INTEGRATED MODELING OF MAIN CHANNEL AND FLOODPLAIN APPLIED TO AQUIDAUANA RIVER, IN BRAZILIAN PANTANAL

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1 INTEGRATED MODELING OF MAIN CHANNEL AND FLOODPLAIN APPLIED TO AQUIDAUANA RIVER, IN BRAZILIAN PANTANAL Adriano Rolim da Paz, Waler Collischonn, Carlos E. M. Tucci (1) Insiuo de Pesquisas Hidráulicas, Universidade Federal do Rio Grande do Sul, Av. Beno Gonçalves, 9500, Caixa Posal 15029, Agronomia, CEP , Poro Alegre (RS), Brazil phone: ; fax: ; {collischonn, ABSTRACT The hydrology and hydrodynamics consiue some of he main governing facors of ecosysem funcioning and hus is mahemaical represenaion plays a key role o ecological sudies and o waer resources planning and managemen. Several mehodologies have been applied o sreamflow simulaion. However, rivers wih large floodplains need a more specific mahemaical mehodology o represen hen, owing o occurrence of huge volumes of waer exchanged beween main channel and floodplain and appearence of secondary fluxes in he floodplain. Rivers in he Upper Paraguay River Basin, in he Brazilian Pananal, presen such hydrologic paern. This paper presens a mehodology o inegraed modeling of main channel and floodplain. The proposed mehodology consiss of combining a one-dimensional hydrodynamic model applied o he main channel and a raser-based model applied o he floodplain. Such mehodology was applied o Aquidauana River, in he river reach beween he river gauging saions of Aquidauana and Poro Ciríaco. The ime period from december/1999 o may/2000 was simulaed and ineresing resuls were achieved, such as he hydrograph falling from upsream o downsream closely o he observed values and he occurrence of a kind of maximum discharge in he hydrograph a Poro Ciriaco river secion. Flood exen propagaion along he floodplain was simulaed by he raser-based model, represening he secondary fluxes independenly of he main river flux. Keywords: floodplain, Pananal, hydrologic modeling 1 INTRODUCTION Hydrodynamics of aquaic sysems plays a key role in ecosysem funcioning, and influences physical, chemical, biological and ecological processes. In river sysems wih large floodplains, he hydrodynamic behavior becomes more ecologically valuable. Sedimen ranspor, nurien cycling, creaion of flooded areas propiious o fish reproducion and egg deposiion, seed ranspor and deposiion are jus some examples ha illusrae how exchanges of waer volumes beween main channel and floodplain may affec he whole ecosysem (Posel and Richer, 2003). Therefore, numerical modeling and simulaion of he hydrologic regime of river main channel and is floodplain is essenial o undersand, represen and predic ecosysem funcioning. Several mehodologies have been applied o mahemaically represen waer flow in rivers wih floodplain. Depending on he purposes of he sudy and on he modeled sysem characerisics, a specific and suiable approach is required o deal wih he waer volumes exchanged beween main channel and floodplain. For example, rivers of he upper Paraguay River basin, a Pananal Welands (Souh America), are characerized by huge volumes of waer exchanged beween main channel and floodplain, mainly due o he limied capaciy of main channel o convey floodwaer (Hamilon e al., 2002; Hamilon, 1999). In he secion of Paraguay River beween Amolar and São Francisco gauging saions, exchanges of waer beween main channel and floodplain may reach a flow up o m 3 /s (Bravo e al., in press).

