2.4.1. Energy Efficiency Solutions

To evaluate the energy savings after the rooftop renovation, the assessment of heat fluxes through the roof were quantified during the heating and cooling seasons. Different thermo-physical properties

of the roofs, indicated in Figure 4, were used according to roof type: Common roof, common insulated roof (red tiles), insulated high-reflectance roof, and insulated green roof.

**Figure 4.** Energy efficiency solutions' scheme.

The roofs have different values of thermal transmittance (*URoof*) that depend on the type of insulations. *URoof* is taken to equal 1.80 <sup>W</sup>/m<sup>2</sup>/<sup>K</sup> for common roofs and 0.24 <sup>W</sup>/m<sup>2</sup>/<sup>K</sup> for insulated roofs (according to Italian standard) and has different solar absorption coefficients (<sup>α</sup>*Roof*) that depend on the roof-covering materials. The <sup>α</sup>*Roof* is equal to 0.6 for common roofs with red tiles, 0.3 for light-color roofs, and 0.87 for green roofs. The quota of solar radiation changes according to the presence of vegetation, the incident global solar radiation (*Ii*), was calculated according to global solar radiation recorded by weather stations, while the quota of incident solar radiation entering a green roof (*In*) depends on the Leaf Area Index (*LAI*), which is the ratio between the green area and the underneath soil area [38], and on the short-wave extinction coefficient (*ks*) [39].

Using green roof technology, the heat flow of solar radiation that enters the system is a net contribution taking into account the solar reflection and green absorption. Equation (2) describes the exponential law developed by Palomo Del Barrio [40] used in this work to assess the effect of green roofs on incident global solar radiation:

$$I\_n = I\_i^{-k\_\* \cdot LAI} \tag{2}$$

where:

*In* is the solar irradiance entering the system (W/m2);

*Ii* is the incident solar irradiance (W/m2);

*ks* is the short-wave extinction coefficient (-), which was assumed to equal 0.29 (values proposed for similar vegetation characteristics in [40]); and

*LAI* is the ratio between the green area and the underneath soil area (-), which was assumed to equal 5 in summer, 3.5 in spring, 3 in autumn, and 0.5 in winter [38,39].

To assess the energy savings of a building, due to the roof component, some simplified assumptions were made: (1) The heat flow rate from internal gains was constant; (2) the heat flow rate dispersed by ventilation was constant; (3) the evapotranspiration of green roofs was not considered; and (4) and the thermal capacity of different roof typologies was equal.

The energy savings for space heating and cooling were quantified calculating the hourly heat flow rates before and after the rooftop retrofit interventions with the following equations [39]:

$$\frac{\Delta Q\_H}{A} = \mathcal{U}\_1 \cdot \left( T\_{a|H} - T\_{a4,1} \right) - \mathcal{U}\_2 \cdot \left( T\_{a|H} - T\_{a4,2} \right) \qquad \frac{\Delta Q\_{\mathcal{C}}}{A} = \mathcal{U}\_1 \cdot \left( T\_{a4,1} - T\_{a|\mathcal{C}} \right) - \mathcal{U}\_2 \cdot \left( T\_{a4,2} - T\_{a4,\mathcal{C}} \right) \tag{3}$$

with:

 with:

$$T\_{sl} = T\_{al,H} - R\_{sl} \cdot \mathrm{Id} \cdot \left( T\_{al,H} - T\_{al} + \alpha \cdot \frac{I}{h\_{\ell}} \right) \tag{4}$$

$$T\_{sl} = T\_{al,\mathcal{L}} + R\_{sl} \cdot \mathrm{Id} \cdot \left( T\_{al} + \alpha \cdot \frac{I}{h\_{\ell}} - T\_{al,\mathcal{L}} \right) \tag{5}$$

where:

Δ*QH* is the energy savings during the heating season (Wh);

Δ*QC* is the energy savings during the cooling season (Wh);

*A* is the roof area (m2);

*U* is the thermal transmittance of the roof (W/m<sup>2</sup>/K);

*Rsi* is the thermal resistance of the roof (m2K/W);

*Tai*,*<sup>H</sup>* is the internal air temperature during the heating season equal to 20 ◦C;

*Tai*,*<sup>C</sup>* is the internal air temperature during the cooling season equal to 26 ◦C;

*Tsa* is the sol–air temperature, which was introduced to take into account not only the external air temperature but also the incident solar irradiation absorbed by the roof (◦C);

*Tsi* is the internal surface temperature of the roof (◦C);

*Tae* is the external air temperature (◦C);

α is the solar absorption of the roof (-);

*Ii* is the incident solar irradiance (W/m2), which with green roof was equal to *In* (see Equation (2)); and *he* is the external thermal adductance (W/m<sup>2</sup>/K).

The primary energy savings for space heating and cooling were quantified as the sum of the hourly energy savings during, respectively, the heating and cooling seasons divided by the efficiency of the systems:

$$\frac{\Delta Q\_{P,H}}{A} = \frac{\sum \Delta Q\_H}{A} \cdot n\_{HS}^{-1} \qquad \qquad \frac{\Delta Q\_{P,\mathbb{C}}}{A} = \frac{\sum \Delta Q\_{\mathbb{C}}}{A} \cdot EER^{-1} \tag{5}$$

where:

Δ*QP*,*<sup>H</sup>* is the primary energy savings during the heating season (Wh);

<sup>Δ</sup>*QP*,*<sup>C</sup>* is the primary energy savings during the cooling season (Wh);

*nH* is the average seasonal efficiency of the heating system (in Italy, for residential buildings, this value varies between 0.65 and 0.75 (-)) [17]; and

*EER* is the average seasonal energy efficiency ratio, which depends on the efficiency of air conditioners (in Italy, for a typical heat pump (air/air) this value is about 3).

Following the energy savings obtained from the retrofit of the rooftop, the GHG emissions' reduction was quantified.
