Modelling complex flood flow evolution in the middle Yellow River basin, China

Transcription

1 Journal of Hydrology (200) 353, avalable at journal homepage: Modellng complex flood flow evoluton n the mddle Yellow Rver basn, Chna Hongmng He a,b, Qan Yu a, *, Je Zhou a, Yong Q. Tan c, Robert F. Chen c a Department of GeoScence, Unversty of Massachusetts-Amherst, Amherst, MA 01003, Unted States b State Key Laboratory of Loess and Quaternary Geology, Insttute of Earth Envronment, Chnese Academy of Scences, P.O. Box 17, Xan, , Chna c Department of Envronmental, Earth and Ocean Scences, Unversty of Massachusetts, Boston, 100 Morrssey BLVD., Boston, MA 02125, Unted States Receved 20 March 2007; receved n revsed form 17 January 200; accepted 31 January 200 KEYWORDS Flood routng; Backwater flow; The mddle Yellow Rver; Rver morphology Summary Flood routng processes n the mddle Yellow Rver basn are complex snce they consst of three types of flood: bdrectonal, convergent and dvergent flood flows between the man channel and ts trbutares. We propose three computaton schemes to smulate the complex flood routng: a smple scheme for a sngle man channel wth no trbutary or backwater, an mproved schemes for convergent or dvergent flow at the confluence, and an mproved scheme for bdrectonal flow. The schemes are examned by analyzng seven hstorcal flood events and three scenaros of flood routng n the mddle Yellow Rver basn. The model was calbrated and valdated based on the smulaton of three dfferent types of flood. As compared wth the observed hydrographs, the results show that the model s able to smulate flood routng processes effcently for the study rver (wth Nash Sutclffe ndces fallng n the range ). The model demonstrates that flood routng durng hstorcal flood events ( ) n the mddle Yellow Rver was altered under boundary condton changes. The shape of the hydrographs changed from hgh and thn to low and wde, whch was accompaned by a delayed occurrence and extended duraton of peak flow after the 1960s. Moreover, these trends were ntensfed after the early 190s. Backwater resulted from dvergent flows and bdrectonal flood flows. An analyss of combned boundary condtons shows that flood wave volume has the strongest mpact on flood duraton, peak dscharge and water level, the tme of occurrence of peak dscharge, and the magntude of backwater. Rver bed slope has the second strongest mpact on flood duraton and the magntude of backwater. Channel roughness has the second strongest mpact on peak dscharge and water level. Publshed by Elsever B.V. * Correspondng author. Tel.: E-mal address: qyu@geo.umass.edu (Q. Yu) /$ - see front matter Publshed by Elsever B.V. do: /j.jhydrol

2 Modellng complex flood flow evoluton n the mddle Yellow Rver basn, Chna 77 Introducton Floods are one of the most common hazards n the mddle Yellow Rver basn, Chna (Yu and Ln, 1996). Heavy flood events transport sedments from upstream to downstream and lead to changes of rver channel morphology and flood routng processes (Speght, 1965; Beven et al., 19; Carson and Grffths, 199; Wharton et al., 199; Marston et al., 1995; Wyzga, 1997; Lee and Chang, 2005; Webb and Leake, 2006). One of the dstnctve features of flood dsasters n the mddle Yellow Rver s that they mostly result water from backng up from downstream to upstream (Qan, 1992; Wang, 2004). Backwater from downstream dam and releases from trbutares extended the areas of floodplan. For decades, mpacts of flood dsasters of backwater have grown n spte of ncreasngly mproved defence measures (Wang et al., 2005). From 1964 to 2003, there were 2 flood dsasters of backwater from the mddle Yellow Rver to the lower Wehe Rver (State Flood Control and Drought Relef Headquarters, 1992). These floods resulted n huge economc losses, ncreased nundated farmlands, and decreased crop productvty (He et al., 2006). An ncreased understandng of evoluton of flood routng of backwater n the mddle Yellow Rver would mprove rsk analyss and regonal emergency response. Because the mddle Yellow Rver s one of the major rvers n the world, the consequences of flood events n the mddle Yellow Rver represent an nternatonal concern. Rver channel morphology has sgnfcant mpacts on flood routng. Quantfcaton of the mpacts nvolves estmatng peak flow and characterzng hydraulc parameters. There were many prevous efforts assessng the mpacts of channel morphology on floods (Speght, 1965; Beven et al., 19; Carson and Grffths, 199; Wharton et al., 199; Wyzga, 1997; Lee and Chang, 2005; Webb and Leake, 2006). Speght (1965) studed the relatonshp between flow and channel characterstcs and dsclosed that mgratng wde trangular channel cross-sectons domnated by pont-bars were more capable of carryng the most probable annual flood than fxed narrow rectangular sectons domnated by levees wth a sandy bed and slt clay banks. Beven et al. (19) examned the relatonshp of morphology to runoff routng and producton n flood routng. They ponted out that morphology may be used as a clue to study hydrologcal responses. Based on the analyss of changes n vertcal channel poston and varatons n flood flows, Wyzga (1997) revealed the mportance of channel ncson for ncreasng flood hazard to downstream reaches. Many models for smulatng flood routng were derved from the Sant-Venant equatons (Daluz, 193; Cunnane, 19; Ramamurthy, 1990; Camacho and Lees, 1999; Carrvck, 2006) and other smplfed wave models such as the knematc wave, non-nerta wave, quas-steady dynamc wave, and gravty wave approxmatons (Walters and Cheng, 190; Begn, 196). The model ntroduced by Chung et al. (1993) analyzed the response functons of flood wave movement n a sem-nfnte channel and n a fnte channel under general condtons. The model consdered effects of downstream boundary condtons on dffusve flood routng and the magntude of backwater. In ther model, the nflow flood hydrograph was controlled by three parameters: the tme to peak, the base tme, and the peak dscharge. Schuurmans et al. (1995) used lnearzed Sant-Venant equatons to analyze open-channel flow wth backwater effects. The model emphaszed the effects of backwater on frequency underestmaton n the neghbourhood of the resonance n flood routng. Thorne and Furbsh (1995) found that bank roughness essentally has backwater effects that resst surface flow downstream. Tsa (2005) theoretcally nvestgated unsteady flow routng wth downstream backwater effects n a mld-sloped rver on the bass of lnearzed Sant-Venant equatons and other routng models. The common ssues reported n prevous studes are that smplfed knematc wave and gravty wave models were unable to account for the downstream backwater effect and were not sutable for modellng the flood wave propagaton n mldsloped rvers. These prevous studes mostly dealt wth the general form of flood routng. There s no approprate soluton to smulate the flood wave propagaton wth a downstream backwater effect of complex flood routng (such as bdrectonal flow, convergent and dvergent flows between the man channel and trbutares). At the same tme, characterstcs of dfferent dranage systems affect flood dfferently, n terms of both duraton and ntensty (Goel et al., 2000). The characterstcs nclude runoff volume, peak flow, and dranage channel morphology. Specal attenton needs to be pad to the nvestgaton of the dstnctve dranage characterstcs of the mddle Yellow Rver n the study of flood routng. On the other hand, the nfluence of trbutary floods on the behavour of water flows n the man channel has not been well studed n the mddle Yellow Rver basn. There s a need to analyze the concurrent floods of multple trbutares for mprovng our understandng of flood routng processes and the assocated trbutary dranage characterstcs n a rver basn. The objectve of ths paper s to nvestgate the characterstcs of flood wave propagaton under dfferent flood routng boundary condtons. By referencng to hstorc flood records n the study area, we analyze the mpacts of flood propagaton on regonal envronmental propertes. Ths study examnes the three computaton schemes that we proposed for smulatng the complex flood flows n the dfferent boundary condtons and of varyng nherent hydraulc features. These schemes are: a smple scheme for sngle man channel wth no trbutary and backwater, an mproved scheme for convergent or dvergent flow at the confluence, and an mproved scheme for bdrectonal flow. The smulaton analyss mproves our understandng of flood routng of backwater and complex flood flow evoluton n the mddle Yellow Rver. Study area The study area s located n the basn of the mddle Yellow Rver (between Tongguan and Huaxan) at a lattude between 35 N and 3 N, and a longtude between 105 E and 112 E (Fg. 1). We focus on the man stem and ts two trbutares, the Wehe Rver and the Luohe Rver. The Luohe Rver s the trbutary of the Wehe Rver whch flows nto the mddle Yellow Rver at Tongguan. The elevaton of Tongguan rules the base level of the Wehe Rver, and nfluences the operaton behavours of the Sanmenxa Reservor (constructon n and reconstructon n ).

