Snow Sublimation

If you live in an area with snow, you’ve probably experienced a snowfall followed by several cold clear days. If it lasted long enough, you may have noticed that the snow gradually starts to disappear (sublimate) even when the air temperature never gets above the melting point. In this post, we’ll look at the speed of that effect.
An approach to estimating the rate of sublimation from Grigull and Sandner results in this approximate expression for the speed of recession of the snow surface: 

where q” is the heat flux, ρ is the density, and h_sg is the heat of sublimation. Now, the density of snow is a tricky thing to get a handle on because it varies from almost ice: ~700-800 kg/m³ for heavy wet snow down to ~50-70 kg/m³ for light fluffy snow. The heat flux is going to have a wide variation as well. Most of the time, we wouldn’t be considering snow on the equator. Let’s think about the 45th parallel which, in the U.S. goes through Oregon, Idaho, and Minneapolis. At that latitude, noonday sun provides about 120 W/m² at the winter solstice and about 300 W/m² at the equinox. We also probably wouldn’t be considering snow in midsummer. Of course, those are only the daily peak heat fluxes, and we need to account for the fact that there is zero heat flux at night, and it builds up to the peak and then diminishes through the day. 

This figure shows the rate of surface sublimation of snow for a range of snow densities and daily peak solar heat fluxes. The shaded area corresponds to settled, but fairly dry snow. Of course, wind, temperature variations, and partial shade or cloud cover would modify these numbers by a lot.

Reference Grigull, U., Sandner, H., Heat Conduction, Hemisphere Publishing Corporation, 1984.