Abstract
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 viewed as bad model performance, and only 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, modellers who use the KGE metric 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. More generally, a strong case can be made for moving away from ad hoc use of aggregated efficiency metrics and towards a framework based on purpose-dependent evaluation metrics and benchmarks that allows for more robust model adequacy assessment.
Highlights
Model performance criteria are often used during calibration and evaluation of hydrological models, to express in a single number the similarity between observed and simulated discharge (Gupta et al, 2009)
There is a tendency in current literature to interpret Kling– Gupta efficiency (KGE) values in the same way as Nash– Sutcliffe efficiency (NSE) values: negative values indicate “bad” model performance, whereas positive values indicate “good” model performance
We show that the traditional mean flow benchmark that results in Nash–Sutcliffe efficiency (NSE) = 0 and the likely origin of√this “bad/good” model distinction, results in Kling–Gupta efficiency (KGE) = 1 − 2
Summary
Model performance criteria are often used during calibration and evaluation of hydrological models, to express in a single number the similarity between observed and simulated discharge (Gupta et al, 2009). It is not an representative benchmark for different flow regimes (for example, the mean is not representative of very seasonal regimes but it is a good approximation of regimes without a strong seasonal component; Schaefli and Gupta, 2007), and Published by Copernicus Publications on behalf of the European Geosciences Union It is a relatively arbitrary choice (for example, Moriasi et al, 2007, define several different NSE thresholds for different qualitative levels of model performance) that can influence the resultant prediction uncertainty bounds
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