Stochastic Optimization Models for Risk-Based Reservoir Management*
- 9 Downloads
The paper provides an overview of publications on reservoir management and formulates a novel stochastic dynamic optimization model for water balance management in the area affected. The proposed stochastic optimization approach allows multiple key performance indicators such as agriculture and energy production, wetland water and flood protection, biodiversity preservation, and reservoir storage. The two-stage feature of the proposed model induces safety constraints on water supply known as chance conditions in stochastic optimization: safety constraints in nuclear energy, stability constraints in insurance business, or constraints on the Conditional Value-at-Risk (CVaR) in finance. The original nonlinear, nonconvex and often discontinuous model can be reduced to linear programming problems.
Keywordsstochastic optimization risk water resource management two-stage problem extreme events
Unable to display preview. Download preview PDF.
- 1.V. M. Gorbachuk, “Optimization models of water quality (based on IIASA data),” V. M. Glushkov Inst. of Cybernetics, Kyiv (1989), pp. 89–60.Google Scholar
- 2.T. Zhao and J. Zhao, “Optimizing operation of water supply reservoir: The role of constraints,” Mathematical Problems in Engineering, Vol. 2014, ID 853186 (2014), DOI: https://doi.org/10.1155/2014/853186.
- 8.B. H. Dias, A. L. M. Marcato, R. C. Souza, et al., “Stochastic dynamic programming applied to hydrothermal power systems operation planning based on the convex hull algorithm,” Mathematical Problems in Engineering, Vol. 2010, Article ID 390940 (2010). DOI: https://doi.org/10.1155/2010/390940.
- 10.T. Zhao, D. Yang, X. Cai, J. Zhao, and H. Wang, “Identifying effective forecast horizon for real-time reservoir operation under a limited inflow forecast,” Water Resources Research, Vol. 48, No. 1 (2012). DOI: https://doi.org/10.1029/2011WR010623.
- 14.T. M. Carpenter and K. P. Georgakakos, “Assessment of Folsom lake response to historical and potential future climate scenarios: 1. Forecasting,” J. Hydrol., Vol. 249, Iss. 1–4, 148–175 (2001).Google Scholar
- 15.H. Yao and A. Georgakakos, “Assessment of Folsom lake response to historical and potential future climate scenarios: 2. Reservoir management,” J. Hydrol., Vol. 249, Iss. 1–4, 176–196 (2001).Google Scholar
- 16.F. X. Wang, L. Wang, H. C. Zhou, O. C. S. Valeriano, T. Koike, and W. L. Li, “Ensemble hydrological prediction-based real-time optimization of a multiobjective reservoir during flood season in a semiarid basin with global numerical weather predictions,” Water Resources Research, Vol. 48, No. 7 (2012). DOI: https://doi.org/10.1002/2017WR021480.
- 17.T. Dysarz, “Control of the reservoirs system during flood: Concept of learning in multi-stage decision process,” Technical Report IR-05-031, International Institute for Applied Systems Analysis, Schlossplatz 1 A-2361 Laxenburg, Austria (2005). URL: http://pure.iiasa.ac.at/7804.
- 18.P. D. Jones, J. M. Murphy, and M. Noguer, “Simulation of climate change over Europe using a nested regional — climate model. I: Assessment of control climate, including sensitivity to location of lateral boundaries,” Q. J. R. Meteorol. Soc., Vol. 121, Iss. 526, 1413–1449 (1995).Google Scholar
- 20.B. C. Bates, S. P. Charles, and J. P. Hughes, “Stochastic downscaling of numerical climate model simulations,” Environ. Model. Software, Vol. 13, Iss. 3–4, 325–331 (1998).Google Scholar
- 21.C. Prudhomme, N. S. Reynard, and S. Crooks, “Downscaling of GCMs for flood frequency analysis: Where are we now?” Hydrol. Process., Vol. 16, Iss. 6, 1137–1150 (2002). DOI: https://doi.org/10.1002/hyp.1054.
