Nash-Sutcliffe Efficiency (NSE) fit function

Calculates the Nash-Sutcliffe Efficiency between observed and modelled values, in its conventional orientation where higher is better (1 = perfect fit).

Usage

nse(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; NSE, ranging -Inf to 1 (1 = perfect fit). Returns NA if undefined (e.g., zero observed variance).

Details

NSE is calculated as: $$\text{NSE} = 1 - \frac{\sum_{i=1}^n (\text{obs}_i - \text{sim}_i)^2}{\sum_{i=1}^n (\text{obs}_i - \bar{\text{obs}})^2}$$

It ranges from -Inf to 1 (1 = perfect fit, 0 = no better than the mean of the observations). It is dimensionless, which makes it a reasonable default when combining fit values across variables with different units or magnitudes - but it is squared-error based, so it over-weights peaks and under-weights errors in the low/baseline range, and it conflates bias, variability and timing error into one number. See kge/kge_prime for a fit function that keeps those separate.

calib_aeme() and run_and_fit() minimise the values returned by FUN_list entries, so nse() is not suitable as a calibration objective directly - use nse_loss (which returns -1 * nse(obs, sim)) for that.

See also

nse_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)
nse(obs, sim)
#> [1] 0.986