Stochastic Analysis of Hydrologic Operation of Green Roofs

Both deterministic and probabilistic models have been developed to study the hydrologic operation of green roofs. Previously developed probabilistic models provide only approximate solutions because of simplifying assumptions. Exact analytical solutions are derived here for not only those variables that are solved for already but also some additional ones of interest. Analysis of the additional variables reveals that, depending on local climates, the average moisture level of a green roof may either always increase or increase first but reach a maximum and then even gradually decrease as the growing medium depth increases. Example results of analysis also demonstrate that with shallow growing medium depths, water required for irrigation may be greater than the runoff that can be reduced by green roofs. Taking advantage of the solution’s analytical tractability, similar insights can be easily obtained for locations of interest and used for the better design and operation of green roofs.