README.md
In MBC: Multivariate Bias Correction of Climate Model Outputs

MBC is an R package for calibrating and applying univariate and multivariate bias correction algorithms for climate model simulations of multiple climate variables. Three iterative multivariate methods are supported: (i) MBC Pearson correlation (MBCp), (ii) MBC rank correlation (MBCr), and (iii) MBC N-dimensional probability density function transform (MBCn). The first two, MBCp and MBCr (Cannon, 2016), match marginal distributions and inter-variable dependence structure. Dependence structure can be measured either by the Pearson correlation (MBCp) or by the Spearman rank correlation (MBCr). The energy distance score (escore) is recommended for model selection. The third, MBCn (Cannon, 2018), which operates on the full multivariate distribution, is more flexible and can be considered to be a multivariate analogue of univariate quantile mapping. All aspects of the observed distribution are transferred to the climate model simulations. In each of the three methods, marginal distributions are corrected by the univariate change-preserving quantile delta mapping (QDM) algorithm (Cannon et al., 2015). Finally, an implementation of the Rank Resampling for Distributions and Dependences (R2D2) method introduced by Vrac (2018) is also included.

Cannon, A.J., 2018. Multivariate quantile mapping bias correction: An N-dimensional probability density function transform for climate model simulations of multiple variables. Climate Dynamics, 50(1-2):31-49. doi:10.1007/s00382-017-3580-6

Cannon, A.J., 2016. Multivariate bias correction of climate model output: Matching marginal distributions and inter-variable dependence structure. Journal of Climate, 29:7045-7064. doi:10.1175/JCLID-15-0679.1

Cannon, A.J., S.R. Sobie, and T.Q. Murdock, 2015. Bias correction of simulated precipitation by quantile mapping: How well do methods preserve relative changes in quantiles and extremes? Journal of Climate, 28:6938-6959. doi:10.1175/JCLI-D-14-00754.1

Francois, B., M. Vrac, A.J. Cannon, Y. Robin, and D. Allard, 2020. Multivariate bias corrections of climate simulations: Which benefits for which losses? Earth System Dynamics, 11:537-562. doi:10.5194/esd-11-537-2020

Vrac, M., 2018. Multivariate bias adjustment of high-dimensional climate simulations: the Rank Resampling for Distributions and Dependences (R2D2) bias correction. Hydrology and Earth System Sciences, 22:3175-3196. doi:10.5194/hess-22-3175-2018