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.
:
where:
*
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 ...
,
*
is a term representing the variability of prediction errors,
*
is a bias term.
The terms
and
are defined as follows:
:
where:
*
is the mean of the simulated time series (e.g.: flows predicted by the model)
*
is the mean of the observed time series
and
:
where:
*
is the variance of the simulated time series, so
is estimated by the standard deviation of simulated data.
*
is the variance of the observed time series
A modified version, KGE', was proposed by Kling et al. in 2012.
References
Hydrology models
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