3 7 H. He et al. Fgure 1 Locaton of study area n the mddle Yellow Rver basn. Annual precptaton n the study area ranges from 300 mm to 1000 mm per year. About 4% of the annual total ( mm) falls n the summer season (from July to August) n the form of ranstorms (ranfall amounts are over 50 mm n 24 h). Floods occur frequently after ranstorms. They transport large amounts of sedments along the Wehe Rver and the mddle Yellow Rver and depost them n the lower Wehe Rver. The fluval sedments gradually change rver channel condtons, such as rver bed elevaton and roughness. Improper human actvty, such as the constructon of Sanmenxa Dam also contrbuted to the shrnkage of rver channels n the study area. Consequently, backwater was caused n the mddle Yellow Rver basn due to hydraulc condton changes. The evoluton of flood routng processes was examned at sx cross-sectons along the Wehe, Luohe Rver and mddle Yellow Rvers. There are four water-gauge cross-sectons from upstream to downstream n the Wehe Rver: Huaxan, Chenchun, Huayn and Tongguan. Two other cross-sectons are at Zhaoy n the Luohe Rver and at Shanyuantou n the mddle Yellow Rver. Materal and methods Data In ths study, nput data to the smulaton model nclude topographc, hydraulc and hydrometrc datasets. Topographc data, such as rver channel roughness, rver bed slope, and dstance between partcular cross-sectons, are extracted from the 30-m Dgtal Elevaton Model (DEM, from IRSA, CAS). Hydraulc and hydrometrc data such as flood flow radus, wdth, and cross-secton area, and flood flow velocty, dscharge and water level n each cross-secton are obtaned from gauge data compled n the State Flood Control and Drought Relef Headquarters (State Flood Control and Drought Relef Headquarters, 1992). Gauge data of 11 flood events are collected n dfferent tme perods from 1954 to 2003, of whch four flood events are used to calbrate the model, and four others are selected to examne the model effcency through smulaton results.

