earthkit.meteo.score.kge¶

earthkit.meteo.score.kge(fcst, obs, over, method='original', return_components=False)¶

Calculates the Kling-Gupta Efficiency (KGE) between a forecast and observations.

Warning

Experimental API. This function may change or be removed without notice.

The KGE is defined as follows:

\begin{align*} \text{KGE} = & \begin{cases} 1 - \sqrt{(\rho - 1)^2 + (\alpha - 1)^2 + (\beta - 1)^2} & \text{if method = "original"} \\ 1 - \sqrt{(\rho - 1)^2 + (\gamma - 1)^2 + (\beta - 1)^2} & \text{if method = "modified"} \\ \end{cases} \end{align*}

Each of the components of the KGE is defined as follows:

\[\beta = \frac{\mu_f}{\mu_o} \alpha = \frac{\sigma_f}{\sigma_o} \gamma = \frac{\alpha}{\beta}\]

where:

\(\rho\) = Pearson’s correlation coefficient between observed and forecast values.
\(f\) and \(o\) are forecast and observed values, respectively
\(\mu_f\) and \(\mu_o\) are the means of forecast and observed values, respectively
\(\sigma_f\) and \(\sigma_o\) are the standard deviations of forecast and observed values, respectively