A grid-based runoff generation and flow routing model for the Upper Blue Nile basin

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1 Hydrologcal Scences Journal ISSN: (Prnt) (Onlne) Journal homepage: A grd-based runoff generaton and flow routng model for the Upper Blue Nle basn ANIL MISHRA & TAKESHI HATA To cte ths artcle: ANIL MISHRA & TAKESHI HATA (26) A grd-based runoff generaton and flow routng model for the Upper Blue Nle basn, Hydrologcal Scences Journal, 51:2, , DOI: /hysj To lnk to ths artcle: Publshed onlne: 19 Jan 21. Submt your artcle to ths journal Artcle vews: 799 Vew related artcles Ctng artcles: 11 Vew ctng artcles Full Terms & Condtons of access and use can be found at Download by: [ ] Date: 23 November 217, At: 3:29

2 Hydrologcal Scences Journal des Scences Hydrologques, 51(2) Aprl A grd-based runoff generaton and flow routng model for the Upper Blue Nle basn ANIL MISHRA 1,2 & TAKESHI HATA 1 1Graduate School of Scence and Technology, Kobe Unversty, Kobe , Japan hata@kobe-u.ac.jp 2 Jacob Blausten Insttute for Desert Research, Ben-Guron Unversty of the Negev, Sede Boker Campus, 8499 Israel Abstract A smple water balance model was used to generate monthly water surplus for.5 grd cells of the Upper Blue Nle basn. An applcaton of a spatally dstrbuted unt hydrograph method s presented to route generated runoff from the grd cells. The work dffers from prevous modellng work on the basn n that t accounts the spatal varablty of the flow parameters. The study llustrates that velocty s a more sgnfcant parameter n determnng the response of the basn. The key nference from the smulaton wth spatally varable parameters s that, f varable velocty zones exst n a basn, then t s mportant to consder the effect of non-unform dsperson coeffcents as well. The study also demonstrated the successful smulaton of the hydrologcal cycle for a local/natonal data-poor basn usng data sets manly from global archves. Key words Blue Nle basn; flow routng model; dstrbuted model; unt hydrograph; water balance Un modèle mallé de génératon de l écoulement et de propagaton pour le bassn supéreur du Nl Bleu Résumé Un modèle smple de blan hydrologque a été utlsé pour générer l écoulement mensuel ssu de malles de.5 couvrant le bassn supéreur du Nl Bleu. Une applcaton d une méthode de type hydrogramme untare dstrbué est présentée pour transférer l écoulement généré ssu des malles. Ce traval dffère des travaux de modélsaton précédents sur le bassn par la prse en compte de la varablté spatale des paramètres d écoulement. Cette étude montre que la vtesse est un paramètre plus sgnfcatf pour détermner la réponse du bassn. La prncpale concluson de la smulaton réalsée avec des paramètres varables dans l espace est que, s l exste des zones de vtesse varable dans un bassn, l est alors mportant de consdérer également l effet des coeffcents de dsperson non unforme. L étude montre en outre la bonne smulaton du cycle hydrologque pour un bassn pauvre en données locales/natonales, en utlsant des jeux de données ssus prncpalement d archves globales. Mots clefs Bassn du Nl Bleu; modèle de propagaton; modèle dstrbué; hydrogramme untare; blan hydrologque INTRODUCTION The Upper Blue Nle, wth a basn area of almost 175 km 2, s the most mportant trbutary of the Nle Rver and provdes over 5% of the Nle s supply of freshwater to the North Afrcan countres, Sudan and Egypt (Conway, 1997). Currently North Afrca s one of the most acute water-shortage regons n the world, where per capta water avalablty s already less than the basc requrement of ~1 m 3 per year (Wallace & Gregory, 22). Egypt, and to a lesser extent Sudan, are almost wholly dependent upon water that orgnates from the Nle. Ths dependency makes the challenges of water resources management n ths regon an nternatonal ssue (Waterbury, 22). Pressure on water resources n the Nle basn are lkely to ncrease dramatcally n the comng years as a result of hgh populaton growth rates n all rparan states, and ncreasng development-related water needs n Ethopa. Nevertheless, n spte of the natonal and nternatonal mportance of the regon, only a few studes have been conducted n the Upper Blue Nle wthn Ethopa and there s only lmted understandng of the basn s detaled clmatc, hydrologcal, topographc and hydraulc Open for dscusson untl 1 October 26

