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As part of the CORDEX project, the fifth-generation Canadian Regional Climate Model (CRCM5) is used over the Arctic for climate simulations driven by reanalyses and by the MPI-ESM-MR coupled global climate model (CGCM) under the RCP8.5 scenario. The CRCM5 shows adequate skills capturing general features of mean sea level pressure (MSLP) for all seasons. Evaluating 2-m temperature (T2m) and precipitation is more problematic, because of inconsistencies between observational reference datasets over the Arctic that suffer of a sparse distribution of weather stations. In our study, we additionally investigated the effect of large-scale spectral nudging (SN) on the hindcast simulation driven by reanalyses. The analysis shows that SN is effective in reducing the spring MSLP bias, but otherwise it has little impact. We have also conducted another experiment in which the CGCM-simulated sea-surface temperature (SST) is empirically corrected and used as lower boundary conditions over the ocean for an atmosphere-only global simulation (AGCM), which in turn provides the atmospheric lateral boundary conditions to drive the CRCM5 simulation. This approach, so-called 3-step approach of dynamical downscaling (CGCM-AGCM-RCM), which had considerably improved the CRCM5 historical simulations over Africa, exhibits reduced impact over the Arctic domain. The most notable positive effect over the Arctic is a reduction of the T2m bias over the North Pacific Ocean and the North Atlantic Ocean in all seasons. Future projections using this method are compared with the results obtained with the traditional 2-step dynamical downscaling (CGCM-RCM) to assess the impact of correcting systematic biases of SST upon future-climate projections. The future projections are mostly similar for the two methods, except for precipitation. [ABSTRACT FROM AUTHOR]