Skip to main content

Value of information analysis of snow measurements for the scheduling of hydropower production


The scheduling of a hydropower plant is challenging because of inflow uncertainty. During spring there is increased uncertainty when the snow melts. By gathering snow measurements, one learns more about the future inflow, and this might lead to lower spillage risk or higher efficiency. In this paper the value of information of snow measurements is studied. The value of information is representative of how much a test is worth. If the price of acquiring and processing snow measurements is less than the value of information, the test is worth doing. The notion of value of information is also useful for comparing various kinds of snow measurements in different situations. For scheduling a least squares Monte Carlo method is used in this paper. The uncertain inflow is represented by discrete scenarios, while the time-varying spot price is assumed known. Data from a Norwegian power plant are used to fit the inflow and snow distributions as well as prices, water reservoir limits and production release alternatives. The numerical tests show that snow measurements have little value when the reservoir is large compared to the total inflow. When the reservoir is smaller, the probability of overflow is bigger, and the snow measurements can be valuable for the scheduling when the data have high accuracy. The increase in value by using the snow measurements is between 0 and 10% in the different parameter settings considered here.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9


  1. Bruland, O., Færevåg, A., Steinsland, I., Liston, G., Sand, K.: Weather SDM: estimating snow density with high precision using snow depth and local climate. Hydrol. Res. 46(4), 494–506 (2015)

    Article  Google Scholar 

  2. Castelletti, A., Fedorov, R., Fraternali, P., Giuliani, M.: Multimedia on the mountaintop: using public snow images to improve water systems operation. In: Proceedings of the 2016 ACM on Multimedia Conference, MM ’16, pp. 948–957. ACM, New York (2016)

  3. Cressie, N.A.C., Wikle, C.K.: Statistics for Spatio-Temporal Data. Wiley Series in Probability and Statistics. Wiley, New York (2011)

    MATH  Google Scholar 

  4. Denault, M., Simonato, J.G., Stentoft, L.: A simulation-and-regression approach for stochastic dynamic programs with endogenous state variables. Comput. Oper. Res. 40(11), 2760–2769 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Desreumaux, Q., Côté, P., Leconte, R.: Role of hydrologic information in stochastic dynamic programming: a case study of the Kemano hydropower system in British Columbia. Can. J. Civil Eng. 41(9), 839–844 (2014)

    Article  Google Scholar 

  6. Eidsvik, J., Mukerji, T., Bhattacharjya, D.: Value of Information in the Earth Sciences: Integrating Spatial Modeling and Decision Analysis. Cambridge University Press, Cambridge (2015)

    Book  MATH  Google Scholar 

  7. Fleten, S.E., Kristoffersen, T.K.: Short-term hydropower production planning by stochastic programming. Comput. Oper. Res. 35(8), 2656–2671 (2008)

    Article  MATH  Google Scholar 

  8. Fosso, O.B., Gjelsvik, A., Haugstad, A., Mo, B., Wangensteen, I.: Generation scheduling in a deregulated system. The Norwegian case. IEEE Trans. Power Syst. 14(1), 75–81 (1999)

    Article  Google Scholar 

  9. Goninon, T., Pretto, P., Smith, G., Atkins, A.: Estimating the economic costs of hydrologic data collection. Water Resour. Manag. 11(4), 283–303 (1997)

    Article  Google Scholar 

  10. Guariso, G., Rinaldi, S., Zielinski, P.: The value of information in reservoir management. Appl. Math. Comput. 15(2), 165–184 (1984)

    Google Scholar 

  11. Howard, R.A., Abbas, A.: Foundations of Decision Analysis. Prentice Hall, Englewood Cliffs (2015)

    Google Scholar 

  12. Kolberg, S., Gottschalk, L.: Updating of snow depletion curve with remote sensing data. Hydrol. Process. 20(11), 2363–2380 (2006)

    Article  Google Scholar 

  13. Lundberg, A., Granlund, N., Gustafsson, D.: Towards automated ’ground truth’ snow measurements—a review of operational and new measurement methods for Sweden, Norway, and Finland. Hydrol. Process. 24(14), 1955–1970 (2010)

    Google Scholar 

  14. Marshall, H.P., Koh, G.: FMCW radars for snow research. Cold Reg. Sci. Technol. 52(2), 118–131 (2008)

    Article  Google Scholar 

  15. Nandalal, K.D.W., Bogardi, J.J.: Dynamic Programming Based Operation of Reservoirs: Applicability and Limits. Cambridge University Press, Cambridge (2007)

    Book  Google Scholar 

  16. Paraschiv, F., Fleten, S.E., Schürle, M.: A spot-forward model for electricity prices with regime shifts. Energy Econ. 47, 142–153 (2015)

    Article  Google Scholar 

  17. Powell, W.B.: Approximate Dynamic Programming. Wiley, New York (2011)

    Book  MATH  Google Scholar 

  18. Rheinheimer, D.E., Bales, R.C., Oroza, C.A., Lund, J.R., Viers, J.H.: Valuing year-to-go hydrologic forecast improvements for a peaking hydropower system in the Sierra Nevada. Water Resour. Res. 52(5), 3815–3828 (2016)

    Article  Google Scholar 

  19. Séguin, S., Fleten, S.E., Côté, P., Pichler, A., Audet, C.: Stochastic short-term hydropower planning with inflow scenario trees. Eur. J. Oper. Res. 259(3), 1156–1168 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  20. Tejada-Guibert, J.A., Johnson, S.A., Stedinger, J.R.: The value of hydrologic information in stochastic dynamic programming models of a multireservoir system. Water Resour. Res. 31(10), 2571–2579 (1995)

    Article  Google Scholar 

  21. Wallace, S., Fleten, S.E.: Stochastic programming models in energy. In: Ruszczynski, A., Shapiro, A. (eds.) Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10, pp. 637–677. Elsevier Science (2003).

Download references


We thank the hydropower company for letting us analyze and present their dataset, and for providing insight on relevant questions. We further thank Oddbjørn Bruland, Knut Sand and Yisak Sultan for discussions on snow measurements and hydropower production, and Tord Olsen for scientific discussions and careful reading of the paper. Fleten acknowledges support from the Research Council of Norway through Project 268093, and recognizes the Norwegian Research Centre for Hydropower Technology—HydroCen (Project 257588).

Author information

Authors and Affiliations


Corresponding author

Correspondence to Jo Eidsvik.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ødegård, H.L., Eidsvik, J. & Fleten, SE. Value of information analysis of snow measurements for the scheduling of hydropower production. Energy Syst 10, 1–19 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: