Kling–Gupta efficiency

The Kling–Gupta efficiency (KGE) is a goodness-of-fit indicator widely used in the hydrologic sciences for comparing simulations to observations. It was created by hydrologic scientists Harald Kling and Hoshin Vijai Gupta.^[1] Its creators intended for it to improve upon widely used metrics such as the coefficient of determination and the Nash–Sutcliffe model efficiency coefficient.

{\text{KGE}}=1-{\sqrt {(r-1)^{2}+(\alpha -1)^{2}+(\beta -1)^{2}}}

where:

${\textstyle r}$ is the Pearson correlation coefficient,
${\textstyle \alpha }$ is a term representing the variability of prediction errors,
${\textstyle \beta }$ is a bias term.

The terms ${\textstyle \alpha }$ and ${\textstyle \beta }$ are defined as follows:

\beta ={\frac {\mu _{s}}{\mu _{o}}}

where:

${\textstyle \mu _{s}}$ is the mean of the simulated time series (e.g.: flows predicted by the model)
${\textstyle \mu _{o}}$ is the mean of the observed time series

and

\alpha ={\frac {\sigma _{s}}{\sigma _{o}}}

where:

${\textstyle \sigma _{s}^{2}}$ is the variance of the simulated time series, so ${\textstyle \sigma _{s}}$ is estimated by the standard deviation of simulated data.
${\textstyle \sigma _{o}^{2}}$ is the variance of the observed time series

A modified version, KGE', was proposed by Kling et al. in 2012.^[2]

References

^ Gupta, Hoshin Vijai; Kling, Harald (2011). "On typical range, sensitivity, and normalization of Mean Squared Error and Nash–Sutcliffe Efficiency type metrics". Water Resources Research. 47 (10). Bibcode:2011WRR....4710601G. doi:10.1029/2011WR010962. ISSN 1944-7973. S2CID 119636876. Retrieved 2023-08-24.
^ Kling, Harald; Fuchs, Martin; Paulin, Maria (2012). "Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios". Journal of Hydrology. 424: 264–277. Bibcode:2012JHyd..424..264K. doi:10.1016/j.jhydrol.2012.01.011.

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