. Th total ara of this basin is about 1075 km. For boundaris, it has Taiwan strait to th wst, Cntral Mountains to th ast, Cho-Shui Rivr to th north and Pi-Kong Rivr to th south (Fig.l). Th annual prcipitation is about 1300 mm which is almost qual to th annual vaporation in th ara. Furthrmor th distribution of annual rainfall is xtrmly unvn, mor than 80% of th annual rainfall bing concntratd in th 4-month priod from Jun to Sptmbr. Gologically spaking, th groundwatr basin can b dividd into two diffrnt zons: (1) Rcnt alluvium: This zon is composd of uncmntd sand, gravl and clay dpositd by th Cho-Shui Rivr. Sand and gravl layrs ar usually covrd by clay. Th largr gravls and cobbls wr dpositd on th ast sid of th basin bcoming smallr towards th wst coast. Th uppr rachs of th Cho-Shui Rivr form th main natural rcharg ara whr groundwatr is most abundant; in th middl of th basin th gravl layrs ar intrsprsd with sand; nar th coastal ara, thick clay and fin sand layrs ar prdominant.

3 Modl for managmnt of groundwatr in Yun-Lin Basin 335 if \4T Pi-Koni 1 Rivr 'Vx'x FTG.l Map of Yun-Lin Basin. Th thicknss of aquifrs varis from 30 to 50 m in this ara. Bnath th first aquifr, which is 70 m undr th ground surfac, thr ar scond and third aquifrs which li 120 m and 200 m undrnath th ground surfac rspctivly. Th gological profils of this basin ar shown in Fig. 2. (2) Trracd gravls: This zon, locatd on th ast sid of th basin, is composd of various sizs of gravl and thrfor is usually vry porous with a high cofficint of prmability. Howvr, in som locations, du to cmntation or th prsnc of larg amounts of clay, th prmability is substantially rducd. Th thicknss of aquifr in this zon rangs from 30 to 50 m. At th prsnt tim th numbr of wlls in this basin totals 6508, about half bing usd to irrigat ha. of paddy ric and upland crops to supplmnt th unrliabl surfac watr supply. In som dry yars, th total withdrawal of groundwatr has xcdd 400 million tons pr yar which gratly surpasss th natural rcharg of th basin. MATHEMATICAL MODEL Gnral quation Sinc th aquifr systm in Yun-Lin is considrd basically to b a confind aquifr systm, from Darcy's Law and th quation of consrvation of mass w can obtain th following gnral quation V. (TV0) -p + q-s-^~-=0 (1)

4 336 Yii-Soong Tsao Lgnd 0 3 Clay, loam L _j sand L -^ ' sand and fcii-13 gravl gravl FIG.2 Gological profils of Yun-Lin Basin.

5 Modl for managmnt of groundwatr in Yun-Lin Basin 337 whr T is th transmissivity tnsor, 0(x,y,t) is th instantanous pizomtric had, p is th discharg from th wll, q is th vrtical rcharg or infiltration flow into th aquifr systm and S is th storag cofficint. Equation 1 is subjct to th limitation of th initial condition 4> = 4>Q (X,Y,tQ) and th prvailing boundary conditions. Sinc this quation taks considration in a clos-boundd D in a twodimnsion spac, its boundary C(C^ + C2) is a picwis continuous curv; thrfor, for Dirichlt condition 0 = <p (x,y,t) on Cj for Numann condition Q.n = -(!"#).n = Q (x,y,t) on C 2 Galrkin's modl If 4> is a solution of Equation 1 as wll as th initial and A boundary conditions, thn thr is an approximat solution 4> such that it satisfis Equation 1 and i.ts conditions A A b R(0) = V. (TV0) -p + q - S JT = 0 According to th mthod of wightd rsidual thr is a wight function W which satisfis A WR(0)dD = 0 (2) If <p is assmbld by M 0 in domain D thn A 4> M 11 A = S 0 =l M D = S D 1 =l A Th rlation btwn 4> in ach lmnt and its Nodal Valu {<p} is as follows Î = [N 6 ] {^} whr [ N] is th intrpolation function or shap function in th lmnt. Using Galrkin's mthod lt W = [ N ] T hnc Equation 2 bcoms M 2 J n T [ N ]V[N ]{0 }dd - L D D (p -q )[N ] T dd =l -y D s [N ] T [ N ]^fid D^O (3)