4 Modellng complex flood flow evoluton n the mddle Yellow Rver basn, Chna 79 Computatonal schemes for complex flood flow evoluton Classfcaton for steady and unsteady flow s necessary n descrbng the flows of nterest. The smplest steady flow s unform flow, n whch no flow varable change wth dstance, and every flow varable s a constant wth respect to dstance and tme (Keskn and Agraloglu, 1997). Dfferent from unform flow s non-unform flow, whch can be further dvded for both gradually vared flow and rapdly vared unsteady flows, and the same general rules for analyss apply as for steady flow. Flow zones can be vewed as under the 1-D flow assumpton; thus, the method of analyss for steady and unsteady flow s the same n ths respect. Based on Sant-Venant equaton, the soluton scheme of the steady or unsteady flow equatons depends on the scheme of ts numercal soluton (Cunnane, 19; Ren and Cheng, 2003). In ths study, the flow routng process of backwater evoluton durng a flood event s vewed as one dmensonal unsteady flow descrbed wth the Sant-Venant equaton based on equatons of contnuty and momentum as below, oq < þ B oz ¼ q ox ot L : oq oq þ 2v þðga BV 2 Þ oz ot ox V2oA ox ox z þ g nmqjqj ¼ 0 AR 4=3 h where Q s flood dscharge (m 3 /s), x s the coordnate horzontal n flow drecton, B s the velocty of propagaton of the knematc wave (m/s), Z s water level (m), q L s the lateral nflow per unt tme per unt channel length (m 2 /s), t s the tme (s), V s flood flow velocty (m/s); g s acceleraton due to gravty (m/s 2 ), A s cross-sectonal area of the flow (m 2 ); R h s the hydraulc radus (m), n m s Mannng roughness coeffcent. The frcton slope S f s approxmated by Mannng s equaton (Keskn and Agraloglu, 1997): < : S f ¼ n2 m VjVj y 4=3 V ¼ 1 n m R 2=3 h S 1=2 f where S f s the frcton slope, n m s the Mannng s roughness coeffcent, R h s the hydraulc radus (m), and VjVj replaces V 2 to account for the possblty of flow reversal. Supposng that at tme t at the th reach the channel roughness coeffcent s n t, the estmated channel roughness changes at tme Dt + t due to sedment varaton (DV ). Ths can be descrbed as below (Keskn and Agraloglu, 1997; Ren and Cheng, 2003): n tþdt ¼ n t C n DS >< Dt ( n tþdt ¼ 0:5nt¼0 ; n tþdt >: 1:5n t¼0 ; n tþdt < 0:5n t¼0 > 1:5n t¼0 where C n s adaptable emprcal coeffcent, DV s sedment varaton and s marked as a postve value when the channel bed s slted and as a negatve value when t s scoured (10 9 m 3 ), Dt s the tme change from the prevous tme step to the present; n t¼0 s the ntal value of the channel roughness coeffcent at the th reach, and s defned through feld work. We use the Pressmann three-pont mplct scheme (He et al., 2006) to solve the channel flow equatons and avod ð1þ ð2þ ð3þ the dsturbng effect of the numercal dffuson on the results of modellng. The flow doman s dvded nto a number of flow reaches. Accordngly, for a pont lke p located n a rectangular grd, the average values and dervatves are gven by of hðf jþ1 þ1 fjþ1 Þþð1 hþðf < j þ1 fj Þ ox Dx ð4þ jþ1 : of f þ1 þfjþ1 f j þ1 ox 2Dt where f s the functon of Q, Z, A, V. The subscrpt of f s the dentty of dfferent rver reaches; the superscrpt of f depcts dfferent tme perods. s the tme weghtng coeffcent. Dx s the length of the th reach n a rver. On substtutng the average values n Eq. (1) for the approprate tems n Eq. (4), the followng equatons are obtaned: ( Q jþ1 1 þ Q j þ C Z j 1 þ G Z jþ1 ¼ D E Q jþ1 1 þ G Q jþ1 F Z jþ1 1 þ F Z jþ1 ¼ u where C ¼ Dx B j 1=2 2hDt D ¼ 1 h ðq j 1 h Q j ÞþC ðz j 1 þ Zj Þ E ¼ Dx 2hDt 2Vj 1=2 þ g 2h F ¼ðgA BV 2 Þ j 1=2 n 2 R 1:33 j jv j 1 jdx / ¼ Dx 2hDt ðq j 1 þ Q j 2ð1 hþ þ V j 1=2 h ðq j 1 Q j Þ þ 1 h ðga BV 2 Þ j 1=2 h ðzj 1 Zj Þ þ Dx V 2 oa j h ox Z 1=2 The approachng method was used to estmate flood nfluence on knematc wave propagaton based on the upper boundary condtons of flood dscharge. Suppose that ^y s an unknown vector at the tme of n +1, then the general form of Eq. (5) can be represented as ^y ¼ Fð^y 1 Þ ð7þ where the subscrpts and + 1 are tmes of teratve computaton. Ths teratve computaton process s acheved by ^y þ1 ¼ x^y þð1 xþ^y 1 ðþ and ends up n case of max j^y ^y 1 j < d ð9þ where d s the value of the control parameter and x s the lax factor. In teraton, the value of prevous tme step s vewed as the ntal value n the next tme step. Boundary condtons are key factors n computaton of hydrologcal modellng. Based on former studes (Mosselman, 1995; Keskn and Agraloglu, 1997; Ren and Cheng, 2003), we develop three computaton schemes to smulate the complcated flood flow evoluton accordng to the complex flood flow stuaton n the mddle Yellow Rver: a smple scheme for sngle man channel wth no trbutary and backwater, an mproved scheme for convergent or dvergent flows at the confluence (Wehe Rver and Luohe Rver, ð5þ ð6þ

5 0 H. He et al. Wehe Rver and mddle Yellow Rver), and an mproved scheme for bdrectonal flows (Fg. 2). Smple boundary scheme for sngle man channel If there are no trbutares and backwater n a sngle channel, then the boundary condton of Eq. (1) s defned as below: ( 1 ¼ Q 1 t nþ1 ð10þ ¼ Z N t nþ1 N where 1 and N are the flood dscharge and the water level at the nth tme step, Q 1 and Z N are the ntal flood flow dscharge and water level, t n+1 s the tme step at n + 1. Eq. (10) s used as the boundary condtons, snce t descrbes the relatonshp between ntal status and flood dscharges and water levels n next tme nterval from upstream to downstream. The approachng method s used to estmate backwater evoluton processes durng flood events based on upper boundary condtons. ( ¼ H þ1 þ I ð ¼ 1; 2;...; N 1Þ ð11þ þ1 ¼ F þ1 þ1 þ G þ1 where H, I, F +1, G +1 are approachng coeffcents, and ntal values are defned as F 1 =0,G 1 = Q 1 Æ t n+1. By usng these approachng functon and boundares, we can calculate flood water levels and dscharge n the man channel where there are no trbutares and backwater. Improved boundary scheme for convergent and dvergent flow Two assumptons are proposed for the stuaton when there s a slght amount of flood flow backwater at the confluence between the Wehe Rver and the Luohe Rver. Frst, we neglect the resstance nfluence of backwater on the boundary condtons. Second, we assume that convergent flow dscharge has a postve value (from the Luohe Rver to the Wehe Rver), and dvergent flow dscharge has a negatve value (from the Wehe Rver to the Luohe Rver). As s shown n Fg. 2A, we defne the boundary condton as >< >: a1 a1 b1 þ b1 ¼ þ 1 2g þ 1 2g a1 A a1 b1 A b1 2 ¼ Z nþ1 2 ¼ Z nþ1 þ 1 2g 1 2g 2 A 2 A ð12þ From Eq. (5), we can relate flood dscharge wth water level at cross-secton a and b as below, ( a1 ¼ F a1 a1 þ G a1 ð13þ b1 ¼ F b1 b1 þ G b1 Fgure 2 Computatonal schemes of flood routng of backwater n the mddle Yellow Rver basn.

