Investigating the absorption and scattering effects of atmospheric particles, i.e., raindrops and fog droplets, is required to establish a comprehensive and accurate channel model. However, for long-distance communication in outdoor scenarios, research on the propagation characterization of fog and rain attenuation in the terahertz (THz) band is insufficient. In this study, fog and rain attenuation characterization with different conditions are characterized. First, fog attenuation at different temperatures and diverse visibility is explored using Rayleigh approximation theory and Mie theory. The results demonstrate that visibility and frequency have a stronger effect than temperature on fog attenuation. Then, rain attenuation as a function of rainfall rate is theoretically determined using Mie theory and the Joss, M-P, and Weibull distribution. The results show that rainfall rate and frequency have greater impact than raindrop distribution on rain attenuation. There are large differences in rainfall attenuation under diverse distributions. Accurate fog and rainfall attenuation information can be used to better estimate path loss and the link budget for terahertz communication in outdoor scenarios.