Upward snow was described in the post JoEtzold linked. It involves the N node - examine the normal. If N.y is > 0, the surface is pointing upward. Helgard renamed the node to be called Snow Percentage, but it is still an N node.

Du and Dv are derivatives, describing the rate of change in U or V with respect to the rendered pixels. I have used these to some extent to anti-alias procedural shaders, sort of like texture filtering. The ones you want for measuring curvature would be dNdU and dNdV, but they don't really work for meshes.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)