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Groundwater Spatial Dynamics and Endogenous Well Location

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Abstract

Groundwater economic models have refined optimal extraction rules while lagging behind in the study of optimal spatial policies. This paper develops a theoretical model to estimate welfare gains from optimal groundwater management when the choice variable set is expanded to include well location decisions as well as optimal groundwater extraction paths. Our theoretical results show that if there is spatial heterogeneity in groundwater, the welfare gains from optimal location of wells are substantial even if extraction rates are unregulated. Furthermore, second-best economically defined spacing regulations may possibly have better efficiency results (and lower implementation costs) than first-best uniform taxes or quotas. An application of the model to a real-world aquifer shows the importance of including well location decisions in spatially differentiated groundwater models and the need for (1) robust estimates of the gains from optimal management and; (2) spatially explicit regulations.

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Notes

  1. The location of a well affects the feasible capacities and locations for the rest of wells. Even if Ω is a convex set, once any well is located, the remaining feasible set is non-convex. The non-convex nature of the problem prevents us from solving it by conventional optimization methods. In order to surpass the non-convexity of the problem and attain an analytical solution, we set the feasible region Ω to be a convex set and allow wells to be, in principle, arbitrarily close to one another. Although, in a more realistic setting well location decisions would be limited by land ownership, we exclude this type of spatial restrictions from the present study to keep the model tractable.

  2. We also assumed that net benefits decrease at least linearly with head loss and falling extraction rates,.

  3. The calculation can be simplified when: (i) the objective functional and state dynamics are linear in the state; (ii) they are no cross-terms involving control and state variables; and (iii) a small and fixed number of users is considered.

  4. The model was calibrated with regional hydrogeological studies and a trial-and-error method that compared observed and simulated water drawdown at several spatial points. A sensitivity analysis was conducted on the value of regional hydraulic conductivity. A 100 % increase in the value assumed did not result in significant changes on water table levels throughout the region (Charlesworth et al. 2008).

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Acknowledgments

I am grateful to the Environmental Protection and Sustainable Development of the Guarani Aquifer System Project for the hydrological and economic data provided on the Concordia-Salto pilot project and to attendees at the Spanish-Portuguese Association of Natural Resources and Environmental Economics and the Sustainable Resource Use and Economic Dynamics conferences for their feedback.

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  1. International Water Management Institute, Martin Odei Block, CSIR Campus, PMB CT 112, Accra, Ghana

    Pamela Giselle Katic

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Katic, P.G. Groundwater Spatial Dynamics and Endogenous Well Location. Water Resour Manage 29, 181–196 (2015). https://doi.org/10.1007/s11269-014-0834-5

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