Genetic Algorithm based Simulation Optimization Approach to Seawater Intrusion

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1 International Symposium on Genetic Algorithm based Simulation Optimization Approach to Seawater Intrusion 1313 Integrated Water Resources Management (IWRM 2014) February 19 21, 2014, CWRDM, Kozhikode, Kerala, India Genetic Algorithm based Simulation Optimization Approach to Seawater Intrusion Pramada S K 1, Minnu K P and Roshni T 2 Civil Engineering Department, National Institute of Technology, Calicut, Kerala , India 1 pramada@nitc.ac.in; 2 roshni.balan@gmail.com ABSTRACT: Many areas of the world use groundwater as their main source of fresh water supply. With the worlds population increasing at alarming rates, the fresh water supply is being continually depleted. Coastal aquifers constitute an important source for water. Due to heavy urbanization, many coastal areas in the world are highly dependent on local fresh groundwater resources. One of the most important threats to groundwater in coastal areas is the seawater intrusion. This paper presents a study where an optimization program based genetic algorithm was developed and applied to a ground water model. A 3D seawater intrusion model has been developed, for the case study of Ernakulam coastal Aquifer System. SEAWAT was used for the development of density dependent model. The developed simulation model was integrated with GA based optimization model. The significant advantage of interfacing a simulation model with an optimization algorithm is that the solution requires no additional simplifying assumptions about the physics of the real system. The integrated simulation model with optimization model permits the determination of optimum pumping from coastal aquifers, which is a viable management option. Keywords: Coastal Aquifer, Seawater Intrusion, Simulation Optimization, SEAWAT, Genetic Algorithm. INTRODUCTION Due to rapid urbanization along the coastal regions, the exploitation of ground water has increased to meet the growing demand from domestic, agriculture, and industrial purposes. Consequent to the continuous pumping and improper management, many coastal aquifers are facing a severe threat of being contaminated with the saltwater. Especially in drought years, the ground water resource is the sole safe guarding arrangement to meet the drinking water requirement in these areas. In order to control the intrusion of seawater into the coastal aquifer system, a good and appropriate management technique should be considered which could determine optimum freshwater supply strategies that will satisfy various hydrological and environmental restrictions. It is expected that with the use of simulation and optimization model, the potential behavior of groundwater in the aquifer can be simulated for present conditions and can be predicted for future scenarios. A saltwater intrusion management model was developed by linking a simulation model with an optimization model to study the movement of salt - fresh water interface. The developed simulation model was integrated with

2 1314 Integrated Water Resources Management (IWRM 2014) GA based optimization model. This coupling technique between optimization and simulation allows the advantages of both modules to be retained within a single framework. In combined simulation-optimization approach, the output from the simulation model forms the input to the optimization model. The developed simulation optimization model is applied to a case study in Ernakulam coastal area, Kerala, India. DESCRIPTION OF THE STUDY AREA The coastal aquifer of interest in this study is the Ernakulam coast, the study area extends from Chellanam to Vypin (Figure 1). Physiographically, Ernakulam district can be divided into three well defined areas namely the coastal plains in the West, the middle region in the center and the hilly ranges in the small areas in North-East and South-East parts of the district. The study area lies between latitudes N and longitudes E. The width of the coastal plains generally ranges from 10 km 15 km. The unconsolidated alluvial formations occupy most of the area on the coastal plains in the western parts of Ernakulam district. On an average, 3000 mm rainfall occurs annually in the district. Out of this, the major contribution is from South-West monsoon season and other seasons contribute less rainfall. In areas, where surface water is not available, drinking water requirement is met from groundwater sources through dug wells, bore wells and tube wells constructed by Kerala Water Authority. Within the past few years, water levels in many wells in this area have declined due to large withdrawals, and the figure will be alarming in the near future if pumping continues at the current higher rate. This will lead to ingress of saltwater. Thus it is essential to study this coastal belt and develop appropriate management strategies with the help of mathematical model considering the geological and hydrological conditions of the area. Fig. 1: Map of the Study Area

