Planning Groundwater Development in Coastal Deltas with Paleo

Water Resources Management (2005) 19: 625–639 DOI: 10.1007/s11269-005-5604-y

C

Springer 2005

Planning Groundwater Development in Coastal Deltas with Paleo Channels S. V. N. RAO1,∗ , S. MURTY BHALLAMUDI2 , B. S. THANDAVESWARA2 and V. SREENIVASULU1 1 National

Institute of Hydrology, Roorkee, UA, India; 2 Indian Institute of Technology, Chennai, TN, India (∗ author for correspondence, e-mail: [email protected]) (Received: 18 March 2004; in final form: 25 October 2004) Abstract. In this study, a management model is presented for planning groundwater development in costal deltas with paleo channels. It is demonstrated that paleo channels are the best locations for locating the wells for large-scale pumping. Groundwater flow in these aquifers is simulated using a three-dimensional (3-D) density-dependent flow and transport model SEAWAT, which is suitable for a coastal and deltaic environment. A simulation-optimization model is used to determine the optimal locations and pumpages for groundwater development for a group of production wells, while limiting the salinity below desired levels. The mixed integer problem is solved using the Simulated Annealing algorithm and the SEAWAT simulation model. A trained Artificial Neural Network (ANN) is used as the virtual SEAWAT model to perform the simulations, in order to reduce the computational burden for application of the model on desktop computers. The applicability of the model is demonstrated on a hypothetical, but near-real, delta system. Key words: artificial neural network, coastal deltas, density-dependent flow, paleo channel, seawater intrusion, simulated annealing

Introduction The complex deltaic processes, including changes in the river course, result in the formation of paleo channels over evolutionary time periods. Spatial variability in the fresh groundwater availability in coastal deltas is vastly influenced by the presence of these paleo channels. The presence of continuous freshwater pockets along some lineaments is often attributed to paleo channels, which may be hydraulically connected to the existing streams at some point upstream. The transmissivity and storativity values of the aquifer along paleo channels are normally higher than those of the aquifer in the surrounding areas. Therefore, groundwater extraction from these paleo channels generally yields a good quantity of freshwater. On the other hand, groundwater extraction from neighboring areas may result in saline water due to seawater intrusion. Remote sensing studies on coastal deltas in India (Ghosh, 1996) have also suggested that paleo channels as promising sites for locating production wells for agricultural purposes. The present study attempts to

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demonstrate, using a Simulation-Optimization model (S/O), the utility of paleo channels as management strategies for planning groundwater development in a deltaic system. The groundwater development in a coastal deltaic system should be such that there is no excessive seawater intrusion due to pumping. Therefore, groundwater management models for deltaic regions should combine the process model for seawater intrusion with an appropriate technique for solving the optimization problem. Two general approaches have been used to simulate seawater intrusion in coastal aquifers. The first approach is based on the simplifying assumption that the transition zone between the saline water and fresh water regions can be represented by a sharp interface (Essaid, 1990; Bakker, 2003). This approach is valid only when the transition zone thickness is small compared to the aquifer thickness. The second approach, known as the disperse interface approach (Huyakorn et al., 1987; Das and Datta, 1999), explicitly represents the presence of this zone. In this approach, complete density dependent flow and transport equations are solved simultaneously. This disperse interface approach should be used whenever the aquifer response is to be simulated realistically. The retarding velocity of the river, in the deltaic plains before joining the sea, results in the deposition of heavier sediment such as sand in the lower layers compared to silt and clay in the upper layers. Therefore, several layers, with increasing particle size (of sediment material) along the depth, are normally present in the paleo channels. This is also true along the paleo channel course. Coarse-grained particles occur in the upper reaches of the paleo channel, while the fine-grained particles occur in the lower reaches of the channel. Thus a deltaic aquifer with paleo channels represents a highly non-homogeneous, layered porous medium. Simulation of seawater intrusion phenomenon in such a system should consider the three-dimensional (3-D) disperse interface approach. In this study, a coupled S/O framework is developed as a tool to aid in the planning of groundwater development in deltaic aquifers with paleo channels. Although several earlier studies have dealt with groundwater management in coastal aquifers (Willis and Finney, 1988; Hallaji and Yazicigil, 1996; Emch and Yeh, 1998; Das and Datta, 1999), no study has explicitly addressed the issue of paleo channels in deltaic systems. In the problem studied here, the groundwater is extracted through a group of production wells to meet the agricultural demand. The aim of the management model is to determine optimal rates of pumpages and their locations in the delta system, while limiting the salinity to desired levels. The proposed management model is formulated as a mixed integer problem wherein the locations of wells are treated as discrete and pumpages are considered as continuous variables. The combined S/O model is developed by interfacing the Simulated Annealing (SA) algorithm (Aarts and Korst, 1989; Dougherty and Maryott, 1991) for optimization with the 3-D disperse interface simulation model, the SEAWAT (Guo and Langevin, 2002). A trained Artificial Neural Network (ANN) is used as the virtual SEAWAT model to perform the simulations, in order to reduce the computational burden. The

