Water Resources Management

, Volume 20, Issue 2, pp 277–290 | Cite as

Response Matrix Minimization Used in Groundwater Management with Mathematical Programming: A Case Study in a Transboundary Aquifer in Northern Greece

Article

Abstract

Groundwater has always been considered to be a readily available source of water for domestic, agricultural and industrial use. The last decades, the lack of policymaking for the utilization of groundwater, has led to overexploitation in many areas. The cooperation of a wide range of scientists such as mathematicians, engineers, computer scientists, environmentalists and economists – operation researchers, have led to the design and construction of commercial computer programs concerned on water management and specifically on the optimal distribution of limited water resources using groundwater management models. These combined models, via simulation and optimization algorithms, result in one optimal solution through operations research and mathematical programming methods. The groundwater management models are based on the method of space superposition or the combination of space and time superposition for steady and unsteady state problems, respectively. In the present study, an algorithm is presented, which minimizes the dimension of the response matrix, concerning on two assumptions: the first is the added fixed cost which represents the water supply pumping well and the second is the removal of time superposition. The study area is a transboundary phreatic aquifer in Northern Greece, in the area of Eidomeni, a small Hellenic village just on the borderline with FYROM. The aquifer has a total area of 10,84 km2, 26 operating – pumping wells, which the 9 of them consist control points of the hydraulic head. The number of the management periods is 12 months.

Key Words

Greece groundwater management mathematical programming optimization response matrix simulation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahlfeld, D. P., 2004, ‘Nonlinear response of streamflow to groundwater pumping for a hydrologic streamflow model,’ Adv. Water Resour, 27, 346–360.CrossRefGoogle Scholar
  2. Ahlfeld, D. P. and Sprong, M. P., 1998, ‘Presence of nonconvexity in groundwater concentration response functions,’ J. Water Res. PL – ASCE, 124(1), 8–14.Google Scholar
  3. Biswas, A. K., 1997, Water Resources. Environmental Planning, Management and Development, McGraw-Hill, New York, p. 737.Google Scholar
  4. Hsiao, C. T. and Chang, L. C., 2002, ‘Dynamic optimal groundwater management with inclusion of fixed costs,’ J. Water Res. PL – ASCE, 128(1), 57–65.Google Scholar
  5. Gorelick, S. M., 1983, ‘A review of distributed parameter groundwater management modelling methods,’ Water Resour. Res. 19(1), 305–319.Google Scholar
  6. Gorelick, S. M., 1990, ‘Large-scale non-linear deterministic and stochastic optimization: Formulations involving simulation of subsurface contamination,’ Math Program, 48, 19–39.CrossRefGoogle Scholar
  7. Greenwald, R. M., 1994, ‘MODflow MANagement: An optimization module for modflow,’ IGWMC–FOS 76 PC, Version 3.02.Google Scholar
  8. Maddock, T., 1974, ‘Non-linear technological functions for aquifers whose transmissivities vary with drawdown,’ Water Resour. Res. 10(3), 877–881.Google Scholar
  9. Mc Donald, M. G., and Harbaugh, A. W., 1988, ‘A modular three-dimensional finite-difference ground-water flow model. U.S. Geological Survey Techniques of Water Resources Investigations,’ Book 6, Chap. A1, p. 586.Google Scholar
  10. Psilovikos, A., 1999a, ‘Optimization models in groundwater management, based on linear and mixed integer programming. An application to a Greek Hydrogeological basin,’ Phys. Chem. Earth Pt B, 24(1–2), 139–144.Google Scholar
  11. Psilovikos, A., 1999b, ‘Optimum management in groundwater resources. Comparison and evaluation with Linear and Non-Linear Programming models,’ PhD Thesis, Department of Rural and Surveying engineering, Aristotle University of Thessaloniki, Greece.Google Scholar
  12. Psilovikos, A. and Tzimopoulos, C., 2003, ‘Time superposition removal from unit response matrix used in groundwater management,’ Hydrotechnica. 13, 87–104.Google Scholar
  13. Psilovikos, A., and Tzimopoulos, C., 2004, ‘Comparison of quadratic and non-linear programming (QP and NLP) optimization models in groundwater management,’ J. Hydroinform 6(2), 175–186.Google Scholar
  14. Spiliotopoulos, A. A., Karatzas, G. P., and Pinder, G. F., 2004, ‘A multiperiod approach to the solution of groundwater management problems using an outer approximation method,’ Eur. J. Oper. Res., 157(1), 514–525.Google Scholar
  15. Theodossiou, N., 2004, ‘Application of non-linear simulation and optimisation models in groundwater aquifer management,’ Wat. Resour. Manag. 18, 125–141.Google Scholar
  16. Tsakiris, G., 1995, Water Resources: I. Technical Hydrology, Symmetria, Athens, p. 675 (In Greek).Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Agriculture Animal Production and Aquatic Environment, School of Agricultural SciencesUniversity of ThessalyN. Ionia Magnisias

Personalised recommendations