Optimal placement of green, blue and yellow roofs under uncertainty

Maximizing the societal benefits for a municipality

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Abstract

Climate change challenges the resiliency of our cities, and lack of spaces in densely paved areas makes it impossible to implement adaptation and mitigation strategies on the street level. However, buildings have often unused roofs, which can be converted into sustainable roofing options. Green roofs are systems which allow for the growth of different types of vegetation, mitigating heat and capturing water. Blue roofs are layers for water collection, which provide temporary storage and slow release of rainwater. Yellow roof is another name to indicate roofs with photovoltaic (PV) panels. Some areas of the city may be more subject to flooding and heat. Some buildings may instead receive more solar radiation. Therefore, prioritizing which option to install where may be the key to the success of sustainable roofing placement. In this study, we construct an optimization model that evaluates the benefits of the roofing option in each potential location and chooses the combination of roofs and roofing options which maximizes the total societal benefits. The reduction of flooding and heat risks and the production of clean energy are modeled considering both climate variables and the city’s characteristics. However, the derived data and parameters are uncertain by nature. Climate data is used in ensembles and is integrated into the problem by formulating the model into a stochastic and robust version. We take Schiedam as our case study area and solve the model. We also perform uncertainty analysis, making use of clustering and classification tree regression. This analysis allows to understand which parameters are driving which type of solutions, and to understand how robust the constructed model is. Moreover, we formulate the same problem in the shape of a multi-time step model, where the decision maker can make the optimal placement decision every year. In this case, it is possible to simplify the decision process into a one-branch tree for which we present a methodology. The results show that our model is robust in terms of placement choice when parameters change, and we discover which parameters drive the main variations. The total benefits are instead much more reliant on the uncertainty of the problem.