Green roofs, as implied by their name, are meant to be sustainable, or at least that was the original intent in their creation. Like any creation, green roofs have taken on a life of their own and expanded into roof gardens that have an aesthetic as well as utilitarian purpose -- and this complicates matters somewhat.
From a strictly sustainable perspective, green roofs should be minimally maintained and consume minimal resources. Sedum green roofs have come very close to achieving this ideal, only needing water in the first year and needing no more maintenance than a normal roof would.
In ideal circumstances the irrigation for these roofs in the first year would be a drip system, which is eighty percent more efficient than spray heads; however, since these are usually temporary systems, they tend to be spray-head systems of some kind, which are inexpensive enough to install and remove that they cost less than the water savings of a drip system.
If the goal is sustainability, why do we ever plant anything other than sedum, extensive green roofs? The value of square footage is king in any real estate market. If a developer or owner can obtain energy savings and get usable garden square footage from their green roof, then why not install a higher-maintenance garden?
Indeed, my belief is that we will start to see more and more garden and habitat green roofs that will require more water and more maintenance. The payoff, besides usable square footage, will be green roofs that produce locally usable foods and provide refuge for wildlife.
These really should utilize drip irrigation driven by the new generation of smart timers that adjust watering based on satellite weather monitoring to deliver water as efficiently as possible.
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You should also read Susan Wisniewski's Ask A Pro Q&A, "What's the difference between a green roof and a white roof?"