A suggestion for computing objective function in model calibration

Ecological Informatics
By:  and 



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).

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title A suggestion for computing objective function in model calibration
Series title Ecological Informatics
DOI 10.1016/j.ecoinf.2014.08.002
Volume 24
Year Published 2014
Language English
Publisher Elsevier
Contributing office(s) Earth Resources Observation and Science (EROS) Center
Description 5 p.
First page 107
Last page 111