## 4 Discussion  
### The Scanning Data Analysis during the Two Solar Eclipses  
During the scanning of the sun, the sun can be assumed to be a point source for the antenna, the solar T\({}_{\rm B}\) increment received by the antenna can be assumed to be a Gaussian function of the radial distance to the antenna beam axis [4; 27]. The T\({}_{\rm B}\) increment is given by:  
\[\Delta T_{sun}(x)=A_{d}\exp[-4\ln 2\bigg{(}\frac{x}{\theta_{A}}\bigg{)}^{2}], \tag{18}\]  
where \(x\) is the angle radius distance from the sun to the center of the antenna beam, \(\theta_{A}\) is the antenna half-power beamwidth, and \(A_{d}\) is the maximum T\({}_{\rm B}\) increment when the antenna is pointing to the center of the sun. During scanning data by the GMR, the antenna beamwidth and the maximum T\({}_{\rm B}\) increment can be easily fitted by the least-square method. That is to say that the sun can be used to measure the antenna pattern of the radiometer. The measurement of principle and method have already been reported in detail in previous papers [17; 18]. We used the upgraded radiometer to track and scan the sun during the two solar eclipses. The GMR recorded the variation of the T\({}_{\rm B}\) at three frequencies (22.235, 25.0, 30.0 GHz) in K-band on 26 December 2019 and 21 June 2020. These two eclipses provided a very good opportunity for us to observe the solar eclipse process with a microwave radiometer. In order to compare the variation of solar radiation T\({}_{\rm B}\), we also scanned and observed the solar T\({}_{\rm B}\) without solar eclipse. During the process of scanning the solar eclipse, we measured T\({}_{\rm B}\) increments at many step angles at three frequencies after correction for the angle distortion, as is shown in Figures 4 and 5 for 26 December 2019 and 21 June 2020,  
Figure 3: The portion of the sun covered by the moon (eclipse obscuration) and the red marker represents the observation site in Xi’an, China. (**a**) 26 December 2019, (**b**) 21 June 2020. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Eclipse Time** & **First Contact** & **Maximum Phase** & **Last Contact** & **Duration** & **Max-Obscuration** \\ \hline
26 December 2019 & 12:21 & 13:29 & 14:36 & 2 h 15 min & 11.4\% \\
21 June 2020 & 14:16 & 15:47 & 17:06 & 2 h 50 min & 74.9\% \\ \hline \end{tabular}
\end{table} 
Table 3: Stages and times of the eclipse events outlined for Xi’an (all times were local time, CST). respectively. The observation results showed that the solar eclipse could be observed by the GMR. According to Equation (17), the scanning data were fitted with Gaussian function using the least squares fitting, and the statistical results are given in Table 4. The results showed that:  
1. the scanning points near the sun showed good symmetry and consistency with the results from a fitting using the Gaussian function. The scanning data were able to be used to measure the antenna pattern;
2. the maximum value of T\({}_{\rm B}\) increment was different for each frequency, but they were related to the antenna beamwidth, and the fitting of beamwidth (\(\beta\)) was not affected by solar eclipse (see Table 4). Because the Earth-Sun distance is very far, the sun can be regarded as a point source during the solar eclipse. Therefore, it did not affect the measurement of antenna beamwidth;
3. during the solar eclipse, the T\({}_{\rm B}\) increment decreased significantly when compared to the main beam without the solar eclipse, because the sun disk was shaded by the moon and the level of solar radiation became small;
4. the T\({}_{\rm B}\) increment was related to the portion of the sun shaded by the moon, when the solar eclipse reached its maximum phase, the decrease of the T\({}_{\rm B}\) increment was at its maximum;
5. because of the variations of the Earth-Sun distance, the T\({}_{\rm B}\) observed by radiometer is different at different times. Figure 4: The variation of T\({}_{\rm B}\) increment during the scanning of the sun at the azimuth on 26 December 2019. BE means “before eclipse” and ME means “maximum eclipse”.