6 Modellng complex flood flow evoluton n the mddle Yellow Rver basn, Chna 1 Therefore, Eq. (12) may be wrtten as >< ¼ F þ G 1c ¼ þ D a1 >: a1 b1 ¼ þ D b1 where D a1 ¼ a1 >< 2g A A a1 D b1 ¼ >: 2g A b1 A b1 ð14þ ð15þ where U a2, U b2 and U c2 are average flood flow veloctes at cross-sectons of the mddle Yellow Rver (cross-secton a 2, man channel), the Wehe Rver (cross-secton b 2, trbutary), and the convergence (cross-secton c 2 ); R a2, R b2 and R c2 are hydraulc rad at each cross-secton (cross-secton a 2, b 2 and c 2 ); n a2, n b2 and n c2 are Mannng roughness coeffcents at each cross-secton (cross-secton a 2, b 2 and c 2 ); DX a2c2 and DX b2c2 are dstances from the man channel (cross-secton a 2, the mddle Yellow Rver) to the confluence secton (cross-secton c 2 ), and from the trbutary channel (cross-secton b 2, the Wehe Rver) to the confluence secton (cross-secton c 2 ); f a2c2, f b2c2 are regonal resstant coeffcents from the man channel (cross-secton a 2, the mddle Yellow Rver) to the confluence secton (cross-secton c 2 ), and from the trbutary channel (cross-secton b 2, the Wehe Rver) to the confluence secton (cross-secton c 2 ). The rest of the parameters have the same physcal meanng as ndcated above. Based on the boundary condtons of Eq. (17), flood dscharge and water levels from the mddle Yellow Rver to the Wehe Rver can be computed. The boundary condton from the Wehe Rver to the mddle Yellow Rver s defned as >< a2 a2 þ b2 þ ðunþ1 a2 2g ¼ c2 ¼ Z c2 þð1þn a2c2 Þ ðunþ1 c2 þ Dx a2c2 2 n 2 a2 ðunþ1 a2 R 4=3 a2 2g þ n2 c2 ðunþ1 c2 R 4=3 c2 ð1þ The approachng coeffcents are defned as F ¼ F a1 þ F b1 G ¼ G a1 þ G b1 þ F a1 D a1 þ F b1 D ð16þ b1 When the flood water level at cross-secton c 1 (Z, at the convergence) s obtaned, we can calculate the flow dscharge at cross-secton c 1 (Q ), and water levels at crosssecton a 1 (Z a1, n the Luohe Rver) and b 1 (Z b1, n the Wehe Rver). At the confluence of the Wehe Rver and the mddle Yellow Rver, there are huge amounts of flood flow convergence, dvergence and backwater, and resstance nfluence of backwater cannot be neglected. For the purpose of the smulaton, we assume that convergent flood flow dscharge has a postve value (Fg. 2B, from Wehe Rver to the mddle Yellow Rver), and that dvergent flood flow dscharge has a negatve value (from the mddle Yellow Rver to the Wehe Rver). Models are constructed to smulate these two dfferent flood flow stuatons. The boundary condton from the mddle Yellow Rver to the Wehe Rver s defned as a2 þ b2 ¼ c2 ð a2 þ Unþ1 a2 Þ 2 ¼ Z 2g c2 þð1þn a2c2 Þ ðunþ1 c2 2g >< þ Dx n 2 a2c2 a2 ðunþ1 a2 2 ð17þ >: b2 þ ðunþ1 b2 2g R 4=3 a2 ¼ Z c2 þð1þn b2c2 Þ ðunþ1 c2 2g þ Dx b2c2 2 n 2 b2 ðunþ1 a2 R 4=3 b2 þ n2 c2 ðunþ1 c2 R 4=3 c2 þ n2 c2 ðunþ1 c2 R 4=3 c2 >: a2 þ ðunþ1 a2 2g ¼ Z b2 þð1þn a2b2 Þ ðunþ1 b2 þ Dx a2b2 2 n 2 a2 ðunþ1 a2 R 4=3 a2 2g þ n2 b2 ðunþ1 b2 R 4=3 b2 where DX a2b2 s the dstance from dvergence (cross-secton a 2 ) to the trbutary channel (cross-secton b 2, the Wehe Rver); f a2b2, s the regonal resstant coeffcent from the man channel (cross-secton a 2, the mddle Yellow Rver) to the trbutary channel (cross-secton b 2, Wehe Rver). Usng Eq. (1), flood dscharge and water levels from the Wehe Rver to the mddle Yellow Rver can be computed. Improved boundary scheme for bdrectonal flow The mproved boundary scheme for bdrectonal flow focused on modellng two flood flows of smlar magntudes travellng n opposte drectons. Other cases of bdrectonal flows of dfferent magntudes have been consdered n the mproved boundary scheme for convergent and dvergent flows. The type of backwater n bdrectonal flood flow s relatvely rare. Bdrectonal flood flows occur when backwater flows back from the mddle Yellow Rver to the Wehe Rver (Fg. 2C). When two flood flows n opposte drectons meet, a zero flood dscharge wll occur. Therefore, we can defne that as, < : m1 m1 ¼ m2 ¼ 0 ¼ Znþ1 m2 ð19þ and approachng coeffcents n Eq. (5) can be calculated from Eq. (19). However, the confluence cross-secton of the two bdrectonal flows s relatvely dffcult to locate as t relates wth the state of ebb-and-flow of the two flood flows, and vares wth tme. Therefore, we use an explct dfference soluton to solve the problem and to calculate flood flow parameters at tme step of ndt. The computaton tme nterval (Dt) s one of the key parameters n our model smulaton. Two factors are mportant n choosng the tme step n the computaton. Frst, the nterval should be short enough to accurately descrbe the rse and fall of the hydrographs beng routed. Second, the computaton nterval should be adjusted by varatons of hydraulc features, such as boundary condtons. By consderng the propagaton of peak dscharge and water level, we defne tme nterval (Dt) and dstance nterval (Dx) by the functons descrbed as below

7 2 H. He et al. Dt ¼ 0:5 t 6 s 0:5 >< Dt ¼ t p =20 s 0:5 6 t 6 s þ 2s Dt ¼ T p =20 t P s þ 2t p >: Dx ¼ c f Dt ð20þ where Dt s the tme nterval (h), t p s the tme of frst occurrence of peak dscharge (h), T p s the tme of peak dscharge occurrence n selected cross-secton (h), s s the tme of peak dscharge occurrence n the outlet (h), C f s the celerty of flood wave propagaton (m/s), and Dt s the dstance nterval (m). The tme ntervals range from 0.5 to 1 h. The dstance ntervals range from 3.1 to 5.5 km for 13 reaches. The ratos of tme nterval to dstance nterval (Dt/Dx) are between 3.5 and 6.3. Varatons of the roughness frcton parameter n m n Eq. (2) ncrease n relaton to the hghest wave number. That mght result n a wave speed greater than n realty. In these stuatons, t usually causes computatonal nstabltes. Ths numercal scheme needs a dsspaton mechansm n order to elmnate accumulaton of dsperson errors. Therefore, t s advsable to ncrease the coeffcent of tme weghtng parameter, h. Tme coeffcents are usually defned as dependng on the stuaton of roughness coeffcent. After a seres of adaptatons, C n n Eq. (3) ranges from 0.4 to 0.6. Consderng the complex of land surface condtons n the mddle Yellow Rver, we defne h as 0.6 and the roughness coeffcent as Estmaton of channel roughness n flood routng s based on Eq. (3). To calculate the channel roughness durng dfferent routng tmes, we need to know the ntal roughness. The ntal roughness s defned by followng steps. Frst, after accountng for flood water levels at dfferent dscharges for each gauge cross-secton, we can get so-surfaces of those dscharges. Second, we can get ntal roughness values when the smulated water levels are compared wth gauged water levels by adaptng roughness values (Table 1). Some of these parameters are determned based on the experence of experts combned wth referencng to hstorc observaton records and lteratures from USGS. Table 1 Channel confguratons used n the study Parameters The Luohe Rver The Wehe Rver The small north manstream (downstream of the mddle Yellow Rver) Channel type Rectangular Rectangular Rectangular Channel length (km) Average channel wdth (m) Average channel slope (%) Intal Mannng s roughness Dscharge Mannng s (m 3 /s) roughness > > > Varable cross-secton nterval (Dx, km) Grd element number Rato of spatal temporal nterval (Dx/Dt)

