## 1 Introduction
As for rain attenuation, authors [23; 24] developed free-space communication channels at 625 GHz and 1550 nm and designed a controllable rainfall weather simulation room; the performance of the two channels was analyzed by measuring the power and bit error rate of each link using a terahertz time-domain spectroscopy system. Given the results, the attenuation of terahertz and the infrared waves was comparable in typical rain conditions. In addition, in [25; 26], the rain attenuation of THz waves was estimated by collecting local rainfall data based on Mie theory, which was compared with the results of the International Telecommunication Union Radiocommunication Sector (ITU-R) model. The main difference was that the former uses rainfall rate data, while the latter uses raindrop size distribution data. The authors of [25] indicated that for rainfall events greater than 10 mm/h, the average attenuation was between 8 dB/km and 18 dB/km, and the results in [26] demonstrated that the rainfall attenuation in Indonesia was smaller than that in the ITU-R model at lower frequencies, while it is larger than the ITU-R model at higher frequencies. The rain attenuation of terahertz waves at 77 GHz and 300 GHz under varying rainfall rates was investigated [27], and a series of measurements were conducted, including attenuation, rainfall rate, and droplet size distribution. In addition, the measured droplet size distribution was later compared with that obtained with commonly used models, such as the Marshall and Palmer (M-P) distribution model and Weibull distribution model, and it was concluded that the Weibull distribution model was more in line with the measured droplet size distribution. Overall, rain and fog attenuation of terahertz waves have been widely investigated by scholars and institutions. Nevertheless, research on the systematic and comprehensive propagation characterization of rain and fog attenuation of terahertz waves is lacking, and there is a need to enhance the numerical simulation of attenuation under various conditions. To address these issues, we aimed to comprehensively characterize the propagation of rain and fog attenuation of terahertz waves. The main contributions of this work are as follows:* In terms of fog attenuation, based on Rayleigh approximation theory and Mie theory, we investigated the influence of advection fog and radiation fog on terahertz waves and determined the attenuation in fog at diverse temperatures and visibility at 0.1-1 THz. In addition, we used a more accurate Rayleigh approximation theory and compared it with the results obtained with a reference [18]. * In terms of rain attenuation, the rain was divided into four types: drizzle, moderate rain, downpour, and rainstorm, based on the rainfall rate, and we comprehensively compared and analyzed the rain attenuation of terahertz waves under Joss, M-P, and Weibull distributions. * The results indicate that visibility and frequency have a more significant effect than temperature on fog attenuation. The differences at 1 THz between the attenuation caused by advection fog and radiation fog are 8461.31 dB, 1986.81 dB, 250.82 dB, and 24.98 dB, corresponding to visibility of 30 m, 50 m, 100 m, and 200 m, respectively. Additionally, rainfall rate and frequency have a greater impact than raindrop distribution on rain attenuation. The rainfall attenuation significantly varies under different distributions, with the maximum difference being 3256.35 dB and the minimum difference being 0.34 dB at 1 THz. The remainder of this paper is structured as follows: In Section 2, the propagation mechanism of terahertz waves and the distribution spectrum of fog droplets and raindrops are discussed. Section 3 presents Mie theory and [PERSON] approximation theory. Section 4 focuses on the analysis of fog and rain attenuation of terahertz waves. In Section 5, the main conclusions of this study are drawn.