PLANNING GROUNDWATER DEVELOPMENT IN COASTAL DELTAS

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Figure 1. Definition sketch of a Hypothetical coastal delta with a paleo channel.

applicability of the model is demonstrated on a hypothetical, but near-real, delta system. Model Formulation A hypothetical 3-D aquifer system as shown in Figure 1 is considered. The problem involves maximizing groundwater pumpages for agricultural purposes from a group of production wells. The delta system is assumed to be non-homogeneous due to presence of paleo channels. Also, it is assumed to be partially developed i.e., there are some pumping wells existing already. It is required to determine optimal location and pumpages from a group of wells in space and time to meet the objective of maximizing the total pumpage. Some of these wells could be located in paleo

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channels, while others are not. Mathematically, the single-objective problem may be formulated in general within the S/O framework as follows: Max.J 1 =

K J I N

Q nsi, j,k

n=1 k=1 j=1 i=1

where, Q nsi, j,k is the pumpage (decision variable) from production wells located at the node (i, j, k) during the time period n. Subject to the following constraints: (a) Concentration (c) in production wells should be less than specified value cs . ci,n j,k < cs

∀ All production wells and during each time period n

(b) Nonlinear flow and transport equations should be satisfied. f (h, c, q)i,n j,k = 0 ∀ All i, j, k and n; h and q represent heads and source/sink terms (c) Not more than one well at a location. This constraint ensures that the model does not allocate more than one well at the same location. (d) Q min < Q nsi, j,k < Q max In the above equations, I, J, K, and N represent the number of rows, columns, layers and time periods relevant to the hypothetical aquifer. The decision variables are restricted to discrete values in respect of location and continuous values in respect of pumpages. Q min and Q max correspond to lower and upper bounds for the pumpages. Solution Methodology The methodology adapted in this study uses a coupled S/O approach (Figure 2). The simulator (SEAWAT model), the optimiser (SA) and the ANN are also briefly discussed below. For more details see Rao et al. (2003, 2004). THE

SEAWAT MODEL

The SEAWAT model has been recently developed by Guo and Langevin (2002) by combining the popular MODFLOW (McDonald and Harbaugh, 1988) and MT3D (Zheng and Wang, 2002) models, with modifications to account for density variations between seawater and freshwater. The pressure head is converted to equivalent freshwater head for the variable density water in space and time. During any computational time step, the flow field is first solved by MODFLOW and this is followed by the solution for concentration using MT3D. The updated density field is then calculated from the new concentrations and is incorporated back into MODFLOW as relative density difference terms. The flow and transport equations are solved


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Figure 2. Scheme of solution procedure using simulated annealing.

several times for the ‘same time step’ until the difference in fluid density between consecutive iterations is less than a tolerance limit. SIMULATED ANNEALING ALGORITHM

Simulated annealing (SA) is a heuristic algorithm (Figure 2) to find near optimum solutions (Kirkpatrick et al., 1983). The basic idea of the method is to generate

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a random configuration (trial point) iteratively through perturbation, and evaluate the objective function and the constraints after determining the state variables by using the simulator. If the trial point results in infeasibility i.e., if the constraints are violated, it is rejected and a new point is generated. If the trial point is feasible and the objective functions value is smaller than the current best value (for a minimization problem), then the point is accepted and the record for the best value is updated. If the trial point results in feasibility but the objective function is higher than the current best value, then the trial point is either accepted or rejected using the Metropolis criterion (Metropolis et al., 1953). The entire process is terminated after performing a fairly large number of trials or chains (iterations). The method uses temperature and other annealing parameters by trial and error in arriving at near-optimal solutions. Details of SA can be found elsewhere (Aarts and Korst, 1989; Dougherty and Maryott, 1991; Cunha, 1999). ARTIFICIAL NEURAL NETWORK

