Kling-Gupta Efficiency (KGE) fit function

Calculates the Kling-Gupta Efficiency (Gupta et al. 2009) between observed and modelled values, in its conventional orientation where higher is better (1 = perfect fit).

Usage

kge(obs, sim, na.rm = TRUE)

Arguments

obs

Numeric vector of observed values.

sim

Numeric vector of simulated (modelled) values.

na.rm

Logical; should missing values (NA) in either vector be removed pairwise before computation? Default is TRUE.

Value

numeric; KGE, with a maximum of 1 (perfect fit). Returns NA if undefined (e.g., zero observed variance or mean).

Details

KGE decomposes fit into three components instead of conflating them the way nse's single squared-error term does:

$$\text{KGE} = 1 - \sqrt{(r - 1)^2 + (\alpha - 1)^2 + (\beta - 1)^2}$$

where the variability ratio (\(\alpha\)) and bias ratio (\(\beta\)) are calculated as:

$$\alpha = \frac{\sigma_{\text{sim}}}{\sigma_{\text{obs}}}, \quad \beta = \frac{\mu_{\text{sim}}}{\mu_{\text{obs}}}$$

with \(r\) being the Pearson correlation, \(\sigma\) the standard deviation, and \(\mu\) the mean. Maximum is 1 (perfect fit). Being dimensionless like NSE, it is also a reasonable choice when combining fit values across variables with different units or magnitudes, and is generally preferred over NSE in current hydrological/environmental modelling practice.

calib_aeme() and run_and_fit() minimise the values returned by FUN_list entries - use kge_loss (which returns -1 * kge(obs, sim)) as a calibration objective.

See also

kge_loss for the minimise-oriented variant used in FUN_list.

Examples

obs <- c(1, 2, 3, 4)
sim <- c(1.1, 2.1, 2.9, 4.2)
kge(obs, sim)
#> [1] 0.9663051