2 The simples mehod of river modeling consiss of using a one-dimensional (1D) model and considering he floodplain as sorage areas or adoping compound cross secions (Cunge e al., 1980). The more complex approach is based on employing wo- (2D) or hree dimensional (3D) models. While 1D mehods are no able o represen he laeral exchanges of waer in a desirable way, applicaion of 2D or 3D hydrodynamic models o rivers and floodplains faces wih problems relaed o a complex floodplain opography, shallow waer dephs, and he weing and drying process (Gillan e al., 2005; Baes e al., 2005; Werner, 2004; Baes and De Roo, 2000). An alernaive approach consiss of using a cell-based model, which represens he floodplain areas by inerconneced cells consiuing a wo-dimensional horizonal nework (Cunge e al., 1980; Miguez and Mascarenhas, 1999; Villanueva, 1998). The main shorcoming of his mehodology is is inabiliy o represen secondary fluxes ha ake place in he floodplain. Owing o he increasingly developmen of geoprocessing echniques and Geographical Informaion Sysems (GIS) and availabiliy of remoe sensing daa, raser-based models have been developed and applied, such as he LISFLOOD-FP (Horri and Baes, 2001a; Baes and De Roo, 2000) and DELFT-FLS (Selling and Duijnmeier, 2003) models. These models represen he floodplain by a recangular grid, and each grid elemen is inerconneced wih is neighbors and some of hem wih he main channel, which is in urn simulaed by a 1D model. Besides simulaing floodplain secondary fluxes, raser-based models allow a beer represenaion of he spaial variabiliy of floodplain characerisics and produce very useful resuls such as inundaion maps which may be readily inegraed o GIS. Benefis of inegraed modeling of river and floodplain by combining 1D and 2D models are highlighed by several auhors (Selling and Verwey, 2005; Gillam e al., 2005; Verwey, 2001; Horri and Baes, 2001b). This paper describes a mehodology of combining a 1D hydrodynamic model and a raser-based floodplain model, and is applicaion o a secion of he Aquidauana River, in he Brazilian Pananal Welands. The ecological imporance of he Pananal, he role of he flood pulse for he ecosysem and he increasing hrea by large developmen programs are discussed by several auhors, such as Junk and Nunes de Cunha (2005), Girard e al. (2003), and Hamilon (1999), for example. Sudying and modeling inundaion paerns of Pananal may consiue an imporan sep owards a beer managemen of such vas complex floodplains. 2 METHODOLOGY In his research, a model for simulaing flow propagaion along he main river channel was combined wih a raser-based model applied o he floodplain. The main flow along river channel was simulaed wih a 1D hydrodynamic model, while a raser-based approach was adoped o model he 2D fluxes over floodplain. A specific module was developed aiming o allow he inegraed modeling of he wo sysems (main channel and floodplain). The following secions describe boh models used and he linkage procedure. 2.1 MAIN CHANNEL MODELING Flow propagaion along river main channel was simulaed wih he 1D hydrodynamic model IPH4 developed by Tucci (1978, 1998). This model solves he complee Sain Venan equaions (equaions 1 and 2) of fluid dynamics using a finie differences mehod wih an implici scheme. Deailed descripion of IPH4 model is presened by Tucci (1978, 1998). h Q + 1 = q (1) b x

3 2 Q Q h + + ga + ga( S f S0 ) = 0 (2) A x where: h is he flow deph; he ime sep; Q is he discharge; x he disance along he longiudinal river lengh; b and A are he widh and area of river cross-secion, respecively; g he local graviy acceleraion; S f he energy slope; S 0 he channel bed slope; q is he sum of laeral discharges along he river reach. 2.2 FLOODPLAIN MODELING A raser-based approach was employed for simulaing flow propagaion along he floodplain, following he mehodology proposed by Baes and De Roo (2000). Such auhors presened he LISFLOOD-FP model, which was also employed in several sudies (Baes e al., 2006; Baes e al., 2005; Huner e al., 2005; Horri and Baes, 2002; Horri and Baes, 2001a; Horri and Baes, 2001b). While cell-based models idenify specific areas o be represened and modeled individually by large cells (Figure 1-a) (Cunge e al., 1980), raserbased models divide he enire floodplain in square-grid elemens (pixels) (Figure 1-b). These grid elemens are inerconneced and waer volumes are exchanged beween neighbouring elemens and also beween grid elemens and he main channel. In his research, he main channel does no occupy any elemens in he floodplain, being represened by a single vecor line and simulaed by he 1D hydrodynamic model described in previous subsecion, following he approach adoped by Baes e al. (2005) and Horri and Baes (2001a). For each floodplain elemen, a horizonal waer level is assumed, and is waer volume varies in funcion of inpu and oupu flows (Baes and De Roo, 2000): V = Q + Q + Q + Q + Q, (3) up down lef righ R FP where: V is he waer volume; is he ime; Q up, Q down, Q lef and Q righ are he discharges exchanged wih he neighbouring elemens locaed above, bellow, in he lef and in he righ, respecively, of such elemen; Q R-FP is he discharge exchanged beween he floodplain elemen and he river reach. This waer balance may be modified o ake ino accoun ohers inpu and oupu of waer, such as precipiaion, evaporanspiraion and soil infilraion. In his research, each floodplain elemen is allowed o exchange waer volumes wih is four neighbours and wih he main river channel if such elemen lies over he river nework (Figure 1-b). A numerical discreizaion explici in ime and regressive in space was adoped, where he waer level in each grid elemen is locaed in is cenre and he discharges exchanged wih is neighbours are relaed o he corresponden elemen faces (Figure 1-c): where: j h h Q Q + Q x y Q + j i 1, j j j 1 j x x y y = i j h, is he waer deph in he elemen (j) in ime ; i j Q, x in x-direcion beween he elemen (j) and he elemen (i+1,j); (4) is he discharge exchanged i j Q, y is he discharge exchanged in y-direcion beween he elemen (j) and he elemen ( j+1); is he ime sep; x and y are he spaial resoluion in x- and y-direcion, respecively. The discharge beween wo grid elemens may be calculaed hrough hydraulic equaions such as flow resisance equaions (Manning, Chèzy) or weir and spill equaions. In his research, Manning equaion was adoped, using a numerical discreizaion in ime and space as follows:

