In this paper we evaluated the Weather Research and Forecasting (WRF) mesoscale meteorological model for stable conditions at clear skies with low wind speeds. Three contrasting terrains with snow covered surfaces are considered, namely Cabauw (Netherlands, snow over grass), Sodankylä (Finland, snow over a needle-leaf forest) and Halley (Antarctica, snow over an ice shelf). We used the full 3D model and the single-column versions of the WRF model. The SCM was driven by realistic forcings of the WRF-3D field. Several sets of SCM forcings were tested: A. no advection, B. varying geostrophic wind in time, C. momentum advection in addition to B, D. temperature and moisture advection in addition to C, and E. forcing the SCM field to the 3D field above a threshold height. The WRF-3D model produced overall good results for wind speed, but the near-surface temperatures and specific humidity were overestimated for Cabauw and Sodankylä, and underestimated for Halley. Prescribing advection for momentum, temperature and moisture gave the best results for the WRF-SCM, and simulations deviated strongly from reality without advection. Nudging the SCM field to the 3D field above a threshold height lead to an unrealistic behaviour of the variables below this height and is not recommended. Detailed prescription of the surface characteristics, e.g. adjusting the snow cover and vegetation fraction, improved the 2¿m temperature simulation. For all three sites, the simulated temperature and moisture inversion was underestimated, though this improved when prescribing advection. Overall, in clear-sky conditions, the stable boundary layer over snow and ice can be modelled to a good approximation if all processes are taken into account at high resolution, and if land surface properties are carefully prescribed.