## 2 Setting of the Analysis
### Weather Data  
Weather open data were collected for three Italian cities belonging to different climatic zones and that are characterized by different standard heating seasons, according to Italian law, DPR 412/1993. In Table 1 the main data of the selected locations are shown. In detail, Milan and Livigno are located in northern Italy and are classified as climatic zones E and F, respectively; San Benedetto del Tronto is located in central Italy and is classified as climatic zone D. Open data are collected considering a period of 8 years (2013-2020) from Arpa Lombardia for Milan and Livigno and from the online platform SIRMIP Marche for San Benedetto del Tronto [18; 19]. Weather stations considered in this paper are, \"Milano Lambrate\" (45\({}^{\circ}\)30\({}^{\prime}\) North, 9\({}^{\circ}\)15\({}^{\prime}\) East,altitude 120 m), \"Livigno La Vallaccia\" (46\({}^{\circ}\)28\({}^{\prime}\) North, 10\({}^{\circ}\)11\({}^{\prime}\) East, altitude 2650 m) and \"San Benedetto\" (13\({}^{\circ}\)53\({}^{\prime}\) North, 42\({}^{\circ}\)55\({}^{\prime}\) East, altitude 6 m), respectively. With reference to Milan and Livigno, hourly data of temperature, humidity ratio, solar radiation, precipitation, wind speed, and wind direction were downloaded. For San Benedetto del Tronto, a lower number of climatic variables are available: for this reason, only hourly values for the temperature, humidity ratio, and solar radiation were downloaded. Nonetheless, with the abovementioned, data detailed dynamic simulations can be performed as well. According to the authors' opinion, the quality of the data were good for almost the totality of the downloaded years for each location, except for San Benedetto del Tronto. For this municipality, 2018 is characterized by a strong lack of data: temperature data are missing for about 58% of the season, and there are no affordable data available for the humidity ratio or solar radiation. Therefore, effective climatic data for S. Benedetto del Tronto related to year 2018 were not considered. However, as discussed, climate data were mostly complete; moreover, the availability of experimental radiation data integrating the outside air temperature helped to more accurately simulate the behavior of the building and its energy balance. Standard test reference years were created by means of Meteonorm v. 7.2 [20] for the three cities mentioned above. The TRY created for Livigno was then corrected, considering the influence of altitude on air temperature, using the correlation proposed by UNI 10349-2014 [21]:  
\[\mathrm{t_{H}}=\mathrm{t_{REF}}-\frac{\mathrm{\Delta z}}{178}, \tag{1}\]  
where \(\mathrm{t_{H}}\) is the corrected temperature, \(\mathrm{\Delta z}\) (m) is the difference between the altitude of the two places considered, and \(\mathrm{t_{REF}}\) is the temperature of the lower place. The correlation is introduced because of the altitude difference between the meteorological station that collects weather data in Livigno and the altitude set in Meteororm (Livigno 1850 m, meteorological station 2650 m). With reference to the humidity ratio, a correction referring to altitude is also introduced, as suggested in [22], considering a linear decrease of humidity ratio, i.e.,  
\[\mathrm{HR_{H}}=\mathrm{HR_{REF}}-0.0041\mathrm{\Delta z}, \tag{2}\]  
where \(\mathrm{HR_{H}}\) is the corrected humidity ratio, and \(\mathrm{HR_{REF}}\) is the humidity ratio of the lower place. Moreover, for Milano, simulations considering the test reference year proposed by the Italian Thermotechnical Committee CTI [23] were performed as well. For all of the considered years, the values of the real heating degree days (HDD) are determined for each location, as shown in Figure 1, considering a reference temperature for its definition of 20 \({}^{\circ}\)C (according to DPR 412/93) and the reference period as prescribed by the UNI 11300/1 norm (from 15 October to 15 April for Milan, from 1 November to 15 April for San Benedetto del Tronto, and from 5 October to 22 April for Livigno).