Multiobjective calibration with Pareto preference ordering: An application to rainfall-runoff model calibration

Automatic calibration routines for hydrologic models with multiple objective capabilities are becoming increasingly popular due to advances in computational power, population-based optimization techniques, and the recognition that a single performance measure such as the root-mean-square error is no longer sufficient to characterize the complex behavior of the catchment. However, as more objective functions are included in the calibration, the number of Pareto-optimal solutions as well as the number of ''near'' Pareto-optimal parameter sets increases. The calibration problem quickly becomes a decision-making problem. In the practical sense, users of automatic calibration routines have to face the task of selecting a set of suitable model parameters from the numerous Pareto-optimal sets. A new method of automatic calibration is proposed, which combines an effective optimization routine, based on multiobjective genetic algorithms, and Pareto preference ordering. In this case, Pareto-optimal points that are also Pareto-optimal in different subspace combinations of the objective functions space are preferred. The proposed method is used to calibrate the MIKE11/NAM rainfall-runoff model for a Danish catchment. The results indicated that the method is able to sieve through the numerous Pareto-optimal solutions and select a small number of preferred solutions. This is extremely useful to modelers who typically are required to provide the best estimated parameter sets with good overall model performance.