A case study of warm air advection over the Arctic marginal sea-ice zone is presented, based on aircraft observations with direct flux measurements carried out in early spring, 1998. A shallow atmospheric boundary layer (ABL) was observed, which was gradually cooling with distance downwind of the ice edge. This process was mainly connected with a strong stable stratification and downward turbulent heat fluxes of about 10-20 W m-2, but was also due to radiative cooling. Two mesoscale models, one hydrostatic and the other non-hydrostatic, having different turbulence closures, were applied. Despite these fundamental differences between the models, the results of both agreed well with the observed data. Various closure assumptions had a more crucial influence on the results than the differences between the models. Such an assumption was, for example, the parameterization of the surface roughness for momentum (zO) and heat (zT). This strongly affected the wind and temperature fields not only close to the surface but also within and above the temperature inversion layer. The best results were achieved using a formulation for zO that took into account the form drag effect of sea-ice ridges together with zT = 0.1 zO. The stability within the elevated inversion strongly depended on the minimum eddy diffusivity Kmin. A simple ad hoc parameterization seems applicable, where Kmin is calculated as 0.005 times the neutral eddy diffusivity. Although the longwave radiative cooling was largest within the ABL, the application of a radiation scheme was less important there than above the ABL. This was related to the interaction of the turbulent and radiative fluxes. To reproduce the strong inversion, it was necessary to use vertical and horizontal resolutions higher than those applied in most regional and large-scale atmospheric models.