This study presents a multivariate bias correction method named R
2D
2 to adjust both the 1d-distributions and inter-variable/site dependence structures of climate simulations in a high-dimensional context, while providing some stochasticity. R
2D
2 is tested on temperature and precipitation reanalyses and illustrated on future simulations. In both cases, R
2D
2 is able to correct the spatial and physical dependence, opening proper use of climate simulations for impact (e.g. hydrological) models.
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