Kling–Gupta efficiency

{{Short description|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.{{Cite journal| doi = 10.1029/2011WR010962| issn = 1944-7973| volume = 47| issue = 10| last1 = Gupta| first1 = Hoshin Vijai| last2 = Kling| first2 = Harald| title = On typical range, sensitivity, and normalization of Mean Squared Error and Nash–Sutcliffe Efficiency type metrics| journal = Water Resources Research| accessdate = 2023-08-24| date = 2011| bibcode = 2011WRR....4710601G| s2cid = 119636876| url = https://onlinelibrary.wiley.com/doi/abs/10.1029/2011WR010962| url-access = subscription}} 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:

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

The terms $\backslash alpha$ and $\backslash beta$ are defined as follows:

:$$

\beta=\frac{\mu_s}{\mu_o}

where:

• $\backslash mu\_s$ is the mean of the simulated time series (e.g.: flows predicted by the model)
• $\backslash mu\_o$ is the mean of the observed time series

and

:$$

\alpha = \frac{\sigma_s}{\sigma_o}

where:

• $\backslash sigma\_s^2$ is the variance of the simulated time series, so $\backslash sigma\_s$ is estimated by the standard deviation of simulated data.
• $\backslash sigma\_o^2$ is the variance of the observed time series

A modified version, KGE', was proposed by Kling et al. in 2012.{{Cite journal| doi = 10.1016/j.jhydrol.2012.01.011| volume = 424| pages = 264–277| last1 = Kling| first1 = Harald| last2 = Fuchs| first2 = Martin| last3 = Paulin| first3 = Maria| title = Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios| journal = Journal of Hydrology| date = 2012| bibcode = 2012JHyd..424..264K}}