Percent Bias (PBIAS) fit function

Calculates the absolute percent bias between observed and modelled values - the average tendency of the modelled values to be larger (positive bias) or smaller (negative bias) than the observed values, expressed as a percentage of the observed total:

Usage

pbias(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; absolute percent bias. Returns NA if the sum of obs is zero.

Details

$$\text{PBIAS} = 100 \times \left| \frac{\sum_{i=1}^n (\text{sim}_i - \text{obs}_i)}{\sum_{i=1}^n \text{obs}_i} \right|$$

Already 0 (perfect fit, no systematic bias) at its best and increasing as fit worsens in either direction, 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. The absolute value is used rather than the signed value, since an equally large over- or under-estimate is an equally poor fit - minimising the signed value would instead push the calibration towards the most negative (under-estimating) bias possible.

Unlike mae/rmse, it is expressed as a percentage of the observed total rather than in the variable's native units, which makes it directly comparable across variables with different units or magnitudes - similar to nse/kge in that respect. On its own it only captures systematic over/under-estimation, not timing, variability or shape - it is typically combined with NSE or KGE (which are largely insensitive to a consistent bias) rather than used alone. See Moriasi et al. (2007) for commonly used PBIAS performance thresholds.

Examples

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