Empirical quantile-mapping bias correction (QUANT)

x' = F_obs^{-1}(F_mod(x)) (Gudmundsson et al. 2012, Eq. 2) with both distributions empirical: piecewise-linear type-7-consistent CDF and quantile function (percentile tables + linear interpolation, Boe et al. 2007 procedure; beyond-range values take the extreme trained quantile). Mapping a sample onto itself is the identity; a pure shift is recovered exactly (test anchors).

Usage

Qmds(x_mod, obs, mod)

Arguments

x_mod

Modelled values to correct.

obs

Observed calibration sample.

mod

Modelled calibration sample.

Value

List with estimate, probs, n_obs, n_mod, method.

References

Gudmundsson, L., Bremnes, J. B., Haugen, J. E. and Engen-Skaugen, T. (2012), HESS 16, 3383-3390, doi:10.5194/hess-16-3383-2012 , Eq. 2, Sec. 2.3.1. Wood et al. (2004) Climatic Change 62, 189-216; Boe et al. (2007) Int J Climatology 27, 1643-1655; Maraun (2013) J Climate 26, 2137-2143.

Examples

Qmds(x_mod = c(1, 2, 3, 4, 5, 6, 7, 8), obs = c(1, 2, 3, 4, 5, 6, 7, 8),
  mod = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $estimate
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $probs
#> [1] 0.0000000 0.1428571 0.2857143 0.4285714 0.5714286 0.7142857 0.8571429
#> [8] 1.0000000
#> 
#> $n_obs
#> [1] 8
#> 
#> $n_mod
#> [1] 8
#> 
#> $method
#> [1] "empirical quantile mapping x' = F_obs^-1(F_mod(x)) (Gudmundsson 2012 Eq. 2, QUANT)"
#>