• Abramowitz, M., , and I. A. Stegun, 1970: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications, 228–233.

    • Search Google Scholar
    • Export Citation
  • Basson, M. A., , and J. A. Van Rooyen, 2001: Practical application of probabilistic approaches to the management of water resource systems. J. Hydrol., 241 , 5361.

    • Search Google Scholar
    • Export Citation
  • Carpenter, T. M., , and K. P. Georgakakos, 2001: Assessment of Folsom Lake response to historical and future climate scenarios: 1. Forecasting. J. Hydrol., 249 , 148175.

    • Search Google Scholar
    • Export Citation
  • Chiew, F. H. S., , S. L. Zhou, , and T. A. McMahon, 2003: Use of seasonal streamflow forecasts in water resources management. J. Hydrol., 270 , 135144.

    • Search Google Scholar
    • Export Citation
  • Dynesius, M., , and C. Nilsson, 1994: Fragmentation and flow regulation of river systems in the northern third of the world. Science, 266 , 753762.

    • Search Google Scholar
    • Export Citation
  • Garbrecht, J., , H. Meinke, , M. V. K. Sivakumar, , R. P. Motha, , and M. J. Salinger, 2005: Seasonal climate forecasts and adoption by agriculture. Eos, Trans. Amer. Geophys. Union, 86 , 227.

    • Search Google Scholar
    • Export Citation
  • Georgakakos, A. P., 1993: Operational trade-offs in reservoir control. Water Resour. Res., 29 , 38013820.

  • Georgakakos, A. P., , H. Yao, , M. G. Mullusky, , and K. P. Georgakakos, 1998: Impacts of climate variability on the operational forecast and management of the upper Des Moines River basin. Water Resour. Res., 34 , 799821.

    • Search Google Scholar
    • Export Citation
  • Georgakakos, K. P., , A. P. Georgakakos, , H. Yao, , and N. E. Graham, 1998: Assessment of benefits of climate forecasts for reservoir management in the GCIP region. GEWEX News, Vol. 8, International GEWEX Project Office, Silver Spring, MD, 5–7.

    • Search Google Scholar
    • Export Citation
  • Georgakakos, K. P., , N. E. Graham, , T. M. Carpenter, , A. P. Georgakakos, , and H. Yao, 2005: Integrating climate-hydrology forecasts and multi-objective reservoir management for Northern California. Eos, Trans. Amer. Geophys. Union, 86 , 122127.

    • Search Google Scholar
    • Export Citation
  • Goddard, L., , S. J. Mason, , S. E. Zebiak, , C. F. Ropelewski, , R. Basher, , and M. A. Cane, 2001: Current approaches to seasonal-to-interannual climate predictions. Int. J. Climatol., 21 , 11111152.

    • Search Google Scholar
    • Export Citation
  • Graf, W. L., 1999: Dam nation: A geographic census of American dams and their large-scale hydrologic impacts. Water Resour. Res., 35 , 13051312.

    • Search Google Scholar
    • Export Citation
  • Graham, N. E., , K. P. Georgakakos, , C. Vargas, , and M. Echevers, 2006: Simulating the value of El Niño forecasts for the Panama Canal. Adv. Water Resour., 29 , 16651677.

    • Search Google Scholar
    • Export Citation
  • Greis, N. P., 1982: Seasonal climate forecasts and water management for the steam-electric generation. J. Appl. Meteor., 21 , 17981814.

    • Search Google Scholar
    • Export Citation
  • Karamouz, M., , and M. H. Houck, 1987: Comparison of stochastic and deterministic dynamic programming for reservoir operating rule generation. Water Resour. Bull., 23 , 19.

    • Search Google Scholar
    • Export Citation
  • Keeney, R. L., , and H. Raiffa, 1993: Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Cambridge University Press, 569 pp.

    • Search Google Scholar
    • Export Citation
  • Lemos, M. C., , T. J. Finan, , R. W. Fox, , D. R. Nelson, , and J. Tucker, 2002: The use of seasonal climate forecasting in policymaking: Lessons from Northeast Brazil. Climatic Change, 55 , 479507.

    • Search Google Scholar
    • Export Citation
  • Livezey, R. E., 1990: Variability of skill of long range forecasts and implications for their use and value. Bull. Amer. Meteor. Soc., 71 , 300309.

    • Search Google Scholar
    • Export Citation
  • Loucks, D. P., , J. R. Stedinger, , and D. A. Haith, 1981: Water Resource Systems Planning and Analysis. Prentice Hall, 559 pp.

  • Nardini, A., , and D. Montoya, 1995: Remarks on a min-max optimization technique for the management of a single multiannual reservoir aimed at hydroelectric generation and water supply. Water Resour. Res., 31 , 11291135.

    • Search Google Scholar
    • Export Citation
  • National Research Council, 2006: Completing the Forecast: Characterizing and Communicating Uncertainty for Better Decisions Using Weather and Climate Forecasts. National Academies Press, 178 pp.

