## 2 Materials and Methods
### Green Roof Technology
Table 4 shows typical roofing materials with solar absorption (\(\alpha\)), solar reflectance (\(\rho\)), and infrared emittance (\(\varepsilon\)) values used in this work to quantify \(SRI\) and \(T_{s}\) before and after roof renovation using the albedo strategy. In the analyzed district, the values of roofing material properties refer to 'generic black shingle' for dark and black roofs, 'gray Ethylene-Propylene Diene Monomer (EPDM)' for medium roofs, and 'white EPDM' for white and renovated roofs. The values of \(SRI\) and \(T_{s}\) were calculated both at building scale and at blocks-of-building scale to evaluate the external conditions. The main problem of this strategy is that over time the solar reflectance values of high- reflectance roofs decrease due to the accumulation of surface dirt and the degradation of the material by about 0.15 mainly during the first year [54]. The emission, however, does not decrease significantly, and washing the roof surfaces could restore the roof solar reflectance to 70%-100% of the original values [55]. Since most roofs are not washed frequently, it is necessary to evaluate aged values of solar reflectance and infrared emittance values to predict energy savings. If aged values of a roof are unknown, it is possible to estimate the aged solar reflectance (\(Aged_{\rho}\)) based on the initial solar reflectance (\(Initial_{\rho}\)) by using the following equation:  
\[Aged_{\rho}=0.7\big{(}Initial_{\rho}-0.2\big{)}+0.2 \tag{8}\]  
Referring to LEED (Leadership in Energy and Environmental Design) environmental protocol is also possible to assess mixed nonroof and roof measures, using the following relation as a function of area surfaces (\(A\)):  
\[\frac{A_{\text{n\tiny{norof\,\,measures}}}}{0.5}+\frac{A_{\text{\tiny{high\, \,reflectance\,\, roof}}}}{0.75}+\frac{A_{\text{\tiny{vegetated\,\, roof}}}}{0.75}\geq A_{\text{\tiny{total\,\,site}}}+A_{\text{\tiny{total\,\, roof}}} \tag{9}\]  
Solar Energy Technology  
Solar thermal (ST) collectors and photovoltaic (PV) panels that exploit renewable energy sources (RES) provide environmental and economic benefits [57; 58; 59]. In this work, the solar technologies were assessed considering the potential roofs' area with better solar exposition. In Italy, the most used types of low-temperature ST collectors are _flat glass collectors_ with high efficiency and low cost and _vacuum tubes_, which have greater efficiency compared to flat glass collectors, due to the lower dispersions by thermal convection inside the vacuum tubes, but higher \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Roof Material** & \(\alpha\) **(-)** & \(\rho\) **(-)** & \(\varepsilon\) **(-)** & \(T_{s}\) **(\({}^{\circ}\)C)** & \(SRI\) **(-)** \\ \hline Smooth bitumen & 0.94 & 0.06 & 0.86 & 83 & \(-0.1\) \\ Generic black shingle & 0.95 & 0.05 & 0.91 & 82 & \(0.1\) \\ Vegetated field & 0.90 & 0.10 & 0.76 & 83 & \(-0.2\) \\ Grey EPDM & 0.77 & 0.23 & 0.87 & 68 & \(0.21\) \\ Red clay tile & 0.67 & 0.33 & 0.90 & 69 & \(0.36\) \\ Red concrete tile & 0.82 & 0.18 & 0.91 & 76 & \(0.17\) \\ Shasta white shingle & 0.74 & 0.26 & 0.91 & 64 & \(0.27\) \\ Light gravel & 0.66 & 0.34 & 0.90 & 57 & \(0.37\) \\ Aluminum & 0.39 & 0.61 & 0.25 & 48 & \(0.56\) \\ White EPDM & 0.31 & 0.69 & 0.87 & 25 & \(0.84\) \\ White coating on shingle & 0.29 & 0.71 & 0.91 & 23 & \(0.87\) \\ White PVC & 0.17 & 0.83 & 0.92 & 11 & \(1.04\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Solar performance of roofing materials [48; 56]. cost [60]. On average, a solar thermal system in Italy has a monthly efficiency of 40-85% with flat collectors and 70-86% with vacuum tubes; a collection area of 0.7-1.2 m\({}^{2}\)/person for flat collectors and 0.5-0.8 m\({}^{2}\)/person for vacuum tubes (considering the production of domestic hot water), with the month of maximum solar radiation being considered for the dimensioning; and a cost of 1000 euro/m\({}^{2}\) for flat collectors and 1200 euro/m\({}^{2}\) for vacuum tubes.