KGE

Kling-Gupta Efficiency (KGE) is a statistical metric used in hydrology to evaluate how well a hydrological model reproduces observed time series. Proposed by Kling, Gupta, and Kaya in 2012, it is designed to capture multiple aspects of model performance in a single value while remaining interpretable for diagnostic purposes. It is commonly applied to rainfall-runoff modeling, streamflow simulations, and related hydrological analyses.

KGE combines three components: the correlation between simulated and observed data, the relative agreement of their variability, and the alignment of their means. It is defined as: KGE = 1 - sqrt( (r - 1)^2 + (α - 1)^2 + (β - 1)^2 ), where r is the Pearson correlation between the simulated and observed series, α is the ratio of the standard deviation of the simulated data to that of the observed data (α = σ_S / σ_O), and β is the ratio of the mean of the simulated data to the mean of the observed data (β = μ_S / μ_O).

Interpretation of KGE values follows the idea that values closer to 1 indicate better agreement between simulated and observed time series. Values can be less than zero if the model performs poorly. Because KGE integrates correlation, amplitude, and mean bias, it provides a diagnostic tool: its components can be examined separately to identify whether misfit stems from timing and shape (r), variability (α), or bias in level (β).

Limitations include sensitivity to outliers, dependence on data aggregation and time step, and potential ambiguities when the three components trade off. Consequently, KGE is often used alongside other metrics to provide a more complete model assessment.