Evaporation losses as a major factor in determining allowable yield from water supply reservoirs: the case of Botswana s major reservoirs

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1 River Bsin Mngemen III 631 Evporion losses s mjor fcor in deermining llowble yield from wer supply reservoirs: he cse of Boswn s mjor reservoirs P. K. Kenbho & B. P. Prid Deprmen of Environmenl Science, Universiy of Boswn Absrc Reservoirs ply n imporn role in soring wer for vrious uses. This sorge is ffeced by rising demnd due o chnges in economic pern nd demnd disribuion. Added o hese is he effec of evporion especilly in semi-rid res wih limied suible reservoir sies. Boswn is one such counry wih fl errins, ephemerl rivers wih sndy beds nd ofen lcks well defined chnnels for poenil dm sies. These hydrogrphic fcors led o he developmen of shllow nd lrge reservoirs, which lose more wer due o evporion. In ssessing performnce of Boswn s mjor reservoirs, modified sequen pek lgorihm hs been used o sudy he effecs of evporion on reservoir sizing nd operion, nd how h ffecs he yield. The sudy concludes h evporion is very criicl for reservoir plnning in semi-rid regions, becuse for every sorge here exiss rnge of yield o be supplied. Ouside his rnge, he effecs of evporion re more difficul o conrol. Keywords: llowble yield, reservoir cpciy, criicl period. 1 Inroducion In semi-rid hydrology, evporion losses re very imporn since hey influence sorge cpciy of surfce reservoirs. The biliy o ccoun for evporion explicily is hus imporn in hese regions (Adeloye e l, [1]). Accouning for evporion in reservoir plnning cn ler he sequence of criicl period (CP, period over which full reservoir goes ino empy wihou spillge) nd hence of he filure periods, when he reservoir is no ble o mee WIT Trnscions on Ecology nd he Environmen, Vol 83, 25 WIT Press ISSN (on-line)

2 632 River Bsin Mngemen III he demnd. This lerion hs been well repored by Monseri nd Adeloye [6] nd Adeloye e l, [1]. While mos of hese sudies dequely ddress he issue of ccommoding evporion losses, nd he subsequen effec on he CP, nowhere do hey focus on idenifying window of yield o be supplied in order o conin he sequence of CP even wih inclusion of evporion. This sudy herefore emps o bridge he gp, by vrying yield o be supplied nd checking how h ffecs he sequence nd mgniude of he CP for Boswn s reservoirs. The modified sequen pek lgorihm (Lele, [2]; Adeloye e l, [1]) is used iniilly o esime he desired sorge cpciies of reservoirs in Boswn o check is performnce, nd subsequenly ssess he effecs of evporion on he CP nd rge yield 2 Sequen Pek Algorihm (SPA) SPA uses mss blnce equion o simule reservoir performnce hrough sequenil deficis from n iniilly full reservoir (McMhon nd Mein, [5]), s given in eqn. (1) nd (1b) K 1 + D + E Q > K = (1), oherwise * K = mx( ), (1b) K where K -1 nd K re he volumeric deficis he sr nd end of ime, respecively; E, Q nd D re volumeric evporion losses, inflows nd * yield, K is he exc esimed cpciy. For he purpose of his pper, he modified SPA is used in order o explicily ccommode sorge-dependen losses (Adeloye e l, 21) s summrized below. The lgorihm lso begins wih he bsic SPA o compue K nd he pproxime sorge cpciy, K '. Approprie sorge ses ( S ) re esimed by subrcing K from K ' ; S is hen used o obin E wih eqns. (2) nd (3) (Loucks e l., [4]; Lele, [2]; Adeloye e l, [1]) A = S + b (2) E = e ( A + A + 1) / 2 (3) where A nd A+ 1 re he surfce res he beginning nd end of, respecively; e is he deph of ne evporion; nd b re consns, obined from sorge-heigh-re relionships he reservoir sie. The resuling bckwrd pss sorge, which includes evporion cn be re-wrien s eqn. 4 below. WIT Trnscions on Ecology nd he Environmen, Vol 83, 25 WIT Press ISSN (on-line)

