# COSMIC-2 RO Profile Ending at PBL Top with Strong Vertical Gradient of Refractivity
## 4 Results
### Statistical Results on the Relationship between the RO Lowest Altitudes and PBL Heights  
The vertical gradients of \(N-\overline{N}^{\text{obs}}(r)\) are calculated at the lowest altitudes of all the COSMIC-2 RO profiles in August 2020 over the SEP and SCP areas. The scatter plots in Figure 7 suggest a relationship between the lowest RO observing altitudes and the strong local vertical gradients of \(N-\overline{N}^{\text{obs}}(r)\) in both SEP and SCP areas. The points on the left of the dashed line, which is line with the vertical gradient of \(N-\overline{N}^{\text{obs}}(r)\) equal to \(-65\) N-unit km\({}^{-1}\), represent the cases where the GPS RO signals in the low altitudes cannot be observed when encountering significant strong vertical gradients of \(N-\overline{N}^{\text{obs}}(r)\). The results in the two areas are not exactly the same in that the strong negative vertical gradients of \(N-\overline{N}^{\text{obs}}(r)\) occur more frequently in the SEP than in the SCP area, especially when the negative vertical gradients are less than \(-200\) N-unit km\({}^{-1}\). This finding is consistent with previous studies that have pointed out that the atmospheric ducting occurs most frequently in the SEP area [30; 31]. In Figure 7, the ERA5 PBL heights near the RO profiles are indicated  
Figure 6: (**a**) Spatial distribution of COSMIC-2 observations of RO profiles on 1 August 2020, in which the lowest height from the Earth surface is indicated in colors. (**b**) Vertical profiles of spherically symmetric refractivity \(N(r)\) from the COSMIC-2 RO observations (red curve) and the ERA5 reanalysis (black curve). Also indicated is the COSMIC-2 data count (gray curve, top x-axis) between 45\({}^{\circ}\)S and 45\({}^{\circ}\)N on 1 August 2020.  
in colors. It is seen that when the vertical gradients are smaller than \(-65\) N-unit km\({}^{-1}\), the lowest altitudes of COSMIC-2 RO observations agree with the PBL heights. It is likely that the inversion at the PBL top hinders the propagation of RO signals. As shown by the black solid curve in Figure 7, however, this kind of RO only accounts for a very small fraction of all the COSMIC-2 RO data in these two areas.  
We notice that there are still quite a few RO profiles on the right side of the dashed line whose lowest altitudes are high, suggesting that some RO profiles are unable to penetrate down into the lower troposphere even though the vertical gradient is weak. The impacts of  
Figure 7: Scatter plots of the lowest heights versus the vertical gradient of \(N-N(r)\) for all COSMIC2 RO profiles in August 2020 over (**a**) the SEP and (**b**) SCP areas. The PBL height for each RO profile is indicated in colors, and the number of the lowest RO data with the vertical gradient of \(N-N(r)\) being greater than \(-65\) N-unit km\({}^{-1}\) (black dashed line) at 0.2-km interval is shown by black curve.  
the horizontal gradient of refractivity on how deep the GPS RO signals can be observed will be investigated in the following section.  
Figure 8 gives a geographic look at the relationship between the lowest RO altitudes and the PBL heights for those RO cases whose negative vertical gradients of \(N-\overline{N}^{\mathrm{obs}}(r)\) at the RO lowest altitudes are smaller than \(-65\) N-unit km\({}^{-1}\). We see correspondence between the lowest RO altitudes (top panels) and the PBL heights (bottom panels) in both the SEP (left panels) and SCP areas (right panels). More cases in the SEP area have higher PBL heights than the SCP area. This observation is consistent with the results in Figure 7 that showed that more significantly strong negative vertical gradients of \(N-\overline{N}^{\mathrm{obs}}(r)\) appeared in the SEP area than the SCP area.