# A Simulation-Optimization Model for Seawater Intrusion Management at Pingtung Coastal Area, Taiwan

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. SEAWAT

^{−3}), ${\mu}_{0}$ is the dynamic viscosity (M·L

^{−1}·T

^{−1}) at the reference concentration and reference temperature, $\mu $ is dynamic viscosity (M·L

^{−1}·T

^{−1}), ${K}_{0}$ is the hydraulic conductivity tensor saturated with the reference fluid (L·T

^{−1}), ${h}_{0}$ is the hydraulic head (L) measured in terms of the reference of a specified concentration, ${\rho}_{0}$ is the fluid density (M·L

^{−3}) at the reference concentration and reference temperature, $z$ is the elevation (L), ${S}_{s,0}$ is the specific storage (L

^{−1}), $t$ is time (T), $\theta $ is porosity (-), $C$ is species concentration (M·L

^{−3}), and ${q}_{s}^{\text{'}}$ is a source or sink (T

^{−1}) of fluid with density ${\rho}_{s}$. The freshwater is usually used as the reference fluid.

^{−3}), ${K}_{d}^{k}$ is the distribution coefficient of species k (M·L

^{−3}), ${C}^{k}$ is the concentration of species k (M·L

^{−3}), $D$ is the hydrodynamic dispersion coefficient tensor (L

^{2}·T

^{−1}), $q$ is specific discharge (L·T

^{−1}), and ${C}_{s}^{k}$ is the source or sink concentration (M·L

^{−3}) of species k.

#### 2.2 Artificial Neural Networks

_{j}and b

_{k}are bias values for hidden and output layers, respectively. ${f}_{1}(\cdot )$ and ${f}_{2}(\cdot )$ are the activation functions for hidden and output layers, respectively.

#### 2.3. Management Model Formulation

#### 2.4. Differential Evolution

## 3. Study Area

#### 3.1. General Background

^{2}, is roughly 55 km long and 20 km wide. The plain is bounded by the Central Mountain Range to the east, the Taiwan Strait to the southwest, and the low hills to the north and northwest (Figure 2a). The topography of the Pingtung Plain varies from the elevated Central Mountain Range in the east to the gently sloping alluvial fan in the west and southwest. Altitudes range from 10 m above sea level at coastal areas to 110 m above sea level in the mountain range. Streamflow in the Pingtung Plain is perennial and occurs primarily in response to rainfall. The major streams in this area are Kaoping River, Donggang River, and Linbian River and all of them discharge into Taiwan Strait (Figure 2a). The average annual precipitation in the plain is about 2400 mm, but the distribution is uneven during a year, with a ratio of wet season (May to October) to dry season (November to April) of 9:1. Due to uneven distribution of rainfall, surface water supply is usually insufficient and groundwater is used to satisfy the water demand. Accompanying with rapid growth of aquaculture activities in the 1970s and the increase of population along the coastal area, the water supply reliance on groundwater resources is severe and causes groundwater level drawdown very quickly.

#### 3.2. Hydrogeology

^{−1}, and from 0.005 to 120 m·day

^{−1}, respectively. Because no wells perforate the aquitards, estimates of hydraulic conductivity in aquitards are based on lithology and range from 8.64 × 10

^{−5}to 8.64 × 10

^{−2}m·day

^{−1}. Estimates of specific storage in the plain range from 7.15 × 10

^{−7}to 5.00 × 10

^{−5}m

^{−1}, and estimates of specific yield range from 1.25 × 10

^{−7}to 3.97 × 10

^{−1}[60]. Regional groundwater flow occurs from northeast to southwest, with an average hydraulic gradient of about 0.002 m·m

^{−1}.

#### 3.3. Seawater Intrusion in Pingtung Plain

^{−1}and the area of contamination is about 50 km

^{2}. The seawater fronts in the deeper aquifers F3-1 and F302 moved into the inland by the rate of 400 m·year

^{−1}, faster than those in the shallow aquifers, and the area of contamination is about 100 km

^{2}, also larger than that in the shallow aquifers.

#### 3.4. Regional Groundwater Flow Model

^{−5}–8.64 × 10

^{−2}m·day

^{−1}[64]. The calibrated parameters are shown in Table 1 and the simulated groundwater levels are shown in Figure 4c. The calibrated regional flow model performed very well (Figure 5) and was adapted for the development of seawater intrusion (SWI) model in this study. The water budget in 1999 obtained from the calibrated regional flow model (Table S1) confirmed that all aquifers were overpumped and the regulation or management might be needed.