- 22.C. Prudhomme, D. Jakob, and C. Svensson, “Uncertainty and climate change impact on the flood regime of small UK catchments,” J. Hydrol., Vol. 277, Iss. 1, 1–23 (2003).Google Scholar
- 24.D. Conway and P. D. Jones, “The use of weather types and air flow indices for GCM Downscaling,” J. Hydrol., Vol. 212–213, Iss. 1–4, 348–361 (1998).Google Scholar
- 25.D. J. Sailor, T. Hu, X. Li, and J. N. Rosen, “A neural network approach to local downscaling of GCM output for assessing wind power implications of climate change,” Renewable Energy, Vol. 19, Iss. 3, 359–378 (2000).Google Scholar
- 26.J. Stehlik and A. Bardossy, “A multivariate stochastic downscaling model for generating daily precipitation series based on atmospheric circulation,” J. Hydrol., Vol. 256, Iss. 1–2, 120–141 (2002).Google Scholar
- 27.R. L. Wilby, C. W. Dawson, and E. M. Barrow, “SDSM — A decision support tool for the assessment of regional climate change impacts,” Environ. Model. Software, Vol. 17, Iss. 2, 145–157 (2002).Google Scholar
- 29.D. S. Wilks, “Simultaneous stochastic simulation of daily precipitation, temperature and solar radiation at multiple sites in complex terrain,” Agric. For. Meteorol., Vol. 96, Iss. 1–3, 85–101 (1999).Google Scholar
- 30.G. Goodsell and R. Lamb, “Estimating long return period floods by continuous simulation using a stochastic rainfall generator,” Report to MAFF, project FD 404 (1999).Google Scholar
- 31.P. Eagelson, “Dynamics of flood frequency,” Water Resources Research, Vol. 8, Iss. 4, 878–898 (1972).Google Scholar
- 32.M. B. Abbott, J. C. Bathurst, J. A. Cung, P. E. O’connell, and J. Rasmussen, “An introduction to the European Hydrological System — Systeme Hydrologique Europeen SHE. 2: Structure of a physically-based, distributed modelling system,” J. Hydrol., Vol. 87, Iss. 1, 61–77 (1986). DOI: https://doi.org/10.1029/WR008i004p00878.
- 33.E. M. Morris, “Forecasting flood flows in grassy and forecasted catchments using a deterministic distributed mathematics model,” in: Hydrological Forecasting — Prévisions Hydrologiques, Proc. of the Oxford Symposium, April 1980; Actes du Colloque d’Oxford, April 1980, IAHS-AISH Publ. No. 129 (1980), pp. 247–255. URL: http://hydrologie.org/redbooks/a129/iahs_129_0247.pdf.
- 34.W. R. Edward, D. A. Woolhiser, and R. E. Smith, “A distributed kinematic model of upland watershed,” Hydrology Paper, Colorado State University, No. 93 (1977). URL: https://mountainscholar.org/bitstream/handle/10217/61820/Hydrologypapers_n93.pdf?sequence=1.
- 35.B. B. Ross, D. N. Contractor, and V. O. Shanholtz, “A finite element model of overland and channel flow for accessing the hydrologic impact of land use change,” J. Hydrol., Vol. 41, Iss. 1–2, 11–30 (1979).Google Scholar
- 36.A. W. Jayawardena and J. K. White, “A finite element distributed catchment model: I. Analytical basis," J. Hydrol., Vol. 34, Iss. 3–4, 269–286 (1977).Google Scholar
- 38.R. P. Ibbitt and T. O’donnell, “Fitting methods for conceptual catchment models,” J. Hydraul. Div., Vol. 97, Iss. 9, 1331–1342 (1971).Google Scholar
- 39.M. H. Diskin and E. S. Simpson, “A quasi-linear spatial distribution cell model for the surface runoff system,” Water Resource Bull., No. 14, 903–918 (1978).Google Scholar
- 40.M. H. Diskin, G. Wyseure, and J. Feyen, “Application of a cell model to the Bellebeek watershed,” Nordic Hydrol., Vol. 15, Iss. 1, 25–38 (1984).Google Scholar
- 42.“A European Flood Forecasting System EFFS,” EFFS Final Report, Project coordinator: WL | Delft Hydraulics (2003). URL: http://effs.wldelft.nl.
