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Bi-objective Extraction-injection Optimization Modeling for Saltwater Intrusion Control Considering Surrogate Model Uncertainty

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Abstract

Data-driven machine learning surrogates are used to substitute complex groundwater numerical simulation models within optimization algorithms to reduce computational burden for large-scale aquifer management. The traditional surrogate-assisted simulation–optimization modeling has been limited due to uncertainty persisting in surrogate model predictions. More advanced methods are imperative to reduce impact of uncertainties from surrogate models on solution optimality. In this regard, we propose an ensemble surrogate-based simulation–optimization methodology for optimal saltwater intrusion (SWI) control through accounting for uncertainty induced by surrogate models. The optimization model includes two conflicting objectives: minimizing total groundwater pumping and injection rate from an extraction-injection horizontal well system while reducing chloride concentration at monitoring locations below a certain level as much as possible. Three types of machine learning surrogates including artificial neural network, random forest and support vector machine were established to replace a high-fidelity physically based saltwater intrusion model. Optimal Latin hypercube design combined with parallel computing on high performance computing (HPC) was performed to generate input–output data of pumping and injection schedules and resulting salinity levels. An innovative Bayesian set pair analysis approach was presented to derive posterior model weights by considering both training and testing data. The newly constructed individual and ensemble machine learning surrogates were then coupled with a bi-objective optimization model to obtain Pareto-optimal extraction-injection strategies in a deep “2000-foot” sand of the Baton Rouge area, Louisiana, where the optimization was solved using a multi-objective genetic algorithm NSGA-II. Results showed that individual and ensemble surrogate models were accurate enough for salinity prediction. Through comparing the Pareto-optimal solutions, the ensemble surrogate-based modeling was confirmed to provide more reliable and conservative strategies for alleviating saltwater intrusion threat while considerably reducing computational cost. The improved Bayesian set pair analysis approach proved to be robust to integrate multiple models by quantifying model uncertainty.

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Data Availability

The historical pumping data were provided by the Capital Area Ground Water Conservation Commission (CAGWCC) of Louisiana. The water quality data were provided by the U.S. Geological Survey (USGS). Other data, models, and codes that support the findings of this study are available from the corresponding author upon request.

References

  • Ajami NK, Duan Q, Sorooshian S (2007) An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction. Water Resour Res 43(1):W01403. https://doi.org/10.1029/2005WR004745

    Article  Google Scholar 

  • Asher M, Croke B, Jakeman A, Peeters L (2015) A review of surrogate models and their application to groundwater modeling. Water Resour Res 51(8):5957–5973. https://doi.org/10.1002/2015WR016967

    Article  Google Scholar 

  • Badaruddin S, Werner AD, Morgan LK (2017) Characteristics of active seawater intrusion. J Hydrol 551(8):632–647. https://doi.org/10.1016/j.jhydrol.2017.04.031

    Article  Google Scholar 

  • Bolstad WM, Curran JM (2016) Introduction to Bayesian statistics. John Wiley & Sons, pp 85–110

  • Breiman L (2001) Random forests. Mach Learn 45:5–32

    Article  Google Scholar 

  • Brodeur ZP, Herman JD, Steinschneider S (2020) Bootstrap aggregation and cross-validation methods to reduce overfitting in reservoir control policy search. Water Resour Res 56(8):e2020WR027184

    Article  Google Scholar 

  • Christelis V, Mantoglou A (2016) Pumping optimization of coastal aquifers assisted by adaptive metamodelling methods and radial basis functions. Water Resour Manag 30(15):5845–5859. https://doi.org/10.1007/s11269-016-1337-3

    Article  Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197. https://doi.org/10.1109/4235.996017

    Article  Google Scholar 

  • Draper D (1995) Assessment and propagation of model uncertainty. J Roy Stat Soc Ser B (Methodol) 57(1):45–70. https://doi.org/10.1111/j.2517-6161.1995.tb02015.x

    Article  Google Scholar 

  • Du C, Yu J, Zhong H, Wang D (2015) Operating mechanism and set pair analysis model of a sustainable water resources system. Front Environ Sci Eng 9(2):288–297. https://doi.org/10.1007/s11783-014-0642-4