3 S [ S (1 + e / 2) + D + e b Q ]/(1 e / 2) = + (4) 1 Since he bckwrd pss srs from he end of he CP, hen he sring S+ 1 is known nd equl o zero, nd he mximum of ll S is he exc cpciy * esime, denoed by K. This process is repeed unil he cpciy seles down, using convergence crierion given by eqn. (5) ' ( K K ) / K.1 (5) ' where K nd K re he esimes of he cive sorge cpciy in ny wo successive ierion, respecively (Adeloye e l, [1]). 3 Reservoirs nd d Reservoirs under sudy re Gborone nd Bok in he souhern pr of Boswn, Shshe nd Lesibogo in he norhern pr of Boswn. Shshe dm is loced on he Shshe River, ner Frncisown Ciy, while Lesibogo dm is on he Molouse River, ner Selibe-Phikwe own. Gborone dm is loced o he souh es of he Ciy of Gborone on he Nowne River, while Bok is on he Mesimolhbe River norh of Gborone Ciy. A summry of he hydrogrphic d is presened in Tble 1 below: River Bsin Mngemen III 633 Tble 1: A summry of hydrogrphic d for he Four Dms used in he sudy. Dm Cch. Are (Km 2 ) Dm Are (Km 2 ) Cpciy (x1 6 m 3 ) MAR (x1 6 m 3 ) Shshe Lesibogo Gborone Bok Averge Deph (m) The norhern pr of Boswn receives relively higher nnul rinfll o he une of 6mm, compred o 35mm in he souhern Boswn. For his reson, norhern cchmens hve higher men nnul runoff (MAR) s shown in Tble 1. 4 D collecion Evporion d were obined from Deprmen of Meeorologicl Services. Cpciy curves needed for consns nd b in eqn. (2) nd (4) were obined from Liebenberg nd Snder [3] nd SMEC [7]. However, since hisoricl sremflow d ll he four sies were smll, simulion exercise ws WIT Trnscions on Ecology nd he Environmen, Vol 83, 25 WIT Press ISSN (on-line)

4 634 River Bsin Mngemen III underken o obin s lrge s 64 yers of record ech sie using Pimn Model (SMEC, [7]). 5 D presenion nd nlysis The SPA resuls for he four dms re presened in Tble 2. Firsly, SPA ws used o esime he cpciies of he reservoirs. This ws done o es he biliy of he mehod in esiming reservoir cpciy. The mehod reurned very good resuls; 99% for Gborone, nd 1% for he res, indicing perfec esimion for ll he dms. Tble 2: Sorge nd Yield esimes from SPA. Dms Cpciy (x1 6 m 3 ) SPA Sor. (x1 6 m 3 ) Effec of evpo (%) Yield/n. (x1 6 m 3 ) Shshe Lesibogo Gborone Bok CP (Monhs) Losses(%) Sorge(%) %Losses due o Evporion Figure 1: Effec of evporion s percenge of cive sorge (Shshe dm). 5.1 Effecs of evporion on sorge nd llowble yield Reservoir cpciies were deermined for specified yield under he cses when evporion ws included nd when i ws no. I ws observed h when including evporion ino SPA mehod, he desired sorge cpciies incresed, indicing significnce of evporion for he dm in quesion (Tble 2). From hese resuls lone, i is cler h he norhern reservoirs hve lower evporion res compred o heir counerprs, wih Bok dm recording he highes re of evporion. I should however be noed h he bove conclusions re resriced o inclusion of evporion on he esimion of reservoir cpciy, nd s such here is need o furher ssess hese effecs on reservoir performnce nd he CP under specified yields. Since he effecs re much fel wihin he CP, n ssessmen of he effecs ws resriced o his period, hough he simulion WIT Trnscions on Ecology nd he Environmen, Vol 83, 25 WIT Press ISSN (on-line)

5 River Bsin Mngemen III 635 ws bsed on he enire record lengh. From Figs 1-4, i is observed h Boswn reservoirs loose more wer due o evporion, wih more wer los when he sorges re low (i.e. below 5%). Also, hese resuls re in greemen wih Tble 2, s on verge, souhern cchmens displyed higher evporion losses of 24%(Gborone) nd 54% (Bok), compred o norhern cchmens, wih low res of 2%(Shshe) nd 11%(Lesibogo). I my lso be noed h lhough Lesibogo dm hs generlly lower res of evporion, mos of hese losses however occur when he dm is 5-75% full, unlike Gborone nd Shshe dms, where he losses re much pronounced below 5% full cpciy. Ineresingly, Bok dm on he oher hnd ends o disply persisen loss of 5% hrough ll he sorge ses, mos likely due o shllow deph (8m). 25 Losses(%) 2 15 %Losses due o Evporion Sorge(%) Figure 2: Effec of evporion s percenge of cive sorge (Lesibogo dm). Losses(%) %Losses due o Evporion Sorge(%) Figure 3: Effec of evporion s percenge of cive sorge (Gborone dm) Alerion of he criicl period due o evporion By sudying relionship beween he llowble yield h reservoir cn suppor, nd he CP, Figs 5-8 hve shed more ligh; h ech sorge hs rnge of yield h i cn supply wihou lering he CP. The CP is no offse if i sys on he zero line indicing h he effecs of evporion re conined wihin h specific rnge of releses (i.e. for CP lg nd CP movemen plos). In ll he WIT Trnscions on Ecology nd he Environmen, Vol 83, 25 WIT Press ISSN (on-line)

