Modified Kling-Gupta Efficiency (KGE') fit function

As kge, but replaces the raw variability ratio with a coefficient-of-variation ratio (Kling et al. 2012):

Usage

kge_prime(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.

Details

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

where the coefficient-of-variation ratio (\(\gamma\)) decouples the variability term from the bias term more cleanly:

$$\gamma = \frac{\sigma_{\text{sim}} / \mu_{\text{sim}}}{\sigma_{\text{obs}} / \mu_{\text{obs}}}$$

This is generally the recommended default over the original KGE. Returned in its conventional orientation where higher is better (1 = perfect fit).

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

See also

kge_prime_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_prime(obs, sim)
#> [1] 0.9661881