After a spring snowstorm the snow mostly had melted. As I walked along the campus sidewalk, I noticed the remaining piles of snow contained many sharp edges. Dirt accumulated mostly on these edges. This seemed odd, because the snow should melt more quickly where dirty and keep such edges from forming.
Once observed it appeared again and again in melting piles of snow. It happened in the shade too. What happens if the snow sublimes, I wondered? Does the sublimating (solid to gas) surface move perpendicular to the plane of the surface?
Here is a smooth model surface. Each point on the surface will be moved perpendiculat to the local plane of the surface. The direction is generally downward, as in melting snow.
After moving the surface, the valleys become more broad and the peaks more pointed.
After more motion the surface near the peaks crosses itself. This produces an unphysical plateau, which disappears upon melting. Of course any dirt on this surface will deposit on the sharp crest separating the broad valleys below.
Patterns in Snow