A green roof is engineered to partially duplicate normal soil only without the depth. In normal soil the earth is deep but with a typical shallow green roof (aka extensive) the soil is no more than 6 inches at the very most.
You replicate an earthen environment using drainage mats and water retention mats so that on one hand the water drains and on the other hand the water is retained like it would into deep soil. You also alter the actual soil. It typically is called a growing medium instead of soil.
The Germans are the leaders in green roofs, arguably the leaders in green building overall, and they have spent a lot of time looking into the best composition of green roof growing medium.
Typically it is a mix of filler and nutrients. The filler usually also acts as a water retention material as well as being something very light. Volcanic rock works great but isn’t local unless you live in Hawaii or something. Expanded clay works really well too. Clay can retain a lot of water for its weight and releases it slowly over time.
I’ve seen the filler be chopped up expanded polystyrene. Gaia Soil does this. That is a cool use of garbage and you can’t get lighter than foam! The foam doesn’t do well in winds though and I’ve seen neighboring back yards filled with little white foam pellets blown from the green roof. I also have some minor concerns about the foam pellets giving off toxins.
The nutrient is usually fertilizer. Eco Brooklyn is currently building a brownstone with composting toilets and I am excited to use the humanure for a green roof. We would water it with gray water. That would be taking urban green building to yet another revolutionary level! Just think of the thousands of gallons of sewage being turned into a lush and hygienic green roof!
In terms of composition about 80% expanded slate (clay) and 20% compost works well. Permatill has some great info on this. They provide growing medium.
Despite all this a green roof is not a normal earth plot and only certain plants will grow on it – namely shallow root plants ok with harsh weather.