The flat roof will be straightforward in the future because it can absorb the maximum of solar energy, independent on the orientation of the building. A flat roof on the other hand accumulates easily humidity in not-vapour-tight thermal insulation like XPS, EPS and mineral wool if there is no perfect vapour screen on the warm side. The perfect vapour screen does not exist and so perfect dry thermal insulation in a flat roof neither. Basically, the reason of this accumulation is the combination of a healthy humidity in house (50% relative), a cold winter and a waterproofing membrane induces humidity where the perfect vapour screen is absent (joints, poor labour, …)
For this reason, the cellular glass compact warm roof (warm roof = water proofing membrane on top of the thermal insulation) is known as the best solution on the condition that the joints are perfectly filled with bitumen. If these joints are partially not filled with bitumen, condensation of the present humidity induces in winter freeze and thaw. This causes open cells and the humidity enters almost permanent in the cells, increasing drastically the thermal conductivity. This has been observed by Prof. Dr. Hugo Hens, KU Leuven in the Belgian climate (interview November 17, 2022). This should certainly not happen when the joints are well filled with bitumen.
A cellular glass roof, installed with bitumen is hard to recycle at the end of its lifetime. In Germany it is not allowed anymore to use oxydized bitumens while installation with other bitumens is more difficult. As a consequence, the dry installation will become a necessity, even for flat roofs. This means that the surface cells have to be filled to be protected against freeze and thaw. According to Prof. Dr. Künzel, (Fraunhofer Holzkirchen, Stuttgart University and developer WUFI-software) (interview November 30, 2022) at least the top surface and sides of the cellular glass need to be coated against freeze and thaw damage. For the moment, there is no such cellular glass product available but some polymer coatings are straightforward.
If freeze and thaw resistant cellular glass should be available, we have the choice to install above (inverted roof) or under the water-proofing-membrane (warm roof). The major advantage of the inverted roof is that the water proofing membrane is protected against UV-light, temperature variations and mechanical damage. These are the causes that the membrane has a reduced lifetime on the warm roof. A nice paper states that the lifetime of a water proofing membrane at least doubles in an inverted roof compared to a warm roof.
Roof 4 is the inverted rood, roof 3 a warm roof with some ballast (protection) and roof 2 the unprotected insulated roof (typical compact roof). Roof 1 is the non-insulated roof. It is clear that an inverted roof with freeze and thaw resistant cellular glass has a life time of about 50 years after which the cellular glass blocks can be reused (no need for disposal or recycling). Using solar energy to the maximum will be a must and so the flat roof. The inverted roof is the logic choice due to its expected lifetime if freeze and thaw resistant cellular glass at (top and side surfaces) is available.
The inverted roof was originally patented by Dow Chemical for XPS like discussed in a previous post. However, XPS is a closed cellular structure based on polystyrene, which has a diffusion coefficient for water vapour, which is about 1 billion larger than in ordinary glass. For that reason, perfectly installed XPS absorbs humidity by diffusion in an inverted roof. This became even worse in the green roof, with its almost constant > 95% relative humidity, again according to Prof. Dr. Künzel by experiments and WUFI-simulations. In 20 years the thermal conductivity doubles and disposal is needed. This disposal is very expensive because the cost goes pro kg. After 20 years, XPS absorbs about 6 times its weight in a green inverted roof …
Although there are a lot of (negative and false) dogma about the inverted roof, in my opinion it will conquer the world with freeze and thaw (top and sides) resistant cellular glass. Disposal of the water proofing membrane after minimum 50 years and reuse of the cellular glass will be the arguments to get rid of the compact warm roof and its bitumen, causing a shorter life time and a high disposal cost. The first signs are already present. Austrian accredited expert Hannes Guggenberger states (telephone November 29, 2022) that he has already 4 years a good experience with a cellular glass inverted roof. If it works in the Austrian climate, I guess it works everywhere in Europe.