4 where Q j x = ± h n 5 / 3 flow j h j h x i+ 1, j 1/ 2 y, (5) i j n, is he Manning s coefficien of resisance of he elemen (j) and flow h is he waer deph available o he flow beween he elemens (j) and (i+1,j) a ime. The waer deph h is defined as he difference beween he highes waer level of he wo elemens and he flow highes bed elevaion (Horri and Baes, 2001a; Baes and De Roo, 2000). The discharges in y-direcion are calculaed analogously. Figure 1 (a) Cell-based floodplain model srucure (adaped from Bravo e al., in press); (b) Raser-based floodplain model srucure; (c) Locaion of discharges and waer deph relaed o floodplain grid elemen (j). 2.3 LINKAGE BETWEEN MAIN CHANNEL AND FLOODPLAIN Linkage beween river main channel and floodplain is achieved by connecing floodplain elemens o river reaches and calculaing he discharges exchanged beween boh modeled sysems. Topological linkage beween floodplain and main channel is done previously o simulaion sar, afer models iniializaion, hrough a GIS-based auomaic procedure (Figure 2). Each floodplain elemen which lies over he river vecor nework is idenified and conneced o he corresponden river reach. In his sep flow equaions and parameers relaed o discharge beween floodplain and main channel are also defined, and may vary wihin each floodplain elemen. For example, one may adop a Manning resisance coefficien spaially variable according wih land use derived from saellie images. The main channel is represened in he 1D model by river reaches associaed wih one upsream and one downsream river cross secions. Due o differences in discreizaion, several floodplain grid elemens are usually conneced o he same river reach. A linear approximaion was adoped in order o deermine waer level and bed elevaion of he river reach a poins locaed beween is upsream and downsream river cross secions, where are locaed he inermediary floodplain elemens. During simulaion, river and floodplain models are combined delayed in ime. This delay is equal o one ime sep adoped o simulaing river main channel (d R ), which is usually several imes greaer han he ime sep used in he raser-based model (d FP ). The 1D model runs for one river ime sep (d R ) and he floodplain model runs np imes unil complee 1 d R (np = d R /d FP ). Then, discharges are calculaed for each exising linkage beween floodplain

