HYDRODYNAMIC MODELING OF RIVER CHENAB FOR FLOOD ROUTING (MARALA TO QADIRABAD REACH) Ghulam Nabi, Dr. Habib-ur-Rehman, Engr. Abdul Ghaffar CED, UET, Lahore CED, UET, Lahore CED, BUZ, Multan.

ABSTRACT The flood flow in a natural channel is purely unsteady, and should be analyzed by using full Saint Venant equations of continuity and momentum conservation. The mathematical modelling is the most commonly used tool to analyze the unsteady flow. The study was meant for the development of a (1-d) hydrodynamic flood routing model based on full Saint Venant equations. The governing equations were discretized by an implicit finite difference scheme (Pressimann Scheme). The system of equations was solved by the Newton Raphson method. The model was applied to river Chenab from Marala to Qadirabad reach for 1992 flood. The flood hydrograph of 1992 was routed through the selected reach by the hydrodynamic model. The series of hydrographs showing attenuation in peak flow at ten-km interval was calculated. A single representative uniform cross section (wide rectangular) was used as channel geometry in the model. It has been found that an average rectangular cross section can be adequately used to simulate flow conditions in a natural river. The developed scheme was also validated for the flood event of 1988 for Khanki to Qadirabad reach. The results of the model reveal that flood flow phenomena in the river Chenab from Marala to Qadirabad reach can be simulated well.

INTRODUCTION (5.7 MAF), respectively. However the flood The Indus Basin River System consists of five may occur in late monsoon season when these major rivers. The most of the rainfall occurs in reservoirs are filled and have no significant monsoon period causing the flood condition in impact on peak flows. the rivers. The brief description of main rivers is as under. Ravi: The river Ravi enters the upstream of Jassar bridge. The river ravi has : The river Sutlej enters Pakistan at 2 catchment area of about 11520 km with the Ganda-Singh-Wala. The total length of upper total length of the catchment is 224 km. India catchment is 720 km. The floods in River Sutlej have completed Thein dam, with live storage are rare due to construction of reservoirs such over 3700 MCM (3 MAF) located about 70 as Ponah Dam and Bhakra Dam having live miles upstream of Jassar bridge, the storage 6166 MCM (5MAF) and 7030 MCM

Madhopur barrage is about 40 km upstream of protection structure cannot always prevent flood Jassar. In 1988 the flood in river Ravi caused damages as expected because i) the flood damages in the Khupura district. protection structures and levees are not designed for all the possible floods. ii) The river Chenab: The Chenab enters Pakistan near aggradations reduce the discharge carrying Marala Barrage about 480 km from its origin. capacity of the channel. iii) Extensive use of river The Salal dam in India is located 64 km valley for agricultural production, industrial use upstream of Marala, which runoff river power and urbanization. Mathematical modelling is the station. The flood damages due to river most commonly used tool to analyze the Chenab are frequent. unsteady flow. Numerical simulation requires less time as well as expenses as compared to Jhelum: The has catchment area physical models, which also involve distortion of about 24600 km2, the most of catchment area scale. Once a system has been modeled it is an is in Kashmir. It has Mangla reservoir of 6166 easy exercise to foresee the consequences of MCM (5 MAF) capacity. The Punch river also such a system, this only involves the change in enter the Mangla reservoir, which chment area data or minor modifications in model it self. about 4100 km2 and peak flows in the order of 11325 cumecs (400,000 cusecs). The Jhelum Flood routing is a procedure to predict the river’s flood in 1992 caused heavy damages to changing magnitude, speed, and shape of life & property. flood wave as it propagates through the

waterways, such as a canal, river, reservoir, or Floods are natural phenomena in many estuary. It is the process of calculating flow countries and Pakistan is no exception, where conditions (discharge, depth) at certain section rivers are flooded frequently. Devastating floods in a channel from the known initial and occurred in river Chenab during 1988 and 1992. boundary conditions in the selected reach. The Marala to Qadirabad reach experiences serious flood hydrograph is modified in two ways. problems of embankments, erosion, bank Firstly the time to peak rate of flow occur later sloughing, and flooding. The floods in the joining at the downstream point this is known as nallas are often sudden and have sharp peaks, translation. Secondly the magnitude of the which usually cause extensive damage and peak rate of flow diminishes at downstream casualties. This sudden flood cause extensive point, the shape of the hydrograph flattens out, damages to the nearby cities. The use of flood so the volume of the water takes longer time to

