# Experimental Evaluation and Numerical Simulation of the Thermal Performance of a Green Roof
## 2 Materials and Methods
### Methodology  
In order to assess the thermal behavior of the green roof and its effectiveness in terms of energy savings, it was necessary to analyze and compare the thermal performance of the two parts of the roof. It is worth to mentioning that the stratigraphies of the two roofs were known but the thermophysical properties of each layer were undetermined. In addition, the green roof is made of five layers, of which the roof-lawn is non-homogeneous, and it consists of a layer of grass and the underlying soil. On the other hand, the original roof is made of only three layers, characterized by conventional materials. For this reason, data obtained from the on-site measurement campaign were used for generating a model through Comsol Multiphysics software [23; 24]. The experimental system registered data useful in setting the boundary conditions in the model. Taking into account the direction of the heat flux caused by the difference in temperature between the two sides of the roof, a thermal input, equal to the experimental surface temperature trend, was set. The internal measured air temperatures and the heat fluxes were employed to calculate proper internal heat transfer coefficients. The stratigraphy of the actual green roof was reproduced in Comsol as a single homogeneous layer, characterized by equivalent thermophysical properties, following the method demonstrated in [25]. Simulations were performed in different periods of the year, all characterized by no thermal inversion between internal and external air temperatures and heat fluxes characterized by the same direction for a better calculation of the internal heat transfer coefficients (\(h_{int}\)) [26]. On-site measurements were used as boundary conditions in the model: external surface temperature values were used as an external forcing function; on the other side of the equivalent layer, a heat transfer based on the equation \(q=h_{int}(T-T_{env})\) was set, where \(T\) is the internal surface temperature and \(T_{env}\) is the temperature of the environment, outside the simulated domain (in this case corresponding to the indoor air temperature). From experimental measurements, \(h_{int}\) values along time were calculated and used in the simulation code. Thus, different equivalent thermophysical properties were iteratively tested and the internal surface temperatures were simulated. The search for equivalent thermophysical properties aimed to obtain the best reproduction of the behavior of the green roof, to obtain the best correspondence between the measured and simulated internal temperatures of the surface. The desired condition to stop searching for the best parameters is represented by a Model Efficiency (EF) value greater than 0.9 [23], expressed as  
\[EF=\frac{\sum_{i=1}^{N}(m_{i}-\overline{m})^{2}-\sum_{i=1}^{N}(s_{i}-m_{i})^{ 2}}{\sum_{i=1}^{N}(m_{i}-\overline{m})^{2}} \tag{6}\]  
where \(m_{i}\) is the measured value at time \(t_{i}\), \(s_{i}\) is the simulated value for each time \(t_{i}\), \(\overline{m}\) is the average of the measured values and \(N\) is the total number of samples. EF can understand equivalent structure to reproduce the original one's behavior, showing values between 0 and 1 (which indicates that measured and simulated data are equal). Finally, the thermophysical properties obtained by the green and the original roofs were used in the energy simulation software TRNSYS in order to obtain the annual energy needs of a detached building. Thus, the comparison between the energy demands allowed the evaluation of the advantages deriving from the installation of a green roof. Considering that the solar reflectance of green roofs varies between 0.3 and 0.5 depending on the plant types [27], here, a reflectivity of 0.3 (typical value for leaves) was used in the model. The detached building was modelled considering walls consisting of a 0.22 m layer of concrete and a 0.04 m XPS layer, plastered on both sides, with a U-value of 0.600 W/(m\({}^{2}\)K).