5 elemens and river reaches. These calculaed exchange discharges are considered as inpu or oupu in river and floodplain models in he nex ime sep. Figure 2 Descripion of he iniializaion and simulaion procedures developed for combining river and floodplain models. 3 STUDY SITE The mehodology was applied o he Aquidauana River, in a 230 km secion beween he gauging saions of Aquidauana and Poro Ciríaco. Aquidauana River is locaed in he upper Paraguay River basin, in Brazilian Pananal Welands (Figure 3-a), which is one of he world s mos exensive weland complexes and was designaed by UNESCO as a Biosphere Reserve in he year Upper Paraguay River and some of is ribuaries are characerized by very fla areas and seasonal occurrence of floodplain inundaion, mainly due o he limied capaciy of he river channels o convey he seasonal floodwaer (ANA/GEF/PNUMA/OEA, 2005; Hamilon e al., 2002; Hamilon, 1999). Comparison beween he upsream and downsream hydrographs of he sudy river reach illusraes he huge volumes of waer exchanged beween main channel and floodplain (Figure 3-b). In he 1D hydrodynamic model, he main channel was discreized in 49 reaches of km lengh each one. Boundary condiions were locaed in he upsream river secion (Aquidauana) and 66 km downsream from he Poro Ciríaco gauging saion, o avoid influence over he calculaed hydrograph a his locaion. Daily discharges were available from ANA (2005), and a 145-day period was simulaed (from 28 December 1999 o 20 May 2000, period indicaed by he dashed recangle in Figure 3-b). Manning s coefficien of resisance was adoped wih values equal o in he main channel and 0.05 in he floodplain, based on lieraure mean values (Werner, 2004; Chow, 1959). A resoluion of 200 m (0.002 o ) was adoped o he raser-based floodplain model. Elevaion daa for he floodplain grid elemens were obained by resampling he globally-wide available Digial Elevaion Model (DEM) produced by he Shule Radar Topography Mission (SRTM), wih resoluion of hree arc second (~90 m) (CGIAR-CSI, 2005). Due o he lack of available daa, bed slope of main channel was derived from he DEM, wih values ranging from 0.20 m/km o 0.11 m/km (Figure 3-c). A ime sep of 15 min was adoped o he 1D hydrodynamic model (d R = 15 min), while a smaller ime sep was necessary o be used in he floodplain raser model (d FP = 2 s) in order o avoid numerical insabiliies. A differen approach would consis of using an adapive ime sep o floodplain model as proposed by

6 Huner e al. (2005). Figure 3 (a) Locaion of he Aquidauana River, in he secion beween he gauging saions of Aquidauana and Poro Ciríaco (adaped from hp://www.ana.gov.br/gefap); (b) Daily discharges a Aquidauana and Poro Ciríaco saions (he dashed recangle indicaes he simulaion period); (c) Sream elevaion profile of Aquidauana River represened in he 1D hydrodynamic model. 4 RESULTS AND DISCUSSION Despie no calibraion was carried ou in boh river and floodplain model parameers, in general he resuls were quie saisfacory. The hydrograph falling from upsream o downsream was reproduced close o observed values (Figure 4). The calculaed discharge peak was reduced from 700 m 3 /s a Aquidauana gauging saion o 210 m 3 /s a Poro Ciriaco, while he acual discharge peak in such saion is abou 180 m 3 /s. The difference in he maximum values reached by calculaed and observed discharges a Poro Ciríaco resuled in a sligh difference in he shape of he corresponden hydrographs. A beer agreemen beween river cross secion profile and floodplain elevaion daa may possibly improve he agreemen beween calculaed and observed hydrographs in erms of he maximum discharge value reached. Figure 4 Observed hydrograph a Aquidauana gauging Saion and calculaed and observed hydrographs a Poro Ciríaco.