    Article  Google Scholar 

  • Garud SS, Karimi IA, Kraft M (2017) Smart sampling algorithm for surrogate model development. Comput Chem Eng 96(Supplement C):103–114. https://doi.org/10.1016/j.compchemeng.2016.10.006

    Article  Google Scholar 

  • Harbaugh AW (2005) MODFLOW-2005, the U.S. Geological Survey modular ground-water model: The ground-water flow process. Techniques and Methods 6-A16. Reston, VA: US Dept. of the Interior, USGS

  • Hou Z, Dai Z, Lao W, Wang Y, Lu W (2019) Application of mixed-integer nonlinear optimization programming based on ensemble surrogate model for dense nonaqueous phase liquid source identification in groundwater. Environ Eng Sci 36(6):699–709. https://doi.org/10.1089/ees.2018.0366

    Article  Google Scholar 

  • Hou Z, Lu W, Xue H, Lin J (2017) A comparative research of different ensemble surrogate models based on set pair analysis for the DNAPL-contaminated aquifer remediation strategy optimization. J Contam Hydrol 203:28–37. https://doi.org/10.1016/j.jconhyd.2017.06.003

    Article  Google Scholar 

  • Jasechko S, Perrone D, Seybold H, Fan Y, Kirchner JW (2020) Groundwater level observations in 250,000 coastal US wells reveal scope of potential seawater intrusion. Nat Commun 11(1):1–9. https://doi.org/10.1038/s41467-020-17038-2

    Article  Google Scholar 

  • Jiang X, Lu W, Hou Z, Zhao H, Na J (2015) Ensemble of surrogates-based optimization for identifying an optimal surfactant-enhanced aquifer remediation strategy at heterogeneous DNAPL-contaminated sites. Comput Geosci 84(11):37–45. https://doi.org/10.1016/j.cageo.2015.08.003

    Article  Google Scholar 

  • Jiang X, Lu W, Na J, Hou Z, Wang Y, Chi B (2018) A stochastic optimization model based on adaptive feedback correction process and surrogate model uncertainty for DNAPL-contaminated groundwater remediation design. Stoch Env Res Risk Assess 32(11):3195–3206. https://doi.org/10.1007/s00477-018-1559-4

    Article  Google Scholar 

  • Ketabchi H, Ataie-Ashtiani B (2015) Assessment of a parallel evolutionary optimization approach for efficient management of coastal aquifers. Environ Model Softw 74:21–38. https://doi.org/10.1016/j.envsoft.2015.09.002

    Article  Google Scholar 

  • Konikow LF, Hornberger GZ, Halford KJ, Hanson RT, Harbaugh AW (2009) Revised Multi-Node Well (MNW2) package for MODFLOW ground-water flow model, U. S. Geological Survey Techniques and Methods 6–A30, p 67 

  • Kuczera G, Kavetski D, Franks S, Thyer M (2006) Towards a Bayesian total error analysis of conceptual rainfall-runoff models: Characterising model error using storm-dependent parameters. J Hydrol 331(1–2):161–177

    Article  Google Scholar 

  • Kumar K, Garg H (2018) Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making. Appl Intell 48(8):2112–2119. https://doi.org/10.1007/s10489-017-1067-0

    Article  Google Scholar 

  • Lal A, Datta B (2018) Development and implementation of support vector machine regression surrogate models for predicting groundwater pumping-induced saltwater intrusion into coastal aquifers. Water Resour Manag 32(7):2405–2419. https://doi.org/10.1007/s11269-018-1936-2

    Article  Google Scholar 

  • Langevin CD, Thorne Jr DT, Dausman AM, Sukop MC, Guo W (2008) SEAWAT version 4: a computer program for simulation of multi-species solute and heat transport (No. 6-A22). Geological Survey (US). https://doi.org/10.3133/tm6A22

  • Lovelace JK (2007) Chloride Concentrations in Ground Water in East and West Baton Rouge Parishes, Louisiana, 2004-05. US Department of the Interior, US Geological Survey. 2007–5069. https://doi.org/10.3133/sir20075069

  • Maier HR, Dandy GC (2000) Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications. Environ Model Softw 15(1):101–124. https://doi.org/10.1016/S1364-8152(99)00007-9

    Article  Google Scholar 

  • Maliva RG, Manahan WS, Missimer TM (2020) Aquifer storage and recovery using saline aquifers: Hydrogeological controls and opportunities. Groundwater 58(1):9–18. https://doi.org/10.1111/gwat.12962