## 4. Results

#### 4.1. Development of the SWI Model

#### 4.1.1. Refinement of Regional Groundwater Flow Model

#### 4.1.2. SWI Model of Pingtung Plain

^{3}), respectively, and the concentrations of seawater and freshwater are 35.0 and 0.0 (g·L

^{−1}), respectively.

#### 4.1.3. Calibration of SWI Model

^{2}, the sensitivity analysis was conducted on the parameters to avoid the problem of over-fitting. Only the parameters with higher sensitivities were selected for calibration and parameters with low sensitivities were fixed at the initial values. The truncated threshold was set based on Hill et al. [70], i.e., those parameters whose sensitivity values are less than about 0.01 times the largest sensitivity value were not estimated. The results of sensitivity analyses and the associated zones of dispersivities with high sensitivities are shown in Figures S1 and S2. Based on results of the analysis, seven dispersivities were selected for calibration and the scatter plot of measured and simulated TDS were shown in Figure 7. The performance of calibration was satisfactory and its coefficient of determination (R

^{2}) was about 0.85. The calibrated values of longitudinal dispersivities ranged from 0.01 to 500 m and they are shown in Table 1. Once the SWI model was calibrated, the surrogate model of ANNs can be used to replace the calibrated model through the training and testing processes.

#### 4.2. The Surrogate Model of ANNs

#### 4.2.1. Management Scenario #1

^{3}·day

^{−1}with the interval of 200 m

^{3}·day

^{−1}was equal to six (0, 200, 400, 600, 800, and 1000 m

^{3}·day

^{−1}). Hence, the total combination of different pumping scenarios is equal to 6

^{4}(=1296) which means the SWI model needs to run 1296 times to generate all necessary data for the training of ANNs. After determining the architecture of the network, the input and output data were first normalized to an interval between −1 and +1. The activation functions of tangent (tansig) and linear (purelin) functions were used for the hidden and output layers, respectively. The entire dataset was randomly divided into the training, validation, and testing sets by 60%, 20%, and 20% of data, respectively. Two criteria, the convergent gradient which should be less than 10

^{−7}and the maximum epoch which is equal to 1000, were implemented during the ANNs training process. If any one of criteria is met, the training process is terminated. The correlation coefficient (R) for the training, validation, and testing datasets was used to evaluate the performance of identified ANNs.

#### 4.2.2. Management Scenario #2

^{3}·day

^{−1}with the interval of 250 m

^{3}·day

^{−1}was equal to five (0, 250, 500, 750, and 1000 m

^{3}·day

^{−1}). Hence, the total combination of different pumping scenarios is equal to 5

^{5}(=3125) which means the SWI model needs to run 3125 times to generate all necessary data for the training of ANNs. After determining the architecture of the network, the input and output data were first normalized to an interval between −1 and +1 as well. The tangent and linear functions were also used as the activation functions for the hidden and output layers, respectively. The partition of each dataset and the stopping criteria of the training process used in the management Scenario #1 were implemented in this management scenario. The R was also used to evaluate the performance of identified ANNs.

#### 4.3. Results of SWI Management

#### 4.3.1. The Setting of DE Algorithm

^{3}·day

^{−1}corresponding to the training process of ANNs. The initial injection rate was randomly generated by the DE algorithm. The convergence criterion of objective function was set equal to 10

^{−6}and the maximum generation is 200.

#### 4.3.2. The Results of Status Quo

#### 4.3.3. The Management Results of Scenario #1

^{3}·day

^{−1}, and the Barriers #3 and #4 has the lowest and highest injection rates, respectively. The second column in Figure 9a showed the simulated concentrations after 20-year of remediation using the optimal injection strategy. The difference of concentrations between 20-year of remediation and the initial condition was shown in the first column of Figure 9b to demonstrate the effectiveness of remediation. A significant reduction of TDS concentrations was observed around the injection wells. In aquifer F1, the concentrations around Donggang decreased significantly from 32,780 ppm to 14,385 ppm but those around Qifeng still maintained at the high level with 32,766 ppm. In aquifer F2, the injection barriers worked well along the coastal areas where the high concentrations were extensively mitigated from 28,626 ppm to 6621 ppm. In aquifer F3-1, the injection strategy seemed ineffective and the plume with high concentrations still covered large areas, especially around the inland. During the optimization process, the concentration constraints were never violated and implied that the setting of MCL value was too high and could be achieved easily. Consequently, the injection strategy was less effective. To improve the effectiveness of remediation, either a more rigorous concentration constraint should be set or the planning horizon of remediation should be extended to achieve the ultimate target of converting brackish water into freshwater.