7 Figure 5 shows calculaed exchange discharges beween main channel and floodplain relaed o five poins along Aquidauana River, which are indicaed in Figure 6. Negaive values mean ha he main channel is loosing waer o he floodplain, while a posiive discharge value means ha waer flows from floodplain o he main channel. For example, a poin P1, which is locaed approximaely 24 km downsream from Aquidauana gauging saion, occurred a maximum flow of 340 m 3 /s from he main channel o he floodplain. Three disinc siuaions may occur: (a) predominance of waer flowing from main channel o he floodplain (poins P1 and P5); (b) main channel receiving waer from he floodplain (poins P2 and P4); (c) alernaing of previous siuaions (poin P3). Hydrographs raced in Figure 5 illusrae he abiliy of he mehodology o deal wih he ineracion beween floodplain and main channel, being able o represen he hree menioned siuaions. Figure 5 Exchange discharges beween floodplain and main channel agains ime, for five differen poins (which locaion is shown in Figure 6). During simulaion, he developed modeling sysem races he flooded area, as shown in Figure 6. Floodplain grid elemens considered we (waer deph > 0) are blue-coloured, wih darker colours indicaing deeper waer. In Figure 6, four simulaed flooded areas are raced, relaed o differen insans of ime. This kind of model oupu is useful o idenify and undersand flow inundaion paerns along he floodplain. For example, one can noe he occurrence of main fluxes parallel o he river main channel, as indicaed by arrows 1 and 2 in he menioned figure. The arrow indicaed by number 3 shows waer flowing from floodplain of Aquidauana River and reaching he Negro River. This resul is in agreemen wih inundaion paern observed during exreme flooding evens, as repored by DNOS (1974). Alhough here were no available saellie images o evaluae he simulaed flooded areas, he major inundaion paern of Aquidauana River was represened in a coheren way. 5 CONCLUSIONS The abiliy o represen he waer flowing from he main channel o he floodplain a a given river cross secion, forming secondary fluxes in he floodplain, and furher reurning o he main channel in disribued poins downsream of he iniial cross secion is he powerful advanage of he mehodology employed. Cell-based models, in urn, allow he sorage of waer in he floodplain only in delimied areas, and he exchange of volumes of waer beween floodplain and main channel occurs a few specific linkage poins. Furher research will focus on exending he sudy area o enire Pananal Welands. Improvemens in he compuaional code will be necessary in order o minimize compuaional coss and make such modeling feasible. Despie of good resuls obained, prioriy will be given o acquiring saellie images aiming o beer validae model resuls,

8 mainly he exen of simulaed flood inundaion. A beer characerizaion of floodplain opography and is agreemen wih he river cross secions profile will be necessary in order o calibrae model parameers and produce more acual resuls. Regardless of such difficulies, his research seems promising and may be valuable o managemen and susainable developmen of Pananal Welands. Figure 6 Simulaed flooded area of Aquidauana River in four differen insans of ime. The we floodplain elemens are blue-coloured, wih darker colour indicaing deeper waer. In background is shown a colour composie of a Landsa image. ACKNOWLEDGEMENTS The firs auhor was suppored by Conselho Nacional de Desenvolvimeno Cienífico e Tecnológico (CNPq). Digial elevaion model daa were supplied by The CGIAR Consorium for Spaial Informaion (CGIAR-CSI) SRTM-90m Daabase, Landsa images were couresy of he U. S. Geological Survey, and discharge daa were provided by Agência Nacional de Águas (ANA). The auhors would also like o hank Paul Baes and Neil Huner for he valuable discussion abou LISFLOOD-FP model.

