The Kling-Gupta efficiency (KGE) is a metric used to evaluate the performance of hydrological models. It provides a more robust and balanced assessment compared to traditional metrics like the Nash-Sutcliffe efficiency (NSE).

Here's a breakdown of the KGE:

• The KGE aims to decompose model performance into three key components:
  • Correlation (r): Measures how well the simulated and observed values are linearly related.
  • Variability bias (α): Measures the ratio of the simulated standard deviation to the observed standard deviation.
  • Mean bias (β): Measures the ratio of the simulated mean to the observed mean.
• By considering these three aspects, the KGE provides a more comprehensive evaluation of model performance.

Formula:

The Kling-Gupta efficiency is calculated as:

$$ KGE = 1 - sqrt((r - 1)^2 + (α - 1)^2 + (β - 1)^2) $$

Where:

• $r$ is the Pearson correlation coefficient between simulated and observed values.
• $α = σ_sim / σ_obs$ (ratio of standard deviations).
• $β = μ_sim / μ_obs$ (ratio of means).
• $σ_sim$ is the standard deviation of the simulated values.
• $σ_obs$ is the standard deviation of the observed values.
• $μ_sim$ is the mean of the simulated values.
• $μ_obs$ is the mean of the observed values.

Interpretation:

• A KGE of 1 indicates perfect model performance.
• Higher KGE values indicate better model performance.
• Unlike the NSE, the KGE can effectively diagnose specific model deficiencies related to correlation, variability, or mean bias.
• The KGE is less sensitive to outliers than the NSE, making it more robust.