6 636 River Bsin Mngemen III dms, i cn be seen h ouside he preferred rnge of yield, he CP eiher moves o compleely differen locion wihin he d record, or is lengh is lered. A summry of hese yields is given in Tble 2, wih he plos shown in Fig Also, he CP is ffeced when he yield is incresed, h is he sorge being pu under pressure o relese more wer hn i hs been designed for, hence displying mixure of posiive nd negive shif (erly CP nd le CP, respecively). In his scenrio, he demnd for wer coupled wih effecs of evporion mke he reservoir more prone o filures. This cn be problem during drough periods when inflows ino he reservoirs re much lower. 8 Losses(%) %Losses due o Evporion Sorge (%) Figure 4: Effec of evporion s percenge of cive sorge (Bok dm). CP(Monhs) 4 CPLg(due o Evp.) 3 CPMov(due o Evp.) CPLengh(NoEvp) 2 CPLengh(Evp) Yield(Monhly MCM) Figure 5: Effec of evporion on llowble yield (Shshe dm). CP(Monhs) CPLg(due o Evp.) CPMov(due o Evp.) CPLengh(NoEvp) CPLengh(Evp) Yield(Monhly MCM) Figure 6: Effec of evporion on llowble yield (Lesibogo dm). WIT Trnscions on Ecology nd he Environmen, Vol 83, 25 WIT Press ISSN (on-line)

7 River Bsin Mngemen III 637 CP(Monhs) CP lg(due o Evp.) CP Mov(due o Evp.) CPLengh(NoEvp) CPLengh(Evp) Yield(MonhlyMCM) Figure 7: Effec of evporion on llowble yield (Gborone dm). CP(Monhs) 3 CP Lg(due o Evp.) 25 CPMov(due o Evp.) 2 CPLengh(NoEvp) 15 CPLengh(Evp) Yield(Monhly MCM) Figure 8: Effec of evporion on llowble yield (Bok dm). 6 Conclusions The pper s objecives were o deermine effecs of including evporive losses on reservoir sizing nd operion, nd how h ffecs he yield o be suppored by ech dm. From he four dms sudied, i hs been esblished h evporion is very criicl no only during reservoir sizing bu lso hroughou is operion. Furhermore, i hs been found h for ech of he reservoir cpciy esimes, here exiss window of llowble yield, wihin which he effecs of evporion cn sill be conined. The CP hen become sensiive s soon s he dm is sressed o relese more wer hn i hs been designed for. When considering he significnce of evporion cross Boswn dms, i cn be concluded h he souhern dms re much suscepible o effecs of evporion hn he norhern dms. From hese four, Bok showed highes res, no wonder i is used s rnsfer sion ino he Gborone dm hrough he Norh-Souh wer rnsfer scheme. While here re severl fcors conribuing o high evporion res in Boswn dms, mos of hese cn be WIT Trnscions on Ecology nd he Environmen, Vol 83, 25 WIT Press ISSN (on-line)

8 638 River Bsin Mngemen III ribued o opogrphic chrcerisics of cchmens (fl errin nd lck of suible sies), nd shpe of dms (shllow nd wide dms). References [1] Adeloye A.J., Monseri M., & Grmnn C., Curing he misbehviour of reservoir cpciy sisics by conrolling shorfll during filures using he modified sequen pek lgorihm. Wer Resources Reserch, 37(1); pp , 21. [2] Lele S. M., Improved lgorihms for reservoir cpciy clculion incorporing sorge-dependen losses nd relibiliy norm. Wer Resources Reserch, 23(1), , [3] Liebenberg & Snder Boswn, The hydrogrphic Survey of Shshe, Gborone, Nowne nd Nnywne dms, Finl Repor. Vol 2, Deprmen of Wer Affirs, Boswn, 2. [4] Loucks P.D., Sedinger J.R., Hih D.A., Wer Resources Sysems Plnning nd Anlysis. Prenice-Hll, Englewood, Cliffs. NJ., [5] McMhon T.A., Mein R.G., River nd Reservoir Yield, Wer Resources Publicion. Lileon. Co, [6] Monseri M., nd Adeloye A.J., Criicl period of reservoirs for plnning purposes. J. Hydrology, 224(1999), , [7] Snowy Mounins Engineering Corporion (SMEC), Boswn Nionl Wer Mser Pln Sudy, Volume 6, Hydrology, Boswn, [8] Vogel R.M., McMhon T.A., Approxime relibiliy nd resilience indices for over-yer reservoirs fed by AR(1) Gmm nd Norml flows. Hydrologicl Sciences. Journl, 41(1) 75-96, WIT Trnscions on Ecology nd he Environmen, Vol 83, 25 WIT Press ISSN (on-line)