^{3}·day

^{−1}. Barriers #3 and #4 still have the lowest and highest injection rates, respectively. The third column in Figure 9a showed the simulated concentrations after 20-year of remediation using the optimal injection strategy. The difference of concentrations between 20-year of remediation and the initial condition was shown in the second column of Figure 9b to demonstrate the effectiveness of remediation. The effectiveness of remediation was very similar to Case 1-1. In general, a significant decrease of TDS concentrations was observed around the injection wells. The injection barriers performed well around Donggang in aquifer F1 and along coastal areas in aquifer F2. However, the effectiveness of injection strategy on Qifeng area in aquifer F1 and entire aquifer F3-1 was still poor. In Case 1-3, the most rigorous MCL (=1000 ppm) was set and the minimal objective function values obtained using the population size of 100 was equal to 9,825.00 m

^{3}·day

^{−1}. The forth column in Figure 9a and third in Figure 9b showed the simulated concentrations and concentration difference after 20-year of remediation, respectively. The results were also similar to Cases 1-1 and 1-2. The effectiveness of injection strategy on the Donggang area in aquifer F1 and coastal areas in aquifer F2 slightly increased, but, for the Qifeng area in aquifer F1 (from 37,206 ppm to 27,219 ppm) and entire aquifer F3-1, it almost did not change and remained with high concentration. The optimal results are summarized in Table 5.

#### 4.3.4. The Management Results of Scenario #2

^{3}·day

^{−1}identified by using the population size of 50. Barriers #1 and #4 have the highest and second highest injection rates, respectively, and Barriers #2 and #3 were inactivated. This result implied that Barriers #2 and #3 might be unnecessary and 15% concentration reduction at the constraint locations can be accomplished by natural recharge. The second column in Figure 11a shows concentrations after 20-year of remediation using the optimal injection strategy. The difference of concentrations 20-year of remediation and the initial condition is also shown in the first column of Figure 11b to demonstrate the effectiveness of remediation. In aquifers F1 and F2, the significant reduction of TDS concentrations was not only around the injection wells, but also extended to the downstream gradient of groundwater. In aquifer F1, the concentrations at the entire downstream gradient of injection barriers were mitigated significantly. In aquifer F2, the concentration around Linyuan also decreased obviously from 24,465 ppm to 13,463 ppm. However, in aquifer F3-1, the radii of influence for the injection wells were still limited to the areas nearby and the injection strategy could not effectively remedy seawater intrusion at the deep aquifer.

^{3}·day

^{−1}. Barrier #4 has the highest injection rate and the most significant increase of injection rate among all barrier compared to Case 2-1. Barriers #2 and #3 were both activated due to the tighter concentration constraints. The third column in Figure 11a and second in 11b showed the simulated concentrations and concentration difference after 20-year of remediation, respectively. In general, the effectiveness of injection strategy was very similar to Case 2-1. The reduction of concentrations around the injection wells and their extents to downstream gradient of groundwater was significant; however, the remediation in aquifer F3-1 was still not very successful. In Case 2-3, the most rigorous MCL (50% of concentration reduction) was set and the minimum objective function values obtained using the population size of 100 was equal to 26,076.5 m

^{3}·day

^{−1}. All of barriers increased their injection rates evidently to satisfy the tightest concentration constraints. The barriers in aquifer F1 have the highest and second highest injection rates, and the Barrier #2 has the most significant increase of injection rate among all barriers compared to Case 2-2. Barrier #3 has the lowest highest injection rates. The fourth column in Figure 11a and third column in Figure 11b show the simulated concentrations and concentration difference after 20-year of remediation, respectively. Compared to Case 2-2, the high concentrations around Xinpi in aquifer F1 were effectively reduced from 19,503 ppm to 645 ppm due to the highest injection rate of Barrier #2. In aquifer F2, a slight increase of remedied areas was observed and its effectiveness of injection strategy was similar to Case 2-2. Again, the remediation of aquifer F3-1 was still limited to the small areas around the wells. The optimal results are summarized in Table 5.