3 Genetic Algorithm based Simulation Optimization Approach to Seawater Intrusion 1315 METHODOLOGY The methodology consists of two phases. The first phase consists of development of a simulation model to compute the head values at different locations for a given pumping strategy. In the second phase the simulation model is externally linked with the optimization model. Whenever the optimization procedure requires the objective function and or constraint evaluation, it calls the simulator and passes the modified input parameters to the simulator and the simulation model execute and do the required evaluation. Genetic algorithm module acts as a driver model where in it calls the simulation model by passing the management decision variables and gets back the corresponding objective function value. The genetic algorithm then adjusts the management decision variables to get a new objective function value and continue the process until there is no further improvement in the objective function by altering the decision variables. The genetic algorithm toolbox in Matlab 7 (The MathWorks, 2003) was used as the optimization routine, in which, it calls the calibrated simulation model during each iteration. A subroutine has been developed to interface the genetic algorithm tool box with the calibrated flow model (to communicate between both modules) using Matlab. Simulation Model SEAWAT2000 is used to simulate the seawater intrusion in the study area. SEAWAT is a finite difference based code designed to simulate coupled variable density ground water flow and solute transport. Visual MODFLOW 4.2 is used as a pre and post processor for SEAWAT for the present study. Model area is 11 km in X direction and 24 km in Y direction. Discretization of study region into grids is required for a finite difference based simulation. Grid spacing Fig. 2 Fig. 3: Vertical Discretization

4 1316 Integrated Water Resources Management (IWRM 2014) is given as 100 m in X and Y direction (Figure 2). The model contains 240 rows and 110 columns. Based on the lithological data obtained, the study area is divided vertically into four layers (Figure 3). The maximum elevation is 3 m and minimum elevation is 240 m. The water level and concentration data for January 2003 was given as initial condition. These initial values are interpolated and assigned as initial head and concentration in the model. Boundary condition applied to flow model is the constant head of 0 m for sea. Constant concentration of TDS mg/l is assigned for seaside. The recharge is also applied to the model to represent interaction with the surface water system. Recharge is assumed as 10% of average rainfall (Bhosale and Kumar, 2000). The local and seasonal fluctuations in the natural ground water recharge cause fluctuations of hydraulic head. Monthly recharge rates in mm/year are used in the model. Calibration is done by changing the values of aquifer parameters. These small changes are continued till getting a close correlation between the observed and calculated heads at the observation wells. An overall correlation coefficient of 0.99 and RMS value of 7.104% are obtained. It indicates the reasonable good match between observed and calculated head. Measured water level for 6 years was used as observed heads in model. The model was run in transient state. The calibrated Head vs. Time graph for wells 1 and 3 are shown in Figure 4 and 5. Fig. 4: Comparison of Observed and Computed Head-Well No. 1 Fig. 5: Comparison of Observed and Computed Head-Well No. 3 The calibration of observed and calculated concentrations is done by small adjustments in values of dispersion coefficient. The calibrated plot of observed and calculated values of concentration is shown in Figure 6. The normalized RMS is 2.693% and correlation coefficient is From the figure it is clear that there is a good match between observed and calculated values. From these measures, it can be inferred that the developed model is adequate for studying the behavior of the aquifer for various groundwater pumping scenarios. Figure 7 shows the head and velocity contour during year In Chellanam location water level is below msl. The simulated TDS concentration for the year 2008 is shown in Figure 8. From the figure it can be seen that the higher TDS concentration is in Chellanam area, which is affected by seawater intrusion.

5 Genetic Algorithm based Simulation Optimization Approach to Seawater Intrusion 1317 Fig. 6: Comparison of Observed and Computed Concentration Fig. 7: Simulated Head and Velocity Contour Fig. 8: Simulated TDS Concentration

