Water Resources Management

, Volume 32, Issue 12, pp 3979–3995 | Cite as

Robust Parameter Set Selection for a Hydrodynamic Model Based on Multi-Site Calibration Using Multi-Objective Optimization and Minimax Regret Approach

  • Li Li
  • Eun-Sung Chung
  • Kyung Soo Jun


A robust parameter set (ROPS) selection method for a hydrodynamic flow model was proposed based on the multi-site calibration by combining multi-objective optimization with the minimax regret approach (MRA). The multi-site calibration was defined by a multi-objective optimization problem for which individual objective functions were used to measure errors at each site. In the hydrodynamic model, coefficients of power functions that show the changing relationships between Manning’s roughness and discharge in each sub-reach were optimized by minimizing the residuals of multiple sites. Different combinations of weights were assigned to sites in the application of an aggregation approach to solve the multi-objective function, and the corresponding Pareto optimal parameter sets were assumed as the ROPS candidates. All performance measures to individual Pareto optimal parameter sets were calculated and the ROPS was determined using MRA. The set which has the lowest maximum regret obtained by averaging the results from calibration and validation was determined as the only ROPS. It was found that the estimated variable roughness and the corresponding computed water levels varied considerably depending on the weights assigned to sites. Using the proposed method, the task to assign proper weights on multiple sites can be easily achieved for multi-site calibration problems. This study provides a multi-criteria decision making method to choose a ROPS that has the lowest potential regret among various alternatives for hydrologic and hydraulic models.


Minimax regret approach Pareto optimal parameter sets Robust parameter set (ROPS) Hydrodynamic model Multi-site calibration Variable roughness 



This study was supported by a grant (NRF-2016R1D1A1B04931844) from the National Research Foundation of Korea, and a grant (13AWMP-B066744-01) from the Advanced Water Management Research Program by the Ministry of Land, Infrastructure and Transport.

Compliance with Ethical Standards

Conflict of Interest

The authors declare no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Graduate School of Water ResourcesSungkyunkwan UniversitySuwonRepublic of Korea
  2. 2.Department of Civil EngineeringSeoul National University of Science and TechnologySeoulRepublic of Korea

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