The parameterization of heat and momentum fluxes over a heterogeneous surface consisting of sea ice and large areas of open ocean (polynyas) has been studied. Various theories required to calculate grid-averaged fluxes are discussed, and a two-dimensional mesoscale boundary layer model has been applied to simulate the flow and heat exchange processes inside a single grid element of a hypothetical atmospheric general circulation model. The theories are compared with model results. Considering the surface fluxes of sensible and latent heat, a mosaic method, based on the use of estimates for local surface temperature, air temperature, specific humidity, and wind speed over the ice-covered and ice-free parts of the grid square, performed well in the comparison. Parameterizing the net longwave radiation, an estimate for the subgrid distribution of cloudiness was useful. Parameterization of surface momentum flux seemed to be most reasonable on the basis of the surface pressure field and a geostrophic drag coefficient depending on the air-surface temperature difference. ¿ American Geophysical Union 1995