# Global GNSS-RO Electron Density in the Lower Ionosphere
## 2 Data and Methods
### \(N_{e}\) Retrievals
#### 2.3.2 D/E-Region  
The bottom-up algorithm is developed to enable and optimize the \(D\)/\(E\)-region \(N_{e}\) retrieval in the situations where the \(F\)-region \(hTEC\) measurements are unavailable for correcting their effects on the lower-ionospheric retrieval. It is difficult to make this correction with the onion-peeling method when the entire \(hTEC\) profile is not available. An example from Equations (9) and (10) is shown in Figure 4, where the \(N_{e}\) profile is retrieved up to the RO top. Since most of the COSMIC 50-Hz RO data have a top height around \(h_{t}\sim\) 125 km (see Appendix B), the \(D\)-region and a good portion of the \(E\)-region can be resolved, but the number of COSMIC-1 ROs started to decrease after 2017. The sampling reduction creates a problem for uniform local time coverage during the later years of COSMIC-1 mission. On the other hand, the operation from Sun-synchronous MetOp satellites has been stable throughout the mission, acquiring 100 Hz ROs up to \(h_{t}\sim\) 90 km for the \(D\)-region. Therefore, the MetOp-A/B/C data are quite useful for studying long-term \(D\)-region \(N_{e}\) variations at two Sun-synchronous local times (8-11 h and 20-23 h).  
Figure 4 is a relatively quiet case where the RIE component in the \(\phi_{iono\_free}\) profile has an amplitude of \(\sim\)3 cm with a small (\(\sim\)5 cm) \(E_{s}\) residual at \(h_{t}\sim\) 100 km. The \(D\)/\(E\)-region component (\(\phi_{p\_D/E}\)) in \(\phi_{exL1}\) is \(\sim\)2 m (Figure 4b), significantly greater than the RIE and \(E_{s}\) errors. This \(\phi_{p\_D/E}\) corresponds to \(\sim\)10 TECu in \(\Delta hTEC\) (Figure 4c). Because the observed \(\Delta hTEC\) is larger than the linearization profile (\(\mathbf{y}_{0}\)) from the state vector (\(\mathbf{x}_{0}\)), the retrieval yields an inverted \(N_{e}\) greater than \(\mathbf{x}_{0}\), as seen in Figure 4d.  
The _D/E_-region \(N_{e}\) retrievals show a good sensitivity to the diurnal variations (Figure 5), since a constant linearization profile is used in Equation 11 without any a priori information on solar zenith angle (\(\chi\)). As expected for the low \(N_{e}\) concentration, the retrieval result is noisier at lower altitudes. More scatters are evident in the early evening hours, especially in the _E_-region, suggesting the potential impacts from ionospheric scintillations [47]. The local time coverage from the COSMIC-2 is fairly uniform on a single day. By the time of this day (i.e., 1 January 2021), the six-satellite constellation had spread out in local time sampling from their initial launch orbits on 25 June 2019. The low inclination (24\({}^{\circ}\)) orbit also helps to cover the tropical diurnal cycle in a relatively shorter period compared to those higher-inclination orbiters.  
The diurnal variation of the retrieved _D/E_-region \(N_{e}\) is generally consistent with FIRI, although it exhibits a large deviation at 60 km (Figure 5). Unlike FIRI, which is symmetric about the local noon, the RO \(N_{e}\) retrievals are skewed slightly toward the afternoon hours. It is clear that the morning-hour onset of the daytime RO \(N_{e}\) lags the FIRI curve, while the retreat from the RO in the evening hours appears lagging behind the noon-symmetric FIRI model. The daytime RO \(N_{e}\) retrievals are slightly higher than the FIRI at 110 km. Given that F10.7 is at 77.7 solar flux unit (sfu) on 1 January 2021, the RO \(N_{e}\) retrievals are generally higher, compared to the FIRI prediction for F10.7 = 75 sfu.  
Figure 4: (**a–d**) Illustration of a COSMIC-1 RO \(N_{e}\) profile retrieved from 1 January 2008. Differences between the \(\Delta tTEC\) measurement profile and the linearized model \(\mathbf{y}_{0}\) are inverted to produce a new state vector \(\mathbf{x}\) for \(N_{e}\).