^{3}·day

^{−1}) was higher than that identified by using the population sizes of 50 and 100 (5,462.34 and 5,446.64 m

^{3}·day

^{−1}). In both Cases 2-2 and 2-3, the lowest averaged values were identified by using the population size of 100. This result indicated that the small population size, i.e., 30, probably has the difficulty to solve a more complicated problem, i.e., more rigorous constraints or more number of decision variables. In this scenario, the number of decision variables was increased by one and the population size should be set large enough, i.e., 100, to obtain a robust solution. The increase of population size could increase the search domain and enlarge the probability of identifying the optimal solutions. Again, the large population size does not guarantee to find the optimal management strategy but a more robust solution can be identified by increasing the population size.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Conflicts of Interest

## References

- Chiang, C.-Y.; Wang, C.-H. Seawater Intrusion in the Groundwater Area of Pingtung Plain. Groundwater and Hydrogeological in the Pingtung Plain, Taiwan; Water Resources Agency MOEA: Taichung, Taiwan, 1998. (In Chinese) [Google Scholar]
- Chang, L.-C. Hydrogeological Survey and Groundwater Resource Estimation in Taiwan—Potential Estimation of Groundwater Recharge and Groundwater Flow Model (3/4); Bulletin of the Central Geological Survey MOEA: Taipei, Taiwan, 2011. (In Chinese) [Google Scholar]
- Werner, A.D. A review of seawater intrusion and its management in Australia. Hydrogeol. J.
**2010**, 18, 281–285. [Google Scholar] [CrossRef] - Werner, A.D.; Bakker, M.; Post, V.E.; Vandenbohede, A.; Lu, C.; Ataie-Ashtiani, B.; Simmons, C.T.; Barry, D.A. Seawater intrusion processes, investigation and management: Recent advances and future challenges. Adv. Water Resour.
**2013**, 51, 3–26. [Google Scholar] [CrossRef] - Shi, L.; Jiao, J.J. Seawater intrusion and coastal aquifer management in china: A review. Environ. Earth Sci.
**2014**, 72, 2811–2819. [Google Scholar] [CrossRef] - Cheng, A.D.; Halhal, D.; Naji, A.; Ouazar, D. Pumping optimization in saltwater-intruded coastal aquifers. Water Resour. Res.
**2000**, 36, 2155–2165. [Google Scholar] [CrossRef] - Mantoglou, A. Pumping management of coastal aquifers using analytical models of saltwater intrusion. Water Resour. Res.
**2003**, 39, 183. [Google Scholar] [CrossRef] - Ataie-Ashtiani, B.; Ketabchi, H. Elitist continuous ant colony optimization algorithm for optimal management of coastal aquifers. Water Resour. Manag.
**2011**, 25, 165–190. [Google Scholar] [CrossRef] - Lu, C.; Shi, W.; Xin, P.; Wu, J.; Werner, A.D. Replenishing an unconfined coastal aquifer to control seawater intrusion: Injection or infiltration? Water Resour. Res.
**2017**, 53. [Google Scholar] [CrossRef] - Mahesha, A. Control of seawater intrusion through injection-extraction well system. J. Irrig. Drain. Eng.
**1996**, 122, 314–317. [Google Scholar] [CrossRef] - Rastogi, A.; Choi, G.W.; Ukarande, S. Diffused interface model to prevent ingress of sea water in multi-layer coastal aquifers. J. Spatial Hydrol.
**2004**, 4, 1–31. [Google Scholar] - Mantoglou, A.; Papantoniou, M.; Giannoulopoulos, P. Management of coastal aquifers based on nonlinear optimization and evolutionary algorithms. J. Hydrol.
**2004**, 297, 209–228. [Google Scholar] [CrossRef] - Shamir, U.; Bear, J.; Gamliel, A. Optimal annual operation of a coastal aquifer. Water Resour. Res.
**1984**, 20, 435–444. [Google Scholar] [CrossRef] - Finney, B.A.; Samsuhadi, A.; Willis, R. Quasi-three-dimensional optimization model of Jakarta basin. J. Water Resour. Plan. Manag.
**1992**, 118, 18–31. [Google Scholar] [CrossRef] - Zheng, C.; Bennett, G. Applied Contaminant Transport Modeling; John Wiley & Sons. Inc.: New York, NY, USA, 2002; p. 621. [Google Scholar]
- Abarca, E.; Vázquez-Suñé, E.; Carrera, J.; Capino, B.; Gámez, D.; Batlle, F. Optimal design of measures to correct seawater intrusion. Water Resour. Res.
**2006**, 42, 203–206. [Google Scholar] [CrossRef] - Bear, J.; Cheng, A.H.-D.; Sorek, S.; Ouazar, D.; Herrera, I. Seawater Intrusion in Coastal Aquifers: Concepts, Methods and Practices; Springer Science & Business Media: Berlin, Germany, 1999; Volume 14. [Google Scholar]
- Badon-Ghyben, W. Nota in Verband Met de Voorgenomen Putboring Nabil Amsterdam’tijdschr; Kononkl. Inst. Ing.: The Hague, The Netherlands, 1888; Volume 27, pp. 1888–1889. [Google Scholar]
- Herzberg, D. Die Wasserversorgung Einiger Nordseebäder. J. Gasbeleucht. Wasserversorg.
