Evaluating model performance: towards a non-parametric variant of the Kling-Gupta efficiency

Goodness-of-fit measures are important for an objective evaluation of runoff model performance. The Kling-Gupta efficiency (<i>R</i>_KG), which has been introduced as an improvement of the widely used Nash-Sutcliffe efficiency, considers different types of model errors, namely the error in the mean, the variability, and the dynamics. The calculation of <i>R</i>_KG is implicitly based on the assumptions of data linearity, data normality, and the absence of outliers. In this study, we propose a modification of <i>R</i>_KG as an efficiency measure comprising non-parametric components, i.e. the Spearman rank correlation and the normalized flow–duration curve. The performances of model simulations for 100 catchments using the new measure were compared to those obtained using <i>R</i>_KG based on a number of statistical metrics and hydrological signatures. The new measure resulted overall in better or comparable model performances, and thus it was concluded that efficiency measures with non-parametric components provide a suitable alternative to commonly used measures.