8 Modellng complex flood flow evoluton n the mddle Yellow Rver basn, Chna 3 In the study area, two upstream channels meet and form a larger channel at the juncton pont (Fg. 1). Accordng to the geometry, the values of each parameter assocated wth the routng are functons wth tme because of channel morphology changes. The physcal setups of the model are shown n Table 1. The modellng works on each of the total of elements of the rver dscretzed wth lengths on the bass of DEM resoluton (30 m). Other dscretzed schemes were descrbed n the Methodology secton. For example, the tme ntervals range from 0.5 to 1 h, the dstance ntervals range from 3.1 to 5.5 km for 13 reaches or the ratos of tme nterval to dstance nterval (Dt/Dx) are between 3.5 and 6.3. Calbraton and valdaton of the model are performed through four flood events (July 27 31, 1962; June 25, 196; August 2, 1970; September 25 October 5, 193). Parameter values are adjusted from the ntal estmates gven n the model wthn the acceptable ranges to acheve the desred proporton after smulaton by usng the traland-error method. The model was calbrated by consderng all the possble combnatons of parameters. Ths procedure s repeated untl optmal parameter values are found by comparng the smulated and observed ranstorm flood event data. Coeffcent of Model Effcency (CME, Nash and Sutclffe, 1970) and Root Mean Square Error (RMSE) are used to evaluate model effcency. Flood contrbuton ndex An ndex was developed to evaluate the contrbuton of rver bed slope, channel roughness, and water volume amount to flood wave propagaton. Ths contrbuton ndex, CI, can be represented as Fgure 3 Calbratng smulaton of the flood routng model n the mddle Yellow Rver basn for the floods of July 27 31, 1962; June 25, 196; August 2, 1970; September 25 October 5, 193. (A) Model calbraton for unlateral flow routng n the Wehe Rver (smple scheme; Juny 25, 196 (m a.s.l)). (B) Model calbraton for flood routng n the Wehe/Luohe Rvers (mproved boundary scheme; August 2, 1970). (C) Model calbraton for flood routng n the Wehe/mddle Yellow Rvers (mproved boundary scheme; July 27 31, 1962). (D) Model calbraton for blateral flow n the Wehe Rver (mproved boundary scheme; September 25 October 5, 193).

9 4 H. He et al. Fgure 3 (contnued) CI ¼ P j, X n ¼1 P where CI value s between 0 and 1. The hgher the ndex value the greater the contrbuton of a gven parameter to flood wave propagaton. P j s smulated value of a certan varable (such as rver bed slope, channel roughness, and water volume) n a gven scenaro (such as roughness of 1962 and 2003, rver bed slope of 1962 and 2003); P P s the total value of a certan varable n all desgned scenaros.

10 Modellng complex flood flow evoluton n the mddle Yellow Rver basn, Chna 5 Results and dscusson Smulaton of three computatonal boundary schemes n flood routng Results of smulatng flood routng processes for the three computatonal schemes are presented below. Before analyzng the modellng results, we frst descrbe calbraton and valdaton of the model. Model calbraton and valdaton The model was calbrated and the results were valdated (Fg. 3) wth the runoff measured durng four flood events (July 27 31, 1962; June 25, 196; August 2, 1970; September 25 October 5, 193). The valdaton was based on measured and estmated dscharges and water levels at varous statons and flood events. The coeffcents of the model effcency ( 1 < CME < 1; Nash and Sutclffe, 1970) ranged from 0.3 to 0.91 (Table 2). Root Mean Square Errors (RMSEs) fall wthn m 3 /s for flow dscharges, and m for water levels. The measured hydrographs are hghly varable n tme. In most scenaros, the modelled results consstently matched the measurements performed durng all flood events on partcular rvers. A major error n smulatng runoff corresponded to the duraton of peak flows. The model was able to descrbe the magntude of backwater generated due to an abrupt fluctuaton of boundary condtons wth tolerable errors. The boundary condtons for the cross-sectons n the Wehe Rver/the mddle Yellow Rver are the most complex. However, the model performance of smulatng flood characterstcs on the complex boundary condtons s satsfactory (Fg. 3C). The Coeffcents of Model Effcency (CME) of the modelled dscharge and water level are 0.77 and 0.3 for the flood event n July 27 31, Root Mean Square Errors (RMSE) of dscharge and water level are 39.4 (m 3 /s) and 0.29 m, respectvely. Smple boundary scheme for sngle man channel Results from smulatng unlateral flow n the Wehe Rver for the flood event on July 6, 1990 were based on the proposed smple boundary scheme. Hydrographs n the rver are relatvely smple as there are no trbutary flows or backwater n the routng process. Unlateral flow routes along a sngle channel and usually happens durng non-flood seasons or n relatvely small flood events (State Flood Control and Drought Relef Headquarters, 1992). Estmated hydrographs of dscharge and water level were developed for the gauge cross-sectons of Huaxan, Chenchun, and Huayn. Fg. 4 shows the observed hydrographs and smulaton results on the bass of a smple boundary scheme for a sngle man channel. It can be observed that the rsng lmbs and the recesson lmbs of the hydrographs have almost the same slopes at successve gauges. Ths ndcates that flood routng along the sngle channel s mostly domnated by temporal dstrbuton of ranstorms. Importantly, backwater does not exst n ths stuaton. By comparng the observed hydrographs and the smulaton results n smple boundary schemes, Table 2 shows model effcency for sngle man channel n the event of July 6, Coeffcents of Model Effcency (CME) of dscharge and water level are 0.3 and 0.5 (July 27 31, 1962), whereas Root Mean Square Error (RMSE) of dscharge and water level are 43.3 m 3 /s and 0.21 m (July 27 31, 1962). Improved boundary scheme for convergent and dvergent flow We adopted the mproved boundary scheme for convergent and dvergent flow to the rver segment from the mddle Yellow Rver to the Wehe Rver for the flood event n August 3 4, Backwater n ths rver segment happens when flood flows from the Wehe to Luohe Rvers converge synchronously, or when a greater flood on the mddle Yellow Rver than that on the Wehe results n flow dvergence at the confluence of the Wehe and Louhe Rvers (Fg. 2). Observed hydrographs and smulated results for convergent and dvergent flows n the rver segment and for the four flood events between 1977 and 2003 are dsplayed n Fg. 5 (the Wehe and Luohe Rvers) and Fg. 6 (the mddle Yellow Rver and Wehe Rver). By comparng wth the unlateral flood flow, the hydrographs of convergent and dvergent flood flows show dstnctve behavours. The rsng lmbs have much steeper slopes than the recesson lmbs n the routng process n the Wehe and the mddle Yellow Rvers. In the Wehe and Luohe Rvers, the rsng lmbs have relatvely gentler slopes than the recesson lmbs. The magntude of backwater n the Wehe Rver/Luohe Rver (Fg. 5) Table 2 Evaluaton of the effcency of the proposed flood routng model based on smulated peak dscharges and water levels for seven hstorcal flood waves n the mddle Yellow Rver basn Nash Sutclffe coeffcent RMSE Flow dscharge Water level Flow dscharge (m 3 /s) Water level (m) July 27 31, June 25, August 2, August 3 4, September 25 October 5, July 6, June 6, August 25,

