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Discussion papers | Copyright
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Technical note 08 Jun 2018

Technical note | 08 Jun 2018

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

Technical note: Pitfalls in using log-transformed flows within the KGE criterion

Léonard Santos, Guillaume Thirel, and Charles Perrin Léonard Santos et al.
  • Irstea, HYCAR Research Unit, 1 rue Pierre-Gilles de Gennes, 92160 Antony, France

Abstract. Log-transformed discharge is often used to calculate performance criteria to better focus on low flows. This prior transformation limits the heteroscedasticity of model residuals and was largely applied in criteria based on squared residuals, like Nash-Sutcliffe efficiency (NSE). In the recent years, NSE has been shown to have mathematical limitations and Kling-Gupta efficiency (KGE) was proposed as an alternative to provide more balance between the expected qualities of a model (namely representing the water balance, flow variability and correlation). As in the case of NSE, several authors used the KGE criterion (or its improved version KGE') with a prior logarithmic transformation on flows. However, we show that the use of this transformation is not adapted to the case of the KGE (or KGE') criterion and may lead to several numerical issues, potentially resulting in a biased evaluation of model performance. We present the theoretical underpinning aspects of these issues and concrete modelling examples, showing that KGE' computed on log-transformed flows should be avoided. Alternatives are discussed.

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Short summary
The Kling and Gupta Efficiency (KGE) is a score used in hydrology to evaluate flow simulation compared to observations. In order to force the evaluation on the low-flows, some authors used the log-transformed flow to calculate the KGE. In this technical note, we show that this transformation should be avoided because it produce numerical flaws that lead to difficulties in the score value interpretation.
The Kling and Gupta Efficiency (KGE) is a score used in hydrology to evaluate flow simulation...