Multi-objective parameter calibration
Multi-objective calibration can help identify parameter sets that represent a hydrological system and enable further constraining of the parameter space. Multi-objective calibration is expected to be more frequently utilized, along with the advances in optimization algorithms and computing resources. However, the impact of the number of objective functions on modeling outputs is still unclear, and the adequate number of objective functions remains an open question. We investigated the responses of model performance, equifinality, and uncertainty to the number of objective functions incorporated in a hierarchical and sequential manner in parameter calibration. The Hydrological Simulation Program – FORTRAN (HSPF) models that were prepared for bacteria TMDL development served as a mathematical representation to simulate the hydrological processes of three watersheds located in Virginia, and the Expert System for Calibration of HSPF (HSPEXP) statistics were employed as objective functions in parameter calibration experiments. Results showed that the amount of equifinality and output uncertainty overall decreased while the model performance was maintained as the number of objective functions increased sequentially. However, there was no further significant improvement in the equifinality and uncertainty when including more than four objective functions. This study demonstrated that the introduction of an adequate number of objective functions could improve the quality of calibration without requiring additional observations.