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The Greenland Ice Sheet is a key contributor to sea level rise. By melting, the ice sheet thins, inducing higher surface melt due to lower surface elevations, accelerating the melt coming from global warming. This process is called the melt–elevation feedback and can be considered by using two types of models: either (1) atmospheric models, which can represent the surface mass balance (SMB), or SMB estimates resulting from simpler models such as positive degree day models or (2) ice sheet models representing the surface elevation evolution. The latter ones do not represent the surface mass balance explicitly as well as polar-oriented climate models. A new coupling between the MAR (Modèle Atmosphérique Régional) regional climate model and the PISM (Parallel Ice Sheet Model) ice sheet model is presented here following the CESM2 (Community Earth System Model; SSP5-8.5, Shared Socioeconomic Pathway) scenario until 2100 at the MAR lateral boundaries. The coupling is extended to 2200 with a stabilised climate (+7 ∘C compared to 1961–1990) by randomly sampling the last 10 years of CESM2 to force MAR and reaches a sea level rise contribution of 64 cm. The fully coupled simulation is compared to a one-way experiment where surface topography remains fixed in MAR. However, the surface mass balance is corrected for the melt–elevation feedback when interpolated on the PISM grid by using surface mass balance vertical gradients as a function of local elevation variations (offline correction). This method is often used to represent the melt–elevation feedback and prevents a coupling which is too expensive in computation time. In the fully coupled MAR simulation, the ice sheet morphology evolution (changing slope and reducing the orographic barrier) induces changes in local atmospheric patterns. More specifically, wind regimes are modified, as well as temperature lapse rates, influencing the melt rate through modification of sensible heat fluxes at the ice sheet margins. We highlight mitigation of the melt lapse rate on the margins by modifying the surface morphology. The lapse rates considered by the offline correction are no longer valid at the ice sheet margins. If used (one-way simulation), this correction implies an overestimation of the sea level rise contribution of 2.5 %. The mitigation of the melt lapse rate on the margins can only be corrected by using a full coupling between an ice sheet model and an atmospheric model.