(ANN)

The optimization process involves calling the simulator several thousands of times to verify the constraints. This involves a significant amount of computational time. This is reduced in this study by replacing the simulator with ANNs (MATLAB, 2000). Briefly the goal of ANN in general is to establish a relation of the form: (Y m ) = f (X n )

(1)

where, X n is an n dimensional input vector consisting of x1 , x2 , . . . , xn ; and Y m is an m dimensional output vector consisting of resulting variables of interest y1 , y2 , . . . , yn ; and f (.) is the commonly used sigmoidal transfer function given by, f (t) = 1/(1 + exp(−t))

(2)

In the present study the input-output vectors are obtained through repeated execution of SEAWAT. The network is trained generally, using a back propagation algorithm that adjust the weights and biases so as to minimize the error function given by: E=

P

(yi − ti )2

(3)

p

where, yi is the ANN output, ti is the desired output, p is the number of output nodes, and P is the number of training patterns or data sets.


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Illustrative Application of Model The illustrative application of the management model presented in this section is intended to evaluate the feasibility and applicability of the methodology for representative conditions. The evaluation and interpretations are however subject to the limitations and assumptions built in the simulation model, and the hypothetical data used in the study. The methodology is designed for application to those situations where it is desired to determine the optimal combination of locations and the corresponding pumpages for m number of wells from among the n possible locations, already identified in the deltaic plain. DESCRIPTION OF STUDY AREA AND DATA

In the course of developing and testing the methodology, a hypothetical data set representing the unconfined deltaic aquifer system is used. The simplified, unconfined aquifer system is represented in the form of a delta (isosceles triangle) of uniform thickness. The delta is 4 km long along the coast and extends up to 4 km normal to the coastline (Figure 1). A 4 layer, 40-rows and 40-column finite difference grid is constructed to represent the simplified hypothetical aquifer system (for real-aquifer problems more layers must be used). The sea face and all other boundaries are assumed vertical. A constant head (zero) is assigned to the nodes along the coast and a specified head boundary condition (varying from 3 m along the river to zero at the coast) is assumed along the two sides of the delta representing river boundary conditions. The concentration along the river boundary is assumed to be zero and constant with respect to time. The sea boundary is similarly assumed to have a time invariant constant concentration of 35-kg/m3 for the bottom 3 layers. The upper layer is assigned the same concentration but is allowed to vary with time such that freshwater/seawater mixed concentrations could be simulated. The problem geometry, the boundary conditions, a typical paleo channel, an existing well (to represent a partially developed aquifer system) and the possible locations of 5 production wells are shown in Figure 1. The hydraulic conductance values in paleo channel is assumed to be 2, 3 and 4 times the value in the surrounding aquifer system for the 1st, 2nd, and 3rd layers respectively. The aquifer details are listed in Table I. The time horizon of the model is considered as three seasons i.e. monsoon, nonmonsoon and monsoon seasons of 180 days each. A large time step of 6 months (180 days) is chosen because recharge occurs only during monsoon season and there is no recharge during the non-monsoon season under typical Indian climatic conditions. It is assumed that a uniform recharge of 0.02 m occurs during the monsoon season. The state variable pertaining to chloride concentration is constrained at certain pre-determined level for all time periods in the production wells (in the cell where the screens are located) as discussed in the formulation. The model is initially run using ‘false transient’ approach with only average recharge for a long time period until steady state conditions in terms of heads and concentrations is achieved

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Table I. Aquifer and other parameters used for SEAWAT model S. No 1 2 3 4 5 6 7 8 9 10 11 12 13

Particulars

Values

Hydraulic conductivity, K x , K y and K z Specific yield (unconfined aquifer) Specific storage of confined aquifer Molecular diffusion Longitudinal and vertical dispersivity Uniform rainfall recharge Grid in X and Y directions Grid in Z direction (z)

20, 20 and 20 m/day 0.225 0.00044 7.7 × 10−5 m/day 66.66 and 13.11 m 0.02 m/monsoon season 100 m z1 = z2 = z3 = 10 m and z4 = 20 m 0.025 0 35 kg/m3 1025 kg/m3 1000 kg/m3

Density difference ratio Concentration of freshwater Concentration of seawater Density of seawater Density of freshwater

