Abstract
When hydrological simulation models are calibrated, the optimized parameter set based on a single event often does not show good accuracy for other events, even using the same performance measure. Therefore, this study improved the robust parameter set (ROPS) selection method for hydrological simulation models to consider multiple rainfall events by combining the Minimax Regret Approach (MRA) with Pareto optimums. A multi-event objective function, which is the linear combination of three weighting values and three Nash-Sutcliffe coefficients, was used and individually solved using a genetic algorithm. All available 63 multi-objective functions with weighting values based on three events were determined and then, the Pareto optimum was derived. These optimized parameter sets were considered as the ROPS candidates for the final selection. This study used two approaches. First, Nash-Sutcliffe efficiencies (NSEs) for the additional three rainfall events were used to identify the ROPS. Second, four performance indices, the NSE, the Peak Flow Error (PFE), the Root Mean Square Error (RMSE) and the Percent Bias (PBIAS), were used for the other three events. From the results, it can be concluded that the optimized parameter set from the best weighted multi-objective function using multiple events can simulate most rainfall events well with relatively high precision for both the NSE only and the four performance indices. Furthermore, it can be extended to combine multiple events from multiple sites.
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08 July 2017
An Erratum to this paper has been published: https://doi.org/10.1007/s12205-017-2972-9
References
Bardossy, A. and Sing, S. K. (2008). “Robust estimation of hydrological model parameters.” Hydrology and Earth System Sciences, Vol. 12, pp. 1273–1283.
Cheng, C. T., Zhao, M. Y., Chau, K. W., and Wu, X. Y. (2006). “Using genetic algorithm and TOPSIS for Xinanjiang model calibration with a single procedure.” Hournal of Hydrology, Vol. 316, pp. 129–140.
Chung, E. S., Won, G. J., Kim, Y., and Lee, H. (2015). “Water resources vulnerability characteristics by district’s population size in a changing climate using subjective and objective weights.” Sustainability, Vol. 6, No. 9, pp. 6141–6157.
Dayaratne, S. T. and Perera, B. J. C. (2004). “Calibration of urban stormwater drainage models using hydrograph modeling.” Urban Water Journal, Vol. 1, No. 4, pp. 283–297.
Di Pierro, F., Khu, S. T., and Savic, D. (2006). “From single-objective to multiple-objective multiple-rainfall events automatic calibration of urban storm water runoff models using genetic algorithms.” Water Science & Technology, Vol. 54, Nos. 6-7, pp. 57–64.
Gamerith, V., Gruber, G., and Muschalla, D. (2011). “Single-and multievent optimization in combined sewer flow and water quality model calibration.” Journal of Environmental Engineering, Vol. 137, No. 7, pp. 551–558.
Garcia-Cascales, M. S. and Lamata, M. T. (2012). “On rank reversal and TOPSIS method.” Math. Comput. Model., Vol. 56, pp. 123–132.
Hwang, C. L. and Yoon, K. (1981). Multiple attribute decision making: Methods and applications, Heidelberg: Springer.
Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Boston, Mass.
Kang, T. U. and Lee, S. H. (2014). “Modification of the SCE-UA to include constraints by embedding an adaptive penalty function and application: Application approach, Water.” Resour. Manag., Vol. 28, pp. 2145–2159.
Khu, S. T. and Madsen, H. (2005). “Multiobjective calibration with Pareto preference ordering: An application to rainfall-runoff model calibration.” Water Resources Research 2005, Vol. 41, W03004, DOI: 10.1029/2004WR003041.
Khu, S. T., Madsen, H., and di Pierro, F. (2008). “Incorporating multiple observations for distributed hydrologic model calibration: An approach using a multi-objective evolutionary algorithm and clustering.” Advances in Water Resources, Vol. 31, pp. 1387–1398.
Kim, Y. and Chung, E. S. (2014). “An index-based robust decision making framework for watershed management in a changing climate.” Sci. Tot. Environ., Vol. 473, pp. 88–102.
Kim, Y., Chung, E. S., and Jun, S. (2015a). “Iterative framework for robust reclaimed wastewater allocation in a changing environment using multi-criteria decision making.” Water Resour. Manage., Vol. 29, No. 2, pp. 295–311.
Kim, Y., Chung, E. S., Won, K., and Gil, K. (2015b). “Robust parameter estimation framework of a rainfall-runoff model using pareto optimum and minimax regret approach.” Water, Vol. 7, pp. 1246–1263.
Li, X., Weller, D. E., and Jordan, T. E. (2010). “Watershed model calibration using multi-objective optimization and multi-site averaging.” Journal of Hydrology, Vol. 380, pp. 277–288.
Loulou, R. and Kanudia, A. (1999). “Minimax regret strategies for greenhouse has abatement: Methodology and application.” Operations Research Letters, Vol. 25, pp. 219–230.
Madsen, H. (2000). “Automatic calibration of a conceptual rainfallrunoff model using multiple objectives.” Journal of Hydrology, Vol. 235, pp. 276–145.
Nash, J. E. and Sutcliffe, J. V. (1970). “River flow forecasting through conceptual models: Part 1–A discussion of principles.” J. Hydrol., Vol. 125, pp. 221–241.
Rossman, L. A. (2010). Storm Water Management Model User’s Manual Version 5.0. United States Environmental Protection Agency.
Saeidifarzad, B., Nourani, V., and Aalami, M. T. (2014). “Chau, K.W. Multi-site calibration of linear reservoir based geomorphologic rainfall-runoff model.” Water, Vol. 6, pp. 2690–2716.
Shinma, T. A. and Reis, L. F. R. (2014). “Incorporating multi-event and multi-site data in the calibration of SWMM.” Procedia Engineering, Vol. 79, pp. 75–84.
Soltanifar, M. and Shahghobadi, S. (2014). “Survey on rank preservation and rank reversal in data envelopment analysis.” Knowl. -based Syst., Vol. 60, pp. 10–19.
Tavana, M., Li, Z., Mobin, M., Komaki, M., and Teymourian, E. (2016). “Multi-objective control chart design optimization using NSGA-III and MOPSO enhanced with DEA and TOPSIS.” Expert Systems With Applications, Vol. 50, pp. 17–39.
Wang, W. (2012). “Multi-site calibration, validation, and sensitivity analysis of the MIKE SHE model for a large watershed in Northern China.” Hydrology and Earth System Science, Vol. 16, pp. 4621–4632.
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Song, C.G., Chung, ES. & Won, K. Use of the Minimax Regret Approach for Robust Selection of Rainfall-Runoff Model Parameter Values Considering Multiple Events and Multiple Performance Indices. KSCE J Civ Eng 22, 1515–1522 (2018). https://doi.org/10.1007/s12205-017-1972-0
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DOI: https://doi.org/10.1007/s12205-017-1972-0