## 3 Verification of the STAR-Derived Excess Phase and Bending Angle Profiles
### STAR Bending Angle Comparison with UCAR and ERA5  
This study processed more than twelve thousand COSMIC-2 E1 occultation profiles collected in October 2019. Because all COSMIC-2 receivers (E1-E6) are of a similar quality (see [35]), we do not further repeat E2-E6 results hereafter. The ERA5 temperature, moisture, and pressure profiles are interpolated onto the times and locations of COSMIC-2 data. The interpolated ERA5 datasets are then converted to bending angle profiles using the forward operator package described in Section 2.6. This section compares the STAR bending angle profiles with ERA5 and UCAR. STAR  
Figure 5: Excess Phase comparison between STAR and UCAR results (STAR-UCAR) for (**a**) rising and (**b**) setting for day 2019.275. The impact height is derived based on the geo-optical method from L1. The Solid line represents difference, and the dashed line represents standard deviation. profiles passed quality control. (See Table 1) are used in the comparisons. We separate our comparisons with L2P/L2C signals and GPS/GLONASS satellites. Figure 6a,b compared STAR-derived bending angle profiles with those from UCAR and ERA5 simulated bending angle profiles spatially and temporally collocated with COSMIC-2 events. The fractional bending angle difference (i.e., (STAR-ERA5)/ERA5 \(\times\) 100%) is shown. Only \"good\" STAR-derived bending angle profiles are included in the comparison. The STAR-derived bending angle profiles are flagged as \"bad\" when the profile's relative bending angle deviated from the background (ERA5 simulation) by more than 15 sigmas at any height below 45 km. For the STAR and ERA5 pairs, those profiles with more than 100% fractional differences at all altitudes below 60 km are excluded to derive the reference bias and standard deviation. Figure 6a shows that the mean fractional bending angle difference between STAR and UCAR from 10 km to 35 km impact heights is less than 0.06%, and the standard deviation is less than 1.3%. However, a distinctive mean STAR-UCAR difference exists for L2P and L2C tracking signals. GPS L2P has a standard deviation of 1.32% (see Table 2). A relatively large STAR-UCAR standard deviation for GPS L2P compared to L2C occurred at impact heights from 20 km to 25 km. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Relative Percent (\%)**} & \multicolumn{2}{c}{**GPS L2C**} & \multicolumn{2}{c}{**GPS L2P**} & \multicolumn{2}{c}{**GLONASS**} \\ \cline{2-7}  & **UCAR** & **ERA5** & **UCAR** & **ERA5** & **UCAR** & **ERA5** \\ \hline BA & \(-0.04\pm 1.15\) & \(-0.34\pm 2.96\) & \(-0.04\pm 1.32\) & \(-0.28\pm 3.81\) & \(-0.06\pm 1.15\) & \(-0.09\pm 3.20\) \\ \hline Refractivity & \(-0.02\pm 0.83\) & \(-0.04\pm 1.06\) & \(-0.04\pm 0.97\) & \(0.09\pm 176\) & \(-0.05\pm 0.91\) & \(0.03\pm 1.08\) \\ \hline \end{tabular}
\end{table} 
Table 2: Mean difference and standard deviation of bending angle and refractivity comparison with UCAR and ERA5 at 10-35 km. Figure 6: (**a**) Relative bending angle profiles compared with UCAR results and (**b**) ERA5 simulated results over October 2019. The profile is grouped as GLONASS L2C (cyan), GPS L2C/L2L (blue), and GPS L2P (red). The solid line represents the relative difference, and the dashed line is the standard deviation. The waggling structure compared with ERA5 is due to the forward operator from refractivity to bending angle calculation using Abel inversion. The most significant standard deviation for L2C and GLONASS is 1.6% at 25 km impact height. The large standard deviation for the L2P profile mainly results from the considerable uncertainty in the raw L2P signals from those rising GPS satellites without L2C broadcasting [49]. The latest UCAR operational software has mitigated this issue (per communication with UCAR). A good agreement in the monthly mean fractional bending angle profile between STAR and ERA5 is shown in Figure 6b.