Optimal design for water conservation and energy savings using green roofs in a green building under mixed uncertainties

Most water conservation and energy saving strategies for residential homes and commercial buildings have higher initial capital investment than traditional ones. Yet, the added benefits of these “green” building strategies should outweigh the increase of initial capital cost at the end of the house lifetime. Using green roof systems to cool houses gives rise to uncertainties from local precipitation patterns and the unstable market related costs and benefits. The optimal area of green roof to balance cost, benefit, and risk remains unknown. To achieve such a complex systems analysis, a grey stochastic programming model was prepared to address the optimal design strategies under mixed uncertainties. Such a cost-benefit-risk trade-off model was formulated for this study through an optimization framework to retrieve the optimal design strategies with respect to a typical Florida residential home (shingle and metal roofs). It is particularly designed to synergistically integrate a green roof with beneficial reuse of gray water and stormwater while achieving some degree of energy savings. The study identifies the optimal green roof area that keeps within the cost of a conventional home over a specific life time, such as 50 years. Research findings show that as the reliability level associated with the chance constraint was decreased, the upper bound of the green roof area did not vary much for either shingle or metal roofs. The lower bound was found to decrease in the same situation, however, due to the higher minimum cost of the cistern in relation to the greater volume of expected rainfall, forcing the required green roof area to decrease.