Simplified Approach to Mixed-Integer Chance-Constrained Optimization with Ensemble Streamflow Forecasts for Risk-Based Dam Operation
Publication: Journal of Water Resources Planning and Management
Volume 149, Issue 12
Abstract
We developed an integrated optimization program to design the release strategy for a dam, given a downstream flow target and considering medium-range ensemble forecasts of downstream tributary flows. A strength of the program is its ability to explicitly limit the risk of downstream flooding through chance constraints. Embedded in the program is an advanced hydrological ensemble prediction system (HEPS). Given the ensemble nature of the downstream flow forecasts (in that they comprise sets of individual scenarios), we formulated the chance constraints as discontinuous mixed-integer equations. This makes the integrated program nondeterministic polynomial-time hard (NP-hard) and thus, intractable to be solved by conventional mixed-integer programming methods based on branch-and-bound. Thus, to solve the program, we took a simplified but innovative approach—possible through exploiting certain simplifying aspects of the problem—where we solved first for the integer (binary) variables following a ranking mechanism, then the continuous variables using nonlinear programming. The results for a case study of Hume Dam and Lake Mulwala in the Murray-Darling Basin, Australia, demonstrates the efficacy of the integrated program and our simplified approach to solving it. The results show the integrated program is able to meet the optimization target when the natural flow from tributaries is low. The results also show that when that natural flow is high, the integrated program’s ability to meet the target to increase with the allowable risk of flooding. However, a higher allowable risk may lead to a higher possibility of flooding, depending on the problem specification. We recommend to run the integrated program on a continual basis because its results depend not only on the optimization for the current day, but also previous days. This study addresses a major need: the ability to use all information from an advanced HEPS, e.g., to limit risk in optimizing the operation of a mixed engineered-natural system, and with that, advances the use of ensemble hydrologic forecasts in water management.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data that support the findings of this study are available from the corresponding author upon reasonable request, or directly from the third-party sources indicated in the main text or acknowledgments, e.g., Water Data Online, the AIFS database, the AWAP, the Australian Geofabric, and BOM ACCESS archives.
Acknowledgments
We thank the BOM for providing the AIFS hourly rainfall observations used in this study. This work was conducted on the traditional lands of the Boonwurrung people of the Kulin Nation. We acknowledge their continuing custodianship of these lands and the rivers that flow through them, and pay our respects to their elders, past and present. We also acknowledge the traditional owners of the catchments in this study.
References
Anvari, S., S. J. Mousavi, and S. Morid. 2014. “Sampling/stochastic dynamic programming for optimal operation of multi-purpose reservoirs using artificial neutral network-based ensemble streamflow predictions.” J. Hydroinf. 16 (4): 907–921. https://doi.org/10.2166/hydro.2013.236.
Bennett, J. C., D. E. Robertson, D. L. Shrestha, Q. J. Wang, D. Enever, P. Hapuarachchi, and N. K. Tuteja. 2014. “A system for continuous hydrological ensemble forecasting (SCHEF) to lead times of 9 days.” J. Hydrol. 519 (Nov): 2832–2846. https://doi.org/10.1016/j.jhydrol.2014.08.010.
Bennett, J. C., D. E. Robertson, P. G. D. Ward, H. A. P. Hapuarachchi, and Q. J. Wang. 2016. “Calibrating hourly rainfall-runoff models with daily forcings for streamflow forecasting applications in meso-scale catchments.” Environ. Modell. Software 76 (Feb): 20–36. https://doi.org/10.1016/j.envsoft.2015.11.006.
BOM (Bureau of Meteorology). 2010. Operational implementation of the ACCESS numerical weather prediction systems. Melbourne, VIC, Australia: BOM.
CEWO (Commonwealth Environmental Water Office). 2020. Water management plan 2020–21. Canberra, ACT, Australia: Commonwealth of Australia.
Clark, M., S. Gangopadhyay, L. Hay, B. Rajagopalan, and R. Wilby. 2004. “The Schaake shuffle: A method for reconstructing space-time variability in forecasted precipitation and temperature fields.” J. Hydrometeorol. 5 (1): 243–262. https://doi.org/10.1175/1525-7541(2004)005%3C0243:TSSAMF%3E2.0.CO;2.
