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The Arctic has warmed more rapidly than the global mean during the past few decades. The lapse rate feedback (LRF) has been identified as being a large contributor to the Arctic amplification (AA) of climate change. This particular feedback arises from the vertically non-uniform warming of the troposphere, which in the Arctic emerges as strong near-surface and muted free-tropospheric warming. Stable stratification and meridional energy transport are two characteristic processes that are evoked as causes for this vertical warming structure. Our aim is to constrain these governing processes by making use of detailed observations in combination with the large climate model ensemble of the sixth Coupled Model Intercomparison Project (CMIP6). We build on the result that CMIP6 models show a large spread in AA and Arctic LRF, which are positively correlated for the historical period of 1951–2014. Thus, we present process-oriented constraints by linking characteristics of the current climate to historical climate simulations. In particular, we compare a large consortium of present-day observations to co-located model data from subsets that show a weak and strong simulated AA and Arctic LRF in the past. Our analyses suggest that the vertical temperature structure of the Arctic boundary layer is more realistically depicted in climate models with weak (w) AA and Arctic LRF (CMIP6/w) in the past. In particular, CMIP6/w models show stronger inversions in the present climate for boreal autumn and winter and over sea ice, which is more consistent with the observations. These results are based on observations from the year-long Multidisciplinary Drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition in the central Arctic, long-term measurements at the Utqiaġvik site in Alaska, USA, and dropsonde temperature profiling from aircraft campaigns in the Fram Strait. In addition, the atmospheric energy transport from lower latitudes that can further mediate the warming structure in the free troposphere is more realistically represented by CMIP6/w models. In particular, CMIP6/w models systemically simulate a weaker Arctic atmospheric energy transport convergence in the present climate for boreal autumn and winter, which is more consistent with fifth generation reanalysis of the European Centre for Medium-Range Weather Forecasts (ERA5). We further show a positive relationship between the magnitude of the present-day transport convergence and the strength of past AA. With respect to the Arctic LRF, we find links between the changes in transport pathways that drive vertical warming structures and local differences in the LRF. This highlights the mediating influence of advection on the Arctic LRF and motivates deeper studies to explicitly link spatial patterns of Arctic feedbacks to changes in the large-scale circulation. [ABSTRACT FROM AUTHOR]