9 REFERENCES ANA (2005), HidroWeb, Sisema de Informações Hidrológicas, Agência Nacional de Águas, Available a: hp://hidroweb.ana.gov.br, accessed on July ANA/GEF/PNUMA/OEA (2005), Modelo de Simulação Hidrológica do Alo Paraguai. Relaório Final, Subprojeo 5.4 Modelo Inegrado de Gerenciameno Hidrológico da Bacia do Alo Paragua Projeo Implemenação de Práicas de Gerenciameno Inegrado de Bacia Hidrográfica para o Pananal e Bacia do Alo Paraguai. Agência Nacional de Águas, Fundo para o Meio Ambiene Mundial, Programa das Nações Unidas para o Meio Ambiene, Organização dos Esados Americanos, 554 p. Baes, P.D., De Roo, A.P. (2000), A simple raser-based model for flood inundaion simulaion, Journal of Hydrology, 236, Baes, P.D., Wilson, M.D., Horr M.S., Mason, D.C., Holden, N., Currie, A. (2006), Reach scale floodplain inundaion dynamics observed using airborne synehic aperure radar imagery: daa analysis and modelling, Journal of Hydrology, 328 (1-2), Baes, P.D., Dawson, R.J., Hall, J.W., Horr M.S., Nicholls, R.J., Wicks, J., Hassan, M.A. (2005), Simplified wo-dimensional numerical modelling of coasal flooding and example applicaions, Coasal Engineering, 52, Bravo, J.M., Allasia, D., Collischonn, B., Collischonn, W., Villanueva, A., Tucc C. (in press), Meodologia para a esimaiva de rocas de água enre a planície e o canal principal em áreas muio planas, Revisa Brasileira de Recursos Hídricos, ABRH. CGIAR-CSI (2005), Void-filled seamless SRTM daa V1-2004, Inernaional Cenre for Tropical Agriculure (CIAT), The CGIAR Consorium for Spaial Informaion, Available a hp://srm.csi.cgiar.org, accessed on Ocober Chow, V.T. (1959), Open Channel Hydraulics, McGraw-Hill, USA, 680 p. Cunge, J.A., Holly, F.M., Verwey, A. (1980), Pracical aspecs of compuaional river hydraulics, Piman Advanced Publishing Program, Boson, 420 p. DNOS (1974), Esudos hidrológicos da bacia do Alo Paragua Relaório Técnico, UNESCO/PNUD, Rio de Janeiro, Brazil, 284 p. Gillan, P., Jempson, M., Rogencamp, G. (2005), The imporance of combined 2D/1D modelling of complex floodplain Taura case sudy, Fourh Vicorian Flood Managemen Conference, Shepparon, Vicoria, Ausralia. Girard, P., Da Silva, C.J., Abdo, M. (2003), River-groundwaer ineracions in he Brazilian Pananal. The case of he Cuiabá River, Journal of Hydrology, 283, Hamilon, S.K., Sippel, S.J., Melack, J.M. (2002), Comparison of inundaion paerns among major Souh American floodplains, Journal of Geophysical Research, 107, 0. Hamilon, S.K. (1999), Poenial effecs of a major navigaion projec (Paraguay-Paraná Hidrovia) on inundaion in he Pananal Floodplains, Regulaed Rivers: Research & Managemen, 15, Horr M.S., Baes, P.D. (2002), Evaluaion of 1D and 2D numerical models for predicing river flood inundaion, Journal of Hydrology, 268, Horr M.S., Baes, P.D. (2001a), Predicing floodplain inundaion: raser-based modelling versus he finie-elemen approach, Hydrological Processes, 15, Horr M.S., Baes, P.D. (2001b), Effecs on spaial resoluion on a raser based model of flood flow, Journal of Hydrology, 253, Huner, N.M., Horr M.S., Baes, P.D., Wilson, M.D., Werner, M.G. (2005), An adapive ime sep soluion for raser-based sorage cell modelling of floodplain inundaion, Advances in Waer Resources, 28, Junk, W.J., Nunes de Cunha, C. (2005), Pananal: a large Souh American weland a a crossroads, Ecological Engineering, 24, Miguez, M.G., Mascarenhas, F.C.B. (1999), Modelação maemáica de cheias urbanas aravés

10 de um esquema de células de escoameno, Revisa Brasileira de Recursos Hídricos, ABRH, v. 4, n.1, Posel, S., Richer, B. (2003), Rivers for life: managing waer for people and naure, Island Press, Washingon, USA, 253 p. Selling, G.S., Duinmeijer, S.P.A. (2003), A saggered conservaive scheme for every Froude number in rapidly varied shallow waer flows, Inernaional Journal for Numerical Mehods in Fluids, 43, Selling, G.S., Verwey, A. (2005), Numerical flood simulaion, in Encyclopedia of Hydrological Sciences, John Wiley & Sons Ld. Tucc C.E.M. (1998), Modelos Hidrológicos, Ediora da UFRGS, 2ª edição, Poro Alegre, Brazil. Tucc C.E.M. (1978), Hydraulic and Waer Qualiy Model for a River Nework, PhD Thesis, Colorado Sae Universiy, USA, 218 p. Verwey, A. (2001), Laes developmens in floodplain modeling 1D/2D inegraion, in Proceeding of he Conference on Hydraulics in Civil Engineering, The Insiuion of Engineers, Ausralia. Villanueva, A.N.O. (1998), Simulação de áreas de inundação dinâmicas: canais composos e welands, PhD Thesis, Insiuo de Pesquisas Hidráulicas, Universidade Federal do Rio Grande do Sul, Poro Alegre, Brazil, 125 p. Werner, M.G. (2004), A comparison of flood exen modelling approaches hrough consraining uncerainies on gauge daa, Hydrology and Earh Sysem Sciences, 8(6),

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