## 4 Outdoor Thermal Heating Performance  
To evaluate the thermal heating performance of MMW/sub-THz waves in rainy weather, we combined the theoretical models for thermal heating by Equation (6), channel propagation by Equations (3)-(5), and free space path loss (FSPL). Calculations were conducted by setting a rain rate of 5 mm/hr and a planar and uniform water layer of 0.2 mm covering the surface of human skin surface due to falling rain, a normal incidence configuration for the largest transmissivity, as shown in Figure 1c, as well as a relative humidity (RH) of 30% in clear weather and 60% in rain, output power of 60 dBm at the transmitter side launched out from an antenna with a gain of 50 dBi, and an illumination time of 240 s. Results are plotted in Figure 4.  
Figure 3: (a) Temperature evolution with respect to illumination time (Hollow circles for experimental data and solid curves for fitted values based on Equation (6)). (b) Response of the heat transfer coefficient on the variation of the temperature difference between the skin and environment. The colors correspond to the same power density as in (a). (c) Calculated evolution of temperature due to electromagnetic illumination with respect to frequency. The colors correspond to the same power density as in (a). (d) Calculated temperature evolution with respect to illumination time under a power density of 284 mW/cm\({}^{2}\) at 33.5 GHz (blue) and 140 GHz (red). The solid and dashed curves correspond to the same weather conditions as in (c).  
Figure 4: (**a**) Temperature evolution versus channel distance (between transmitter and skin surface) due to the radiation of a 60 dBm output power from a transmitter over an illumination time of 240 s. (**b**) Temperature variation with respect to rainfall rate under different radiation power densities (at 33.5 GHz) over a propagation distance of 10 m. (**c**) Temperature variation versus relative humidity under different water layer thicknesses.  
A negative correlation between skin temperature and channel propagation distance is shown in Figure 4a, due to the distance dependence of channel propagation losses, as shown in Figure 2. The temperature increase caused by the 140 GHz channel is smaller than that by the 33.5 GHz channel due to the higher propagation losses and lower transmissivity into the skin tissue, as shown in Figure 1a. This means the thermal heating effect by sub-THz frequencies would not be an urgent concern for human skin if the propagation distance or output power density is limited. It should also be noted that the equilibrium temperature in rain is much lower than that in clear weather, which is opposite to our predictions in Figure 3d, due to the power losses caused by the water layer covering the skin surface. This indicates that the influence of falling rain and water vapor humidity is not so obvious when compared with power loss caused by the water layer.  
To further investigate the dependence of the equilibrium temperature by the 33.5 GHz signal on the rainfall rate and relative humidity, we calculated evolutional curves due to the variation of rainfall rate and humidity and show the results in Figure 4b,c respectively. The horizontal lines imply the negligible influence of rain conditions, which exert negligible propagation degradation compared to the FSPL and the power losses due to the presence of a water layer on the skin surface. This means the major deterioration of the thermal-heating effect in rain is from the rainwater falling on the skin surface and the output power density at the transmitter side.