pass a lower section. This second Operation Model). Saint-Venant equations were modification to the hydrograph is called solved by an implicit method. The model was attenuation applied on various rivers satisfactorily. Greco[5] (1977) developed a model named as Flood The objective of this article is to present Routing Generalized System (FROGS) to calibration and validation results of 1-d simulate flood wave propagation in natural or hydrodynamic flood routing model. artificial channel. The complete Saint-Venant

equations were solved by an implicit finite Past Studies difference scheme. The model was simulated for Lai [1] (1986) studied different methods for flood event in 1951. Yar [6] developed a numerical modelling of unsteady flow in open hydraulic model for simulation of unsteady flow channel. He concluded that among different in meandering rivers with flood plain. This 1-d numerical methods the implicit finite difference model was based on the complete solution of method gave good results. Warwick and Saint-Venant equations by implicit finite Kenneth.[2] (1995) made comparison of two difference method. Huge data is required to hydrodynamic models (HYNHYD) and RIVMOD simulate hydraulic and topographic conditions. developed by U.S Environmental Protection Fread [7] developed the dynamic wave model Agency. Both models were based on explicit (FLDWAV) for one-dimensional unsteady flow in method. The explicit method requires relatively a single or branched waterways. The Saint small computational time step, about five Venant equations were solved by four-point seconds time step was used to ensure model implicit finite difference scheme. This model was stability. A larger computational time step can be successfully applied to simulate downstream used if the continuity and the momentum flood wave caused by failure of Tento Dam in equations were solved by an implicit method Idaho. Tainaka and Kuwahara [8] (1995) instead of an explicit method. The model results developed a hydrodynamic model for sand spit compared well with the observed data. Wurbs[3] flushing at river mouth during a flood. (1987) studied the Dam Break flood wave

models and applied only selected ones from

several leading routing models. Dynamic routing

model is preferred when a maximum level of

accuracy is required. U.S. National Weather

Service 4 (1970) developed a dynamic wave routing model, DWOPER (Dynamic Wave

Figure 1: Generalize Pressimenn Scheme

The hydraulic equations were solved along with time (s), ql is the lateral inflow to the channel, the sediment equation. A leapfrog finite Sf is the friction slope. difference scheme with uniform grid spacing was used to formulate the differential equations. The The equations (1) and (2) were numerically hydrodynamic and the morphological equations solved using implicit box scheme of were coupled. The model computes water level, Preissmann and Cunge (1961). It has some velocity, and sediment transport rate. This model advantages such as variable spatial grid may was applied to Natori River in Japan. The model be used and steep fronts may be properly results were satisfactory. Amein and Fang[9] simulated by varying the weighing coefficients (1970) developed a hydrodynamic flood routing θ and φ . This scheme gives better solution model solving the complete Saint Venant for linearized and non-linearized form of equation by an implicit method. The fixed mesh governing equations for a particular value of Δx implicit method is more stable as compared to and Δt. The detailed numerical solution can be explicit method. found in Fread (1973). The Schematic diagram of Preissmann scheme is shown in Figure 1. MODEL FORMULATION The pressimann scheme in generalized form The continuity and momentum equations were may be written as. used for formulation of hydrodynamic model.

The continuity and momentum equations are: ⎪⎧ n+1 n+1 ⎪⎫ ⎪⎧ n n ⎪⎫ (x,t) =θ (φ + (1 − φ) + (1 −θ ) (φ + (1 −θ ) ) ∫ m ⎨ ∫∫⎬ ⎨ ∫∫⎬ ⎩⎪ j+1 j ⎭⎪ ⎩⎪ j+1 j ⎭⎪ (3) ∂A ∂Q + = ql (1) ∂t ∂x ∂∫ (m) 1 ⎪⎧ ⎛ n+1 n+1 ⎞ ⎛ n n ⎞⎪⎫ = ⎨θ ⎜ − ⎟ + ()1 − θ ⎜ − ⎟⎬ ∂x Δx ⎜ ∫ ∫ ⎟ ⎜ ∫ ∫ ⎟ (4) ⎩⎪ ⎝ j+1 j ⎠ ⎝ j+1 j ⎠⎭⎪ Q2 ∂( ) ∂Q A A ∂A Q + β + g - gA( So - S f ) - ql = 0 (2) ∂t ∂x T ∂x A n+1 n+1 n n ∂∫ (m) 1 ⎪⎧ ⎛ ⎞ ⎛ ⎞⎪⎫ = ⎨φ ⎜ − ⎟ + ()1 − φ ⎜ − ⎟⎬ ∂t Δt ⎜ ∫ ∫ ⎟ ⎜ ∫ ∫ ⎟ (5) Where Q is discharge or volume flow rate at ⎩⎪ ⎝ j+1 j ⎠ ⎝ j+1 j ⎠⎭⎪ distance x (m3 s-1), A is cross-sectional area (m2), x is distance along the flow (m) and t is In Equations (3) to (5) j and n are grid locations and θ and φ are the weighing factors for the

time and space, respectively. As an example The Newton-Raphson method was used to the value of Q at jth spatial grid point and nth solve this system of equations. In this method n time grid point will be denoted by Qj . The trial values were assigned to the unknown known time level is denoted by superscript n, variables Q and A in each node. These values unknown time level by n+1. Applying finite were iterated to refine the solution. To difference approximation Equation (3) to (5) to determine the correction for each iteration, the Equation (1) and (2) gave two equations partial derivative of equation (1) and (2) and of for every box with four unknowns. This boundary equations with respect to process is called discretization of the n+1 n+1 n+1 Q j , A j ,Q j+1 , A j+1 was required. After governing equations. A system of nonlinear taking the partial derivative, the equations are algebraic equations was obtained. After arranged in matrix form. discretization, the finite difference relationship

made a system of nonlinear algebraic A X = B (6) equations with four unknowns. As there were

N nodle points on a reach, so there were (N-1) Where A is a matrix having the partial rectangular grids and (N-1) interior nodes so derivative and X is a column vector consist of the equations applied at each node produced 2 correction, B is the column vector having (N-1) equations. However two unknowns were known values called residuals. The detailed common to any two contiguous rectangular form of above equation is given in Amein and grids. So there are 2N unknowns and 2 (N-1) Fang (1970). equations, two additional equations were

required for the system to be determinate. STUDY AREA These two equations were provided by The study area is situated on the north eastern boundary conditions, one at upstream end and part of the Punjab province between longitude second at down stream end. The resulting 32o 30' to 33o 00' E and latitude 73o 40' to 74o,50' system of equation was solved by Newton- as shown in Figure 2 . The length of the Chenab Raphson method, which was firstly applied by river reach selected for the study purpose is 88 Amein and Fang (1970) to an implicit non- km (from Marala to Qadirabad). linear formulation of Saint Venant equations.

Figure 2: Location of the study area

The average slope is 0.38 meter per km. Two width = 2050 m was used in hydrodynamic major tributaries, Jammu Tawi and Munawar model. The bed slope calculated from data Tawi join the at upstream of the was 0.0004. The elevations are taken Marala barrage, which is located about 10 km reference to mean sea level. The Manning's Below Marala barrage the river flows in plain roughness coefficient is taken as n = 0.025. area, where it attains the flatter slope. The flow The steady state flow condition was taken as data consist of, flood hydrograph at Marala initial flow conditions. The initial discharge was Headworks, flood hydrograph at Khanki 850 cumecs. The initial flow depth was Headworks and Flood hydrographs at assumed as normal depth. The initial depth Qadirabad Barrage.The collected data was calculated by Manning's formula was 0.75 m. processed before using in the hydrodynamic Inflow flood hydrograph of 1992 flood from 06- models. A representative cross-section was 09-1992, at 6.00 a.m to 20-09-1992, at 6.00 prepared to use in the model. a.m at Marala barrage was used as upstream boundary condition. The Manning's equation APPLICATION OF THE MODEL AND was used as downstream boundary condition. RESULTS Flood hydrograph at Marala barrage was input Marala to Khanki of hydrodynamic model and the output was The Marala to Khanki reach is 56 Km long. outflow hydrograph at Khanki headworks. The basic data used for this reach is given below: The wide rectangular channel having

The outflow hydrograph computed by the model as the kinematic model does not show hydrodynamic model and observed hydrograph wave attenuation. A series of flood hydrograph at Khanki Headwork compare well as shown in showing attenuation in peak at 10 km interval is Figure 3. The flood wave attenuates as it shown in Figure 4. The distance between each propagates through waterway. The hydrograph is same and therefore attenuation hydrodynamic model differs from simplified of peak is also equal.