**1901**, 44, 815–844. [Google Scholar] - Singh, A. Simulation and optimization modeling for the management of groundwater resources. I: Distinct applications. J. Irrig. Drain. Eng.
**2013**, 140, 04013021. [Google Scholar] [CrossRef] - Voss, C.I.; Provost, A.M. Sutra; US Geological Survey Water Resource Investigation Reports: Reston, VA, USA, 1984; pp. 84–4369. [Google Scholar]
- Lin, H.-C.J.; Richards, D.R.; Yeh, G.-T.; Cheng, J.-R.; Cheng, H.-P. Femwater: A Three-Dimensional Finite Element Computer Model for Simulating Density-Dependent Flow and Transport in Variably Saturated Media; DTIC Document; DTIC: Fort Belvoir, VA, USA, 1997. [Google Scholar]
- Guo, W.; Bennett, G. Seawat Version 1.1—A Computer Program for Simulations of Ground Water Flow of Variable Density; Missimer International Inc.: Fort Myers, FL, USA, 1998. [Google Scholar]
- Willis, R.; Finney, B.A. Planning model for optimal control of saltwater intrusion. J. Water Resour. Plan. Manag.
**1988**, 114, 163–178. [Google Scholar] [CrossRef] - Das, A.; Datta, B. Development of multiobjective management models for coastal aquifers. J. Water Resour. Plan. Manag.
**1999**, 125, 76–87. [Google Scholar] [CrossRef] - Javadi, A.; Abd-Elhamid, H.; Farmani, R. A simulation-optimization model to control seawater intrusion in coastal aquifers using abstraction/recharge wells. Int. J. Numer. Anal. Methods Geomech.
**2012**, 36, 1757–1779. [Google Scholar] [CrossRef] - Ahlfeld, D.P.; Mulligan, A.E. Optimal Management of Flow in Groundwater Systems; Academic Press: San Diego, CA, USA, 2000; Volume 1. [Google Scholar]
- Wanakule, N.; Mays, L.W.; Lasdon, L.S. Optimal management of large-scale aquifers: Methodology and applications. Water Resour. Res.
**1986**, 22, 447–465. [Google Scholar] [CrossRef] - Culver, T.B.; Shoemaker, C.A. Optimal control for groundwater remediation by differential dynamic programming with quasi-newton approximations. Water Resour. Res.
**1993**, 29, 823–831. [Google Scholar] [CrossRef] - Culver, T.B.; Shoemaker, C.A. Dynamic optimal ground-water reclamation with treatment capital costs. J. Water Resour. Plan. Manag.
**1997**, 123, 23–29. [Google Scholar] [CrossRef] - Singh, A. Simulation and optimization modeling for the management of groundwater resources. II: Combined applications. J. Irrig. Drain. Eng.
**2014**, 140, 04014002. [Google Scholar] [CrossRef] - Ketabchi, H.; Ataie-Ashtiani, B. Coastal groundwater optimization—Advances, challenges, and practical solutions. Hydrogeol. J.
**2015**, 23, 1129–1154. [Google Scholar] [CrossRef] - Singh, A. Optimization modelling for seawater intrusion management. J. Hydrol.
**2014**, 508, 43–52. [Google Scholar] [CrossRef] - Aguado, E.; Remson, I. Ground-water hydraulics in aquifer management. J. Hydraul. Div.
**1974**, 100, 103–118. [Google Scholar] - Gorelick, S.M. A review of distributed parameter groundwater management modeling methods. Water Resour. Res.
**1983**, 19, 305–319. [Google Scholar] [CrossRef] - Ndambuki, J.; Otieno, F.; Stroet, C.; Veling, E. Groundwater management under uncertainty: A multi-objective approach. Water SA
**2000**, 26, 35–42. [Google Scholar] - Deininger, R.A. Systems Analysis of Water Supply Systems; Wiley: Hoboken, NJ, USA, 1970. [Google Scholar]
- Maddock, T. Ground-water planning model—A basic for a data collection network. In Proceedings of the International Symposium on Uncertainties in Hydrologic and Water Resource Systems, Tuscon, AZ, USA, 11–14 December 1972. [Google Scholar]
- Maddock, T. The operation of a stream-aquifer system under stochastic demands. Water Resour. Res.
**1974**, 10, 1–10. [Google Scholar] [CrossRef] - Rosenwald, G.W.; Green, D.W. A method for determining the optimum location of wells in a reservoir using mixed-integer programming. Soc. Pet. Eng. J.
**1974**, 14, 44–54. [Google Scholar] [CrossRef] - Heidari, M. Application of Linear System's Theory and Linear Programming to Ground Water Management in Kansas; Wiley: Hoboken, NJ, USA, 1982. [Google Scholar]
- Hallaji, K.; Yazicigil, H. Optimal management of a coastal aquifer in southern turkey. J. Water Resour. Plan. Manag.
**1996**, 122, 233–244. [Google Scholar] [CrossRef] - Johnson, V.M.; Rogers, L.L. Accuracy of neural network approximators in simulation-optimization. J. Water Resour. Plan. Manag.
**2000**, 126, 48–56. [Google Scholar] [CrossRef] - Bhattacharjya, R.K.; Datta, B. Optimal management of coastal aquifers using linked simulation optimization approach. Water Resour. Manag.
**2005**, 19, 295–320. [Google Scholar] [CrossRef] - Bhattacharjya, R.; Datta, B. Ann-ga-based model for multiple objective management of coastal aquifers. J. Water Resour. Plan. Manag.
**2009**, 135, 314–322. [Google Scholar] [CrossRef] - Kourakos, G.; Mantoglou, A. Pumping optimization of coastal aquifers based on evolutionary algorithms and surrogate modular neural network models. Adv. Water Resour.
**2009**, 32, 507–521. [Google Scholar] [CrossRef] - Dhar, A.; Datta, B. Saltwater intrusion management of coastal aquifers. I: Linked simulation-optimization. J. Hydrol. Eng.