3 192 Anl Mshra & Takesh Hata characterstcs (Johnson & Curts, 1994; Conway, 1997). Conway (2) provdes a revew of the nature and varablty of the clmate and hydrology of the Upper Blue Nle basn. The Blue Nle s characterzed by severe seasonalty wth average annual flow of about 5 km 3 measured at the basn outlet at El Dem staton near the Sudan Ethopa border. More than 8% of ths flow occurs durng the flood season between July and September, whle only 4% of that flow occurs durng the drest perod January Aprl. Whlst mproved forecastng of the Blue Nle low flows has potentally sgnfcant benefts to reservor management n the downstream rparans, partcularly Sudan (Mshra et al., 23, 24), a comprehensve modellng study would contrbute to the scentfc understandng of ths major, yet lttle studed hydrologcal system. The upper and lower basns of the Blue Nle Rver are shown n Fg. 1. Fg. 1 The upper and lower basns of the Blue Nle Rver. There have been several attempts to develop basn-scale hydrologcal modellng on the Blue Nle, ncludng the work undertaken by Gleck (1991), Schaake (1993), Johnson & Curts (1994), Conway & Hulme (1993, 1996), Strzepek et al. (1996), Conway (1997) and Olvera et al. (2). Johnson & Curts (1994) and Conway (1997) appled smple water balance models to a number of sub-catchments n the Blue Nle basn. Statstcal analyss by Atta & Abulhoda (1992) and Eltahr (1996) show that ENSO epsodes are negatvely teleconnected wth the floods of the Blue Nle and Atbara rvers that orgnate n Ethopa. Conway & Hulme (1996) studed the applcaton of hydrologcal models of the Blue Nle and Lake Vctora sub-basns to assess the magntude of potental mpact of clmate change on Man Nle dscharge. Olvera et al. (2) used the generalzed verson of the unt hydrograph model to route Nle flow. Although they dentfed the mportance of accountng for the spatal varablty of the flow parameters for the three major Nle trbutares, they used unform streamflow parameters for the Blue Nle basn. Such unformly dstrbuted

4 A grd-based runoff generaton and flow routng model for the Upper Blue Nle basn 193 parameters may overlook well-known hydrologcal processes that take place n the complex terran such as n the Upper Blue Nle basn. The present study ams to contrbute to overcomng ths potental shortcomng. The sze and complexty of the Upper Blue Nle, together wth the lack of hydrologcal data, s a severe constrant to the applcaton of sophstcated hydrologcal models (Conway, 1997). However, as more and more data have been collected n computerzed databases and, n partcular, n GIS, the data avalablty has mproved sgnfcantly (Andersen et al., 21). Global data sets are becomng ncreasngly avalable and data from the Internet can often be used to substtute for ground-based observatons (Kte, 21). In ths study a grd-based macro-scale model has been organzed as a set of nteractng components of water balance and water transport models usng data manly from the publc doman. To the authors knowledge ths s the frst tme that a complete quantfcaton of the hydrologcal cycle for the Upper Blue Nle basn has been smulated. Prevous studes were lmted to separate components: water balance smulaton at basn scale or rver routng smulatons at sub-catchment scale only. Moreover, the work dffers from prevous modellng work on the basn n that t s based on the mportance of accountng the spatal varablty of flow parameters. SOIL WATER BALANCE MODEL Water balance models were developed by Thornthwate (1948) and revsed by Thornthwate & Mather (1955) and Budyko (1974, 1982). Monthly water balance models have been wdely used and modfed to address a wde spectrum of water resources problems (Wllmott et al., 1985; Xu & Sngh, 1998). They have been utlzed for long-range streamflow forecastng (Arnell, 1999; Xu & Vandewele, 1995) and to explore the mpact of clmatc change (Xu & Haldn, 1996). Varous studes consdered a varety of models and parameter estmaton algorthms, whch ranged from relatvely complex conceptual models wth 1 15 parameters to those much smpler wth two to fve parameters (Vandewele et al., 1992; Makhlouf & Mchel, 1994). Monthly water balance models can take a smpler form and use a smaller number of parameters than correspondng daly hydrologcal models (Xong & Guo, 1999). The present study also employs a smple water balance model for the water resources assessment of the Upper Blue Nle basn. The model s supported by a hydro-clmate-gis database, whch was developed n the course of authors study of ths regon. Methodology A sol-water balance model estmates the sol-water surplus (or defct) relatve to water holdng capacty gven a precptaton tme seres, potental evaporaton estmates, and assumptons about the relatonshp lnkng actual evapotranspraton to tme-varyng sol water. The water surplus s defned as water whch does not evaporate or reman n sol storage and s avalable to generate surface and subsurface runoff. Water surplus can be estmated usng a smple bucket model (Thornthwate,

