In general closed cell foam is the best choice for unvented cathedral ceilings.
Unvented roof unvented cathedral ceiling insulation.
It is also one of the most expensive and most building inspectors will not allow it to be left uncovered for fire code reasons.
Foil faced iso board can be cost effective insulation for finished attics and cathedral ceilings.
In particular using fiberglass insulation in an un vented cathedral ceiling is most likely to give way to discovery of advanced hidden damage and or mold over the life of the building and may give shorter roof shingle life as well as causing higher indoor temperatures than with a vented roof cavity design.
Moisture problems in unvented or poorly vented cathedral ceilings are not uncommon especially in cold climates where water vapor can enter the joist space and condense on the underside of the sheathing in cold weather.
Unvented attics and cathedral ceilings 2 air permeable insulation only irc r806 5 5 2 attic while the irc refers to this assembly as air permeable insulation only it also involves installation of rigid board insulation above the roof sheathing.
This document provides a brief description of different types of unvented roof assemblies and the benefits of unvented roof construction.
Rigid foam above roof sheathing you can install all of the insulation above the roof sheathing but the foam has to be thick enough to meet minimum code requirements for ceiling r value.
With an unvented cathedral ceiling it is critical to keep moist air and water vapor away from the roof sheathing where it can build up and lead to wood decay.
These assemblies are created by eliminating ventilation openings and moving the thermal moisture and air control boundaries to the plane of the roof deck.