## 2 Materials and Methods
### Comfort Indices Calculation  
The calculation of comfort indicators considers the environmental and physiological variables reported in the introduction. The details of the PET equation are reported in the work of [21]. The procedure was implemented in R in the rPET package that is  
Figure 5: Vertical profile of the 3D point cloud illustrating the vertical profile of thick vegetation and the terrain. available for replicability of the method ([[https://github.com/fpirotti/rPET](https://github.com/fpirotti/rPET)]([https://github.com/fpirotti/rPET](https://github.com/fpirotti/rPET)), accessed on 20 September 2022). Several climatic variables are measured and available from the IoT sensors, i.e., air temperature, wind velocity, barometric pressure, and humidity. An important variable, the mean radiant temperature (Tmr), is the factor that changes in different shade situations and affects the values and relative comfort indicator significantly when other factors are constant. As defined by [22; 23], the mean radiant temperature is what changes when the human body is exposed to full sunlight or the sunlight is partially obstructed (shadow). One formula used for calculating Tmr is the following:  
\[Tmr=\left[(Tg+273.15)^{4}+2.5\times 10^{-8}\cdot WV^{0.6}.(Tg-Ta)\right]^{0.25}-273.15 \tag{1}\]  
where \(Tg\) is globe temperature in degrees Celsius, \(WV\) is wind velocity in m\(\cdot\)s\({}^{-1}\), and \(Ta\) is air temperature in degrees Celsius. Globe temperature can be measured using specific instrumentation, but in this case, it has to be estimated. We use the following equations from [24; 25] to estimate \(Tg\):  
First, we calculate atmospheric vapour pressure and then the thermal emissivity. \[Ea=\left[\exp\left(\frac{17.67\cdot(Td-Ta)}{Td+243.5}\right)\cdot(1.0007+0.0000 0346\cdot P)\cdot 6.112\cdot\exp\left(\frac{17.502\cdot Ta}{Ta+240.97}\right)\right] \tag{2}\]  
\[\varepsilon_{a}=0.575\cdot Ea^{1/7} \tag{3}\]  
where \(Ea\) is atmospheric vapour pressure, \(Ta\) is air temperature, \(Td\) is dew point temperature (\({}^{\circ}\)C), and \(\varepsilon_{a}\) is the thermal emissivity. We then calculate two arguments \(B\) and \(C\) as follows:  
\[B=S\cdot\left(\frac{f_{db}}{4\cdot\sigma\cdot\cos(z)}+\frac{1.2}{\sigma}\cdot f _{dif}\right)+\varepsilon_{a}\cdot Ta^{4} \tag{4}\]  
where \(\sigma\) is the Stephen-Boltzmann constant and is equal to 5.67 \(\times\) 10\({}^{-8}\) (W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-4}\)) and \(S\) is solar irradiance (W\(\cdot\)m\({}^{-2}\)), and \(f_{db}\) and \(f_{dif}\) are the fraction of direct-beam and diffuse sun radiation respectively. \[C=\frac{0.315\cdot u^{0.58}}{5.3865\cdot 10^{-8}} \tag{5}\]  
where \(u\) is wind speed in meters per hour (\(WV\) m\(\cdot\)s\({}^{-1}\) * 3600 s\(\cdot\)h\({}^{-1}\)). Finally, by combining \(C\), \(B\), and \(Ta\) the globe temperature can be calculated:  
\[g=\frac{B+C\cdot Ta+7,680,000}{C+256,000} \tag{6}\]  
Once \(Tg\) is estimated, Equation (1) is used to extract mean radiant temperature that is used in the calculation of the comfort indices. It is worth noting that mapping these values implies that there are different values of mean radiant temperature depending on the position in space. The different values of mean radiant temperature are due to different proportions of direct beam illumination, which is the factor that changes significantly depending on how much shadow is cast in the area. Comfort indices also require other information, such as if the person is male or female, the clothing level, and the metabolic rate. Below are some values of possible metabolic rates (met) where 1 met = 58.2 W/m\({}^{2}\).