## 2 Materials and Methods
### Numerical Simulation and Assessment Criteria  
Using a well-established simulation software, EnergyPlus 8.7.0, developed by the National Renewable Energy Laboratory (NREL), Washington, DC, U.S.A., the energy demand and indoor air temperature are simulated. To better understand the impact of climate change on historic buildings, six scenarios are defined according to building status and climate conditions as shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & **Construction** & **Retrofit Solutions** & \(\mathbf{U_{b}}\) & \(\mathbf{U_{a}}\) \\ \hline \hline \multirow{4}{*}{External wall} & \multirow{4}{*}{2.59} & \multirow{4}{*}{0.28} & \multirow{4}{*}{0.28} & \multirow{4}{*}{0.28} \\  & &  
To verify the effectiveness of the envelope retrofit, the energy performance simulation focuses on space heating, while other end uses such as hot water supply and lighting are not included. The heating energy demand of the building is calculated based on the temperature setpoint of 22 \({}^{\circ}\)C (occupied), which is the comfort temperature recommended by CIBSE Guide A [34]. The heating period of Climate zone I is defined according to the Italian regulation, based on Heating Degree Days (HDD): 15 October-15 April, 14 h/day. Since there are no limitations to heating period and heating hours for Climate zone II, a heating period from 15 September to 15 April is defined based on the comparison of HDD between Climate zone I and II. The occupancy (Figure 6), lighting, and electric appliances profiles are based on ISO 17772-1 [35] and the 2014 Building America House Simulation Protocols [36]. 17772-1 offers an informative occupant schedule for the energy calculations of residential buildings, shops, and offices. However, this schedule does not make any distinction between the living room and bedroom, which makes the comfort assessment inaccurate. Therefore, the fraction of occupants in 17772-1 is distributed for the living room and bedroom according to their ratio in the 2014 Building America House Simulation Protocols. For this study, the indoor temperature in the summer is calculated in free-floating conditions, without any mechanical cooling system. The airtightness of the building envelope before retrofitting is set to 10 ac/h at 50 Pa. This result is based on available studies. Although empirical measurements of airtightness in historic buildings are still limited, there is enough evidence to make an estimation. For instance, the average infiltration rate of 53 historic houses from Estonia, Finland, and Sweden is 8.43 ac/h at 50 Pa [37]. In the UK, the infiltration rate of 471 homes ranged from 9.9 to 16.5 ac/h. When restricting the construction year from pre-1900 to 1949, the infiltration rate ranges from 10.5 to 16.5 ac/h [38]. The value after retrofit is defined according to the Italian CasaClima standard (A): 1.5 ac/h at 50 Pa [39]. Natural ventilation is considered to be active when the room is occupied, indoor temperature is higher than 24 \({}^{\circ}\)C, outdoor temperature is above 18 \({}^{\circ}\)C, and indoor temperature is 3 \({}^{\circ}\)C higher than the outdoor temperature. It is modelled using simplified ventilation calculations in EnergyPlus's Wind and Stack Open Area model. Moreover, the ventilation rate is checked with the requirement of UNI 10339: 1995, based on an average ventilation level of residential buildings with a normal level of comfort expectation. The assumptions and variables used for the simulations are reported in Table 5.  
Figure 5: Simulation scenarios defined according to building and climate conditions, P = Present climate condition (2008–2011); F1 = Near future climate condition (2041–2050); F2 = Far future climate condition (2091–2100); Un-retrofitted = historic building in the original state; and Retrofitted = historic building undergone energy retrofit.