Kling–Gupta Efficiency
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The Kling–Gupta efficiency (KGE) is a goodness-of-fit indicator widely used in the
hydrologic sciences Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and drainage basin sustainability. A practitioner of hydrology is called a hydro ...
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 In statistics, the coefficient of determination, denoted ''R''2 or ''r''2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s). It is a statistic used in t ...
and the Nash–Sutcliffe model efficiency coefficient. : \text =1-\sqrt where: * r is the
Pearson correlation coefficient In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviatio ...
, * \alpha is a term representing the variability of prediction errors, * \beta is a bias term. The terms \alpha and \beta are defined as follows: : \beta=\frac where: * \mu_s is the mean of the simulated time series (e.g.: flows predicted by the model) * \mu_o is the mean of the observed time series and : \alpha = \frac where: * \sigma_s^2 is the variance of the simulated time series, so \sigma_s is estimated by the standard deviation of simulated data. * \sigma_o^2 is the variance of the observed time series A modified version, KGE', was proposed by Kling et al. in 2012.


References

Hydrology models {{Hydrology-stub