Bias Correction for the Unbiased Mapping of GCM Changes to Local Stations, Preserving the Changes in Variability from Raw GCMs

Quantile mapping bias correction algorithms are commonly used to correct systematic distributional biases in precipitation and temperature outputs from General Circulation Models (GCMs). These methods perform well at removing the bias of the mean and the standard deviation in the historical period, although these methods have been reported to distort the raw GCM changes, incorporating unwanted bias. Most of the quantile mapping methods have focused on the mean quantities, without paying attention to changes in the rest of the distribution nor the standard deviation. An exception to this is the quantile delta mapping (QDM), which explicitly preserves the relative changes in precipitation quantiles. Nonetheless, because QDM does not take into account changes in the standard deviation of the GCMs, bias due to big changes in the standard deviation of a GCM output cannot be corrected by QDM. In this work we propose a new method referred to as unbiased quantile mapping (UQM), which by construction preserves the changes of the moments of the GCMs. As a results UQM, just as QDM, preserves relative changes in precipitation quantiles of the raw GCMs. This work uses synthetic experiment to compare the performance of the UQM method against QDM, the standard quantile mapping (QM) and the detrended quantile mapping (DQM) methods. The results show how UQM is the only bias correction method that captures the changes in both the mean and the standard deviation from the GCMs. Finally, the performance of the proposed method is further studied using several GCMs in a variety of locations.