5 194 Anl Mshra & Takesh Hata 1948; Wllmott et al., 1985). In the smple bucket model, the basc equatons for calculatng water surplus are: S ( w() t w* ) ( t) = () t w* Δt () w( t 1) w t Δt = Δt + P () t E() t S () t = () t w() t w = f w () t > w* (1) (2) w = f w() t w* (3) where S(t) s water surplus; P(t) s precptaton; E(t) s evapotranspraton; w(t) s sol mosture storage; and w * s the sol water holdng capacty. Tme seres of the mean monthly temperature and precptaton nterpolated to a.5 (lattude longtude) grd cell for the Blue Nle basn were obtaned from the Unversty of Delaware ( These data are from the Global Ar Temperature and Precptaton Data Archve compled by Wllmott & Matsuura (1995). In the current study, ndependent water balance predctons are made usng the water balance model (equaton (1)) for.5 grd cells representng the Upper Blue Nle basn. The model s smlar to a large-scale modellng approach used for the Amazon and Zambez basns by Vörösmarty et al. (1989) and Vörösmarty & Moore (1991). Snce the ntal sol mosture storage s unknown, the followng ntalzaton procedure s appled to force the net change n sol mosture from the begnnng to the end of a specfed balancng perod to zero,.e. w() w(n + 1) < ξ, where n s the number of tme steps of a complete computaton perod (12 months), and ξ s the userspecfed tolerance (ξ =.1% s used n ths research). Calculatons commence at the end of the wet season when t s assumed that the sol s at feld capacty. Sol water stocks are then depleted durng the dry season n accordance wth the mosture retenton functon. For each wet month, sol mosture s determned by ncrementng antecedent values by the excess of avalable water over evapotranspraton. Global estmates of plant-extractable water capacty are avalable on a.5 grd (Dunne & Wllmott, 1996). As used n ths study, the term plant-extractable water capacty s equvalent to avalable water-holdng capacty. One reason gven for developng ths global database was to elmnate the need for assumng spatally nvarant plant-extractable water capacty n sol-water balance computatons made over large areas. Informaton about sand, clay, organc content, plant rootng depth and horzon thckness was used to estmate the plant-extractable water capacty (Dunne & Wllmott, 1996). Thornthwate evaporaton calculaton s consdered n the model and s derved for the.5 grd cell for the basn. As a sol dres t becomes ncreasngly dffcult to remove mosture aganst ncreasng pore tenson. To estmate the actual evapotranspraton n the sol-water budget method, a sol-mosture extracton functon, smlar to that used by Vörösmarty et al. (1989), s appled, whch relates the actual rate of evapotranspraton to the potental rate of evapotranspraton based on the current sol mosture content and mosture retenton propertes of the sol. The functon has been appled under the restrctve condton that sol mosture s wthdrawn at maxmum rate untl the rato drops below.7, at whch tme a lnear declne n avalablty s assumed (Thornthwate & Mather, 1957). Monthly water surplus calculaton s made usng

