Inter-variable dependencies are key properties to characterise many climate phenomena - such as compound events - and their future changes. Yet, climate simulations often have statistical biases. Hence, univariate (1dBC) and multivariate bias correction (MBC) methods are regularly applied. Inter-variable properties (e.g., correlations) can be altered by BC corrections. Then, it is necessary to assess how hypotheses of BC methods on climate change affect the adjustments. This can lead to better choices of BC methods. Here, we investigate whether an MBC method should try reproducing, preserving or modifying the changes in rank correlations between daily temperature and precipitation over Europe. An original “perfect model experiment” is set up and applied to two different climate simulation ensembles over 2001-2100: 40 runs from the CESM global climate model and 11 runs from the CMIP6 exercise. The results highlight that, within the multi-run single GCM ensemble (CESM), accounting for correlation changes bring valuable information for long-term projections but that a stationary hypothesis provides less biased correlations, up to medium-term projections (2060). For the multi-model ensemble (CMIP6), the non-stationary hypothesis provides larger biases than the stationary approach, up to the end of the century. Not correcting the model rank correlations (1dBC) provides the worst results. Whenever an ensemble is available, the best results come from accounting for the “robust’ part of the change signal (i.e., average change from different runs). This pleads for using ensembles and their robust information, in order to perform robust bias corrections.
