## 2 Materials and Methods
### Green Roof Technology
Regarding PV modules, the efficiency of converting solar energy into electricity varies mainly according to the type of technology chosen. The average efficiency values vary from 22% (high efficiency _monocrystalline silicon_) to 4% (_amorphous silicon_). The cost of a PV solar system depends on the installed power, which is around 2000 euro/kWp where kWp is the peak power). The capturing surface depends on the efficiency of the module and ranges from 5.5 m\({}^{2}\)/kWp for high efficiency monocrystalline silicon to 11 m\({}^{2}\)/kWp for amorphous silicon. In assessing the efficiency of converting solar energy, it is also necessary to consider the energy losses of all system components, in addition to solar panels; it is estimated to be around 20-25%. The GIS tool 'Area solar radiation' was used to quantify how much solar radiation each rooftop in the district receives throughout the year. The sun and sky models were elaborated, considering the monthly data of atmosphere transparency (\(\tau\)) and ratio of diffuse radiation to global radiation (\(\omega\)) identified from the 'Photovoltaic Geographical Information System PVGIS' of Joint Research Centre (JRC). In particular, considering the period 2013-14, \(\tau\) was taken to equal 48%, 62%, and 72% in winter, midesaon, and summer periods, respectively, and \(\omega\) was taken to equal to 48%, 45%, and 35%, similarly. According to European Standard (EN) 12975-2:2006 and Italian Standard (UNI) 11300-4:2016, the two typologies of ST collectors have, on average, respectively, zero-loss efficiencies \(\eta_{0}\) of 0.94 and 0.88, linear heat loss coefficients \(a_{1}\) of 3.34 and 1.57 W/m\({}^{2}\)/K, quadratic heat loss coefficients \(a_{2}\) of 0.02 and 0.01 W/m\({}^{2}\)/K\({}^{2}\), and, for the whole system, a performance ratio of 75%. Then, their monthly efficiencies vary from 0.37 to 0.87 for the flat glass collectors and from 0.69 to 0.87 for the vacuum tubes. The PV modules have an efficiency of 15% (standard efficiency polycrystalline silicon module), and both PV and ST have a system performance around 75%. The hypothesized ST areas were dimensioned in order to not have an overproduction of hot water during summertime. The monthly energy consumption was simulated for a district of Turin as follow:  
* For the residential sector, space heating consumption refers to measured data for the season 2013/2014 [17] and domestic hot water consumption was calculated taking into account that a person needs 50 L of water per day at a temperature of 45 \({}^{\circ}\)C (water temperature variation is 30 \({}^{\circ}\)C). For the nonresidential sector, space heating and domestic hot water consumption were quantified knowing, for different users, the specific consumption in kWh/m\({}^{3}\) and the heated volume (m\({}^{3}\)) [16];
* For the residential sector, electrical consumption refers to the average monthly consumption of 1206 families for the years 2013 and 2014 [61]. For the nonresidential sector, electrical consumption (kWh\({}_{\text{el}}\)) was quantified knowing specific annual consumption in kWh\({}_{\text{el}}\)/m\({}^{3}\) and the heated volume (m\({}^{3}\)) [62].