In the Lite and Standard systems, we only recommend plants which have extreme drought resistance through some means other than the root system.  This means succulent, water-holding plants like Sedums, Alliums, Sempervivums, and Delospermas in the northern temperate regions, and similar species farther south.
The best LiveRoof plants will both store water and have a special type of metabolism called ‘Crassulacean Acid Metabolism’ (CAM). CAM plants are unique in that under drought conditions their stomates (leaf pores) are open at night rather than during the day, as is the case with most plants.  CAM plants exchange gasses (oxygen and carbon dioxide) in the dark when it is cooler and less windy.  CAM plants are up to ten times more efficient with water conservation than non-CAM plants.
In the Deep and Maxx systems, with irrigation, a broader plant palette is possible.
In all cases, consult with your local LiveRoof licensed representative for recommendations of the best plants for the climate.
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