**2009**, 14, 1263–1272. [Google Scholar] [CrossRef] - Rao, S.; Sreenivasulu, V.; Bhallamudi, S.M.; Thandaveswara, B.; Sudheer, K. Planning groundwater development in coastal aquifers/planification du développement de la ressource en eau souterraine des aquifères côtiers. Hydrol. Sci. J.
**2004**, 49, 155–170. [Google Scholar] [CrossRef] - Christelis, V.; Mantoglou, A. Pumping optimization of coastal aquifers assisted by adaptive metamodelling methods and radial basis functions. Water Resour. Manag.
**2016**, 30, 5845–5859. [Google Scholar] [CrossRef] - Nikolos, I.K.; Stergiadi, M.; Papadopoulou, M.P.; Karatzas, G.P. Artificial neural networks as an alternative approach to groundwater numerical modelling and environmental design. Hydrol. Process.
**2008**, 22, 3337–3348. [Google Scholar] [CrossRef] - Papadopoulou, M.P.; Nikolos, I.K.; Karatzas, G.P. Computational benefit using artificial intelligent methodologies for the solution of an environmental design problem: Saltwater intrusion. Water Sci. Technol.
**2010**, 62, 1479–1490. [Google Scholar] [CrossRef] [PubMed] - Guo, W.; Langevin, C.D. User’s Guide to Seawat: A Computer Program for Simulation of Three-Dimensional Variable-Density Ground-Water Flow; USGS: Tallahassee, FL, USA, 2002. [Google Scholar]
- Harbaugh, A.W.; Banta, E.R.; Hill, M.C.; McDonald, M.G. Modflow-2000, the U.S. Geological Survey Modular Ground-Water Model-User Guide to Modularization Concepts and the Ground-Water Flow Process; Open-File Report; U.S. Geological Survey: Reston, VA, USA, 2000. [Google Scholar]
- Zheng, C.; Wang, P.P. Mt3dms: A Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems: Documentation and User’s Guide; DTIC Document; DTIC: Fort Belvoir, VA, USA, 1999. [Google Scholar]
- Rumelhart, D.; Hinton, G.; Williams, R. Learning Internal Representations by Error Propagation, Parallel Distributed Processing; MIT Press: Cambridge, UK, 1986; Volume 1, pp. 318–362. [Google Scholar]
- Price, K.; Storn, R.M.; Lampinen, J.A. Differential Evolution: A Practical Approach to Global Optimization; Springer Science & Business Media: Berlin, Germany, 2006. [Google Scholar]
- Vesterstrom, J.; Thomsen, R. A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. In Proceedings of the IEEE Congress on Evolutionary Computation, CEC2004, Portland, OR, USA, 19–23 June 2004; pp. 1980–1987. [Google Scholar]
- Karterakis, S.M.; Karatzas, G.P.; Nikolos, I.K.; Papadopoulou, M.P. Application of linear programming and differential evolutionary optimization methodologies for the solution of coastal subsurface water management problems subject to environmental criteria. J. Hydrol.
**2007**, 342, 270–282. [Google Scholar] [CrossRef] - Chiu, Y.-C. Application of differential evolutionary optimization methodology for parameter structure identification in groundwater modeling. Hydrogeol. J.
**2014**, 22, 1731–1748. [Google Scholar] [CrossRef] - Chiang, C.-Y. Hydrogeological Survey of Pingtung Plain with the Project of Groundwater Observation Network in Taiwan; Bulletin of the Central Geological Survey MOEA: Taipei, Taiwan, 2002; pp. 1012–6821. (In Chinese) [Google Scholar]
- Peng, T.-R.; Liu, T.-S.; Guo, H.-Y. Groundwaters Salinization in Chemical Compositions of Coastal Area in Pingtung Plain; The Chinese Society of Soil and Fertilizer Sciences: Taipei, Taiwan, 2000; pp. 353–362. (In Chinese) [Google Scholar]
- Chiang, C.-Y. Seawater Intrusion in the Pingtung Plain; Bulletin of the Central Geological Survey MOEA: Taipei, Taiwan, 6821 2000; pp. 1012–6821. (In Chinese) [Google Scholar]
- Cheng, Y. An Optimal Water Allocation for the Ailiao Irrigation District in Pingtung County, Taiwan. Ph.D. Thesis, National Cheng Kung University, Tainan, Taiwan, 2008. (In Chinese). [Google Scholar]
- Central Geological Survey. MOEA Report of Hydrogeologic Investigation for Pingtung Plain; Central Geological Survey: Taipei, Taiwan, 1997. (In Chinese) [Google Scholar]
- Mehl, S.W.; Hill, M.C. Modflow–LGR—Documentation of Ghost Node Local Grid Refinement (Lgr2) for Multiple Areas and the Boundary Flow and Head (Bfh2) Package; US Geological Survey Techniques and Methods: Reston, VA, USA, 2013. [Google Scholar]
- Hydrological Year Book of Taiwan. Taiwan Water Resources Agency MOEA: Taipei, Taiwan, 1997. (In Chinese)
- Hydrological Year Book of Taiwan. Taiwan Water Resources Agency MOEA: Taipei, Taiwan, 1998.
- Water Resource Bureau. Hydrological Year Book of Taiwan; Taiwan Water Resources Agency MOEA: Taipei, Taiwan, 1999. (In Chinese) [Google Scholar]
- Doherty, J.; Brebber, L.; Whyte, P. Pest: Model-Independent Parameter Estimation; Watermark Computing: Corinda, Australia, 1994; pp. 551–554. [Google Scholar]
- Hill, M.C.; Banta, E.R.; Harbaugh, A.W.; Anderman, E.R. Modflow-2000, the US Geological Survey Modular Ground-Water Model; User Guide to the Observation Sensitivity and Parameter-Estimation Processes and Three Post-Processing Programs; 2331-1258; US Geological Survey: Denver, CO, USA, 2000. [Google Scholar]