    Article  Google Scholar 

  • Ouyang Q, Lu W, Miao T, Deng W, Jiang C, Luo J (2017) Application of ensemble surrogates and adaptive sequential sampling to optimal groundwater remediation design at DNAPLs-contaminated sites. J Contam Hydrol 207:31–38. https://doi.org/10.1016/j.jconhyd.2017.10.007

    Article  Google Scholar 

  • Pham HV, Tsai FT-C (2017) Modeling complex aquifer systems: a case study in Baton Rouge, Louisiana (USA). Hydrogeol J 25(3):601–615. https://doi.org/10.1007/s10040-016-1532-6

    Article  Google Scholar 

  • Platt JC (1999) Fast training of support vector machines using sequential minimal optimization. In: Schölkopf B, Burges CJC, Smolar AJ (eds) Advances in Kernel Methods-Support Vector Learning. MIT Press, Cambridge

    Google Scholar 

  • Post VE, Werner AD (2017) Coastal aquifers: Scientific advances in the face of global environmental challenges. J Hydrol 551(8):1–3. https://doi.org/10.1016/j.jhydrol.2017.04.046

    Article  Google Scholar 

  • Probst P, Wright MN, Boulesteix AL (2019) Hyperparameters and tuning strategies for random forest. Wiley Interdiscip Rev Data Mining Knowledge Discovery 9(3):e1301. https://doi.org/10.1002/widm.1301

  • Rajabi MM, Ataie-Ashtiani B, Janssen H (2015) Efficiency enhancement of optimized Latin hypercube sampling strategies: Application to Monte Carlo uncertainty analysis and meta-modeling. Adv Water Resour 76:127–139. https://doi.org/10.1016/j.advwatres.2014.12.008

    Article  Google Scholar 

  • Roy DK, Datta B (2017) Multivariate adaptive regression spline ensembles for management of multilayered coastal aquifers. J Hydrol Eng 22(9):04017031. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001550

    Article  Google Scholar 

  • Rumelhart DE, McClelland JL, The PDP Research Group (1986) Parallel distributed processing: Explorations in the microstructure of cognition. MIT Press, Cambridge, p 516

  • Schölkopf B, Smola AJ, Bach F (2002) Learning with Kernels: Support vector machines, regularization, optimization, and beyond. MIT Press, Cambridge, p 626

    Google Scholar 

  • Schöniger A, Wöhling T, Samaniego L, Nowak W (2014) Model selection on solid ground: Rigorous comparison of nine ways to evaluate B ayesian model evidence. Water Resour Res 50(12):9484–9513

    Article  Google Scholar 

  • Shi L, Lu C, Ye Y, Xie Y, Wu J (2020) Evaluation of the performance of multiple-well hydraulic barriers on enhancing groundwater extraction in a coastal aquifer. Adv Water Resour 144(4):103704. https://doi.org/10.1016/j.advwatres.2020.103704

    Article  Google Scholar 

  • Siade AJ, Cui T, Karelse RN, Hampton C (2020) Reduced-dimensional Gaussian process machine learning for groundwater allocation planning using swarm theory. Water Resour Res 56(3):e2019WR026061. https://doi.org/10.1029/2019WR026061

    Article  Google Scholar 

  • Song J, Yang Y, Wu J, Wu J, Sun X, Lin J (2018) Adaptive surrogate model based multiobjective optimization for coastal aquifer management. J Hydrol 561:98–111. https://doi.org/10.1016/j.jhydrol.2018.03.063

    Article  Google Scholar 

  • Sreekanth J, Datta B (2011) Coupled simulation‐optimization model for coastal aquifer management using genetic programming‐based ensemble surrogate models and multiple‐realization optimization. Water Resour Res 47(4):W04516. https://doi.org/10.1029/2010WR009683

  • Sreekanth J, Moore C (2018) Novel patch modelling method for efficient simulation and prediction uncertainty analysis of multi-scale groundwater flow and transport processes. J Hydrol 559(4):122–135. https://doi.org/10.1016/j.jhydrol.2018.02.028

    Article  Google Scholar 

  • Tomaszewski DJ (1996) Distribution and movement of saltwater in aquifers in the Baton Rouge area, Louisiana, 1990-92. Baton Rouge, LA: Louisiana Department of Transportation and Development, p 44

