Bias adjustment to preserve changes in variability: the unbiased mapping of GCM changes

Standard quantile mapping (QM) performs well, as a bias adjustment method, in removing historical climate biases, but it can significantly alter a global climate model (GCM) signal. Methods that do incorporate GCM changes commonly consider mean changes only. Quantile delta mapping (QDM) is an exception, as it explicitly preserves relative changes in the quantiles, but it might present biases in preserving GCMs changes in standard deviation. In this work we propose the unbiased quantile mapping (UQM) method, which by construction preserves GCM changes of the mean and the standard deviation. Synthetic experiments and four Chilean locations are used to compare the performance of UQM against QDM, QM, detrended quantile mapping, and scale distribution mapping. All the methods outperform QM, but a tradeoff exists between preserving the GCM relative changes in the quantiles (QDM is recommended in this case), or changes in the GCM moments (UQM is recommended in this case).