11 6 H. He et al. Fgure 4 Smulaton of unlateral flow (smple boundary scheme for sngle man channel) n the Wehe Rver (July 6, 1990). Fgure 5 Smulaton of flood flow n the Wehe/Luohe Rvers (mproved boundary scheme; August 3 4, 1977). was much smaller than that n Wehe Rver/the mddle Yellow Rver (Fg. 6), although the backwater n both rvers traced back to Chenchun. At Tongguan fluctuaton of flood wave n the Wehe/Louhe Rvers (Fg. 6), occurred more frequently than that n the Wehe/the mddle Yellow Rvers due to flood flows (Fg. 5). Ths phenomenon was due to the greater magntude of backwater effects dsplayed n Fg. 6. Model effcency of evaluatng the mproved boundary scheme for convergent and dvergent flow was summarzed n Table 2. Coeffcents of Model Effcency (CME) are 0.0 for the event n 1977 and 0.75 for the event n 2003 for flow dscharge, and 0.7 (1977) and 0.79 (2003) for water level. Root Mean Square Errors (RMSE) are 47.2 and 52.3 m 3 /s for the flow dscharge n 1977 and 2003, and 0.26 and 0.34 m for the water level n 1977 and 2003, respectvely. The analyss of flow routng processes for the four flood events n 1962, 1970, 1977, and 2003 ndcates that backwater usually occurred when flow dscharges n the man rver were greater than that n trbutary. For example, the observed peak dscharges at Shanyuantou on the mddle Yellow Rver and at Huanxan on the Wehe Rver amounted to 10,400 and 3750 m 3 /s n 1962, to 140 and 4320 m 3 /s n 1970, to 4470 and 9460 m 3 /s n 1977 and to 5670 and 4250 m 3 /s n The occurrence of backwater n the Wehe Rver was based on functon (21) by analyzng the relatonshp between flow dscharges and water levels n the Wehe Rver >< S DQ HY 6 0 pffffffffffffffff Q maxtg Q HX P 25 ð21þ >: V ztg P 0:06 where S DQ HY s the slope of water level from Daoqao to Huayn, Q maxtg s the peak dscharge at Tongguan (m 3 /s), pffffffffffffffff Q HX s the daly mean flow dscharge n a gven year (m 3 /s), and V ztg s the rate of water level rse (m/h). The end of backwater reached peak values around the tme that

12 Modellng complex flood flow evoluton n the mddle Yellow Rver basn, Chna 7 Fgure 6 Smulaton of flood flow n the Wehe/mddle Yellow Rvers (mproved boundary scheme; August 25, 2003). peak flow occurred n Tongguan. For example, backwater occurred 2 3 h earler n Huanyn (39th hour n 1962) and Chenchun (49th hour n 1977, 133rd hour n 2003) than peak dscharge n Tongguan (41st hour n 1962, 52nd hour n 1977, 135th hour n 2003) n 1977 and 2003, respectvely. However, the shapes of the hydrographs (both flow dscharge Fgure 7 Smulaton of blateral flow n the Wehe Rver (mproved boundary scheme; June 6, 1992).

13 H. He et al. and water level) at the end of backwater (such as Huayn and Chenchun) were smlar to those of the hydrographs n Tongguan. Improved boundary scheme for bdrectonal flow The results of smulatng bdrectonal flow n whch two floods of smlar magntudes converge n the opposte drectons were examned usng data from hstorc flood records. One example of the occurrence of backwater resultng from bdrectonal flow was on Jun 6, 1992 when flood water flowed from the mddle Yellow Rver (5200 m 3 /s n Shanyuantou) to the Wehe Rver (4550 m 3 /s n Huaxan). Fg. 7 shows the observed hydrographs and smulated results for ths event. A magntude of the backwater resultng from bdrectonal flow s relatvely small compared wth that whch occurs when flood flow dverts from the man stream to the trbutary. The rsng lmbs and the recesson lmbs fluctuated due to the effect of backwater. Table 2 lsted model effcency of mproved boundary scheme for bdrectonal flow (June 6, 1992). Coeffcents of Model Effcency (CME) of dscharge and water level are 0.7 and 0.3 (June 6, 1992), whereas Root Mean Square Errors (RMSE) of dscharge and water level are 41. m 3 /s and 0.20 m (June 6, 1992). Through the analyss of seven hstorcal flood events n the mddle Yellow Rver basn (1962, 1970, 1977, 193, 1990, 1992, and 2003), the model dentfed that the shape of the flood hydrographs changed over tme from hgh and thn to low and wde (Fgs. 3 7). These changes were accompaned by a delayed occurrence and an extended duraton of peak flow of progressvely later floods. These trends were ntensfed from the early 190s. For example, flood hydrographs at the Huaxan gauge demonstrate that peak dscharges, water levels, flood duratons and backwater condtons changed consderably between 1962 and Peak dscharges of the floods of 1962 (3750 m 3 /s) and 2003 (3595 m 3 /s) were smlar. However, snce 1962 peak water level rased by. m (333.2 m a.s.l. n 1962 and 342 m a.s.l. n 2003), the occurrence of peak flow delayed by about 99 h (10th hour n 1962 and 109th hour n 2003), and flood duraton (wth threshold dscharge beng 950 m 3 /s) extended by 177 h (42 h n 1962 and 219 h n 2003). In turn, flood hydrographs at the Tongguan gauge show that the peak dscharge of the 2003 flood (5200 m 3 / s) amounted to only one-thrd of that n 1962 (15,300 m 3 / s) but flood duraton (wth threshold dscharge beng 950 m 3 /s) extended by 137 h (9 h n 1962 and 226 h n 2003). Backwater traced back for 23 km (Chenhun n 1962 and Huanyn n 2003), and peak dscharge of the backwater ncreased by 95 m 3 /s ( 1 m 3 /s n 1962 and 103 m 3 /s n 2003). From the above nformaton t s evdent that flood flow propagaton n the mddle Yellow Rver basn experenced sgnfcant change durng the study perod. Effects of boundary condtons on flood routng Boundary condtons of rver flows refer to geometrc features and surface roughness of the rver channel at gven water volumes. We analyzed the effects of boundary condtons on flood routng processes based on the case of the lower Wehe Rver channel. Ths rver channel has been shaped by the nteracton between fluval eroson and deposton, and channel morphology for centures (State Flood Control and Drought Relef Headquarters, 1992). After the constructon of the Sanmenxa Reservor n the 1960s, fluval deposton became the domnant factor for alteraton of the channel morphology n the lower Wehe Rver (He et al., 2006). In return, the altered rver channel boundary condtons mposed sgnfcant mpacts on flood routng, especally for backwater (Table 1). Table 3 presents the combnatons of smulatng flood routng wth the features of backwater under dfferent scenaros. The results dentfed those parameters of the model whch affected flood routng n the lower Wehe Rver. These parameters are rver bed slope, channel roughness, and water volume. The smulaton scenaros were consdered n two categores. In the frst category, the channel roughness and rver bed slope of 1962 and 2003 are combned wth the boundary condtons of 1977 (Table 3; For example, water volume 1B-roughness of 1962 and rver bed slope of 1962, r1962s1962; 1C-roughness of 1962 and rver bed slope of 2003, r1962s2003; 1D-roughness of 2003 and rver bed slope of 1962, r2003s1962; 1E-roughness of 2003 and rver bed slope of 2003, r2003s2003). In the second category, the channel roughness and rver bed slope of 1962 and 1977 are combned wth boundary condtons of 2003 (Table 3; 2B-channel roughness of 1962 and rver bed slope Table 3 Desgned scenaros of smulatng flood routng n the lower Wehe Rver for combned ntal boundary condtons Types Combnatons Intal dscharge Intal roughness Intal slope 1A Gauged, r1977s B r1962s C r1962s D r2003s E r2003s A Gauged, r2003s B r1962s C r1962s D r1977s E 1977s r s rver bed roughness, s s rver bed slope.

14 Modellng complex flood flow evoluton n the mddle Yellow Rver basn, Chna 9 of 1962, r1962s1962; 2C-channel roughness of 1962 and rver bed slope of 1977, r1962s1977; 2D-channel roughness of 1977 and rver bed slope of 1962, r1977s1962; 2E-channel roughness of 1977 and rver bed slope of 2003, r1977s2003). Two of the consdered combnatons of the model parameters, namely 1A (channel roughness and rver bed slope of 1977, r1977s1977) and 2A (channel roughness and rver bed slope of 2003, r2003s2003) represent condtons for the actually observed flows n the routng process. By conductng smulatons of flood routng on the bass of the two above scenaros, we nvestgated the effects of rver bed slope, channel roughness, and water volume on flood routng n the lower Wehe Rver (Fgs. and 9). Below we dscuss the smulaton results separately for each of the boundary condtons. Effects of dfferent rver bed slopes on backwater routng Fg. shows that wth flood wave volume and channel roughness of 1997, a reducton n rver slope from 3.2& (r1962s1962) to 2.0& (r1962s2003) would decrease peak dscharge at Tongguan by 140 m 3 /s (14,560 m 3 /s of r1962s1962 and 13,00 m 3 /s of r1962s2003), delay the occurrence of peak flow by 1 h (4 h of r1962s1962 and 49 h of r1962s2003), extended flood duraton by h (90 h of r1962s1962, and 9 h of r1962s2003) and rase peak water level by 0.5 m (327.5 m a.s.l. of r1962s1962 and 32 m a.s.l. of r1962s2003). However, under both boundary condtons, backwater would trace back to Chenchun. Fg. 9A and B shows that backwater flow at Chenchun would present dfferent behavours. Peak dscharge of backwater would ncrease by 7 m 3 /s ( m 3 /s of r1962s1962, and 15 m 3 /s of r1962s2003), and would occur 3 h earler (45 h of r1962s1962 and 42 h of r1962s2003), backwater duraton would ncrease by 4 h ( h of r1962s1962, and 12 h of r1962s2003), and water level would be hgher by 0.2 m (32.5 m a.s.l. of r1962s1962 and 32.7 m a.s.l. of r1962s2003). Effects of dfferent rver channel roughness on backwater routng The effect of dfferent rver channel roughness on flood routng was smulated under the same condtons of flood wave volume and rver bed slope. Fg. shows that wth flood wave volume and rver bed slope of 1977, the ncrease n channel roughness (Mannng coeffcent) from (r1962s1962) to (r2003s1962) would decrease peak dscharge at Tongguan by 1300 m 3 /s (14,560 m 3 /s of r1962s1962 and 13,260 m 3 /s of r2003s1962), delay the occurrence of peak flow by 4 h (4 h of r1962s1962 and 52 h of r2003s1962), extend flood duraton by 11 h (90 h of r1962s1962, and 101 r2003s1962), and rase peak water level by 0. m (327.5 m a.s.l. of r1962s1962 and 32.3 m a.s.l. of r2003s1962). Agan, under both boundary condtons, backwater would trace back to Chenchun (Fg. 9A and B). Flood routng of backwater at Chenchun shows that wth the ncrease n the channel roughness of the lower Wehe Rver, peak dscharge would ncrease by 2 m 3 /s ( m 3 /s of r1962s1962, and 10 m 3 /s of r2003s1962) and would occur 2 h earler (45 h of r1962s1962 and 43 h of r2003s1962), backwater duraton would ncrease by 3 h ( h of r1962s1962, and 11 h of r2003s1962), and water level would rse by 0.4 m (32.5 m a.s.l. of r1962s1962 and 32.9 m a.s.l. of r2003s1962). Effects of dfferent water volume on backwater routng Effects of dfferent water volume n flood routng were smulated under the same condtons of channel roughness and rver bed slope (Fgs. and 9). Frstly, Fg. shows that wth Fgure Smulated flood routng under combned scenaros at Tongguan on the Wehe Rver.

