Application of inverse routing methods to euphrates river iraq
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Application of inverse routing methods to euphrates river iraq Application of inverse routing methods to euphrates river iraq Document Transcript

  • International Journal of Civil Engineering and TechnologyENGINEERING – 6308 INTERNATIONAL JOURNAL OF CIVIL (IJCIET), ISSN 0976 AND (Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEME TECHNOLOGY (IJCIET)ISSN 0976 – 6308 (Print)ISSN 0976 – 6316(Online)Volume 4, Issue 1, January- February (2013), pp. 97-109 IJCIET© IAEME: www.iaeme.com/ijciet.aspJournal Impact Factor (2012): 3.1861 (Calculated by GISI) © IAEMEwww.jifactor.com APPLICATION OF INVERSE ROUTING METHODS TO EUPHRATES RIVER (IRAQ) Mustafa Hamid Abdulwahid Department of Civil Engineering, University of Babylon, Iraq, mstfee@gmail.com Kadhim Naief Kadhim Department of Civil Engineering, University of Babylon, Iraq, Altaee_Kadhim@yahoo.com ABSTRACT The problem of inverse flood routing is considered in the paper. The study deals with Euphrates River in Iraq. To solve the inverse problem two approaches are applied, based on the Dynamic wave equations of Saint Venant and the storage equation using Muskingum Cunge Method, First the downstream hydrograph routed inversely to compute the upstream hydrograph, Five models have been made for inverse Muskingum Cunge Method (CPMC, VPMC3-1, VPMC3-2, VPMC4-1, VPMC4-2) and two models for inverse finite difference scheme of Saint Venant Equations (explicit and implicit). Then the sensitivity analysis studied for each parameter in each method to find out the effect of these parameters on the solution and study the stability and accuracy of the result (inflow hydrograph) with each parameter value change. Finally, the computed inflow hydrograph compared with the observed inflow hydrograph and analyze the results accuracy for each inverse routing method to evaluate the most accurate one. The results showed that the schemes generally provided reasonable results in comparison with the observed hydrograph and hydraulic results for inverse implicit scheme of Saint Venant equations are more accuracy and less oscillation than that obtained by the inverse explicit scheme and these hydraulic results are more accuracy than hydrologic results using Muskingum Cunge Method. Keywords: CPMC, VPMC3-1, VPMC3-2, VPMC4-1, VPMC4-2 97
  • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEMEI. INTRODUCTION Euphrates is important river in Iraq, flowing from Turkish mountains and pour in ShattAlarab southern Iraq which withdrawing water from the pool upstream of the AL HindyaBarrage. The river is surrounded by floodplains and considered as an important region of theIraqi agricultural incoming. The inverse flood routing appears to be a useful for watermanagement in Euphrates plains. The considered reach of length about 59.450 km between AlHindya Barrage ( 32o 43’ 40" N - 44o 16’ 04" E ) and Al Kifil gauging station ( 32o 12’ 53" N- 44o 21’ 43" E ), where the river branches into Al Kuffa and Al Abbasia branches while thereis no branches within the studied river reach.II. INVERSE FLOOD ROUTING USING SAINT VENANT EQUATIONS The basic formulation of unsteady one dimensional flow in open channels is due toSaint Venant (1871). It can be written in the following form: (1) Continuity equation. (2) Momentum equation. where: t = time, x = longitudinal coordinate, y = channel height, A = cross-sectional flowarea, Q = flow discharge, B = channel width at the water surface, g = gravitationalacceleration, qL = lateral inflow, Sf = friction slope. Figure( 1) . Euphrates river considered reach [ Google Map ]. 98
  • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEME The equations (1, 2) are solved over a channel reach of length L for increasing time t, andthey are carried out in the following domain: 0 ≤ x ≤ L and t ≥ 0, Figure (1) Figure 1 Direction of integration of the Saint Venant equations while (a) is conventional solution and (b) is inverse solution [Szymkiewicz. (2010)].The following auxiliary conditions should be imposed at the boundaries of the solutiondomain (Szymkiewicz, 2010):− Initial conditions: Q (x,t) = Qinflow(t) and h(x,t) = hinflow(t)for x=L and 0 ≤ t ≤ T;− Boundary conditions: Q(t,x) = Qo(x) or h(t,x) = ho(x)for t=0 and 0 ≤ x ≤ L, Q(t,x) = QT(x) or h(t,x) = hT(x) for t=T and 0 ≤ x ≤ L.where Q(x,t), h(x,t), Qo(t), QL(t), ho(t) and hL(t) are known functions imposed, respectively,at the channel ends. The Saint Venant partial differential equations could be solvednumerically by finite difference formulation. The derivatives and functions in Saint VenantEquation are approximated at point (P) which can moves inside the mesh to transform thesystem of Saint Venant Equation to a system of non-linear 4 algebraic equations. Twoweighting factors must be specified, i.e., (θ) for the time step and (ψ) for the distance step asshown in Figure (2). [Dooge and Bruen,(2005)]. Figure (3): Grid point applied in weighted four point scheme. [Dooge and Bruen,(2005)]. The spatial derivatives of the function ( ) at point (P) becomes [Szymkiewicz, (2008)]: 99 View slide
  • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEME The derivatives and functions approximated at point P transform the system of equations (1and 2) to the following system of non-linear algebraic equations [Alattar M. H. (2012)]:where i is index of cross section, j is index of time level, and ψ and θ are the weightingsparameters ranging from 0 to 1.III. INVERSE FLOOD ROUTING USING MUSKINGUM CUNGE METHOD The main features of flood wave motion are translation and attenuation; both arenonlinear features resulting in nonlinear deformation. The linear convection – diffusionequation, scheme stated in terms of the discharge [Miller and Cunge, (1975)]: 100 View slide
  • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEMEwhere: Q = discharge , A = flow area, t = time, x = distance along the channel, y = depth offlow, qL = lateral inflow per unit of channel length, the kinematic flood wave celerity ( ) andthe hydraulic diffusivity (µ) are expressed as follows:where Bo is the top width of the water surface for wide channel, and is the reference flowdepend on its computation method, i.e. (CPMC) and (VPCM). an improved version of theMuskingum - Cunge method is due to Ponce and Yevjevich, (1978). where : i = index of cross section, j = index of time level, QL = total volume discharge, =lateral flow discharge with :where X is dimensionless weighting factor, ranging from 0.0 to 0.5 and the ( C ) value is theCourant number, i.e., the ratio of wave celerity ( ck ) to grid celerity ( x / t) : The Muskingum - Cunge equation is therefore considered an approximation of theconvective diffusion Equation (8). As a result, the parameters K and X are expressed asfollows [Ponce and Yevjevich, (1978)]:From equation (11) Koussis et al.,(2012) develop the explicit reverse routing scheme. Figure(3). 101
  • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEMEThe bi’s are related to the ais of equation (12) and written as follows: Figure (3). Reverse flood routing in a stream reach of length L [Koussis et al.,(2012)]. The values of Qo and ck in equation (15) is obtained as follows [Samimi et al., (2009)] : 1) In Constant Parameters Muskingum Cunge Method (CPMC) ck and Qo are keptunchanged during the entire computation. In other words they were computed based on aconstant “reference discharge”. Ponce, (1983) proposed reference discharge: Where is the base flow taken from the inflow hydrograph. 2) In Variable Parameters Muskingum Cunge Method (VPMC) Ponce et al.,(1978) claimedthat variable routing parameters could more properly reflect the nonlinear nature of flood wavethan the constant parameters do. However, the variable parameter schemes induce volume lossduring the computation. Ponce et al. (1994) argued that the volume loss is the price that shouldbe paid to model the nonlinear characteristic of flood wave. In the variable parameters Muskingum - Cunge method (VPMC), the computation ofrouting parameters is based on a reference discharge that is determined within eachcomputational cell. Therefore, the routing parameters will vary from a time step to anotheraccording to the nonlinear variations of the discharge. The reference discharge is determinedby averaging the discharge of the nodes of each computational cell. Basically, two schemes were proposed for determining the reference discharge in eachcomputational cell. The first scheme uses known discharge values of three nodes of the cell,which is referred to three points averaging scheme. The second one includes the unknowndischarge value of the forth node, that is (i+1, j+1), in the computation of the referencedischarge. This scheme is usually referred to as four points averaging scheme and clearly 102
  • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEMErequires trial and error procedures to determine the reference discharge. Each of the averagingschemes encompasses three computational techniques which were presented as follows [Tanget al., (1999)]: and ( m = 1.5 ) for wide channel [U.S. Army Corps ofEngineers, (1994)].This method is clearly requires trial and error procedures to determine the reference discharge( Qo ). Where the value of Qo (4) and ck (4) is obtained by one of the numerical iterationtechniques. In the present study only five methods (CPMC, VPMC3-1, VPMC3-2, VPMC4-1, andVPMC4-2) have been applied to estimate the reference discharge and flood wave celerity thatneeded to estimate the parameters of Muskingum Cunge inverse routing Method.The values of t and x are chosen for accuracy and stability. First, t should be evaluated bylooking at the following three criteria and selecting the smallest value: (1) the user definedcomputation interval, (2) the time of rise of the inflow hydrograph divided by 20 ( Tr / 20 ),and (3) the travel time through the channel reach [Ponce, (1983)].For very small value of x, the value of in equation (15) may be greater than (0.5) leading tonegative value of (X) so x is selected as [Ponce, (1994)]: 103
  • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEMETo satisfy ( 0 < X < 0.5) and preserve consistency and stability in the method , where thesolution will be more accurate when X 0.5 [Koussis et al.,(2012)].IV. INVERSE ROUTING RESULTS Five models have been made for inverse Muskingum Cunge Method (CPMC,VPMC3-1, VPMC3-2, VPMC4-1, VPMC4-2) and two models for inverse finite differencescheme of Saint Venant Equation (explicit and implicit) used to route the flood wave inEuphrates river (28/11/2011 – 13/12/2011). Table (1) shows the actual and computedhydrographs. the time intervals of 12 hour is used to satisfy the limitations of MuskingumCunge Method and for more smooth curvature line of the hydrographs that calculated indifferent methods and the average bed slope founded to be ( So = 4.3 cm / km ), For inverseexplicit finite difference scheme of Saint Venant equations the weight factors were ( ¥=5 Ø=0)this founded to gave the most accurate results and these values of weight factors arecompatible with the [Chevereau, (1991)] study and for Inverse implicit scheme the weightfactors were ( ¥=0.5 Ø=0). Figure (4) Figures (5) and (6) shows model stability analysis with change of the weight factorsfor explicit finite difference scheme of Saint Venant equations, The results show thatthe time weight factor is very sensitive for model stability and only model of (Ø=0) is astable model, but less sensitive for space weight factor. 104
  • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEMEThe Channel bed slope is one of important parameters effects on river routing results[U.S. Army Corps of Engineers, (1994)] , Figure (7) and Figure (8) shows that themodel is stabile with steep slope and the stability decreasing with mild slope with thesame distance interval ( i.e. x = 59450 m ) in inverse constant parameter MuskingumCunge scheme and the model stability decrease with less distance intervals, The modelwith slope of ( 0.000023 ) and less is instable with dispersion numerical solution withthe same parameters of this study case. Note that the Courant number not depend onslope and remain (C = 0.352) for all models for different slope values, While themodels with different space intervals both of Courant number and weight factorchanged. Table (1). Comparison of computed results of inverse flood routing by various methods. 105
  • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEMEFigure (5). Computed upstream discharge hydrograph in explicit 12 hour interval scheme in different time weight factor. 106
  • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEME Figure (8). Computed upstream discharge hydrograph in inverse Muskingum Cungescheme with different model space intervals with 12 hour time interval and (Slope = 0.0001 ). For one part model the space interval is ( x = 59450 m ); Courant number ( C = 0.352 )and ( X = 0.387 ), The two parts model ( x = 30000 m, 29450 m ); ( C = 0.697 ) and ( X =0.275 ) and the three parts model ( x = 20000 m, 20000 m, 19450 m ); ( C = 0.697 ) and ( X =0.275 ).V. ACCURACY ANALYSIS FOR INVERSE ROUTING RESULTS According to the inverse routing results in table (1) the actual observed upstreamhydrograph is appointed for the error analysis by evaluate the deviation ratio of the results foreach model in different analytic methods with the actual observed inflow. the error percentageis define as equation [Szymkiewicz, (2010)]:Where the QObserved inflow in is upstream station and QComputed is the computed inflowby one of the applied inverse routing methods. The values of the mean errors are listed inTable (2) which summarizes the considerations of each method. Knowing that the percentageof the accuracy was determined as :The root mean square of error method (RMSE) equation (30) computes the magnitude of errorin the computed hydrographs [Schulze et al., (1995)]. 107
  • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEME Where: I-SV is the inverse implicit routing scheme of Saint Venant equations, E-SV is theinverse explicit routing scheme of Saint Venant equations, CPMC is the constant parametersestimation for inverse hydrologic routing of Muskingum Cunge method, VPMC is the variableparameters estimation for inverse hydrologic routing of Muskingum Cunge method.The errors of the measuring field data effect on the accuracy analysis for comparison of theseactual measured field data with calculated results in different inverse routing methods, theseerrors may align against or toward the one of the applied reverse routing methods and theaccuracy analysis will be less adequate. in addition to that the hydraulic and hydrologicinverse routing methods have many approximations and assumptions for its equations that