## 3 Path Loss Simulation and Illuminated Field Intensity Observation in an Air-to-Ground Scenario  
Figure 5 presents a conceptual figure of the air-to-ground scenario in the SAR application across Pohang (S4) and Heuksando (S6) in Korea. We observed the illumination intensity of the electromagnetic wave on the ground surface by wave propagation characteristics according to atmospheric conditions. In the scenario, we assumed that the airborne radar located in the middle of \(S_{4}\) and \(S_{6}\) was steering to the ground with the scan angle of \(\theta_{E}\). Herein, \(h_{a}\) is the altitude of the airborne transmitter, while \(r\) and \(\theta_{A}\) are the scanning range and the azimuth beam angle from flight direction, respectively. To calculate the illuminated field intensity on the terrain, propagation path losses were simulated using the MATLAB PETOOL [29], where the simulation parameters were a Gaussian beam pattern, a beamwidth, an elevation steering angle, an operating frequency, and the digital terrain elevation data. The detailed values of the simulation parameters are listed in Table 3.  
Figure 4: Two-dimensional interpolation results at a fixed altitude of 5000 m in the Korean Peninsula (15 February 2019): (**a**) IDW method; (**b**) nearest-neighbor method; (**c**) linear method; (**d**) cubic method. Figure 6 shows the path loss simulation results between Pohang (S4) and Heuksando (S6) as a function of the range and altitude, where the white dotted line represents the main beam direction. Figure 6a shows the path loss obtained by assuming the standard atmospheric condition of \(\
abla M=118\) throughout the entire troposphere. Figure 6b shows the path loss obtained using the observation-based atmospheric condition on 15 February 2019, where the refractivities between Pohang (S4) and Heuksando (S6) were interpolated with the proposed IDW method, using the data measured in twenty sites. On the terrain surface ranging from 90 km to 190 km, the average path loss was179.7 dB in standard atmospheric conditions (\(\
abla M=118\)), while the average path losses using the observation-based atmospheric conditions interpolated from the measured data was 182.1 dB. To verify the PETOOL simulation software, we adopted another well-known simulation software named Advanced Refractive Effects Prediction System (AREPS) [31] and a standard recommendation of ITU-R P.528 [32]. For the AREPS simulation software, the input parameters were set to the same simulation conditions as PETOOL. For example, a Gaussian source with a 2\({}^{\circ}\) half-power beamwidth (HPBW) was used for a source pattern, and the normal atmospheric condition (\(\
abla M=118\)) was uniformly distributed along the height without having terrain data. Figure 6c presents the comparison of the path loss simulation results at the height of 1.8 m according to the range, where solid, dashed, and dotted lines indicate the AREPS, PETOOL, and ITU-R P.528 models, respectively. The path results of both simulators showed a good agreement with each other, and the ITU-R model followed the trend of the path loss line well. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Altitude of the airborne transmitter (\(h_{a}\)) & 5000 m \\ Scanning range (\(2r\)) & 387.4 km \\ Angle between flight direction and main beam direction (\(\theta_{A}\)) & 0–360\({}^{\circ}\) \\ Beam pattern & Gaussian \\ Beam width & 2\({}^{\circ}\) \\ Steering angle (\(\theta_{\mathrm{E}}\)) & 2\({}^{\circ}\) \\ Polarization & Vertical \\ Tx frequency & 10 GHz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Two-dimensional path loss simulation setup. Figure 5: Air-to-ground scenario in the synthetic aperture radar (SAR) application across Pohang (S4) and Heuksando (S6) in Korea.