Over-Roof venting depth – GreenBuildingAdvisor

The question of how deep a ventilation space is required for over-roof ventilation in an extreme snow region (climate zone 7) to keep the underside of the roof sheathing close to the exterior temperature (to prevent ice damning) is required has come up—builder wants 1 1/2″? This particular roof has R-70 rigid above the roof deck, with R-50 rigid at the roof overhangs, a 7:12 slope, and the over-roof soffit venting at the fascia.  

In Dr Joe Lstiburek’s article BSD-102, (2006) he shows a 2×4 rafter creating the ventilation space. Peter J Arsenault  in a course sponsored Huber Engineering Woods an ZIP system® (12/2018) wrote A minimum 2″ airspace is then provided as an ‘over-roof’…The ventilation space also helps keep the underside  of the over-roof surface cold, thus avoiding snow melting and forming ice dams.”

So our question is whether there are any case studies or some sort of algorithm showing the best depth, for such a roof. Additionally whether slope is a factor in determining the best depth.

Thanks