  • Vapnik V (2013) The nature of statistical learning theory. Springer science & business media. 38(4):409–409

  • Viana FA, Haftka RT, Steffen V (2009) Multiple surrogates: how cross-validation errors can help us to obtain the best predictor. Struct Multidiscip Optim 39(4):439–457. https://doi.org/10.1007/s00158-008-0338-0

    Article  Google Scholar 

  • Williams HP (2013) Model building in mathematical programming. John Wiley & Sons, pp 35–42

  • Xiao C, Liang X, Zhang F, Feng B, Xie S (2009) Advances in water resources and hydraulic engineering. Springer, Berlin Heidelberg, New York

    Google Scholar 

  • Yan S, Minsker B (2006) Optimal groundwater remediation design using an adaptive neural network genetic algorithm. Water Resour Res 42(5):W05407. https://doi.org/10.1029/2005WR004303

  • Yin J, Tsai FT-C (2020) Bayesian set pair analysis and machine learning based ensemble surrogates for optimal multi-aquifer system remediation design. J Hydrol 580(1):124280. https://doi.org/10.1016/j.jhydrol.2019.124280

    Article  Google Scholar 

  • Yin J, Pham HV, Tsai FT-C (2020) Multiobjective spatial pumping optimization for groundwater management in a multiaquifer system. J Water Resour Plan Manag 146(4):04020013. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001180

    Article  Google Scholar 

  • Yu L, Wang S, Lai KK (2007) Basic learning principles of artificial neural networks. Foreign-exchange-rate forecasting with artificial neural networks. International Series in Operations Research & Management Science, vol 107. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-71720-3_2

  • Zhao KQ, Xuan AL (1996) Set pair theory-a new theory method of non-define and its applications. Syst Eng 14(1):18–23

    Google Scholar 

  • Zheng C, Wang PP (1999) MT3DMS: a modular three-dimensional multi-species transport model for simulation of advection, dispersion and chemical reactions of contaminants in groundwater systems; documentation and user’s guide. U.S. Army Engineer Research and Development Center Contract. Report SERDP-99-1, Vicksburg, p 202

  • Zhou X, Ma Y, Tu Y, Feng Y (2013) Ensemble of surrogates for dual response surface modeling in robust parameter design. Qual Reliab Eng Int 29(2):173–197. https://doi.org/10.1002/qre.1298

    Article  Google Scholar 

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Acknowledgements

This research was supported by National Key Research and Development Program (No. 2021YFC3200500), the National Natural Science Foundation of China (No. 52109080), and Fundamental Research Funds for the Central Universities (B220201013). The authors acknowledge the Capital Area Ground Water Conservation Commission (CAGWCC) for providing water pumping data and the U.S. Geological Survey (USGS) for providing water quality data. High Performance Computing (HPC) Platform in Hohai University is acknowledged for providing technique support.

Funding

This research was supported by National Key Research and Development Program (No. 2021YFC3200500), the National Natural Science Foundation of China (No. 52109080), and Fundamental Research Funds for the Central Universities (B220201013). High Performance Computing (HPC) Platform in Hohai University is acknowledged for providing technique support.

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Authors and Affiliations

  1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China

    Jina Yin & Chunhui Lu

  2. Yangtze Institute for Conservation and Development, Hohai University, Nanjing, China

    Jina Yin & Chunhui Lu

  3. Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA, USA

    Frank T.-C. Tsai

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  1. Jina Yin
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  2. Frank T.-C. Tsai
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Contributions

Jina Yin: Conceptualization, Data curation, Methodology, Funding acquisition, Validation, Formal analysis, Writing—original draft. Frank T.-C. Tsai: Conceptualization, Methodology, Supervision, Resources, Validation, Writing-review & editing. Chunhui Lu: Funding acquisition, Data curation, Methodology, Resources, Supervision, Validation, Writing-review & editing.

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Correspondence to Chunhui Lu.

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Yin, J., Tsai, F.TC. & Lu, C. Bi-objective Extraction-injection Optimization Modeling for Saltwater Intrusion Control Considering Surrogate Model Uncertainty. Water Resour Manage 36, 6017–6042 (2022). https://doi.org/10.1007/s11269-022-03340-9

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