Water Resources Management

, Volume 33, Issue 2, pp 775–795 | Cite as

An Ensemble Meta-Modelling Approach Using the Dempster-Shafer Theory of Evidence for Developing Saltwater Intrusion Management Strategies in Coastal Aquifers

  • Dilip Kumar RoyEmail author
  • Bithin Datta


The optimum abstraction policy of coastal groundwater resources is prescribed by solving a meta-model based saltwater intrusion management model. Groundwater parameter uncertainties are explicitly incorporated into the developed meta-models in order to address the uncertainties present in coastal aquifer processes. Nevertheless, the accuracy and consequent reliability of such a management model depends upon the right choice of meta-models or a combination of meta-models. The optimal combination of meta-models, also referred to as an ensemble meta-model, can be selected by applying the Dempster-Shafer (D-S) theory of evidence. D-S evidence theory provides a platform upon which to base the selection of the best meta-model or combination of meta-models to formulate the preferred ensemble. This study demonstrates the application of D-S theory to provide an ensemble of meta-models for developing saltwater intrusion management models in coastal aquifers. The prediction accuracy of the developed ensemble meta-model is compared with that of the best standalone meta-model in the ensemble. The results confirm that the ensemble meta-model performs equally well when compared with the best meta-model in the ensemble. The developed meta-models and their ensemble are then used to develop computationally feasible multiple objective saltwater intrusion management models by utilizing an integrated simulation-optimization approach. The solution results of the management models demonstrate the superiority of the ensemble meta-model approach over standalone meta-models in obtaining Pareto optimal groundwater abstraction patterns. The evaluation of the proposed methodology is demonstrated using an illustrative multilayer coastal aquifer system subjected to groundwater parameter uncertainties.


Coastal aquifer Management model Meta-models Ensemble Dempster-Shafer theory 



The authors would like to appreciate the open source MATLAB Toolbox “Surrogate Model Optimization Toolbox” [] written by Juliane Müller.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Discipline of Civil Engineering, College of Science and EngineeringJames Cook UniversityTownsvilleAustralia
  2. 2.Cooperative Research Centre for Contamination Assessment and Remediation of the EnvironmentUniversity of New CastleCallaghanAustralia

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