An easy-to-use and physically based analytical probabilistic model is developed to evaluate the long-term average hydrologic performance of green roofs. The probabilistic models of local rainfall characteristics are introduced first, the hydrologic and hydraulic processes occurring on and inside a green roof system are then described mathematically, and the closed-form mathematical expressions depicting the storm-water management performance of a green roof system are finally obtained using the derived probability distribution theory. Simplifying assumptions are made to mathematically describe the hydrologic and hydraulic processes. The validity of these assumptions and the overall probabilistic approach is demonstrated by comparing its outcomes with results from a series of continuous simulations using long-term rainfall data from Detroit, Michigan and observations from a real case study in Portland, Oregon.
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