## 2 Methodology and Modeling
### Passive Solution Tests
#### 2.6.3 Roofs and Ceilings  
The effect of roofing on the thermal environment was analyzed for both flat and inclined roof types, with tests consistent across locations. Brazil and Portugal shared the same base roof, while Turkey's roof differed. A total of nine tests across ten alternatives were conducted, starting with alternative 1 as the base.  
In alternative 2, a green roof was added to the flat roof, while in alternative 3 it was white plaster. In alternative 4, 8 cm of XPS insulation was introduced between the base roof and the white plaster. Inclined roof tests began in alternative 5, adding an unconditioned space above the conditioned areas. The interzone slab was made of 100 mm heavyweight concrete with a U-value of 1.26 W/(m\({}^{2}\cdot\)K), and the inclined roof construction resulted in a U-value of 3.21 W/(m\({}^{2}\cdot\)K). Alternatives 6 and 7 introduced XPS insulation either in the slab or roof. Alternatives 8 to 10 replicated these configurations but replaced the concrete slab with a gypsum board (U-value 3.10 W/(m\({}^{2}\cdot\)K)).  
The U-values for each configuration are summarized in Table 6.  
To account for ventilation requirements, the infiltration rates for inclined roofs were adjusted according to [PERSON] et al. [63] based on average wind speeds [38]. The infiltration rates for the unconditioned spaces are summarized in Table 7.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Alternative** & **Description** & \(\mathbf{U}\)**, **BR** & \(\mathbf{U}\)**, **PT** & \(\mathbf{U}\)**, **TK** \\ \hline Alt. 1\_Roof & Base & 1.27 & 1.27 & 0.71 \\ Alt. 2\_Roof & Flat green roof & 1.27 & 1.27 & 0.71 \\ Alt. 3\_Roof & Flat, white exterior & 1.23 & 1.23 & 0.69 \\ Alt. 4\_Roof & Flat, 8 cm of XPS with white exterior & 0.34 & 0.34 & 0.28 \\ Alt. 5\_Roof & Inclined roof, concrete ceiling & 3.21/1.26 & 3.21/1.26 & 3.21/1.26 \\ Alt. 6\_Roof & Inclined, concrete, 8 cm of XPS (slab) & 0.34 (slab) & 0.34 (slab) & 0.34 (slab) \\ Alt. 7\_Roof & Inclined, concrete, 8 cm of XPS (roof) & 0.40 (roof) & 0.40 (roof) & 0.40 (roof) \\ Alt. 8\_Roof & Inclined roof, gypsum ceiling & 3.21/3.10 & 3.21/3.10 & 3.21/3.10 \\ Alt. 9\_Roof & Inclined, gypsum, 8 cm of XPS (slab) & 0.40 (slab) & 0.40 (slab) & 0.40 (slab) \\ Alt. 10\_Roof & Inclined, gypsum, 8 cm of XPS (roof) & 0.40 (roof) & 0.40 (roof) & 0.40 (roof) \\ \hline \hline \end{tabular}
\end{table}
Table 6: U-values (W/(m\({}^{2}\cdot\)K)) for roof solutions across locations: Brazil (BR), Portugal (PT), and Turkey (TK).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Alternative** & **Description** & \(\mathbf{U}\)**, **BR** & \(\mathbf{U}\)**, **PT** & \(\mathbf{U}\)**, **TK** \\ \hline Alt. 1\_ExtWall & Base & 1.69 & 1.38 & 0.87 \\ Alt. 2\_ExtWall & Exterior brown plaster & 1.69 & 1.33 & 0.85 \\ Alt. 3\_ExtWall & Exterior white plaster & 1.69 & 1.33 & 0.85 \\ Alt. 4\_ExtWall & 4 cm of XPS with exterior white plaster & 0.6 & 0.55 & 0.44 \\ Alt. 5\_ExtWall & 8 cm of XPS with exterior white plaster & 0.36 & 0.34 & 0.3 \\ Alt. 6\_ExtWall & 12 cm of XPS with exterior white plaster & 0.26 & 0.25 & 0.23 \\ \hline \hline \end{tabular}
\end{table}
Table 5: U-values, in W/(m\({}^{2}\cdot\)K), for each exterior wall solution and location: Brazil (BR), Portugal (PT), and Turkey (TK).