- 43.A. P. J. De Roo, B. Gouweleeuw, J. Thielen, J. Bartholmes, P. Bongioanninicerlini, E. Todini, P. D. Bares, M. Horritt, N. Hunter, K. Beven, F. Pappenberger, E. Heise, G. Rivin, M. Hils, A. Hollingsworth, B. Holst, J. Kwadijk, P. Reggiani, M. Van Dijk, K. Sattler, and E. Sprokkereef, “Development of a European flood forecasting system,” International Journal of River Basin Management, Vol. 1, No. 1, 49–59 (2003).CrossRefGoogle Scholar
- 45.J. Y. You and X. Cai, “Hedging rule for reservoir operations: 1. A theoretical analysis,” Water Resources Research, Vol. 44, No. 1 (2008). DOI: https://doi.org/10.1029/2006WR005481.
- 47.A. Kiczko, “Multi-criteria decision support system for Siemianowka,” Interim Report IR-08-026, Intern. Inst. for Applied Systems Analysis, Laxenburg, Austria (2008).Google Scholar
- 48.R. Buizza, A. Hollingsworth, F. Lalaurette, and A. Ghelli, “Probabilistic predictions of precipitation using the ECMWF ensemble prediction system,” Weather and Forecasting, Vol. 14, Iss. 2, 168–189 (1999).Google Scholar
- 49.R. Romanowicz and M. Osuch, “An integrated data based mechanistic lowland catchment model for the Upper Narew,” Publs. Inst. Geophys. Pol. Acad. Sc. E-9 (405) (2008). URL: http://adsabs.harvard.edu/abs/2009EGUGA..11.9177R.
- 50.W. J. Junk, P. B. Bayley, and R. E. Sparks, “The flood pulse concept in river-floodplain system,” Proc. of the Intern. Large River Symposium (LARS), Canadian J. of Fisheries and Aquatic Sciences, Vol. 106, 110–127 (1989). URL: https://www.nrem.iastate.edu/class/assets/aecl518/Discussion%20Readings/Junk_et_al._1989.pdf.
- 51.K. Tockner, F. Malard, and J. V. Ward, “An extension of the flood pulse concept,” Hydrological Processes, Vol. 14, Nos. 16–17, 2861–2883 (2000).Google Scholar
- 52.J. Kubrak, T. Okruszko, D. Miroslaw-Swiatek, and I. Kardel, “Recognition of hydraulic conditions in the Upper Narew river system and their influence on the wetland habitats in the river valley,” Publs. Inst. Geophys. Pol. Acad. Sc. (387), 209–237 (2005).Google Scholar
- 53.T. Okruszko, S. Tyszewski, and D. Puslowska, “Water management in the Upper Narew valley,” Zeszyty Problemów Podstawowych Nauk Rolniczych (Pol)., No. 428 (1996).Google Scholar
- 54.”IWOR Protection plan of the Narew national park,” Technical report, IWOR and IMUZ, Falenty (2000).Google Scholar
- 55.Y. P. Li, G. H. Huang, S. L. Nie, et al., “Inexact multistage stochastic integer programming for water resources management under uncertainty,” J. of Environmental Management, Vol. 88, Iss. 1, 93–107 (2008).Google Scholar
- 57.V. M. Gorbachuk, Yu. M. Ermoliev, and T. Yu. Ermolieva, «A two-stage model of ecological–economic decisions,” Bull. Odessa National University. Economics, Vol. 21, Iss. 9, 142–147 (2016).Google Scholar
- 59.Y. Ermoliev and D. Von Winterfeldt, “Systemic risk and security management,” in: Y. Ermoliev, M. Makowski, and K. Marti (eds.), Managing Safety of Heterogeneous Systems, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin–Heidelberg (2012), pp. 19–49.Google Scholar