iscause the deviation of the measured results of discharge and stage hydrograph compared withthe observed data.The many field data approximation also decreases the models accuracy like neglecting of themany channel geometric properties had an indirectly little effecting on the inverse riverrouting i.e. the temperature, meandering and existing of the sapling and grass and neglectingof the small lateral flow i.e. rainfall and seepage.VI. CONCLUSION For the hydraulic and hydrologic inverse routing methods, The inverse hydraulicmethods represented by (explicit and implicit schemes) considered the hydraulic propertieswith the actual cross sections along the reach with more details than the other methods, thisreflect that the inverse hydraulic method give more accurate results than those at the inverseMuskingum Cunge methods and the implicit scheme of hydraulic method for Saint Venantequations gave more adequate results than the explicit scheme, where the implicit schemeaccuracy was ( 96.96% ) and for explicit ( 96.22% ). Channel bed slope is a sensitiveparameter effects on river routing results, this conclusion agree with [U.S. Army Corps ofEngineers, (1994)]. The present study of Muskingum Cunge Methods shows that the model isstabile with steep slope and the stability decreasing with mild slope with the same distanceinterval (i.e. the x = 59450 m), and the model stability decrease with less distance intervals,The models with slope of (0.000023) and less are instable with dispersion numerical solution 108
  • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 1, January- February (2013), © IAEMEwith the same parameters of this study case. The results show that the time weight factor offinite difference explicit scheme of Saint Venant equations is very sensitive for model stabilityand only model of (Ø=0) is a stable model , this compatible with [Liu et al, (1992)] as heconcluded that the inverse computations produced better results with (Ø=0). While the modelis less sensitive for space weight factor (¥) and the model remain stable for wide range ofspace weight factor values. For implicit scheme the value of time weight factor (¥=5) and (Ø=0.5) is founded that it gave the more stable results.VII. REFERENCESFor the hydraulic and hydrologic inverse routing methods, The inverse hydraulic methodsrepresented by (explicit and implicit schemes) considered the hydraulic properties with theactual cross sections along the reach with more details than the other[1] Alattar M. H. (2012) :” Application of Inverse Routing Methods on Sement of EuphratesRiver“. M.Sc. thesis, College of Engineering, University of Babylon, Iraq.[2] Chevereau, G. (1991):” Contribution à létude de la régulation dans les systèmeshydrauliques à surface libre”. Thèse de Doctorat de lInstitut National Polytechnic deGrenoble, 122 p.[3] Dooge, C.I. and Breuen, M. (2005): "Problems in reverse routing". Center of WaterResources Research, University College of Dublin, Earlsfort Terrace, Dublin, Ireland.[4] Koussis, A. D. (2012): " Reverse flood routing with the inverted Muskingum storagerouting scheme", Nat. Hazards Earth Syst. Sci., 12, 217–227.[5] Miller W.A. and Cunge J.A. (1975):” Simplified Equations of Unsteady Flow in OpenChannels”. Water Resources Publications, Fort Collins, Colorado, 5: Pages 183 -257.[6] Ponce, V. M. & Yevjevich, V. (1978) : ” Muskingum - Cunge method with variableparameters”. Hydraulic. Div. ASCE, 104 (12), 1663-1667.[7] Ponce, V. M. (1983) :” Accuracy of physically based coefficient methods of floodrouting”. Tech. Report SDSU Civil Engineering Series No. 83150, San Diego StateUniversity, San Diego, California, Ponce, V.M. (1994):” Engineering Hydrology”, Principlesand Practice, Prentice Hall, New Jersey.[8] Saint Venant, B. de (1871): “Théorie de liquids non-permanent des eaux avec applicationaux cave des rivieres et à l’introduction des marées dans leur lit (Theory of the unsteadymove-ment of water with application to river floods and the introduction of tidal floods in theirriver beds)”, Acad. Sci. Paris, Comptes Rendus 73, pp. 148-154 and 33, pp. 237-249.[9] Samimi S.V. , Rad R. A. , Ghanizadeh, F. (2009): ” Polycyclic aromatic hydrocarboncontamination levels in collected samples from vicinity of a highway ” . J. of Environ. HealthSci. & Eng., 6:47-52. Iran.[10] Schulze, E. D.ct al. (1995): ”Above-ground biom ass and nitrogen nutrition in a chronosequence of pristine Lahurian Larix stands in Eastern Siberia”. Canadian Journal of ForestResearch 25: 943—960.[11] Szymkiewicz, R. (2010) :”Numerical Modeling in Open Channel Hydraulics “,University of Technology, Gdansk, Poland.[12] Tang, X., Knight, D. W., SAMUELS, P. G., (1999):”Volume conservation in VariableParameter Muskingum - Cunge Method”, J. Hydraulic Eng. (ASCE), 125(6), pp. 610–620.[13] U.S. Army Corps of Engineers (1994):” FLOOD-RUNOFF ANALYSIS”DEPARTMENT OF THE ARMY EM U.S. Army Corps of Engineers Washington, DC20314-1000 USA. 109