6 A grd-based runoff generaton and flow routng model for the Upper Blue Nle basn 195 equaton (1) for the 1979/8 1984/85 data perod whch s ncluded n the database. The smulaton perod was chosen based on the avalablty of streamflow data for valdaton from the basn outlet at El Dem staton located near the Sudan Ethopa border. Although short, ths 5-year perod ncludes dry, wet and average condtons. Snce the grd water-holdng capactes were not reached from the model run (equaton (1)) and under predcted runoff for the majorty of months, a modfcaton of the model s consdered wth an extracton functon, whch s descrbed below. Modfed water balance model The use of monthly tme steps nvolves the mplct assumpton that ran falls contnuously at a low ntensty throughout the month and under-predcts runoff. As a result, a correcton factor must be appled to avod under-predctng runoff. Alley (1984) and others have used an extracton functon to compensate for ths shortcomng. Vörösmarty et al. (1998) (also Vörösmarty et al., 1989; Vörösmarty & Moore, 1991) conducted a comparable study of a set of potental evaporaton functons that are commonly employed n global-water scale balance method. Furthermore, they also evaluated the accuracy wth whch each E p functon can smulate runoff when drven by a pror parameter assgnments and data sets commonly employed n global-scale modellng studes. Snce the basn s water holdng capactes were not reached for most months, an extracton functon was ntroduced to compensate for the tme-scale lmtaton of monthly data and to mplctly compute streamflow. Ths functon nvokes an ntal abstracton to be removed from the budgetng calculatons and automatcally dstrbutes a porton of ranfall to runoff. In the absence of excess sol mosture, the followng modfed approach extracts a fracton of precptaton and declares runoff before remanng precptaton s passed to the sol: () w( t 1) w t Δt = Δt + P ()( t 1 α ) + P() t α E() t ex ex where α ex P, the runoff extracton term, accounts for event or quck flow whch cannot be modelled usng monthly averaged values: ( 1) w t α ex = (5) w* Thus the modfed balance equaton s: () w( t 1) ( 1) ( 1) w t w t w t = + P() t + P() t t t 1 Δ Δ w* w* E() t The α ex value s derved based on sol mosture condtons for the space-tme grd and potental water holdng capacty of the grd. Snce the ntal sol mosture storage s unknown, the water balancng procedure (equaton (6)) s appled to force the net change n sol mosture from the begnnng to the end of a specfed balancng perod to zero. In equaton (6), w(t) and w(t 1) denote the sol mosture n the current and the prevous tme step, respectvely; and w* s the water-holdng capacty for each grd. (4) (6)

7 196 Anl Mshra & Takesh Hata Fg. 2 Dstrbuton of α ex for the Blue Nle basn. Fgure 2 shows the dstrbuton of the α ex parameter value for the Blue Nle basn for the study perod. Durng the wet season the coeffcent reaches ts peak value when the sol s at potental capacty. In contrast, sol water stocks are depleted durng the dry season wth the decreasng coeffcent value. Fgure 3 shows the extracted grd surface runoff for the study perod obtaned from the modfed monthly water balance model. The extracted grd runoff was then used as nput value for the runoff routng routne for the basn. FLOW ROUTING MODEL The tme seres representng the runoff of a watershed can be calculated from the tme seres of the water surplus by a runoff routng model. There are many dfferent runoff routng models (RRM) for large-scale rver basns, and most of them belong to the class of lnear-reservor models. In such models, the grd cells are lnear reservors (characterzed by a transfer coeffcent, T -1 ), dschargng nto one another along the dranage network. As revewed by Arora & Boer (1999), the transfer coeffcents are also related to veloctes gven the length of cells and can be: constant over tme and space (e.g. Ok & Sud, 1998), constant n tme but spatally dependent on topography (Hageman & Dumenl, 1998) and/or mean dscharge (Lston et al., 1994; Vörösmarty et al., 1989), or varable n both space and tme, as a functon of topography, channel characterstcs and dscharge (Arora & Boer, 1999). In ths study a two-parameter routng response functon s determned for each cell, whch s related to flow tme (flow velocty) and shear effects (dsperson coeffcent) n the cell. Flow path response functons and responses at the outlet to nstantaneous unt nputs n the cells are calculated by a convoluton ntegral of the responses of the cells located wthn each reach. The watershed response s obtaned as the sum of the flow response to spatally

8 A grd-based runoff generaton and flow routng model for the Upper Blue Nle basn 197 a) Year 198 b) Year 1981 c) Year 1982 d) Year 1983 e) Year 1984 Fg. 3 Spatal dstrbuton of annual extracted surface runoff. dstrbuted precptaton excess. The dgtal flow path networks for the Upper Blue Nle basn (Fg. 4) were constructed usng HYDRO 1K DEM (USGS, 22) and were used to route dscharge from each grd.

