A model performance score that combines correlation, bias and variability errors into one number, with 1 as a perfect fit.
The Kling-Gupta efficiency (KGE) is a score for comparing simulated and observed time series, most often streamflow. It was introduced by Gupta, Kling, Yilmaz and Martinez in 2009 as an answer to problems with the Nash-Sutcliffe efficiency. A modified version, often written KGE', was proposed by Kling and colleagues in 2012. KGE splits model error into three parts. The correlation r shows whether the timing and shape of the hydrograph are right. The variability ratio α is the standard deviation of the simulation divided by that of the observations. The bias ratio β is the mean of the simulation divided by the mean of the observations. A perfect model has r, α and β all equal to 1. KGE measures the distance from that ideal point and subtracts it from 1. In KGE', α is replaced by the ratio of the coefficients of variation, so bias and variability errors do not overlap. For example, a model with r = 0.9, α = 0.8 and β = 1.1 gives (0.9 - 1)² + (0.8 - 1)² + (1.1 - 1)² = 0.01 + 0.04 + 0.01 = 0.06. The square root is 0.245, so KGE = 1 - 0.245 = 0.755. Looking at the parts shows the main fault is that the model underestimates the spread of flows. KGE ranges from minus infinity to 1. Unlike NSE, KGE = 0 does not mark the mean flow benchmark. A model that predicts the observed mean at every step scores about -0.41, so KGE values between -0.41 and 0 still beat the mean. KGE and NSE values should not be compared directly. KGE gives the three parts equal weight, which may not suit every purpose; weighted versions exist. Its correlation and standard deviation terms are still driven mainly by high flows, so it can hide poor low-flow performance. Reporting r, α and β next to the total makes the score more useful.