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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/hess-2019-327
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2019-327
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Technical note 01 Jul 2019

Technical note | 01 Jul 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).

Technical note: Inherent benchmark or not? Comparing Nash-Sutcliffe and Kling-Gupta efficiency scores

Wouter J. M. Knoben1, Jim E. Freer2, and Ross A. Woods2 Wouter J. M. Knoben et al.
  • 1Department of Civil Engineering, University of Bristol, Bristol, BS8 1TR, United Kingdom
  • 2School of Geographical Science, University of Bristol, Bristol, BS8 1BF, United Kingdom

Abstract. A traditional metric used in hydrology to summarize model performance is the Nash-Sutcliffe Efficiency (NSE). Increasingly an alternative metric, the Kling-Gupta Efficiency (KGE), is used instead. When NSE is used, NSE = 0 corresponds to using the mean flow as a benchmark predictor. The same reasoning is applied in various studies that use KGE as a metric: negative KGE values are often viewed in the literature as bad model performance and positive values are seen as good model performance. Here we show that using the mean flow as a predictor does not result in KGE = 0, but instead KGE = 1−√2 ≈ −0.41. Thus, KGE values greater than −0.41 indicate that a model improves upon the mean flow benchmark – even if the model's KGE value is negative. NSE and KGE values cannot be directly compared, because their relationship is non-unique and depends in part on the coefficient of variation of the observed time series. Therefore, we argue that modellers should not let their understanding of NSE values guide them in interpreting KGE values and instead develop new understanding based on the constitutive parts of the KGE metric and the explicit use of benchmark values to compare KGE scores against.

Wouter J. M. Knoben et al.
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Wouter J. M. Knoben et al.
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Short summary
The accuracy of model simulations can be quantified with so-called efficiency metrics. The Nash-Sutcliffe efficiency (NSE) has been often used in hydrology, but recently the Kling-Gupta efficiency (KGE) is gaining in popularity. We show that lessons learned about which NSE scores are acceptable, do not necessarily translate well into understanding of the KGE metric.
The accuracy of model simulations can be quantified with so-called efficiency metrics. The...
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