9 198 Anl Mshra & Takesh Hata Source-to-snk method 1 Km 2 Km 3 Km Fg. 4 Dgtal flow path networks for the Blue Nle flow. An assumpton of lnearty s made n the source-to-snk routng model (Olvera & Madment, 1999). A decomposton of the nputs at the source nto a seres of smaller segments results n an dentcal output at the snk. Olvera (1996) outlnes three major features that characterze a lnear hydrologcal system. These nclude longtudnal decomposablty, whch allows rvers to be splt nto smaller segments and modelled separately; areal decomposablty, whch allows basns to be subdvded and modelled as a seres of separate watersheds; and superpostonng of sub-area responses, whch allows the results of smulatons n dfferent watersheds to be aggregated. The second mportant assumpton made n the source-to-snk approach s that the transformaton parameters relatng system nput to output are tme nvarant (Asante, 2). For a source-to-snk model, ths mples that the physcal locaton of the flow path lnkng a source to a snk does not vary wth tme. In addton, the parameters at each locaton along that flow path reman constant throughout the routng perod (Olvera & Madment, 1999). Model components Sources are runoff producng unts and are the areas where water enters the surface water system as runoff, whereas snks are runoff-recevng unts (Olvera et al., 2).

10 A grd-based runoff generaton and flow routng model for the Upper Blue Nle basn 199 The rver basn s vewed as a seres of sources each defned and parameterzed n relaton to an observaton pont or snk located further downstream. Sources nteract wth the snk through a response functon. A response functon s defned for each flow path whch descrbes the shape of hydrograph at the snk gven an nstantaneous nput at the source. The response functon ncludes a measure of the travel tme, storage effects along the flow path. For a spatally unform hydrologcal system the unt hydrograph model can be wrtten as (Olvera & Madment, 1999): () = A I() τ u ( t τ)τ d Q t t w (7) where t s tme; Q s the flow at the watershed outlet; A w s the watershed area; I s the excess precptaton; u s the watershed response (unt hydrograph); and τ s the tme when watershed receves an nput of unt amount appled nstantaneously. Smlarly, for a spatally dstrbuted lnear system subdvded nto unform non-overlappng subareas, ths equaton takes the form (Madment et al., 1996; Olvera & Madment, 1999): Q N w () t A I () τ U ( t τ)τ d = = 1 t where N w s the number of sub-areas, A s the area of sub-area, I s the excess precptaton ntensty n sub-area (sub-area nput), and U s the response at the watershed outlet to a unt nstantaneous nput n sub-area. Because of the addtvty property that characterzes lnear systems, the overall watershed response can be calculated as the sum of the sub-area responses. In ths study sub-areas are taken as.5 grd cells of the Blue Nle basn. The nput runoff for each source of grdded area s obtaned from the modfed sol water balance model, whch was explaned n the prevous secton. The response at the watershed outlet cell to an nstantaneous unt nput n an upstream watershed cell s called the flow path response functon. Flow path response functons represent the translaton (advecton) and redstrbuton (dsperson) processes n the flow path,.e. lag tme from the watershed cell to the watershed outlet (Olvera & Madment, 1999). If the grd cells are assumed to convey one-dmensonal and unsteady flow and the nertal terms n the St Venant momentum equaton are neglected, the flow process can be modelled by the dffuson wave equaton (Lettenmaer & Wood 1993; Olvera & Madment, 1999). Then, f lateral nflow s not consdered, the flow s represented by: Q t + c Q x d Q 2 2 x = where x s the dstance along the flow drecton; t s the tme; Q s the flow at any tme t and locaton x of cell ; c s the knematc wave celerty n cell ; and d s the dsperson coeffcent n cell. For a tme-nvarant flow velocty, v, at each cell the knematc wave celerty, c, s equal to the flow velocty, because c = dq /da (Chow et al., 1988) and, t follows, c = d(v A)/dA = v. For a unt-mpulse nput, the soluton of equaton (9) for Q at the cell outlet s the cell response functon u, assumng the (8) (9)