Cloke, H. L., F. Pappenberger, S. J. van Andel, J. Schaake, J. Thielen, and M.-H. Ramos. 2013. “Hydrological ensemble prediction system (HEPS).” Hydrol. Processes 27 (1): 1–4. https://doi.org/10.1002/hyp.9679.
Cote, P., and R. Leconte. 2016. “Comparison of stochastic optimization algorithms for hydropower reservoir operation with ensemble streamflow prediction.” J. Water Resour. Plann. Manage. 142 (2): 04015046. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000575.
Datta, B., and M. H. Houck. 1984. “A stochastic optimization model for real-time operation of reservoirs using uncertain forecasts.” Water Resour. Res. 20 (8): 1039–1046. https://doi.org/10.1029/WR020i008p01039.
Delaney, C. J., R. K. Hartman, J. Mendoza, M. Dettinger, L. Delle Monache, J. Jasperse, F. M. Ralph, C. Talbot, J. Brown, D. Reynolds, and S. Evett. 2020. “Forecast informed reservoir operations using ensemble streamflow predictions for a multipurpose reservoir in northern California.” Water Resour. Res. 56 (9): e2019WR026604. https://doi.org/10.1029/2019WR026604.
DELWP (Department of Environment, Land, Water, and Planning). 2015. Business case for flexible rates of fall in river levels downstream of Hume Dam—The six inch rule: A sustainable diversion limit adjustment measure. Melbourne, VIC, Australia: DELWP.
Duan, Q., S. Sorooshian, and V. K. Gupta. 1994. “Optimal use of the SCE-UA global optimization method calibrating watershed models.” J. Hydrol. 158 (3–4): 265–284. https://doi.org/10.1016/0022-1694(94)90057-4.
Eheart, J. W. 1996. “Groundwater remediation design when pretty good is good enough.” In Proc., North American Water and Environment Congress & Destructive Water, Reston, VA: ASCE.
Eum, H.-I., Y.-O. Kim, and R. N. Palmer. 2011. “Optimal drought management using sampling stochastic dynamic programming with a hedging rule.” J. Water Resour. Plann. Manage. 137 (1): 113–122. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000095.
Faber, B. A., and J. R. Stedinger. 2001. “Reservoir optimization using sampling SDP with ensemble streamflow prediction (ESP) forecasts.” J. Hydrol. 249 (1–4): 113–133. https://doi.org/10.1016/S0022-1694(01)00419-X.
Fan, F. M., D. Schwanenberg, R. Alvarado, A. A. dos Reis, W. Collischonn, and S. Naumman. 2016. “Performance of deterministic and probabilistic hydrological forecasts for the short-term optimization of a tropical hydropower reservoir.” Water Resour. Manage. 30 (Aug): 3609–3625. https://doi.org/10.1007/s11269-016-1377-8.
Ficchi, A., L. Raso, D. Dorchies, F. Pianosi, P.-O. Malaterre, P.-J. van Overloop, and M. Jay-Allemand. 2016. “Optimal operation of the multireservoir system in the Seine River Basin using deterministic and ensemble forecasts.” J. Water Resour. Plann. Manage. 142 (1): 05015005. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000571.
Gill, P. E., W. Murray, M. A. Saunders, and M. H. Wright. 1984. “Sequential quadratic programming methods for nonlinear programming.” In Vol. 9 of Computer aided analysis and optimization of mechanical system dynamics. NATO ASI series (Series F: Computer and system sciences), edited by E. J. Haug. Berlin: Springer.
Gneiting, T., and M. Katzfuss. 2014. “Probabilistic forecasting.” Annu. Rev. Stat. Appl. 1 (Jan): 125–151. https://doi.org/10.1146/annurev-statistics-062713-085831.
Haguma, D., R. Leconte, and P. Cote. 2018. “Evaluating transition probabilities for a stochastic dynamic programming model used in water system optimization.” J. Water Resour. Plann. Manage. 144 (2): 04017090. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000883.
Hapuarachchi, H. A. P., et al. 2022. “Development of a national 7-day ensemble streamflow forecasting service for Australia.” Hydrol. Earth Syst. Sci. 26 (18): 4801–4821. https://doi.org/10.5194/hess-26-4801-2022.
Harrigan, S., C. Prudhomme, S. Parry, K. Smith, and M. Tanguy. 2018. “Benchmarking ensemble streamflow prediction skill in the UK.” Hydrol. Earth Syst. Sci. 22 (3): 2023–2039. https://doi.org/10.5194/hess-22-2023-2018.