    • Search Google Scholar
    • Export Citation
  • Oliveira, R., , and D. P. Loucks, 1997: Operating rules for multireservoir systems. Water Resour. Res., 33 , 839852.

  • Peng, C-S., , and N. Buras, 2000: Dynamic operation of a surface water resources system. Water Resour. Res., 36 , 27012710.

  • Pulwarty, R. S., , and K. T. Redmond, 1997: Climate and salmon restoration in the Columbia River basin: The role and usability of seasonal forecasts. Bull. Amer. Meteor. Soc., 78 , 381397.

    • Search Google Scholar
    • Export Citation
  • Rabitz, H., 1989: Systems analysis at the molecular scale. Science, 246 , 221226.

  • Simmons, D. M., 1975: Nonlinear Programming for Operations Research. Prentice Hall, 448 pp.

  • Weiss, E. B., 1982: The value of seasonal climate forecasts in mapping energy resources. J. Appl. Meteor., 21 , 510517.

  • World Commission on Dams, 2000: Dams and Development, A New Framework for Decision-Making. Earthscan, 404 pp.

  • Yao, H., , and A. Georgakakos, 2001: Assessment of Folsom Lake response to historical and future climate scenarios: 2. Reservoir management. J. Hydrol., 249 , 176196.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 33 33 13
PDF Downloads 18 18 2

Potential Benefits of Seasonal Inflow Prediction Uncertainty for Reservoir Release Decisions

View More View Less
  • 1 Hydrologic Research Center, San Diego, California
© Get Permissions
Restricted access

Abstract

This paper examines the conditions for which beneficial use of forecast uncertainty may be made for improved reservoir release decisions. It highlights the parametric dependencies of the effects of uncertainty in seasonal inflow volumes on the optimal release and objective function of a single reservoir operated to meet a single volume target at the end of the season under volume and release constraints. The duration of the “season” may be one or several months long. The analysis invokes the application of Kuhn–Tucker theory, and it shows that the presence of uncertainty introduces complex dependence of the optimal release and objective function on the reservoir parameters and uncertain inflow forcing. The seasonal inflow volume uncertainty is represented by a bounded symmetric beta distribution with a given mean, which is considered to be unbiased, and a half-range QR. The authors find that the use of predicted inflow uncertainty is particularly beneficial during operation with a volume target that is either near reservoir capacity or near zero reservoir volume, with the optimal release being directly dependent on QR in these situations. This positive finding is moderated by the additional finding that errors in the estimation of predicted QR can result in significant operation losses (larger deviations from the target volume) that are due to suboptimal release decisions. Furthermore, the presence of binding release constraints leads to loss of optimal release and objective function benefits due to the seasonal inflow uncertainty predictions, suggesting less rigid release policies for improved operations under uncertain forecasts. It is also shown that the reservoir capacity values for which optimal reservoir operations are most sensitive to seasonal inflow uncertainty predictions are found to be at most 5 times the uncertainty range of the predicted seasonal inflow volume and to be at least as large as the uncertainty range of predicted inflow volumes. Suggestions for continued research in this area are offered.

* Additional affiliation: Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California

Corresponding author address: K. P. Georgakakos, 12780 High Bluff Dr., Suite 250, San Diego, CA 92130. Email: kgeorgakakos@hrc-lab.org

Abstract

This paper examines the conditions for which beneficial use of forecast uncertainty may be made for improved reservoir release decisions. It highlights the parametric dependencies of the effects of uncertainty in seasonal inflow volumes on the optimal release and objective function of a single reservoir operated to meet a single volume target at the end of the season under volume and release constraints. The duration of the “season” may be one or several months long. The analysis invokes the application of Kuhn–Tucker theory, and it shows that the presence of uncertainty introduces complex dependence of the optimal release and objective function on the reservoir parameters and uncertain inflow forcing. The seasonal inflow volume uncertainty is represented by a bounded symmetric beta distribution with a given mean, which is considered to be unbiased, and a half-range QR. The authors find that the use of predicted inflow uncertainty is particularly beneficial during operation with a volume target that is either near reservoir capacity or near zero reservoir volume, with the optimal release being directly dependent on QR in these situations. This positive finding is moderated by the additional finding that errors in the estimation of predicted QR can result in significant operation losses (larger deviations from the target volume) that are due to suboptimal release decisions. Furthermore, the presence of binding release constraints leads to loss of optimal release and objective function benefits due to the seasonal inflow uncertainty predictions, suggesting less rigid release policies for improved operations under uncertain forecasts. It is also shown that the reservoir capacity values for which optimal reservoir operations are most sensitive to seasonal inflow uncertainty predictions are found to be at most 5 times the uncertainty range of the predicted seasonal inflow volume and to be at least as large as the uncertainty range of predicted inflow volumes. Suggestions for continued research in this area are offered.

* Additional affiliation: Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California

Corresponding author address: K. P. Georgakakos, 12780 High Bluff Dr., Suite 250, San Diego, CA 92130. Email: kgeorgakakos@hrc-lab.org

Save