Green roofs (GRs) are well-known for source control of runoff quantity in sustainable urban stormwater management. By considering the inherent randomness of rainfall characteristics, this study derives the probability distribution of rainfall retention ratio Rr and its statistical moments. The distribution function of Rr can be used to establish a unique relationship between target retention ratio Rr, T, achievable reliability AR, and substrate depth h for the aleatory-based probabilistic (AP) GR design. However, uncertainties of epistemic nature also exist in the AP GR model that makes AR uncertain. In the paper, the treatment of epistemic uncertainty in the AP GR model is presented and implemented for the uncertainty quantification of AR. It is shown that design without considering epistemic uncertainties by the AP GR model yields about 50% confidence of meeting Rr, T. A procedure is presented to determine the design substrate depth having the stipulated confidence to satisfy Rr, T and target achievable reliability ART.
Derive the probability distribution of the rainfall retention ratio of green roof (GR) and its statistical moments.
Present an aleatory-based probabilistic (AP) model for GR design.
The paper shows that the design without considering epistemic uncertainties by the AP GR model yields about 50% confidence of meeting target retention ratio.
Propose a methodology to treat epistemic uncertainty in the AP model for the uncertainty quantification of achievable reliability.
Demonstrate the analysis procedures via a numerical example to determine GR substrate depth having the stipulated confidence to satisfy target retention ratio and target reliability.