Mean Absolute Error (MAE) fit function

Calculates the mean absolute error between observed and modelled values:

Usage

mae(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; mean absolute error, in the same units as obs/sim.

Details

$$\text{MAE} = \frac{1}{n} \sum_{i=1}^n |\text{sim}_i - \text{obs}_i|$$

Already 0 (perfect fit) at its best and increasing as fit worsens, so it is minimise-oriented as-is and needs no _loss companion - pass it straight into FUN_list, which calib_aeme and run_and_fit minimise.

MAE stays in the variable's native units, so it is not directly comparable across variables with different units or magnitudes - summing MAE from, say, a temperature fit (degC) and an oxygen fit (mg/L) in a multi-variable FUN_list lets whichever variable happens to have the larger natural magnitude dominate the combined fit. Prefer a dimensionless metric such as nse_loss or kge_loss when combining fits across variables; MAE/RMSE are more suited to single-variable calibration or to reporting fit in interpretable, original units.

Examples

obs <- c(1, 2, 3, 4)
sim <- c(1.1, 2.1, 2.9, 4.2)
mae(obs, sim)
#> [1] 0.125