Hashimoto, T., J. R. Stedinger, and D. P. Loucks. 1982. “Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation.” Water Resour. Res. 18 (1): 14–20. https://doi.org/10.1029/WR018i001p00014.
Horne, A. C., J. A. Webb, M. Mussehl, A. John, L. Rumpff, K. Fowler, D. Lovell, and L. Poff. 2022. “Not just another assessment method: Reimagining environmental flows assessments in the face of uncertainty.” Front. Environ. Sci. 10 (May): 808943. https://doi.org/10.3389/fenvs.2022.808943.
Karamouz, M., and H. V. Vasiliadis. 1992. “Bayesian stochastic optimization of reservoir operation using uncertain forecasts.” Water Resour. Res. 28 (5): 1221–1232. https://doi.org/10.1029/92WR00103.
Kaur, S., A. C. Horne, R. Nathan, J. M. Szemis, L. Gibson, A. M. Costa, J. A. Webb, and M. Stewardson. 2019. “Examining trade-offs in piggybacking flow events while making environmental release decisions in a river system.” J. Water Resour. Plann. Manage. 145 (6): 04019019. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001048.
Kelman, J., J. R. Stedinger, L. A. Cooper, E. Hsu, and S.-Q. Yuan. 1990. “Sampling stochastic dynamic programming applied to reservoir operation.” Water Resour. Res. 26 (3): 447–454. https://doi.org/10.1029/WR026i003p00447.
Kianfar, K. 2011. “Branch-and-bound algorithms.” In Wiley encyclopedia of operations research and management science, edited by J. J. Cochran. Hoboken, NJ: Wiley.
Kim, Y.-O., H.-I. Eum, E.-G. Lee, and I. H. Ko. 2007. “Optimizing operational policies of a Korean multireservoir system using sampling stochastic dynamic programming with ensemble streamflow prediction.” J. Water Resour. Plann. Manage. 133 (1): 4–14. https://doi.org/10.1061/(ASCE)0733-9496(2007)133:1(4).
Li, M., D. E. Robertson, Q. J. Wang, J. C. Bennett, and J.-M. Perraud. 2021. “Reliable hourly streamflow forecasting with emphasis on ephemeral rivers.” J. Hydrol. 598 (Jul): 125739. https://doi.org/10.1016/j.jhydrol.2020.125739.
Li, M., Q. J. Wang, D. E. Robertson, and J. C. Bennett. 2017. “Improved error modelling for streamflow forecasting at hourly time steps by splitting hydrographs into rising and falling limbs.” J. Hydrol. 555 (Dec): 586–599. https://doi.org/10.1016/j.jhydrol.2017.10.057.
Loaiciga, H. A., and M. A. Marino. 1986. “Risk analysis for reservoir operation.” Water Resour. Res. 22 (4): 483–488. https://doi.org/10.1029/WR022i004p00483.
MDBA (Murray-Darling Basin Authority). 2013. Preliminary overview of constraints to environmental water delivery in the Murray-Darling Basin. Canberra, ACT, Australia: MDBA.
MDBA (Murray-Darling Basin Authority). 2015. River Murray from Hume Dam to Yarrawonga Weir reach report: Constraints management strategy. Canberra, ACT, Australia: MDBA.
Meema, T., Y. Tachikawa, Y. Ichikawa, and K. Yorozu. 2021. “Real-time optimization of a large-scale reservoir operation in Thailand using adaptive inflow prediction with medium-range ensemble precipitation forecasts.” J. Hydrol.: Reg. Stud. 38 (Dec): 100939. https://doi.org/10.1016/j.ejrh.2021.100939.
Michalewicz, Z., D. Dasgupta, R. G. le Riche, and M. Schoenauer. 1996. “Evolutionary algorithms for constrained engineering problems.” Comput. Ind. Eng. 30 (4): 851–870. https://doi.org/10.1016/0360-8352(96)00037-X.
Morgan, D. R., J. W. Eheart, and A. J. Valocchi. 1993. “Aquifer remediation design under uncertainty using a new chance constrained programming technique.” Water Resour. Res. 29 (3): 551–561. https://doi.org/10.1029/92WR02130.