6 1318 Integrated Water Resources Management (IWRM 2014) Optimisation Model Development Optimization is the process of finding the best solution from a set of available. The calibrated simulation model is used in the combined simulation optimization framework. Genetic Algorithm module acts as the optimization module. In the context of groundwater management problems, which involve complicated non-linear objective function and constraints; traditional optimization methods often fail to give a globally optimal solution. Recently developed heuristic algorithms was found to be efficient in solving the complex groundwater management problem within a combined simulation-optimization framework. In this study, an attempt has been made to develop a methodology to solve the optimization problems encountered in coastal well field by combining simulation and a heuristic optimization technique namely Genetic Algorithm. The genetic algorithm is a method for solving optimization problems that is based on natural selection, and this process is driven by the concept of biological evolution. The genetic algorithm repeatedly modifies the population of individual solutions. At each step, the genetic algorithm selects individuals at random from the current population to be parents and uses them to produce the children for the next generation. Over successive generations, the population evolves towards an optimal solution. The genetic algorithm can be applied to solve a variety of optimization problems that are not well suited for standard optimization algorithms, including problems in which the objective function is discontinuous, non differentiable, stochastic, or highly nonlinear. Also, the method does not use gradient information and makes relatively few assumptions about the problem being solved. The simulation model is linked explicitly to the management model as an independent module. The simulation model is treated as a subroutine that is called by the optimization procedure. The genetic algorithm toolbox in Matlab was used as the optimization module and an interfacing program was written to link the optimization toolbox with the simulation module. The optimization method was applied to derive the optimal pumping strategy for the system. The Aquifer System has been divided into 5 zones. These zoning was carried out to facilitate the quantification of optimal pumping for control of saltwater intrusion in those zones and for easier implementation. The problem is formulated as an optimization problem to maximize pumping considering the constraints on water levels and pumping. The quantity of water being pumped from each zone during the year 2008 was calculated based on the given rates and that was given as upper limit in the optimization and the lower limit is set to zero. The constraint on hydraulic head is given a safe value of 0.5 m i.e. the hydraulic head in the aquifer should be above 0.5 m of mean sea level so that there is no danger of saltwater intrusion. The objective function has the following form: ZQ ( ) = qi Maximize i= 1 ST * h j h j 0.5, j = 1,..., m * 0 < qi < qi, i = 1,..., n N (1) (2) (3)

7 Genetic Algorithm based Simulation Optimization Approach to Seawater Intrusion 1319 where h j : computed hydraulic head at the observation point j; * h j : minimum allowed hydraulic head (m.s.l) at the observation point j; q i : pumping rate from zone i; q : maximum allowed pumping rate from zone i; m n * i : number of observation points (wells); : number of zones The results of the optimization model are given in Table 1. Figure 9 shows the optimum rate for each well. From these results, it can be concluded that the high rate of pumping over the past years the optimization models suggests that pumping from the first zone should be curtailed completely and reduced pumping rates from the third zone. With the optimum pumping strategy, it was not possible to obtain the desired water level at the first zone. A trial run was made with the optimum pumping to find out how long the same rate needs to be maintained to achieve the desired level. It is found that the optimal pumping strategy needs to be continued atleast for further 18 months. Table 1: Optimum Pumping for each Zone Well Location Normal Pumping Rates Optimum Pumping Rates m 3 /day Chellanam Kumbalangi Edakochi Cheralai Ernakulam South Fig. 9: Optimal Pumping Rate from each Well

8 1320 Integrated Water Resources Management (IWRM 2014) CONCLUSIONS It is concluded that there is an increasing trend of rapid movement of interface in the Chellanam, Edakochi area where as in the Kumbalangi, Cheralai, Ernakulam South there is no definite clue for seawater intrusion. The water levels in this zone are just above the mean sea level and in order to keep the water level to be well above the mean sea level in further time periods, the developed monthly optimization-simulation model has to be run for each time period to find out the optimal pumping values. REFERENCES Bhosale, D. and Kumar, C.P. (2002). Simulation of Seawater Intrusion In Ernakulam Coast, International Conference On Hydrology and Management, December 2002, Hyderabad, 2: Mohan, S., Pramada, S.K. (2006). Real Time Control of a well Field with a Groundwater Simulation-Optimisation Model, Conference on Environmental Conservation organized by BITS Pilani, Rajasthan, September 1 3: Langevin, C.D., Shoemaker, W.B. and Weixing (2003). MODFLOW 2000, the U.S. Geological survey modular groundwater model Documentation of the SEAWAT 2000 Version with variable density flow process and the integrated MT3DMS Transport process, US Geological survey, open file report, The MathWorks, Inc. (2003). MATLAB Users Manual, Natick, MA, US.

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