15 90 H. He et al. Fgure 9 Smulated flood routng under desgned scenaros at Chenchun and Huayn on the Wehe Rver. channel roughness and rver bed slope of 1962, a reducton n flood wave volume from the one typcally of the 1977 flood (caused by 43 mm of precptaton) to that typcal of the 2003 flood (caused by 556 mm of precptaton) would decrease peak dscharge at Tongguan by 0 m 3 /s (14,560 m 3 /s of 1977 and 560 m 3 /s of 2003), shorten flood duraton by 10 h (90 h n 1977, and 0 h n 2003) as well as the duraton of the rsng lmb of flood by h (4 h n 1977 and 40 h n 2003), and decrease peak water level by 0.7 m (327.5 m a,s,l n 1977 and 326. m a.s.l. n 2003). In both cases backwater would trace to Chenchun (Fg. 9). In turn, wth channel roughness and rver bed slope of 1977, the same reducton n flood wave volume would decrease peak dscharge at Tongguan by /s (14,230 m 3 /s n 1977 and 5610 m 3 /s n 2003), shorten flood duraton by 17 h (107 h n 1977, and 90 h n 2003) as well as the duraton of the rsng lmb of the flood by 10 h (55 h n 1977 and 45 h n 2003) and decrease peak water level by 0.2 m (32.5 m a.s.l. n 1977 and 32.3 m a.s.l. n 2003). Agan, n both cases backwater would trace back to Chenchun. Fnally, wth channel roughness and rver bed slope of 2003, the same reducton n flood wave volume would decrease peak Fgure 10 Integrated analyss of flood routng under combned scenaros n the mddle Yellow Rver (the vertcal axs of the graphs s flood contrbuton ndex whch desgns to evaluate the contrbuton to flood wave propagaton of rver bed slope, channel roughness, and water volume amount n flood routng).

16 Modellng complex flood flow evoluton n the mddle Yellow Rver basn, Chna 91 dscharge at Tongguan by 6390 m 3 /s (11,590 m 3 /s n 1977 and /s n 2003), shorten flood duraton by 1 h (237 h n 1977, and 219 h n 2003), as well as the duraton of the rsng lmb of the flood by 10 h (55 h n 1977 and 45 h n 2003), and decrease peak water level by 1.7 m (331.0 m a.s.l. n 1977 and m a.s.l. n 2003). Wth both flood wave volumes, backwater would trace back to Chenchun. Fg. 10 shows the effects of model parameters, such as rver bed slope, channel roughness, and flood wave volume on flood routng. Flood wave volume has the greatest mpact on flood duraton, peak dscharge and water level, the tme of occurrence of peak dscharge, and magntude of backwater, whereas, channel roughness has the second strongest mpact on flood duraton and magntude of backwater. Condtonally, channel roughness also has the second strongest mpact on peak dscharge and water level. Of the model parameters, flow dscharge has the strongest nfluence on flood wave propagaton and backwater effects. At hgh flood dscharges, bed slope has the stronger effect on flood routng than channel roughness, whereas at relatvely low flood dscharges, roughness s more mportant. Conclusons The study examned the methodology of combnng hydrodynamc computatonal schemes wth rver basn characterstcs of multple trbutares n the mddle Yellow Rver basn n Chna. Unlke many others, the proposed schemes lnk envronmental and geomorphologc characterstcs to flood wave propagaton wth a downstream backwater effect of complex flood routng. Clearly, calbraton and valdaton wth hstorcal flood events mprove our understandng of backwater characterstcs n bdrectonal flow as well as convergent and dvergent flows between the man channel and trbutares. Moreover, the hydrodynamc computatonal schemes developed n the study are able to ncrease numercal stablty requred n computng complex flood routng processes, snce the stablty of the numercal scheme s strongly assocated wth the adaptaton of channel descrtzaton n computaton. The study demonstrated that usng dedcated computaton schemes accordng to dfferent types of floods can mprove our understandng of the mechansm of flood flow propagaton. By examnng the smple scheme, mproved scheme and the scheme for bdrectonal flow, the results provded several mportant nsghts nto the complex flood routng processes related to the occurrence of backwater effect. It was dentfed that some characterstcs of the nflow hydrograph are senstve to modellng accuracy, such as the geometrc form of the hydrograph and ts peak flow. In general, the study concludes wth followng summares: Frst, the boundary condtons can sgnfcantly alter flood routng processes. The backwater resultng from dvergent flows and bdrectonal flood flows can delay the occurrence and extend the duraton of peak flow. Ths concluson s supported by the smulaton results for convergent and dvergent flood flows n the mddle of Yellow Rver basn for the years Especally, the shape of hydrographs changed from tall and thn to low and wde. The evdence for the delayed occurrence and extended duraton of peak flows after the 1960s and for the ntensfcaton of the trends after the early 190s s mportant for the management of the Yellow Rver and ts trbutares. Second, the study dentfed varables nfluencng the flood routng process. The analyss of combned boundary condtons showed that water volume has the greatest mpacts on flood duraton, peak dscharge and water level, the tme of occurrence of peak dscharge, and the magntude of backwater. Rver bed slope has the second strongest mpacts on flood duraton and the magntude of backwater. In turn, channel roughness has the second strongest mpacts on peak dscharge and water level. However, the nfluence that rver bed slope and channel roughness exert on flood routng wll depend on nternal boundary condtons and the amount of backwater n the study reach. Fnally, the model successfully descrbed that abrupt fluctuaton of boundary condtons ncreases the magntude of backwater. The smulaton ndcated that the backwater occurs under the condtons of convergent and dvergent flows, as well as bdrectonal flows. For the convergent and dvergent flows, backwater s usually generated when flow dscharges n the man rver are greater than those n the trbutares. For the bdrectonal flows, backwater s caused by convergence of two flood waves of smlar magntudes from the opposte drectons. The evdence of ntensfed backwater events after the 190s confrmed that human actvtes, such as the constructon of the Sanmenxa Dam, exerted sgnfcant nfluence on flood characterstcs n the mddle Yellow Rver basn due to the flood routng boundary condtons. Due to the populaton ncreases world wde, the mpacts of human actvty on hydrologcal system need to be understood n order to prevent unexpected consequences. The hydrodynamc computatonal schemes proposed n ths artcle should represent a sgnfcance value nternatonally. Acknowledgements The study was partally supported by a grant of the Chnese Academy of Scences (KZCX3-SW-146), and a grant of USA Offce of Navy Research (Grant No.: N ). Authors sncerely apprecate the constructve comments and edtoral suggestons from two anonymous revewers. References Begn, Z.B., 196. Curvature rato and rate of rver bend mgraton update. Journal of Hydraulc Engneerng 112 (10), Beven, K.J., Wood, E.F., Svapalan, M., 19. On hydrologcal heterogenety catchment morphology and catchment response. Journal of Hydrology 100 (1 3), Camacho, L.A., Lees, M.J., Multlnear dscrete lag-cascade model for channel routng. Journal of Hydrology 226 (1 2), Carrvck, J.L., Applcaton of 2D hydrodynamc modellng to hgh-magntude outburst floods: an example from Kverkfjoll, Iceland. Journal of Hydrology 321 (1 4), Carson, M.A., Grffths, G.A., 199. Gravel transport n the braded Wamakarr Rver: mechansms, measurements and predctons. Journal of Hydrology 109 (3 4), Chung, W.H., Aldama, A.A., Smth, J.A., On the effects of downstream boundary condtons on dffusve flood routng. Advance of Water Resource 19,