Figure 3. Observed and computed flood hydrograph at Khanki

Figure 4. Series of hydrographs showing attenuation of

Khanki to Qadirabad reach used as upstream boundary condition. The Khanki to Qadirabad reach is 29 km long. The Manning's equation was used as downstream channel width was 1750 m, the bed slope was boundary condition. In Khanki to Qadirabad 0.00041. The Manning's roughness coefficient n reach the inflow hydrograph is the flood = 0.025. Normal flow condition was used as hydrograph at Khanki headworks.The outflow initial flow condition. The initial discharge was hydrograph is computed at Qadirabad. The used 1026 cumecs. The initial flow depth computed and the observed hydrograph calculated by Manning's formula was 0.75 m. compared well with each other as shown in The flood hydrograph of 1992 from 06-09-1992, Figure 5. at 6.00 a.m. to 20-09-1992, at 6.00 a.m was

Figure 5. Comparison between computed and observed flood Hydrograph at Qadirabad

Time (hours)

Figure 6. Series of hydrograph showing attenuation of peak

Figure 7. Comparison between observed and computed hydrographs at Khanki.

The attenuation in peak of flood hydrographs The distances are same so attenuation in peak computed at 10 Kms intervals is shown in Fig.6. is also same. VALIDATION OF HYDRODYNAMIC MODEL

Marala to Khanki the Marala to Khanki reach. The flood The validation of hydrodynamic model was done hydrograph of 1988 from 24-09-1988 to 30-09- for the flood event of 1988. The model was run 1988 was used as input hydrograph at Marala. for the both reach Marala to Khanki and Khanki The output hydrograph was computed at to Qadirabad. The results observed in both Khanki. The Figure 7 shows the comparison reaches are shown in Figure 7. The same between computed and observed hydrograph at topographic and cross sectional data was used Khanki. for the validation of the hydrodynamic model for

There were small discrepancies between may be error in observed data. observed and computed values in the recession As the hydrodynamic model is generalized limb of hydrograph. This difference maybe due model developed for the flood routing, in the to the following reasons. flood study the peak flow is very important. The Figure 7 shows that model had I. There may some initial storage after successfully simulated the peak discharge. So passing the peak discharge, the storage the discharge in the recession limb are not so volume is also mixed with outflow important as compared to peak discharge. discharge, so the discharge in recession is increased. Khanki to Qadirabad II. The river cross sections change every The flood hydrograph of 1988 was routed from year specially in the flood season due to Khanki to Qadirabad reach. The same heavy sediment load. topographic and cross sectional data was used. III. The lateral inflow is not included in the The inflow hydrograph at Khanki was used from hydrodynamic model. The Marala to 25-09-1988 to 01-10 1988. The outflow Khanki reach is 56 km long and many hydrograph was computed at Qadirabad. There Nallas are joining the river which is good agreement between computed and increases the discharge. observed hydrographs at Qadirabad as ahown IV. The observed hydrograph at Khanki in Figure 8. and Qadirabad are almost similar to each other, but in real situation is that CONCLUSIONS the hydrographs at upstream and 1. The steady state flow depth computed downstream cannot be equal. There for an initial discharge provide

satisfactory initial conditions. simulating the shape of output flood 2. Because the hydrodynamic model is hydrograph as well as the time lag. The based on Implicit finite difference attenuation observed can be accurately method (Pressimann Scheme), irregular predicted by the model. mesh interval can be used along the 4. The hydrodynamic model can be used river reach. Similarly unequal time step successfully if large number of cross can be used. sections are not available in a channel 3. The hydrodynamic model is capable of reach.

Figure 8. Comparison between observe and computed flood hydrographs at Qadirabad

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