Over-Roof venting depth

This is a homeowner forum question, not a finished project or study, so there's no new program or product to report — just a technical question worth understanding if you have a snow-prone roof with a lot of foam insulation added on top.

The question comes from someone building a roof in a very cold, heavy-snow region (climate zone 7) who is adding thick rigid foam insulation above the existing roof deck — R-70 over the main roof, R-50 at the overhangs, on a steep 7:12 slope. Above that foam, builders often add a narrow gap, called "over-roof venting," that lets outside air flow between the foam and the new roof surface. The point is to keep the top layer of the roof at outdoor temperature, so snow on the roof doesn't melt from below and refreeze at the eaves as ice dams. The builder in this case wants to make that gap only 1.5 inches deep, while some published sources call for 2 inches or a full 2x4-deep space (roughly 3.5 inches).

The homeowner asking wants to know if there's real data or a formula for how deep that vent gap needs to be, and whether roof slope changes the answer. No such study or rule is cited in the discussion yet. If you're planning a similar over-roof foam job in a cold, snowy climate, this is the kind of detail worth asking about, since gap depth affects how well the system prevents ice dams.