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

TLDR

Goodness‑of‑fit measures are crucial for objectively evaluating runoff model performance, and the Kling‑Gupta efficiency improves upon the Nash‑Sutcliffe efficiency by accounting for errors in mean, variability, and dynamics. In this study, we propose a modification of RKG that incorporates non‑parametric components. The modified RKG replaces parametric assumptions with non‑parametric components, using Spearman rank correlation and a normalized flow‑duration curve, and its performance was evaluated on 100 catchments against the original RKG using statistical metrics and hydrological signatures. The new measure achieved overall better or comparable model performance, indicating that non‑parametric efficiency measures are a suitable alternative to commonly used metrics.

Abstract

Goodness-of-fit measures are important for an objective evaluation of runoff model performance. The Kling-Gupta efficiency (RKG), 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 RKG is implicitly based on the assumptions of data linearity, data normality, and the absence of outliers. In this study, we propose a modification of RKG 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 RKG 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.