Abstract
Abstract 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 and its statistical moments. The distribution function of can be used to establish a unique relationship between target retention ratio , 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 . A procedure is presented to determine the design substrate depth having the stipulated confidence to satisfy and target achievable reliability .
Highlights
The use of green roofs (GRs) is becoming popular in sustainable urban stormwater management
Evaluations of the hydrologic performance of GRs have been made by field monitoring of prototype or laboratoryscale facilities over a selected period of time (e.g., Carter & Rasmussen ; Getter et al ; Soulis et al ; Johannessen et al )
By considering the inherent randomness of rainfall amount of individual rainstorm event and inter-event dry period, this study extends the work of Zhang & Guo ( ) to derive the probability density functions (PDFs) of the GR retention ratio Rr, based on which the analytical expression for the exact mean and variance of the retention ratio are derived
Summary
The use of green roofs (GRs) is becoming popular in sustainable urban stormwater management. As shown in Equations (10) and (22), a unique functional relation can be established between the distributional properties of Rr (i.e., distribution, statistical moments, and achievable reliability) and h because Rc,max, as shown in Equation (4), is a function of h This unique relation for substrate depth h, target retention ratio Rr,T , and achievable reliability AR(Rr,T ; h), defined by Equation (22), would not exist when model parameters describing the rainfall-runoff transformation processes are subject to epistemic uncertainties. Under such circumstance, treating model parameters that characterize soil, plant, and climatic properties as deterministic constants would render a GR design not achieving the target performance with desired confidence. Ci is bounded within [(θwp=θ fc), 1] of which the lower bound of the bounding interval depends on two soil moisture characteristics subject to uncertainty
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