11 2 Anl Mshra & Takesh Hata response functon s a frst-passage-tme dstrbuton (Naden, 1992; Troch et al., 1994; Olvera & Madment, 1999; Olvera et al., 2): u = 2t π ( t t ) ( v l d ) 1 exp 4 2 [ 1 ( t t )] ( t t ) ( v l d ) where t s the expected flow tme through the cell and l s the flow length wthn the cell,.e. l = v t. Because the cell flow length, l, s known, the only two parameters whch need to be determned are the flow velocty, v and the dsperson coeffcent, d. (1) Estmaton of flow velocty Tme nvarance of the flow velocty v s a property of lnear routng systems (Olvera, 1996). A basc assumpton made here wth regard to the flow velocty feld s that t depends on local constant parameters such as bottom roughness, land slope, dranage area, etc. and not on tme-varyng varables such as flow or storage (Madment et al., 1996). Accordngly, the flow velocty s tme- and dscharge-nvarant. Ths requrement for constant resdence tmes n the elements of the system makng up the unt hydrograph was recognzed by Clark (1945). The US Sol Conservaton Servce (SCS, 1985) presented a formula for overland flow velocty as functon of land surface slope, S: b v = as (11) Equaton (11) s a smplfcaton of the Mannng formula for open channel flow n whch b =.5 and the coeffcent a = R 2/3 /n. The value of a s a functon of the land cover wth the effect measured by the value of n and R. By comparng the land and flow regmes of the basn, the value of a for each grd of the Blue Nle catchment s obtaned from McCuen (1998), as s shown n Table 1. The land surface slope, S, s measured usng GIS functon, and thus the mean value of overland velocty v =.43 m s -1 for the basn s obtaned from equaton (11). Spatally dstrbuted velocty s assgned to each cell and the tme lag between the sub-area nput and response at the watershed outlet s found by ntegratng the flow tme along the path from the sub-area to the outlet. Snce equaton (11) s appled to the entre watershed and not smply to the land surface, the fact that velocty ncreases gong downstream n the rver system needs to be taken nto account. As the water deepens, the effectve resstance of the bed and banks on the flow dmnshes because Table 1 Coeffcent a (functon of land cover) vs land use and flow regme (roughness coeffcent, n). Land use/flow regme n a Forest, dense.8.7 Forest, lght Ground ltter Grass, dense Grass, short Agrcultural land Alluval fans Upland gulles

12 A grd-based runoff generaton and flow routng model for the Upper Blue Nle basn 21 the hydraulc radus ncreases (Leopold et al., 1964). To accommodate ths factor, Madment et al. (1996) modfed equaton (11) to the form: b c S A v = v (12) m b [ S A ] c m where v s the velocty assgned to a cell whose local slope s S and upstream dranage area s A; the coeffcents b and c are constants; v m s the average value of the velocty n all cells n the watershed area; and [S b A c ] m s the correspondng watershed average value of the slope-area term. The upstream dranage area of all cells, A, and slope, S, n the landscape are automatcally computed usng the GIS flowaccumulaton functon appled to the flow network developed from HYDRO1K DEM (USGS, 22) data. The ncluson of the dranage area A n the formula s a substtute for hydraulc radus n Mannng s equaton, whch allows the velocty to ncrease wth dranage area and neatly fnesses the ssue of whch cells le n the stream system and whch le on the land surface (Madment et al., 1996). Thus, the model was set up wth spatally varable velocty obtaned from equaton (12) for each.5 grd cell of the basn. Dsperson coeffcent The dsperson coeffcent s usually taken to be the longtudnal dsperson and shows the turbulence of shearng effects whch determne the hydraulcs of the channel (Snell & Svapalan, 1994). In many applcatons n water qualty modellng, the dsperson coeffcent s derved from channel propertes (Fscher, 1967). Dfferent methods to calculate the dsperson coeffcent have been proposed by Troch et al. (1994). In ths study, a GIS-based method s appled to obtan spatally dstrbuted dsperson coeffcents for the basn. The dsperson coeffcent can be expressed n terms of the frst two moments of the dstrbuton path lengths (Snell & Svapalan, 1994; Saco & Kumar, 22): ( L) [ L] v var D = (13) 2E where D (n m 2 s -1 ) s a functon of the ensemble catchment averaged velocty and the rato of the frst and second moments of the dstrbuton of the flow dstances expressed through the mean and varance of the flow dstances. Total varance along a flow path can be determned as the sum of the varance along the component segments (Asante, 2). Varance along the total flow path s obtaned from the flow for each grd path, whch s determned from the GIS functon. Comparson wth observed flows The STS model was run for El Dem staton (snk), Sudan, at the outlet of the Upper Blue Nle basn. Monthly observed flow data for the data perod were obtaned from the Mnstry of Irrgaton and Water Resources, Sudan. A constant dscharge baseflow separaton was performed to the observed flow whch s shown n Fg. 5. The flow perod was separated nto fve annual blocks. The lowest flow

