Searching for an optimized single-objective function matching multiple objectives with automatic calibration of hydrological models

Abstract. In the calibration of hydrological models, evaluation criteria are explicitly and quantitatively defined as single- or multi-objective functions when utilizing automatic calibration approaches. In most previous studies, there is a general opinion that no single-objective function can represent all of the important characteristics of even one specific kind of hydrological variable (e.g., streamflow). Thus hydrologists must turn to multi-objective calibration. In this study, we demonstrated that an optimized single-objective function can compromise multi-response modes (i.e., multi-objective functions) of the hydrograph, which is defined as summation of a power function of the absolute error between observed and simulated streamflow with the exponent of power function optimized for specific watersheds. The new objective function was applied to 196 model parameter estimation experiment (MOPEX) watersheds across the eastern United States using the semi-distributed Xinanjiang hydrological model. The optimized exponent value for each watershed was obtained by targeting four popular objective functions focusing on peak flows, low flows, water balance, and flashiness, respectively. The results showed that the optimized single-objective function can achieve a better hydrograph simulation compared to the traditional single-objective function Nash-Sutcliffe efficiency coefficient for most watersheds, and balance high flow part and low flow part of the hydrograph without substantial differences compared to multi-objective calibration. The proposed optimal single-objective function can be practically adopted in the hydrological modeling if the optimal exponent value could be determined a priori according to hydrological/climatic/landscape characteristics in a specific watershed. This is, however, left for future study.