Kling-Gupta efficiency

This goodness-of-fit measure was developed by Gupta et al. (2009) to provide a diagnostically interesting decomposition of the Nash-Sutcliffe efficiency (and hence MSE), which facilitates the analysis of the relative importance of its different components (correlation, bias and variability) in the context of hydrological modelling Kling et al. (2012), proposed a revised version of this index, to ensure that the bias and variability ratios are not cross-correlated.

where CC is the Pearson coefficient value and rm is the average of observed values and cm is average of forecast values and rd is standard deviation of observation values and cd is standard deviation of forecast values.