Boundary layer growth and advection of heat over snow and soil patches: Modelling and parametrization

Melting snow is generally patchy; upward sensible heat fluxes from patches of snow-free ground warm the air and contribute energy for snowmelt. A simple model is presented for advection of heat over partial snowcovers and compared with measurements of temperature profiles over snow and snow-free ground. Approximations for flux and temperature profiles in the internal boundary layers over snow patches are used to develop parametrizations for local and average surface fluxes into the snow. In comparison with results from the advection model for regular patterns of alternating snow patches and snow-free ground, a tile model is found to give a good parametrization for average heat fluxes over the whole surface but does not match the local fluxes into snow and snow-free ground separately; an extended tile model that gives better results is developed from the flux profile parametrization. For complex snowcover patterns with a fractal distribution of patch sizes, average fluxes are found to be close to those obtained for a regular pattern with an effective patch size linearly related to the average patch size of the complex pattern.