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Sadhana

, Volume 29, Issue 5, pp 477–497 | Cite as

A stochastic dynamic programming model for stream water quality management

  • P. P. Mujumdar
  • Pavan Saxena
Article

Abstract

This paper deals with development of a seasonal fraction-removal policy model for waste load allocation in streams addressing uncertainties due to randomness and fuzziness. A stochastic dynamic programming (SDP) model is developed to arrive at the steady-state seasonal fraction-removal policy. A fuzzy decision model (FDM) developed by us in an earlier study is used to compute the system performance measure required in the SDP model. The state of the system in a season is defined by streamflows at the headwaters during the season and the initial DO deficit at some pre-specified checkpoints. The random variation of streamflows is included in the SDP model through seasonal transitional probabilities. The decision vector consists of seasonal fraction-removal levels for the effluent dischargers. Uncertainty due to imprecision (fuzziness) associated with water quality goals is addressed using the concept of fuzzy decision. Responses of pollution control agencies to the resulting end-of-season DO deficit vector and that of dischargers to the fraction-removal levels are treated as fuzzy, and modelled with appropriate membership functions. Application of the model is illustrated with a case study of the Tungabhadra river in India.

Keywords

Fuzzy decision stochastic optimization water quality streamflow 

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References

  1. Bellman R E, Zadeh L A 1970 Decision-making in a fuzzy environment.Manage. Sci. B17: 141–164MathSciNetGoogle Scholar
  2. Burn D H 1989 Water-quality management through combined simulation-optimization approach.J. Environ. Eng., ASCE 115: 1011–1024CrossRefGoogle Scholar
  3. Burn D H, Lence B J 1992 Comparison of optimization formulations for waste-load allocations.J. Environ. Eng., ASCE 118: 597–612Google Scholar
  4. Burn D H, McBean E A 1985 Optimization modeling of water quality in an uncertain environment.Water Resources Res. 21: 934–940Google Scholar
  5. Burn D H, McBean E A1986 Linear stochastic optimization applied to biochemical oxygen demand — Dissolved oxygen modelling.Can. J. Environ. Eng. 13: 249–254Google Scholar
  6. Carmichael J J, Strzepek K M 2000 A multiple-organic-pollutant simulation/optimization model of industrial and municipal wastewater loading to a riverine environment.Water Resources Res. 36: 1325–1332CrossRefGoogle Scholar
  7. Dai T, Labadie J W 2001 River basin network model for integrated water quantity/quality management.J. Water Resources Planning Manage. 127: 295–305CrossRefGoogle Scholar
  8. Ellis J H 1987 Stochastic water quality optimization using embedded chance constraints.Water Resources Res. 23: 2227–2238Google Scholar
  9. Fugiwara O, Gnanendran S K, Ohgaki S 1986 River quality management under stochastic stream flow.J. Environ. Eng., ASCE 112: 185–198Google Scholar
  10. Fugiwara O, Gnanendran S K, Ohgaki S 1987 Chance constrained model for river water quality management.J. Environ. Eng., ASCE 113: 1018–1031Google Scholar
  11. Kindler J 1992 Rationalizing water requirements with aid of fuzzy allocation model.J. Water Resources Planning Manage., ASCE 118: 308–323Google Scholar
  12. Labadie J W 1997 Reservoir system optimization models.Water Resources Up-date, Universities Council on Water Resources 108: 83–110Google Scholar
  13. Lence B J, Eheart J W 1990 Risk equivalent seasonal discharge programs for multidischargers streams.J. Water Resources Planning Manage., ASCE 116: 170–186Google Scholar
  14. Lence B J, Takyi A K 1992 Data requirements for seasonal discharge programs: An application of a regionalized sensitivity analysis.Water Resources Res. 28: 1781–1789CrossRefGoogle Scholar
  15. Lohani B N, Thanh N C 1978 Stochastic programming model for water quality management in a river.J. Water Pollution Contr. Fed. 50: 2175–2182Google Scholar
  16. Lohani B N, Thanh N C 1979 Probabilistic water quality control policies.J. Environ. Eng., ASCE 105: 713–725Google Scholar
  17. Loucks D P, Lynn W R 1966 Probabilistic models for predicting stream quality.Water Resources Res. 2: 593–605Google Scholar
  18. Loucks D P, Stedinger J R, Haith D A 1981Water resources systems planning and analysis (Englewood Cliffs, NJ: Prentice Hall) 427–545Google Scholar
  19. Mujumdar P P 2001 Uncertainty concepts in stream water quality management models.Research perspectives in hydraulics and water resources engineering (eds.) Rama Prasad, S Vedula (Singapore: World Scientific)Google Scholar
  20. Mujumdar P P, Sasikumar K 2002 A fuzzy risk approach for seasonal water quality management of a river system.Water Resources Res. 38: 5XXX1–5XXX9CrossRefGoogle Scholar
  21. Rossman L A 1989 Risk equivalent seasonal waste load allocation.Water Resources Res. 25: 2083–2090Google Scholar
  22. Sasikumar K, Mujumdar P P 1998 Fuzzy optimization model for water quality management of a river system.J. Water Resources Planning Manage., ASCE 124: 79–88CrossRefGoogle Scholar
  23. Sasikumar K, Mujumdar P P 2000 Application of fuzzy probability in water quality management of a river system.Int. J. Syst. Sci. 31: 575–591MATHCrossRefGoogle Scholar
  24. Streeter H W, Phelps E B 1925 A study of the pollution and natural purification of the Ohio River, III. Factors concerning the phenomena of oxidation and reaeration. U.S. Public Health Service, Pub. Health Bulletin No. 146, February, 1925. Reprinted by U.S., DHES, PHA, 1958.Google Scholar
  25. Takyi A K, Lence B J 1994 Incorporating input information uncertainty in a water quality management model using combined simulation and optimization.Int. UNESCO Symp. on Water Resources Planning in a Changing World Karlsruhe, GermanyGoogle Scholar
  26. Takyi A K, Lence B J 1996 Chebyshev model for water-quality management.J. Water Resources Planning Manage., ASCE 122: 40–48CrossRefGoogle Scholar
  27. Takyi A K, Lence B J 1999 Surface water quality management using a multiple-realization chance constraint method.Water Resources Res. 35: 1657–1670CrossRefGoogle Scholar
  28. Wotton C L, Lence B J 1995 Risk-equivalent seasonal discharge programs for ice-covered rivers.J. Water Resources Planning Manage., ASCE 121: 275–282CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2004

Authors and Affiliations

  • P. P. Mujumdar
    • 1
  • Pavan Saxena
    • 1
  1. 1.Department of Civil EngineeringIndian Institute of ScienceBangaloreIndia

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