Mousavi, S. J., M. Karamouz, and M. B. Menhadj. 2004. “Fuzzy-state stochastic dynamic programming for reservoir operation.” J. Water Resour. Plann. Manage. 130 (6): 460–470. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:6(460).
Nasir, H. A., A. Care, and E. Weyer. 2016. “A randomised approach to multiple chance-constrained problems: An application to flood avoidance.” In Proc., 2016 IEEE 55th Conf. on Decision and Control. New York: IEEE.
Nasir, H. A., T. Zhao, A. Care, Q. J. Wang, and E. Weyer. 2018. “Efficient river management using stochastic MPC and ensemble forecast of uncertain in-flows.” IFAC PapersOnLine 51 (5): 37–42. https://doi.org/10.1016/j.ifacol.2018.06.196.
Ng, T. L., and J. W. Eheart. 2008. “A multiple-realizations chance-constrained model for optimizing nutrient removal in constructed wetlands.” Water Resour. Res. 44 (4): W04405. https://doi.org/10.1029/2007WR006126.
Ng, T. L., D. E. Robertson, and J. C. Bennett. 2019. “Estimating Lake Mulwala diversions for calibration of a semi-distributed hydrologic model of the Murray River.” In Proc., 23rd Int. Congress on Modelling and Simulation. Canberra, ACT, Australia: The Modelling and Simulation Society of Australia and New Zealand.
Nohara, D., and T. Hori. 2018. “Reservoir operation for water supply considering operational ensemble hydrological predictions.” J. Disaster Res. 13 (4): 650–659. https://doi.org/10.20965/jdr.2018.p0650.
Ouarda, T. B. M. J., and J. W. Labadie. 2001. “Chance-constrained optimal control for multireservoir system optimization and risk analysis.” Stochastic Environ. Res. Risk Assess. 15 (Jun): 185–204. https://doi.org/10.1007/s004770100066.
Perraud, J.-M., R. Bridgart, J. C. Bennett, and D. E. Robertson. 2015. “SWIFT2: High performance software for short-medium term ensemble streamflow forecasting research and operations.” In Proc., 21st Int. Congress on Modelling and Simulation. Canberra, ACT, Australia: The Modelling and Simulation Society of Australia and New Zealand.
Perrin, C., C. Michel, and V. Andreassian. 2003. “Improvement of a parsimonious model for streamflow simulation.” J. Hydrol. 279 (1–4): 275–289. https://doi.org/10.1016/S0022-1694(03)00225-7.
Raso, L., D. Schwanenberg, N. C. van de Giesen, and P. J. van Overloop. 2014. “Short-term optimal operation of water systems using ensemble forecasts.” Adv. Water Resour. 71 (Sep): 200–208. https://doi.org/10.1016/j.advwatres.2014.06.009.
Raupach, M. R., P. R. Briggs, V. Haverd, E. A. King, M. Paget, and C. M. Trudinger. 2009. Australian water availability project (AWAP): CSIRO marine and atmospheric research component: Final report for Phase 3. Canberra, ACT, Australia: CSIRO Marine and Atmospheric Research.
Raupach, M. R., P. R. Briggs, V. Haverd, E. A. King, M. Paget, and C. M. Trudinger. 2012. “Australian water availability project (AWAP).” Accessed December 10, 2018. http://www.csiro.au/awap.
Read, L. K., and R. M. Vogel. 2015. “Reliability, return periods, and risk under nonstationary.” Water Resour. Res. 51 (8): 6381–6398. https://doi.org/10.1002/2015WR017089.
Robertson, D. E., D. L. Shrestha, and Q. J. Wang. 2013. “Post-processing rainfall forecasts from numerical weather prediction models for short-term streamflow forecasting.” Hydrol. Earth Syst. Sci. 17 (9): 3587–3603. https://doi.org/10.5194/hess-17-3587-2013.
Saavedra Valeriano, O. C., T. Koike, K. Yang, T. Graf, X. Li, L. Wang, and X. Han. 2010. “Decision support for dam release during floods using a distributed biosphere hydrological model driven by quantitative precipitation forecasts.” Water Resour. Res. 46 (10): W10544.
