## 2 Materials and Methods
### Numerical Simulation and Assessment Criteria
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Parameters**} & \multicolumn{2}{c}{**Value**} \\ \cline{2-3}  & \multicolumn{2}{c}{**Climate Zone I**} & \multicolumn{2}{c}{**Climate Zone II**} \\ \hline  & Heating period & 15 October–15 April, 14 h/day & 15 September–15 May, whole day \\ \hline \multirow{2}{*}{Setpoint temperature} & Occupied hours & 22 \({}^{\circ}\)C & 22 \({}^{\circ}\)C \\  & Un-occupied hours & 18 \({}^{\circ}\)C & 18 \({}^{\circ}\)C \\ \hline \multirow{2}{*}{Occupants’ density} & Residence & 28.3 m\({}^{2}\)/person \\ \cline{2-3}  & Shops and offices & 17 m\({}^{2}\)/person \\ \hline \multirow{2}{*}{Infiltration rate} & Before retrofit & 10 ac/h, at 50 Pa \\ \cline{2-3}  & After retrofit & 1.5 ac/h, at 50 Pa \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Ventilation rate \\ (ventilation is active when:) \\ \end{tabular} } & The room is occupied, indoor temperature is higher than 24 \({}^{\circ}\)C, and the difference between indoor and outdoor temperature is higher than 3 \({}^{\circ}\)C \\ \hline \multirow{2}{*}{HVAC system} & Without any mechanical cooling or ventilation system; heating system is simulated with ideal loads air system \\ \cline{2-3}  & & \\ \end{tabular}
\end{table} 
Table 5: Assumptions and variables used for the simulations. Figure 6: Occupancy profiles of living area (a) and commercial area (b) in the Portiel houses. Two approaches have been used in the evaluation of indoor overheating levels in the present study. Firstly, a deterministic approach using fixed thresholds from CIBSE Guide A [34] was used. Secondly, the results are analysed according to the adaptive thermal comfort model proposed in EN 15,251 [40]. Both approaches offer temperature benchmarks in the form of operative temperature. CIBSE Guide A recommends 23-25 \({}^{\circ}\)C for air-conditioned living rooms during the summer and defines the \"benchmark peak temperature\" for free-running buildings, which is 3 \({}^{\circ}\)C higher than the summer comfort temperature. Accordingly, the prescribed benchmark peak temperature is 28 \({}^{\circ}\)C for the living room [41]. The advantage of this approach is its simplicity, but the downside is that it assumes the particular combinations of the occupant metabolic rate and clothing insulation levels. The alternative method, the adaptive approach [42], argues that occupants can adapt the indoor thermal conditions through window operation or clothing arrangement. It was developed from extensive field studies and defined the comfort temperature range in free-running buildings as a function of the outdoor running mean temperatures. Its upper and lower limits used in this study are shown in Equations (1) and (2). \[\theta_{max}=0.33\theta_{m}+18.8+3 \tag{1}\]  
\[\theta_{min}=0.33\theta_{m}+18.8-3 \tag{2}\]  
where \(\theta_{rm}\) is the running mean outdoor temperature. These limits apply when 10 \({}^{\circ}\)C \(<\theta_{rm}<30\)\({}^{\circ}\)C for the upper limit and 15 \({}^{\circ}\)C \(<\theta_{rm}<30\)\({}^{\circ}\)C for lower limit. However, the outdoor running mean temperature of South Tyrol could be higher than 30 \({}^{\circ}\)C, resulting in some overheating hours being out of the range. Therefore, it is defined in this study that when \(\theta_{rm}\geq 30\)\({}^{\circ}\)C, \(\theta_{max}\) equals to the upper limit when \(\theta_{rm}=30\)\({}^{\circ}\)C. Both assessment criteria are applied in the living room of the Portici houses during occupied hours. Tropical nights, summer days, and heatwaves (HWs) are analysed in current and future climate. Tropical nights occur when the daily minimum temperature is higher than 20 \({}^{\circ}\)C, and summer days take place when the daily maximum temperature is higher than 25 \({}^{\circ}\)C. Heatwaves, on the other hand, can occur during the \"extended summer\" period (i.e., April-September) and have been defined using the methodology developed by [PERSON] et al.