(i.e. to simulate near-real conditions arising from boundary and rainfall recharge stresses). Two cases are considered in the present study. Case-I represents the effect of paleo channels exclusively. Case-II represents conditions for near real partially developed deltaic aquifer system with a paleo channel. CASE

(I): EFFECT OF PALEO CHANNELS

The present study seeks to answer a central question: are paleo channels best locations for wells that yield enough freshwater? The intuitive answer is yes, considering the process of paleo channel formation and their aquifer properties, as discussed in the introduction. However, a more specific answer is required in terms of quantity (pumpages) and quality (salinity) for planning purposes. To evaluate the effect of a paleo channel, a hypothetical symmetrical aquifer system as shown in Figure 3 is considered. It is required to determine the maximum pumpage (or potential) from one well over 3 time periods (seasons). The pumping well could be located either at A, i.e. located in a paleo channel, or at B, which is a mirror image location of A about the axis of symmetry. It may be noted that location B is far away from the paleo channel. The screens for the wells are located in the third layer. The unconfined aquifer is recharged from rainfall only during the monsoon season (i.e. 1st and 3rd seasons), while there is no recharge during the non-monsoon season. The lower and upper bounds of pumpages were fixed at 200 m3 /day and 2000 m3 /day, respectively. The SEAWAT model takes approximately 19 s to run for 3 stress periods on a Pentium 4 micro PC. Since the optimization process would involve several thousands of


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Figure 3. Definition sketch of paleo channel connecting well at A in a deltaic system.

function calls, obviously the use of SEAWAT would result in enormous CPU time. Therefore, a virtual simulator was developed using ANN to replace the SEAWAT. The data sets included random input pumpages (within the range of above data set) for the 3 stress periods and the corresponding output responses of SEAWAT model in terms of chloride concentration at well A at the end of each time period. Repeated execution of SEAWAT model (1000 times) provides the data patterns required for ANN training. The same procedure was repeated for the case when the well is located at B, while ensuring the same initial conditions for both cases. In the present hypothetical study involving SEAWAT simulations (implicit finite difference option), the spatial and temporal discretisations were kept sufficiently small to ensure numerical stability in computing heads and concentrations. The coupling parameter DNSCRIT (in the advection package) between flow and transport was set at 0.1 kg/m3 for convergence. For real field problems this convergence parameter must be set still smaller. However, this will drastically increase the computational time. The Courant number was set to 1 in the MT3D input file and the grid Peclet number was verified near well locations to be less than 2 for a random set of pumpages. The model was also run with shorter time steps to verify numerical accuracy of heads and concentrations. A three layer feed-forward network was trained using ANN toolbox of MATLAB (2000). The network uses a sigmoidal transfer function and a linear function. The supervised training is accomplished with the help of a back propagation algorithm as implemented in MATLAB. A typical network with 1–6–1 architecture is shown in Figure 4. The training results in optimal values of network weights and biases. The procedure is repeated for the second set at location B. The S/O model was run to determine the maximum pumpages at location A and B separately. The concentration is constrained at 1 kg/m3 for both the cases. The annealing parameters are chosen based on the guidelines defined by Dougherty and Maryott (1991) and Cunha (1999). The initial temperature is set such that more than 80% of the configurations were accepted in the beginning. Since the simulator

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Figure 4. A typical neural network.

is replaced with ANN, longer chain lengths were possible. The chain length (equilibrium criterion) were set at 80–90 times the number of decision variables and cooling factor (rate of reducing temperature) was varied in the range 0.3–0.5. The SA procedure is terminated when four successive temperature reductions did not yield improvement in the solution. The evolution of model solution using SA procedure for location A and B is shown in Figure 5. The results clearly demonstrate improvement in objective function in respect of location A on the paleo channel. It is important to note that the initial solution itself in respect of location A is much better than the solution at B indicating paleo channels as very good locations for locating production wells. CASE

(II): NEAR-REAL DELTA SYSTEMS

Real deltaic aquifer systems are complex in terms of shape, number of layers, type (confined/unconfined/semi-confined), boundary conditions, aquifer properties and stresses along space and time. The non-homogeneity and anisotropy of paleo channels, their end conditions, hydraulic connectivity with existing streams in 3D-space are generally unknown. These require large-scale field investigations. Further real delta systems are generally partially developed with existing pumpages. These pumpages are likely to interfere with proposed pumpages arising from new development. Thus their combined effect can be only predicted by using a management model as proposed in this study.


