Kling–Gupta efficiency - Misplaced Pages

Performance indicator for hydrologic models

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. 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.

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.

This statistics-related article is a stub. You can help Misplaced Pages by expanding it.

This hydrology article is a stub. You can help Misplaced Pages by expanding it.