## 1 Introduction  
As the outer tissue of the human body, the skin acts as an interface with the environment and thus is the first to be exposed to electromagnetic radiation, especially at high illumination powers. When the irradiation power density is higher than 10 mW/cm\({}^{2}\), the thermal effect is mainly studied, which is directly manifested by increasing skin temperature and damage to biological tissues [1]. There have been several safety guidelines/standards set by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) and the IEEE International Committee on Electromagnetic Safety (ICES) Technical Committee (TC) 95 [2; 3; 4] to protect humans from excessive exposure. Reference levels of 20 mW/cm\({}^{2}\) at 6 GHz to 10 mW/cm\({}^{2}\) at 300 GHz have been derived for local body exposure based on laboratory measurements or simulations [5; 6; 7]. However, further research on skin response in the atmospheric environment is required for outdoor applications of MMW/sub-THz techniques, such as remote security inspection, high-speed data coverage, and active denial system.  
MMW/sub-THz waves suffer from high sensitivity to outdoor weather conditions [8; 9; 10; 11; 12; 13; 14; 15]. The path availability and channel performance are reduced even in clear weather, as atmosphere gases and air turbulence can lead to serious channel degradation [13]. Outdoor measurements just on channel deterioration have been conducted [11; 16], but no confirmative conclusions could be obtained. That's because of the challenges in measuring the impact of weather conditionsover a long observation time and the difficulties in obtaining the re-occurrence of similar weather conditions to verify the results of independent measurements due to the time-varying rainfall rates and raindrop size distributions, as an example. Several groups have tried to build weather-emulating chambers in a controlled laboratory environment to generate reproducible weather for experimental measurements [13; 17]. However, there are some distinctions between emulated and actual weather [8]. Therefore, a combined approach relying on both theoretical models and case studies is still valuable and necessary.  
In this article, we present a comprehensive theoretical analysis that explores the bio-thermal heating effect of MMW/sub-THz waves on human skin under outdoor weather conditions. To the best of our knowledge, similar research has not yet been conducted, highlighting the importance of our investigation for future applications of this frequency band in outdoor settings. The methodology we propose can be adapted and applied to various weather conditions by measuring or determining the relevant parameters. Additionally, we emphasize that studying the thermal responses of rat skin provides a feasible approach to understanding the potential effects on human skin, considering their structural similarities. The article is organized as follows: Section 2 presents the dielectric properties of skin and water, and proposes theoretical models for the propagation of MMW/sub-THz waves in clear weather and rain. Section 3 shows theoretical models to predict the thermal heating effect and Section 4 presents theoretical models for thermal heating in outdoor weather with investigations on the influence of humidity and rainfall rate. Section 5 shows the conclusion and implications of this work.