Goodness-of-fit criteria for hydrological models: Model calibration and performance assessment

This study provides guidelines for the selection of proper goodness-of-fit criteria for the calibration and evaluation of hydrological models. Popular goodness-of-fit criteria and good practices for hydrological modeling are reviewed. The review discusses the advantages and disadvantages of several criteria and is followed by a case study that focuses on the review's main findings. The main recommendation is for hydrologists to avoid using threshold values to assess model performance and preferably set a proper benchmark series. The case study was developed using the GR5J hydrological model and data from 179 watersheds in the Brazilian Cerrado biome. Several single- and multi-objective functions are used in optimization runs to assess the outcome for different goodness-of-fit criteria. The model performance is evaluated for each optimization run considering overall conditions, i.e., entire time series, and conditions under low- and peak-flow conditions. The study case reinforces that the popular Nash-Sutcliffe efficiency index should be avoided as an objective function. Alternatively, the Kling-Gupta efficiency index showed to be a more reliable criterion, resulting in lower bias for both calibration and validation, and balanced results for both low- and peak-flow conditions. Additionally, combining different criteria in multi-objective functions can result in robust trade-offs. General guidelines are summarized and additional emphasis is given to tropical watersheds where low flows deserve due attention.