13 22 Anl Mshra & Takesh Hata Fg. 5 Observed flow and separated baseflow at El Dem staton. recorded durng each annual block was defned as baseflow, and all flows n excess of ths were defned as snk dscharges. The routng model was run n four dfferent sets. The model was set up frst wth a spatally dstrbuted flow velocty, obtaned from equaton (12) wth the spatally varable dsperson coeffcent, and the run was dentfed as VDVV (varable dsperson coeffcent and varable velocty) flow. In the second run, the model was set up wth a constant velocty, obtaned from equaton (11) wth the spatally varable dsperson coeffcent, and the run was dentfed as VDCV (varable dsperson coeffcent and constant velocty) flow. The thrd setup was run wth the varable velocty, equaton (12) wth the constant dsperson coeffcent, and the run was dentfed as CDVV (constant dsperson coeffcent and varable velocty) flow. The fnal setup was run wth the constant velocty, equaton (11) wth the constant dsperson coeffcent, and the run was dentfed as CDCV (constant dsperson coeffcent and constant velocty) flow. Fgure 6 shows the observed vs smulated flows for all runs. Although the dfference between the observed values and smulated flows s small n all four runs, t s obvous that velocty s a more sgnfcant parameter n determnng the response of a basn. To quantfy the performance of the four dfferent smulatons, they were compared n terms of hydrograph, usng the NSE (normalzed standard error) objectve functon: m 1 2 ( Qe Qo ) m 1 NSE = (14) Qo where Q o and Q e are observed flow and estmated flow. Value of the NSE crteron s expected to be mnmum for a better smulaton. The objectve functon ndcator (Fg. 7) also gves better value for the smulaton wth the spatally dstrbuted parameter. It can be seen from Fg. 7 that spatally dstrbuted flow parameters (velocty) provde a better ft to the observed data. Results ndcate that the VDVV and CDVV smulatons provde better values than wth the constant flow parameters

14 6 7 Observed flow Observed flow 5 Smulated flow (VDVV) A grd-based runoff generaton and flow routng model for the Upper Blue Nle basn 23 6 Smulated flow (VDCV) Flow (m 3 s -1 ) Flow (m 3 s -1 ) (a) (b) observed flow smulated flow (VVCD) Observed flow Smulated flow (CVCD) Flow (m 3 s -1 ) 2 1 Tme (days) Flow (m 3 s -1 ) (c) Tme (days) Fg. 6 Observed vs smulated flows (VDVV: varable dsperson coeffcent and varable velocty; VDCV: varable dsperson coeffcent and constant velocty; CDVV: constant dsperson coeffcent and varable velocty; CDCV: constant dsperson coeffcent and constant velocty) (d)

15 24 Anl Mshra & Takesh Hata Fg. 7 Values of the objectve functon for the four dfferent smulatons: VDVV varable dsperson coeffcent and varable velocty; VDCV varable dsperson coeffcent and constant velocty; CDVV constant dsperson coeffcent and varable velocty; and CDCV constant dsperson coeffcent and constant velocty. VDCV and CDCV. The shapes of hydrograph n the runs were determned by response functon, whch ncludes a measure of the travel tme and storage effects along the flow path. The dscrepances between the hydrographs n the VDVV and CDVV smulatons reflect possble flow loss mechansms along the flow path. Future research wll study the ncluson of flow loss mechansms n the routng process along the flow path (such as effect of evaporaton to the atmosphere or the accountng of localzed areas of floodplan storage), whch can provde more realstc physcal response of a basn. CONCLUSIONS The results of ths study allow one to assess the relatve mportance of the dfferent hydrologcal processes that take place n a large watershed. Frstly, the study shows that a modfed water balance wth an extracton functon s able to partton fast and slow components of runoff. The extracton functon compensates for the tme-scale lmtaton of monthly data. Wthout ths modfcaton, the model would predct zero runoff durng many months when observed streamflow actually occurs. Secondly, the study shows that the spatally varable velocty s the most sgnfcant parameter n determnng the response of a basn, whle constant flow parameters may overlook well-known hydrologcal processes that take place n the complex terran such as n the Blue Nle basn. The key nference from the runs wth spatally varable parameters s that, f varable velocty zones exst n a basn, then t s mportant to consder the effect of non-unform dsperson coeffcent as well. An mportant concluson from the senstvty analyss of the source-to-snk routng model s that the accountng for the spatal varablty of streamflow parameters can make an ncremental, though postve