**Figure 2.**(

**a**) The study area of Pingtung Plain in Taiwan; and (

**b**) the cross-section (A–A′) representation of the hydrogeological framework.

**Figure 3.**The concentrations of TDS in Pingtung Plain: (

**a**) aquifer F1; (

**b**) aquifer F2; and (

**c**) aquifer F3-1.

**Figure 4.**Regional groundwater flow model of Pingtung plain: (

**a**) measured head in January, 1999; (

**b**) grid cells and zones of parameters (hydraulic conductivity, specific storage, and specific yield); and (

**c**) simulated groundwater levels in December 2010.

**Figure 5.**The scatter plot of sim and meas. of water levels by regional flow model (Chang [2]).

**Figure 6.**The refined groundwater flow model of Pingtung Plain coastal area: (

**a**) the model grids; (

**b**) simulated groundwater levels at Xinpi; and (

**c**) simulated groundwater levels at Qifeng.

**Figure 8.**The deployment of injection barriers for two management scenarios: (

**a**) Scenario #1; (

**b**) aquifer F1 in Scenario #2; (

**c**) aquifer F2 in Scenario #2; (

**d**) aquifer F3-1 in Scenario #2.

**Figure 9.**The optimized results in management Scenario #1: (

**a**) the simulated TDS concentrations after 20-year of remediation using identified optimal injection strategy #1; and (

**b**) the difference of concentrations between 20-year of remediation and the initial condition.

**Figure 10.**The averaged results from six times of repeated optimization processes for each different population size in management Scenario #1.