6 338 Yii-Soong Tsao According to Grn's first formula, th first trm of Equation 3 bcoms L T [N ]V[N ]{0 }dd = - L T V[N ] T.V[N ]{0 r,,t }dd + f 'A N D u c 9[N 1- {0 }dc = - 5 T V[N ] T.V[N ]{0 }dd + I [N S ] T Q ddc D C Th last trm in Equation 4 is th Numann condition of th boundary of th lmnt. Lt r 6i f r -, T r, r-, f r, T r,, H = ) T V N ].V[N dd C = ) S N N ]dd D D [F S ] = L (p-q)[n ] T dd + î Q [N ] T [N S ]dc u v- Th Equation 3 can thn b writtn as: (4) 2 ([ H 6 ] {</> 6 }+[ C 6 ] {0 }+[ F ] ) =[ 0] ( 5 ) =l Tim-dpndnt problm Lt [0] = [0] t + 0([0] t+at - [0] fc ) O<0<1 From Taylor Sris Equation 5 can thus b writtn as 01 H] +Si[c]{*} t+at = [-(1^)[H] +^[clh*} t -[F] t^ A t (6) Whn 0=0 is forward diffrnc 0=1 is backward diffrnc 6 = h is cntral diffrnc i.., th Crank- Nicholson schm ESTABLISHMENT AND VALIDATION OF THE YUN~LIN MATHEMATIC MODEL A finit lmnt mathmatic modl was stablishd for th Yun-Lin Basin aftr a prolongd priod and xtndd ffort to gathr th ncssary hydrological, gological and watr managmnt data in th basin. Th procdur of stablishmnt and validation of th modl wr as follows: (1) Dtrmination of th siz of lmnts: Each lmnt was dtrmind to b 4 km x 4 km in siz by taking considration of th

7 Modl for managmnt of groundwatr in Yun-Lin Basin 339 quantity and quality of th data as wll as th limitation of th CPU capacity of th mini-computr ; hnc th whol basin is dividd into 78 such lmnts with 101 nodal points as shown in Fig.3. FIG.3 Elmnts, Nodal Points and Rgions. (2) Tim chosn for validation: In validation of th modl, th 1956 groundwatr contours wr usd bing drivd from th arlist groundwatr contour map that is availabl. In 1956 th dvlopmnt of groundwatr in th Yun-Lin basin was at its vry bginning, thrfor th withdrawal of groundwatr, as wll as th changs of groundwatr lvl, wr rlativly small compard with thos of latr yars. By choosing 1956 as th tim for validation, th intrfrnc from th undsirabl factors would b kpt to a minimum and th task of validation of th modl was mad asir. (3) Dtrmination of S and T: From th pumping tsts conductd bfor 1956, a considrabl numbr of T valus for various wlls can b found, S valus ar also availabl but to a lssr xtnt. Aftr som study, th whol basin was again dividd into 19 zons according to th availabl data of formation constants, i.. within ach zon th sam st of formation constants wr usd. Each zon contains an intgral numbr of lmnts. (4) Dlimitation of rgions: Th condition of th basin varis du to diffrncs in gological structur, aquifr charactristics, prcipitation, surfac watr supply, crop

8 340 Yii-Soong Tsao pattrn, irrigation practic, rcharg and pumping pattrns. Aftr som trials, th whol basin was dividd into six rgions, ach rgion containing an intgal numbr of lmnts as shown in Fig.3. Within ach such rgion th ovrall conditions ar considrd to b similar. (5) Dtrmination of boundary conditions : From th groundwatr contours, as wll as data obtaind from th past, it was obvious that th groundwatr lvls in th mountain ara on th ast sid of th basin sldom chang, thrfor, Dirichlt Condition was st for th ast sid of th basin. On th south sid, th rlation btwn th Pi-Kong Rivr and groundwatr was found to b immatrial, hnc Numann Condition was assumd with zro flux. As for th othr two sids, aftr som tst runs, two diffrnt st of boundary conditions wr usd as shown in Fig.4. Th simulatd rsults wr vry clos to th actual contour no mattr which st of boundary condition was usd, th corrlation cofficints bing bttr than N. B F1 ux = 0 D. B ci = C D. B «s - o D. B N. B 4---C Fluxi-0 D. B <f, : C N. B Flux 0 N. B F!ux = 0 (!) (2) FIG.4 Boundary Condition. To chck th modl furthr, th April 1977 groundwatr contour map was usd as th initial condition to simulat th groundwatr contours of April 1978, and thn compard with th actual valus of that dat. Th rsults wr found to b vry good with corrlation cofficints bttr than 0.99 for both sts of boundary conditions. Th priod was chosn for validation bcaus during this priod an xtnsiv ffort was mad to collct data, with pumping tsts bing conductd for 300 wlls, whil dischargs from th 6508 wlls wr ithr masurd or stimatd from th powr bill. Th T and S valus wr found to hav changd significantly from th 1956 valus, hnc adjustmnts wr mad accordingly bfor th simulation. Th clos rsults obtaind in validation indicat that th modl is sound nough for th simulations followd, as wll as th intndd applications in futur. SIMULATION RESULTS A sris of simulations wr carrid out to find th managmnt solutions to chck th ill-ffcts causd by ovr-xtraction of groundwatr. With th gnral watr shortag in this basin

