The Kling–Gupta efficiency (KGE) is a
goodness-of-fit
The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measure ...
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
The Nash–Sutcliffe model efficiency coefficient (NSE) is used to assess the predictive skill of hydrological models. It is defined as:
:
\text =1-\frac
where \overline_o is the mean of observed discharges, Q_m^t is modeled discharge at time ...
.
:
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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