Bias-corrects a modelled series by \(x' = F_{obs}^{-1}(F_{mod}(x))\) (Gudmundsson et al. 2012, eq. 2) using empirical percentile tables with linear interpolation. Because the CDF and quantile function used are exact inverses of one another, mapping the calibration sample onto itself returns it unchanged and a constant offset between model and observations is removed exactly.
Value
A list with estimate (corrected values),
probs (the intermediate CDF values), n_obs,
n_mod, method.
References
Gudmundsson, L. et al. (2012). Technical note: downscaling RCM precipitation to the station scale. Hydrology and Earth System Sciences, 16, 3383-3390.
Examples
morie_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)"
#>