16 A grd-based runoff generaton and flow routng model for the Upper Blue Nle basn 25 mprovement n the predcted response of a basn. Another mportant fndng, though broader n scope, s the successful demonstraton of the use of data sets from global archves to acheve what may not otherwse be achevable usng nformaton avalable from local or natonal sources. Fnally the applcaton of a scale-ndependence routng model wth fne-resoluton data nputs (clmate, terran) would ad n a more complete nterpretaton of the mpact of clmate varablty (e.g. ENSO) and progressve change on water resources across the Blue Nle basn. Acknowledgements Ths work s part of a study supported by the grants-n-ad (no ) from the Japan Socety for the Promoton of Scence. The authors are grateful to the staff of the Agrcultural Research Corporaton and Mnstry of Irrgaton and Water Resources, Sudan for ther knd cooperaton. The authors wsh to thank the anonymous revewers for ther valuable and constructve comments. REFERENCES Alley, W. M. (1984) On the treatment of evapotranspraton, sol mosture accountng and aqufer recharge n monthly water balance models. Water Resour. Res. 2, Andersen, J., Refsgaard, J. C. & Jensen, K. H. (21) Dstrbuted hydrologcal modellng of the Senegal Rver basn: model constructon and valdaton. J. Hydrol. 247, Arnell, N. W. (1999) A smple water balance model for the smulaton of streamflow over a large geographc doman. J. Hydrol. 217, Arora, V. K. & Boer, G. J. (1999) A varable velocty flow routng algorthm for GCMs. J. Geophys. Res. 14, Asante, K. O. (2) Approaches to contnental scale rver flow routng. PhD Dssertaton, The Graduate School of the Unversty of Texas at Austn, USA. Atta, B. B. & Abulhoda, A. B. ( 1992) The ENSO phenomenon and ts mpact on the Nle's hydrology. In: Clmate Fluctuatons and Water Management (ed. by M. A. Abu-Zed & A. K. Bswas), Butterworth Henemann, London, UK. Budyko, M. I. (1974) Clmate and Lfe. Academc Press, New York, USA. Budyko, M. I. (1982) The Earth s Clmate: Past and Future. Internatonal Geophyscs Seres, vol. 29. Academc Press, New York, USA. Chow, V. T., Madment, D. R. & Mays, L. W. (1988) Appled Hydrology. McGraw-Hll, New York, USA. Clark, C. O. (1945) Storage and unt hydrograph. Trans. Am. Soc. Cvl Engrs 11, Conway, D. (1997) A water balance model of the Upper Blue Nle n Ethopa. Hydrol. Sc. J. 42(2), Conway, D. (2) The clmate and hydrology of the Upper Blue Nle Rver. The Geogr. J. 166, Conway, D. & Hulme, M. (1993) Recent fluctuatons n precptaton and runoff over the Nle sub-basns and ther mpact on man Nle dscharge. Clmatc Change 25, Conway, D. & Hulme, M. (1996) The mpacts of clmate varablty and future clmate change n the Nle basn on water resources n Egypt. Water Resour. Dev. 12, Dunne, K. A. & Wllmott, C. J. (1996) Global dstrbuton of plant extractable water capacty of sol. Int. J. Clmatol. 16, Eltahr, E. A. B. (1996) El Nño and the natural varablty n the flow of the Nle Rver. Water Resour. Res. 32, Fscher, H. B. (1967) The mechancs of dsperson n natural streams. J. Hydraul. Dv. ASCE HY6, Gleck, P. K. (1991) The vulnerablty of runoff n the Nle basn to clmatc changes. The Envronmental Professonal 13, Hageman, S. & Dumenl, L. (1998) A parameterzaton of the lateral water flow for the global scale. Clmate Dynamcs 14, Johnson, P. A. & Curts, P. D. (1994) Water balance of Blue Nle Rver basn n Ethopa. J. Irrg. Dran. Engng 12, Kte, G. (21) Modellng the Mekong: hydrologcal smulaton for envronmental mpact studes. J. Hydrol. 253, Leopold, L. B., Wolman, M. G. & Mller, J. P. (1964) Fluval Processes n Geomorphology. W. H. Freeman, New York, USA. Lettenmaer, D. P. & Wood, E. F. (1993) Hydrologc forecastng. Chapter 26 n: Handbook of Hydrology (ed. by D. R. Madment), McGraw-Hll Inc., New York, USA. Lston, G. E., Sud, Y. C. & Wood, E. F. (1994) Evaluatng GCM land surface hydrology parameterzatons by computng rver dscharges usng a runoff routng model. J. Appl. Met. 33,

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