A suggestion for computing objective function in model calibration

a r t i c l e i n f o A parameter-optimization process (model calibration) is usually required for numerical model applications, which involves the use of an objective function to determine the model cost (model-data errors). The sum of square errors (SSR) has been widely adopted as the objective function in various optimization procedures. However , 'square error' calculation was found to be more sensitive to extreme or high values. Thus, we proposed that the sum of absolute errors (SAR) may be a better option than SSR for model calibration. To test this hypothesis, we used two case studies—a hydrological model calibration and a biogeochemical model calibration—to investigate the behavior of a group of potential objective functions: SSR, SAR, sum of squared relative deviation (SSRD), and sum of absolute relative deviation (SARD). Mathematical evaluation of model performance demonstrates that 'absolute error' (SAR and SARD) are superior to 'square error' (SSR and SSRD) in calculating objective function for model calibration, and SAR behaved the best (with the least error and highest efficiency). This study suggests that SSR might be overly used in real applications, and SAR may be a reasonable choice in common optimization implementations without emphasizing either high or low values (e.g., modeling for supporting resources management). Numerical models have been widely used in environmental science for understanding the natural processes, predicting impacts of global changes, and decision making for the sustainable management of resources. As knowledge of physical processes grows, models become more sophisticated and more parameters may be introduced (Beck, 1999; Brun et al., 2001; Legates and McCabe, 1999). We can see examples of the continuous developments of process-based models such as in ecology. These mathematical models include some parameters that need to be calibrated through an optimization procedure, which is to sample the parameter values from the allowable ranges until the value of the objective function (i.e., a function of differences between observations and simulations) is minimized or maximized From a literature review, a number of objective functions were used for model calibration in hydrology such as mean squared error, absolute mean/maximum error, residual bias, and Nash objective function (Boyle et al. However, the sum of square errors (SSR) is the most commonly used objective function for a variety of optimization processes even in recent years In evaluating model performances mathematically, studies have illustrated that the correlation-based measures characterized by 'square error' such as square …