Boundary-layer growth and advection of heat over snow and soil patches: modelling and parameterization

Melting snow is generally patchy; upward sensible heat fluxes from patches of snow-free around warm the air and contribute energy for snowmelt. A simple model is presented for advection of heat over partial snow covers 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 parameterizations 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 parameterization for average heat fluxes over the whole surface, but it 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 parameterization. For complex snow-cover 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. Copyright (c) 2006 Environment Canada. Published by John Wiley & Sons, Ltd.