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Figure 5. Objective function value evaluated independently: (a) with well at A and (b) with well at B.

In the present study, it is difficult to consider all the above factors. However, for illustration purposes, a paleo channel (in the first layer) and an existing well with fixed pumping (1700 m3 /d) is considered in this study. It is proposed to develop additional groundwater potential for two new wells out of 5 possible locations (see Figure 1). One of the five wells is located on a paleo channel. This provides the required check to determine whether the model prefers a paleo channel well location (#1) for the simplified near-real delta system. However, this may not be necessarily true in all real systems with all the complexities mentioned in the previous paragraph. The existing well was located close to the coast such that seawater intrusion is induced. Three time steps (180 days each) are considered as in previous section. As in previous case the data sets for near-real system for ANN training were generated through repeated execution of SEAWAT model. During each run pumpages were randomly generated within a range (200–2000 m3 /day) for the two wells for each time period (season). These pumpages were allocated to any two random locations, out of 5 possible locations. For the remaining locations, pumpages were assigned zero values. Thus input-output for each time period involving 5 pumpages and 5 responses from SEAWAT model in terms of chloride concentrations at production well locations were written to an output file. In all, 15 responses were obtained at 5 locations for the 3 stress periods. The procedure was repeated to obtain 2000 data patterns as discussed in case (I). The ANN training was achieved on lines as discussed in the previous section to obtain weights and biases. A typical set of arbitrarily selected data sets for calibration and validation between SEAWAT and ANN simulated chloride concentrations for a production well is shown in Figure 6.

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Figure 6. Calibration and validation sets for chloride concentrations arbitrarily selected for a location between SEAWAT and ANN simulated values.

The S/O model (Figure 2) was run to determine optimal location and pumpages. The chloride concentration in all production wells was constrained at 0.75-kg/m3 for all the time periods. The annealing parameters for the SA procedure were determined by trial and error as discussed in the previous section. Evolution of solution is shown in Figure 7. The optimal solution (Table II) is along expected lines. The model invariably chooses location #1 (paleo channel) for the two wells required to be selected among five wells. Therefore paleo channels could be inferred as best locations for production wells in terms of quality and quantity. However this inference could be different if the paleo channel with high hydraulic conductivity extended into sea (Mantoglou, 2003). Computational Time The CPU time in general depends on a number of factors. This includes the time consumed by the simulator, the number of decision variables, the tightness of constraints, the speed of the processor, and the annealing parameters (initial temperature, cooling factor, number of configurations tested for each temperature i.e., chain Table II. Optimal pumping solution (m3 /day) and their location Locationa

1

2

3

4

5

During 1st stress period During 2nd stress period During 3rd stress period

1851.5 1421.8 1532.9

1980.8 – –

– – –

– – 1556.4

– 1856.2 –

a As

in Figure 1.


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Figure 7. Evolution of solution using SA algorithm.

length and termination criterion) used. The SA procedure in the present methodology introduces a computational time burden that has two distinct components. The first component is due to the time consumed by the function calls to the simulator and is associated with every trial feasible configuration. This is virtually reduced to near zero with ANN as the simulator. The second component is the average time consumed for generating feasible configurations after satisfying all constraints until equilibrium and termination criterions are met. The second component is kept to a minimum through efficient coding i.e. by terminating infeasible trial configurations at the earliest stage. The total CPU time is determined by sum of the two components multiplied by the total number of iterations or chains. At initial temperature the number of iterations is large mainly due to infeasible solutions. At