Schwanenberg, D., F. M. Fan, S. Naumann, J. I. Kuwajima, R. A. Montero, and A. A. dos Reis. 2015. “Short-term reservoir optimization for flood mitigation under meteorological and hydrological forecast uncertainty: Application to the Três Marias Reservoir in Brazil.” Water Resour. Manage. 29 (5): 1635–1651. https://doi.org/10.1007/s11269-014-0899-1.
Shrestha, D. L., D. E. Robertson, J. C. Bennett, and Q. J. Wang. 2015. “Improving precipitation forecasts by generating ensembles through postprocessing.” Mon. Weather Rev. 143 (9): 3642–3663. https://doi.org/10.1175/MWR-D-14-00329.1.
Simonovic, S. P., and M. A. Marino. 1980. “Reliability programming in reservoir management: 1. Single multipurpose reservoir.” Water Resour. Res. 16 (5): 844–848. https://doi.org/10.1029/WR016i005p00844.
Stedinger, J. R., B. F. Sule, and D. P. Loucks. 1984. “Stochastic dynamic programming models for reservoir operation optimization.” Water Resour. Res. 20 (11): 1499–1505. https://doi.org/10.1029/WR020i011p01499.
Strycharczyk, J., and J. R. Stedinger. 1987. “Evaluation of a ‘reliability programming’ reservoir model.” Water Resour. Res. 23 (2): 225–229. https://doi.org/10.1029/WR023i002p00225.
Trezos, T., and W. W.-G. Yeh. 1987. “Use of stochastic dynamic programming for reservoir management.” Water Resour. Res. 23 (6): 983–996. https://doi.org/10.1029/WR023i006p00983.
Turner, S. W. D., J. C. Bennett, D. E. Robertson, and S. Galelli. 2017. “Complex relationship between seasonal streamflow forecast skill and value in reservoir operations.” Hydrol. Earth Syst. Sci. 21 (9): 4841–4859. https://doi.org/10.5194/hess-21-4841-2017.
Wang, F., L. Wang, H. Zhou, O. C. Saavedra Valeriano, T. Koike, and W. Li. 2012. “Ensemble hydrological prediction-based real-time optimization of a multiobjective reservoir during flood season in a semiarid basin with global numerical weather predictions.” Water Resour. Res. 48 (7): W07520. https://doi.org/10.1029/2011WR011366.
Wu, W., R. Emerton, Q. Duan, A. W. Wood, F. Wetterhall, and D. E. Robertson. 2020. “Ensemble flood forecasting: Current status and future opportunities.” WIREs Water 7 (3): e1432. https://doi.org/10.1002/wat2.1432.
Xu, B., S. E. Boyce, Y. Zhang, Q. Liu, L. Guo, and P.-A Zhong. 2017. “Stochastic programming with a joint chance constraint model for reservoir refill operation considering flood risk.” J. Water Resour. Plann. Manage. 143 (1): 04016067. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000715.
Xu, B., X. Huang, P.-A. Zhong, and Y. Wu. 2020. “Two-phase risk hedging rules for informing conservation of flood resources in reservoir operation considering inflow forecast uncertainty.” Water Resour. Manage. 34 (Jul): 2731–2752. https://doi.org/10.1007/s11269-020-02571-y.
Xu, W., C. Zhang, Y. Peng, G. Fu, and H. Zhou. 2014. “A two stage Bayesian stochastic optimization model for cascaded hydropower systems considering varying uncertainty of flow forecasts.” Water Resour. Res. 50 (12): 9267–9286. https://doi.org/10.1002/2013WR015181.
Zhao, T., X. Cai, and D. Yang. 2011. “Effect of streamflow forecast uncertainty on real-time reservoir operation.” Adv. Water Resour. 34 (4): 495–504. https://doi.org/10.1016/j.advwatres.2011.01.004.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 149 • Issue 12 • December 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Jun 7, 2022
Accepted: Apr 22, 2023
Published online: Oct 3, 2023
Published in print: Dec 1, 2023
Discussion open until: Mar 3, 2024
ASCE Technical Topics:
- Case studies
- Computer programming
- Computing in civil engineering
- Dams
- Design (by type)
- Engineering fundamentals
- Floods
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid mechanics
- Forecasting
- Geotechnical engineering
- Hydraulic design
- Hydrologic engineering
- Hydrology
- Mathematics
- Methodology (by type)
- Research methods (by type)
- Statistics
- Streamflow
- Water and water resources
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.