**Figure 11.**The optimized results in management Scenario #2: (

**a**) the simulated TDS concentrations after 20-year of remediation using identified optimal injection strategy #2; and (

**b**) the difference of concentrations between 20-year of remediation and the initial condition.

**Figure 12.**The averaged results from six times of repeated optimization processes for each different population size in the management Scenario #2.

Model Parameter | Regional Flow Model (Calibrated by Chang [2]) | SWI Model(Calibrate Based on Historical TDS Data) | ||||
---|---|---|---|---|---|---|

Aquifer F1 | Aquifer F2 | Aquifer F3-1 | Aquifer F1 | Aquifer F2 | Aquifer F3-1 | |

Grid cell size in x and y-directions (m) | 1000 × 1000 | 333 × 333 | ||||

Grid cell size in z-direction (m) | 9–85 | 4–93 | 5–100 | 4.3–17.67 | 1.6–20 | 10.3–27.7 |

Horizontal hydraulic conductivity (m·day^{−1}) | 0.15–231.55 | 0.03–200.30 | 0.61–230.00 | 0.15–100.00 | 17.12–200.30 | 1.98–230.00 |

Vertical hydraulic conductivity (m·day^{−1}) | 0.003–4.63 | 0.0006–4.00 | 0.01–4.60 | 0.003–2.00 | 0.34–4.00 | 0.04–4.60 |

Specific storage (m^{−1}) | 6 × 10^{−6}–6 × 10^{−5} | 6.8 × 10^{−6}–5 × 10^{−5} | 6 × 10^{−6}–4 × 10^{−5} | 6 × 10^{−6}–4 × 10^{−5} | 1 × 10^{−5}–2 × 10^{−5} | 6.75 × 10^{−6}–1.8 × 10^{−5} |

Specific yield (-) | 0.06–0.30 | --- | --- | 0.06–0.21 | --- | --- |

Dispersivity (m) | --- | --- | --- | 0.01–400.00 | 0.01–300.00 | 0.001–500.00 |

**Table 2.**The testing results of the number of neurons for the hidden layer in ANNs for the management Scenario #1.

Number of Neurons | Mean Square Error (MSE) |
---|---|

3 | 4.6813 |

5 | 0.72893 |

7 | 0.2347 |

9 | 0.14783 |

Data Set | Correlation Coefficient (R) | |
---|---|---|

Scenario #1 | Scenario #2 | |

Training | 0.99785 | 0.96787 |

Validation | 0.99787 | 0.96741 |

Testing | 0.99779 | 0.96516 |

All | 0.99784 | 0.9674 |

Mechanism of Vector Selection | Random (Uniform Distribution) |
---|---|

Number of decision variables | 4 in Scenario #1 and 5 in Scenario #2 |

Lower bound of decision variables | 0 |

Upper bound of decision variables | 1000 |

Population size | 30, 50, 100 |

Max iterations | 200 |

Scale factor F | 0.85 |

Crossover probability | 1 |

Cases | Objective Function | Injection Rate #1 | Injection Rate #2 | Injection Rate #3 | Injection Rate #4 | Injection Rate #5 |
---|---|---|---|---|---|---|

Scenario #1 | ||||||

Case 1-1 | 4840.15 | 944.85 | 1193.85 | 893.45 | 1808.00 | --- |

Case 1-2 | 6415.30 | 1429.75 | 1619.85 | 1178.00 | 2187.70 | --- |

Case 1-3 | 9825.00 | 2633.50 | 2436.65 | 1991.65 | 2763.20 | --- |

Scenario #2 | ||||||

Case 2-1 | 5446.64 | 2505.50 | 0.64 | 0.028 | 1833.60 | 1106.88 |

Case 2-2 | 12964.55 | 2694.70 | 1069.84 | 1040.41 | 5010.80 | 3148.80 |

Case 2-3 | 26076.50 | 6766.50 | 7253.52 | 1277.22 | 5341.10 | 5438.16 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Huang, P.-S.; Chiu, Y.-C.
A Simulation-Optimization Model for Seawater Intrusion Management at Pingtung Coastal Area, Taiwan. *Water* **2018**, *10*, 251.
https://doi.org/10.3390/w10030251

**AMA Style**

Huang P-S, Chiu Y-C.
A Simulation-Optimization Model for Seawater Intrusion Management at Pingtung Coastal Area, Taiwan. *Water*. 2018; 10(3):251.
https://doi.org/10.3390/w10030251

**Chicago/Turabian Style**

Huang, Po-Syun, and Yung-Chia Chiu.
2018. "A Simulation-Optimization Model for Seawater Intrusion Management at Pingtung Coastal Area, Taiwan" *Water* 10, no. 3: 251.
https://doi.org/10.3390/w10030251