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final temperature the uphill moves are too many. The total number of iterations is problem specific and therefore can be determined only after actual model execution. The computational time for the near-real case was less than 15 min. Summary and Conclusions The study examines and evaluates the effect of paleo channels as management strategies for planning groundwater development in coastal deltas. The problem is conceptualized and solved as a mixed-integer optimization problem with some reference to hydro-geo-climatic condition in east India. The scope of the study is however limited as a hypothetical example is used to illustrate the methodology. Elaborate field investigations (pertaining to aquifer properties of paleo channels/surrounding areas) and groundwater model calibration will be a pre-requisite for actual model application with the proposed methodology. Results of the present study are consistent with the intuition that paleo channels are best locations for groundwater development in terms of quality and quantity. The present study also indicates that ANN is a good substitute for managing computational burdens inherent to combined S/O procedures involving heuristic optimization algorithms. However real field problems involving large number of decision variables and constraints may require parallel processors to efficiently manage the computational burden. Acknowledgments The authors are thankful to the anonymous reviewers for their valuable comments. The authors are grateful to Dr. K. D. Sharma, Director, NIH Roorkee, for the support, encouragement and permission to publish this paper. The authors acknowledge the help of Sri P. R. S. Rao, Research Assistant, for the neat figures and tables in this manuscript. References Aarts, E. and Korst, J., 1989, Simulated Annealing and Boltzmann Machines, Wiley, New York. Bakker, M., 2003, ‘A Dupuit formulation for modeling seawater intrusion in regional aquifer systems’, Water Resour. Res. 39(5), 1131. Cunha, M. D. C., 1999, ‘On solving aquifer management problems with simulated annealing algorithms’, Water Resour. Mgt. 13, 153–169. Dougherty, D. E. and Maryott, R. A., 1991, ‘Optimal groundwater management. 1. Simulated Annealing’, Water Resour. Res. 27(10), 2493–2508. Das, A. and Datta, B., 1999, ‘Development of multi objective management models for coastal aquifers’, J. of Water Res. Plan. Mgt. ASCE 125(2), 76–87. Essaid, H. I., 1990, ‘A multilayered sharp interface model of coupled freshwater and saltwater flow in coastal systems: Model development and application’, Water Resour. Res. 26(7), 1431–1454. Emch, P. G. and Yeh, W. W. G., 1998, ‘Management model for conjunctive use of coastal surface water and groundwater’, J. Water Res. Plan. Res. ASCE 124(3), 129–139.


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Guo, W. and Langevin, C. D., 2002, ‘User guide to SEAWAT: A computer program for simulation of three-dimensional variable-density groundwater flow’, USGS Open File Report, 1–434. Ghosh, T. K., 1996, ‘Application of SAR DATA for developing groundwater sites in drought affected areas in Andhra Pradesh, India’, J. Asian-Pacific Rem. Sens. GIS 8(2), 25–27. Huyakorn, P. S., Anderson, P. F., Mercer, J. W. and White, W. O. Jr., 1987, ‘Saltwater intrusion in aquifers. Development and testing of a three-dimensional finite-element model’, Water Resour. Res. 23(2), 293–312. Hallaji, K. and Yazicigil, H., 1996, ‘Optimal management of a coastal aquifer in southern Turkey’, J. Water Res. Plan. Mgt. ASCE 122(4), 233–244. Kirkpatrick, S., Gelatt, C. D. Jr., and Vecchi, M. P., 1983, ‘Optimization by Simulated Annealing’, Science 220(4598), 671–680. Mantoglou, A., 2003, ‘Pumping management of coastal aquifers using analytical models of saltwater intrusion’, Water Resour. Res. 39(12), 5–11. McDonald, M. G. and Harbaugh, A. W., 1988, ‘A modular 3D finite difference groundwater flow model – Techniques of Water Resources Investigations of the USGS’, Ch. A1, Bk 6. MATLAB, 2000, “Neural network tool box for use with Matlab.” User Guide. Ver. 4. The Mathwork, Inc. 3, Apple Hill Drive, MA., USA. Metropolis, N., Rosenbluth, A. W., and Teller, A. H., 1953, ‘Equation of state calculations by fast computing machines’ J. Chem. Phys. 21(6), 1087–1092. Rao, S. V. N., Thandaveswara, B. S., Bhallamudi, S. M., and Srinivasulu, V., 2003, ‘Optimal groundwater management in Deltaic regions using simulated annealing and neural networks’, Water Resour. Mgt. 17, 409–428. Rao, S. V. N., Srinivasulu, V., Bhallamudi, S. M., Thandaveswara, B. S., and Sudheer, K. P., 2004, ‘Planning groundwater development in coastal aquifers’, Hydrol. Sci. J. 49(1), 155–170. Willis, R. and Finney, W. A., 1988, ‘Planning model for optimal control of saltwater intrusion’, J. Water Res. Plng. Mgt. ASCE 114(2), 163–177. Zheng, C. and Wang, P. P., 2002, ‘A modular Groundwater Optimizer incorporating MODFLOW/MT3DMS’, Groundwater Systems Research Limited, University of Alabama, 2–8.