Aircraft observations from two Arctic field campaigns are used to characterize and model surface heat and moisture exchange over the marginal ice zone (MIZ). We show that the surface roughness lengths for heat and moisture over uninterrupted sea ice vary with roughness Reynolds number (R*; itself a function of the roughness length for momentum, z0, and surface wind stress), with a peak at the transition between aerodynamically smooth (R*<0.135) and aerodynamically rough (R*>2.5) regimes. A pre-existing theoretical model based on surface-renewal theory accurately reproduces this peak, in contrast to the simple parameterizations currently employed in two state-of-the-art numerical weather prediction models, which are insensitive to R*. We propose a new, simple parameterization for surface exchange over the MIZ that blends this theoretical model for sea ice with surface exchange over water as a function of sea ice concentration. In offline tests, this new scheme performs much better than the existing schemes for the rough conditions observed during the 'Iceland Greenland Seas Project' field campaign. The bias in total turbulent heat flux across the MIZ is reduced to only 13 W m(-2) for the new scheme, from 48 and 80 W m(-2) for the Met Office Unified Model and ECMWF Integrated Forecast System schemes, respectively. It also performs marginally better for the comparatively smooth conditions observed during the 'Aerosol-Cloud Coupling and Climate Interactions in the Arctic' field campaign. The new surface exchange scheme has the benefit of being physically-motivated, comparatively accurate and straightforward to implement, although to reap the full benefits an improvement to the representation of sea ice topography via z0 is required.