Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Modeling and uncertainty analysis of seawater intrusion based on surrogate models


When using a simulation model to study seawater intrusion (SI), uncertainty in the parameters directly affects the results. The impact of the rise in sea levels due to global warming on SI cannot be ignored. In this paper, the Monte Carlo method is used to analyze the uncertainty in modeling SI. To reduce the computational cost of the repeated invocation of the simulation model as well as time, a surrogate model is established using a radial basis function (RBF)–based neural network method. To enhance the accuracy of the substitution model, input samples are sampled using the Latin hypercube sampling (LHS) method. The results of uncertainty analysis had a high reference value and show the following: (1) The surrogate model created using the RBF method can significantly reduce computational cost and save at least 95% of the time needed for the repeated invocation of the simulation model while maintaining high accuracy. (2) Uncertainty in the parameters and the magnitude of the rise in sea levels have a significant impact on SI. The results of prediction were thus highly uncertain. In practice, it is necessary to quantify uncertainty to provide more intuitive predictions.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11


  1. Baoxiang Z, Fanhai M (2011) Delineation methods and application of groundwater source protection zone[C]//2011 International Symposium on Water Resource and Environmental Protection. IEEE, 1: 66-69.

  2. Bear J, Cheng AHD, Sorek S, Ouazar D, Herrera I (Eds.) (1999) Seawater intrusion in coastal aquifers: concepts, methods and practices (Vol. 14). Springer Science & Business Media.

  3. Chen S, Cowan CF, Grant PM (1991) Orthogonal least squares learning algorithm for radial basis function networks. IEEE Trans Neural Netw 2(2):302–309

  4. Elshall AS, Tsai FTC (2014) Constructive epistemic modeling of groundwater flow with geological structure and boundary condition uncertainty under the Bayesian paradigm. J Hydrol 517:105–119

  5. Ghassemi F, Jakeman AJ, Jacobson G, Howard KWF (1996) Simulation of seawater intrusion with 2D and 3D models: Nauru Island case study. Hydrogeol J 4(3):4–22

  6. Gorissen D, Couckuyt I, Demeester P, Dhaene T, Crombecq K (2010) A surrogate modeling and adaptive sampling toolbox for computer based design. J Mach Learn Res 11(Jul):2051–2055

  7. Guanxing H (2006) Tests of Hydro-geological parameters with isotope technique in Longkou Reservoir Area [J][J]. Journal of Geotechnical Investigation & Surveying, 4

  8. Guo J, Lu W, Yang Q, Miao TS (2019) The application of 0–1 mixed integer nonlinear programming optimization model based on a surrogate model to identify the groundwater pollution source. J Contam Hydrol 220:18–25

  9. Helton JC, Davis FJ (2003) Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab Eng Syst Saf 81(1):23–69

  10. Hill MC, Tiedeman CR (2006) Effective groundwater model calibration: with analysis of data, sensitivities, predictions, and uncertainty[M]. John Wiley & Sons

  11. 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).

  12. Laporte E, Le Tallec P (2012) Numerical methods in sensitivity analysis and shape optimization. Springer Science & Business Media.

  13. Lin J, Snodsmith JB, Zheng C, Wu J (2009) A modeling study of seawater intrusion in Alabama Gulf Coast, USA. Environ Geol 57(1):119–130

  14. Looss B, Lemaître P (2015) A review on global sensitivity analysis methods. In: Uncertainty management in simulation-optimization of complex systems. Springer, Boston, pp 101–122

  15. Luo J, Lu W, Xin X, Chu H (2013) Surrogate model application to the identification of an optimal surfactant-enhanced aquifer remediation strategy for DNAPL-contaminated sites. J Earth Sci 24(6):1023–1032

  16. McKay MD, Beckman RJ, Conover WJ (1979) Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2):239–245

  17. Morgan LK, Stoeckl L, Werner AD, Post VE (2013) An assessment of seawater intrusion overshoot using physical and numerical modeling. Water Resour Res 49(10):6522–6526

  18. Narayan KA, Schleeberger C, Bristow KL (2007) Modelling seawater intrusion in the Burdekin Delta irrigation area, North Queensland, Australia. Agric Water Manag 89(3):217–228

  19. Nicholls RJ, Cazenave A (2010) Sea-level rise and its impact on coastal zones. Science 328(5985):1517–1520

  20. Oude Essink GHP, Van Baaren ES, De Louw PG (2010) Effects of climate change on coastal groundwater systems: A modeling study in the Netherlands. Water Resour Res, 46(10).

  21. Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257

  22. Queipo NV, Haftka RT, Shyy W, Goel T, Vaidyanathan R, Tucker PK (2005) Surrogate-based analysis and optimization. Prog Aerosp Sci 41(1):1–28

  23. Rubinstein RY, Kroese DP (2016) Simulation and the Monte Carlo method (Vol. 10). John Wiley & Sons.

  24. Saltelli A, Chan K, Scott EM (eds) (2000) Sensitivity analysis (Vol. 1). Wiley, New York

  25. Saltelli A, et al. (2004) Sensitivity analysis in practice: a guide to assessing scientific models. John Wiley & Sons

  26. Tian-chyi JY, Mao D, Zha Y, Wen JC, Wan L, Hsu KC, Lee CH (2015) Uniqueness, scale, and resolution issues in groundwater model parameter identification[J]. Water Science and Engineering 8(3):175–194

  27. Wang X, Sun J, Jin X (2007) Prediction of water quality index in Qiantang River based on BP neural network model[J]. Journal-Zhejiang University Engineering Science 41(2):361

  28. Werner AD, Bakker M, Post VE, Vandenbohede A, Lu C, Ataie-Ashtiani B et al (2013) Seawater intrusion processes, investigation and management: recent advances and future challenges. Adv Water Resour 51:3–26

  29. Zhang Q, Volker RE, Lockington DA (2004) Numerical investigation of seawater intrusion at Gooburrum, Bundaberg, Queensland, Australia. Hydrogeol J 12(6):674–687

  30. Zio E (2013) The Monte Carlo simulation method for system reliability and risk analysis (Vol. 39). Springer, London

Download references


The authors thank the editor and anonymous reviewers for their insightful comments and suggestions.


This work was financially supported by the Development Program of China (No. 2016YFC0402800).

Author information

Correspondence to Wenxi Lu.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Responsible editor: Marcus Schulz

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Miao, T., Lu, W., Guo, J. et al. Modeling and uncertainty analysis of seawater intrusion based on surrogate models. Environ Sci Pollut Res 26, 26015–26025 (2019).

Download citation


  • Seawater intrusion
  • Sea level rise
  • Uncertainty analysis
  • RBF neural network
  • Surrogate model