## 5 Numerical Results  
In this section, we elaborate on our numerical results. We consider several typical scenarios for weather conditions: (i) cloudless or slightly cloudy, sunny conditions, (ii) cloudy conditions, and (iii) rainy conditions. We also consider different Earth regions. To create a sample set of clouds corresponding to a specific selected region, we use computer simulations with parameters detailed in Section 2. The dimensions of zone \(A\) are chosen to be \(10^{4}\times 10^{4}\) m. To calculate cloud temperatures, we use uniform distribution over the appropriate interval for a particular type of cloud. In the same way, we approach the formation of the height of a particular cloud and its presence in general, focusing on the currently selected scenario. In the case of clouds whose temperature is lower than \(-2~{}^{\circ}\)C, we utilize tabular values for the content of liquid crystals. The default system parameters are summarized in Table 4.  
Note that the impact of temperature is mainly attributed to both the atmospheric attenuation coefficient and typical clouds for different times of the year. It has to be accounted for in both estimations of the absorption coefficient in Section 4.1 by utilizing appropriated tabulated data from the HITRAN database and when deciding upon the cloud formations. In our numerical results, we consider the year-averaged temperature for different considered Earth regions (north, middle, and equator). As an example of the middle zone, Germany was considered with a year-averaged temperature at the sea level of 8.7 \({}^{\circ}\)C, while for the equator, we considered Kenya with the year-averaged value of 29.1 \({}^{\circ}\)C. For the north region, we considered Finland with the corresponding value of 5.0 \({}^{\circ}\)C. Note that, as the altitude increases, the difference between regions gets smaller. Thus, the overall differences caused by different atmospheric attenuation are negligibly lying within 1-2 dB. However, the formations of clouds also vary depending on the time of the year in different Earth regions. We considered those typical for the summertime. In general, when applying it, one needs to fine-tune the model with the appropriate choice of environmental parameters. We start by demonstrating the difference between the proposed model accounting for both atmospheric absorption and attenuation by clouds and the standard free-space propagation model (FSPL) in Figure 5. Here, we consider the middle Earth zone and two cloud conditions--rainy and cloudy weather. As one may observe, the difference between the proposed model for rainy conditions and FSPL is 10 dB. For cloudy conditions, it reaches 12 dB. These observations confirm that for accurate aircraft-to-ground THz channel modeling, one needs to account for the impairments considered in this paper. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Characteristic** & **Value** & **Description** \\ \hline \(f\) & 0.1–10 THz & Carrier frequency \\ \hline \(d\) & 7000–14,000 m & Ground-to-aircraft distance \\ \hline \(P_{T}\) & 10–200 W & Transmit power \\ \hline \(G_{T}\) & 20–80 dB & Transmit antenna gain \\ \hline \(G_{R}\) & 20–40 dB & Receive antenna gain \\ \hline \(S_{T}\) & 0 dB & SNR outage threshold \\ \hline \(N_{0}\) & \(-174\) dBm/Hz & Thermal noise \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The default system parameters. We proceed by illustrating the utilization of the proposed model for different weather conditions, sunny, cloudy, and rainy in the equator Earth zone in Figure 6. Specifically, Figure 6a,b show Rx power as a function of frequency and aircraft altitude. As one may observe in Figure 6a, logically, sunny conditions produce the best propagation environment across the whole THz band. The difference between sunny and cloudy conditions is approximately 15-20 dB and slightly increases as the carrier frequency increases. Note that these differences are solely attributed to the blockage by clouds and atmospheric absorption as no additional weather effects are present.