## 3 Verification of the STAR-Derived Excess Phase and Bending Angle Profiles
### Excess Phase Comparisons  
Figure 4 shows three scenarios of different excess phase profiles processed from level 1a data (see Figure 2). Figure 4a-c depicts raw carrier phase time series from the opnGns files, which lasts about 2-3 min, corresponding to the GNSS satellite's rising/setting time viewed from the LEO satellite. The difference (residual) between the calculated raw carrier phase and carrier phases model from receivers is provided in high-rate observations. Here, phase cycle slips can be seen clearly as the discontinuity from maxima to minima with two adjacent elements. These cycle slips are usually on a scale of a few wavelengths (e.g., 0.19 m for L1).  
Figure 4: From carrier phase to excess phase conversion with three scenarios of C2E1 (left: GPS setting for G14 at 2019.275 01:43:00 middle: GLONASS setting for R20 at 2019.275 11:31; Right: GPS rising for G09 at 2019.275 11:08). The top row (**a–c**) shows the raw carrier phase (black line) and the calculated range (direct distance) between the GNSS satellite and the LEO satellite (blue line) for three cases. The second row (**d–f**) shows the phase residual (carrier phase minus receiver phase model) before cycle slip removal. The third row (**g–i**) shows the residual excess phase after cycle slip removal. The fourth row (**j–l**) shows the excess Doppler (black line represents STAR results, green lines are UCAR results) and L1 SNR (Unit: \(v/v\)) (orange lines). The fifth row (**m–o**) shows excess Doppler differences.  
For L1, the method from [32] can effectively remove the cycle slips for high SNRs by checking the discontinuity in the phase difference (from the model) and restoring the phase continuity by adding integer numbers to the wavelength through minimization. However, there are still uncertainties in the lower troposphere, where atmospheric multi-path occurs. The residual phase time series can also be correlated with the GPS bit time series to remove additional cycle slips [48]. The cycle slip corrected residual carrier phases in our processing are added to the phase model to derive the excess phase for each frequency with clock bias correction and geometric range correction (Figure 4g-i). The excess Doppler is defined as the time derivatives of the excess phase. Figure 4j-l shows that the STAR excess Doppler (blue line) is of excellent agreement with those from UCAR (green line) for these three scenarios.  
STAR-derived COSMIC-2 excess phases are very consistent with those derived from UCAR. Figure 5 compared the excess phases from STAR and UCAR for one day (\(\sim\)800 occultations) for C2E1 on 2 October 2019. The mean differences and standard deviations are 0.01 \(\pm\) 0.04 m (Figure 5a) for rising profiles and \(-\)0.01 \(\pm\) 0.03 m (Figure 5b) for setting profiles at 10 km, respectively. The close 0.2 m difference in the lower troposphere may be due to the remaining residual clock bias of some profiles. The mean difference and standard deviation increase below 10 km, where atmospheric multi-path effects occur. The excess phase difference increases dramatically below 10 km, indicating the cycle slip detection problem. Note that the excess phase is set to zero at the start time of setting or stop time of rising.