9 Modl for managmnt of groundwatr in Yun-Lin Basin 341 in mind, th main objctiv of th simulations was to find solutions which minimiz th rduction of xtraction whil still controlling th ill-ffcts. Th location of groundwatr contour at zro lvation is usd as th critrion for th simulations. Sinc th bst data availabl ar in th priod , all th simulations ar carrid out in this priod for comparison (Fig.5). Lgnd Actual Ground Watr lvl 5,1*,3 tc. Simulatd 50m,UCta,30m tc. rspctivly(ground Watr lvl) A,B,C,D Simulatd t m,2 m,3' n,k m Ground Watr lvl rspctivly * Simulatd Ground Watr lvl of any odd numbr tims 5. FIG.5 Simulation Rsult of Yun-Lin Ara (April 1977-April 1978). Simulation 1: Th xtraction of groundwatr in rgion 1 was varid whil xtraction in othr rgions wr unchangd. Sinc this rgion is th natural rcharg zon of th basin, it is found that in this rgion xtraction of groundwatr can b incrasd as much as 50% without undsirabl consquncs i.., th zro groundwatr contour will rmain at th sam location as at prsnt. Simulation 2: By varying xtractions in rgion 2 only, th xtraction of groundwatr in this rgion roughly accounts for on third of th total xtraction of th whol basin. Th rsult of simulation shows this ara can sustain a slight incras of xtraction without causing th zro groundwatr contour to mov inland.

10 342 Yii-Soong Tsao Simulation 3: Th xtraction in rgion 3 is about 48 million tons pr yar with th zro groundwatr contour passing through this rgion; it was found that in this rgion th xtraction cannot b incrasd any mor; slight rduction of xtraction will b advisd. Simulation 4: Rgion 4 is th on with lowst groundwatr lvls, hnc it is rgardd as th most critical rgion of this study. Th xtraction at prsnt tim is about 28 million tons pr yar. From th simulation it was found that th zro groundwatr contour will rspond snsitivly to th rduction of xtraction in this rgion. Simulation 5: Th xtraction in rgion 5 is only about 18 million tons pr yar, thrfor, th chang of xtraction in this ara will not hav significant consquncs in othr rgions. Howvr, this rgion is locatd at th wst shor of th island adjacnt to Taiwan Strait with groundwatr lvls blow th sa lvl, hnc a larg cut in xtraction is dmd ncssary. Simulation 6: Rgion 6 xtracts 49 million tons of groundwatr pr yar, about 14.5% of th total xtraction of th whol basin. Sinc T valus in this rgion ar th lowst in Yun-Lin Basin, any chang of xtraction has amplifying ffct on th groundwatr lvl. A larg cut is dmd ncssary hr also. Simulation 7: Th total xtraction was kpt unchangd by varying th xtraction of ach rgion with various combinations. It was found by incrasing th xtractions in Rgion 1 and 2, and dcrasing th xtractions in th rmaining rgions, th watr lvl in th whol rgion can b raisd, and th zro groundwatr lvl will mov to th sa shor. CONCLUSIONS Th most important finding was that all ill-ffcts can b chckd by modifying th distribution of wll filds without matrially rducing th xtraction of groundwatr. Th rduction of groundwatr xtraction in rgions 3, 4, 5 and 6 can b offst by incrasing pumping in rgions 1 and 2. Th rduction of groundwatr xtraction in th coastal aras has to b carrid out as soon as possibl. Th govrnmnt was right in forbidding nw wll-drilling in ths aras, but a larg cut in groundwatr xtraction in ths rgions is urgntly ndd as ar furthr stps such as shifting th xisting paddy filds to upland crops, incrasing surfac watr supply, and conjunctiv us of groundwatr and surfac watr tc.; ail ths ar asy to suggst but hard to carry out. Dtaild studis and wll-prpard plans ar

11 Modl for managmnt of groundwatr in Yun-Lin Basin 343 ndd to raliz such schms. For xampl, if th popl in rgion 1 ar to giv up thir chap surfac watr for th coastal ara, and to pump th comparativly costly groundwatr, som compnsation plan must b prpard to obtain thir agrmnt. Th accuracy and fficincy of this modl ar largly limitd by th quantity and quality of th data, sinc th multi-aquifr squnc in th Yun-Lin ara is a vry complx systm, and mor data and mor rsarch ar ndd in this basin to tak full advantag of th modl. In th mantim, fforts ar still bing mad to apply and improv this modl. Thr ar othr aras in Taiwan that suffr from th ill-ffcts causd by ovr xtraction of groundwatr, such as Taipi Basin and Pin-tung ara. This modl can b asily modifid to simulat th groundwatr phnomna in ths aras. REFERENCES Taiwan Sugar Company: A Rconnaissanc Rport on th Groundwatr in th Alluvium of th Cho-Shui Rivr, Taiwan Groundwatr Dvlopmnt Burau: Scond Rconnaissanc Rport on th Groundwatr Rsourcs in th Alluvium of th Cho-shui Rivr, Liao, W.L., Th problms causd by ovr-pumping of groundwatr in Yun-Lin and Chia-Yi Ara, Watr Consrvation, No. 12, Willis, R., Optimal managmnt of th subsurfac nvironmnt, Hydrological Scincs Bulltin, Vol. 21, No. 2, Jun Willis, R. & Nwman, B.A., A Managmnt Modl for Groundwatr Dvlopmnt, procdings on th Windr Computr Simulation Confrnc, AFIPS Prss, Tsao, Y.S. & Tan, Y.C., A study on th application of groundwatr modls in multi-layr confind aquifr; Taiwan Watr Consrvancy, 1979.

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