# Global GNSS-RO Electron Density in the Lower Ionosphere
## 2 Data and Methods
### RO Excess Phase (\(\phi_{ex}\)) Measurements
Although the RO \(\phi_{ex\_iono}\) is dominated by \(-\phi_{p\_iono}\), ionospheric bending effects are not negligible because of the long pathlength in RO wave propagation. On the other hand, phase advance results from a faster phase speed of wave propagation in the ionospheric plasma, which will shorten \(\phi_{ex\_iono}\). The two competing effects both manifest themselves in the GNSS-RO \(\phi_{ex}\) profile shown in Figure 1b. Figure 1: (**a**) GNSS-RO excess phase \(\phi_{iono\_free}\) profile from COSMIC-1 superimposed by the neutral atmospheric bending \(\phi_{atm}\) (in red) component derived from fitting the data \(h_{t}\) = 30–60 km; (**b**) Illustration of different excess phase components in GNSS-RO for L1 excess phase \(\phi_{ex1,L}\), L2 excess phase \(\phi_{ex1,L2}\), atmospheric bending \(\phi_{atm}\), ionospheric component (\(\phi_{ex\_iono}=\phi_{ex}-\phi_{atm}\)) for \(L1\) and \(L2\), \(F\)-region contributions \(\phi_{bend\_F}-\phi_{p\_F}\), and \(D\)/\(E\)-region phase advance \(-\phi_{p\_D/E}\). A thin sporadic-\(E\) (\(E_{s}\)) layer is identified at 107 km with an enhanced excess phase in both \(-\phi_{ex1,L}\) and \(-\phi_{ex1,L2}\) data. The number of \(N_{e}\) retrievals may decrease with the dual-frequency approach, to some extent, compared to the \(\phi_{exL1}\)-only approach. Data quality control is obviously more demanding from the joint use of \(\phi_{exL1}\) and \(\phi_{exL2}\) profiles, because large spikes in either measurement can cause a bad \(Ne\) retrieval. Because GNSS-RO \(\phi_{ex}\) measurements generally have better signal-to-noise ratio (SNR) for \(\phi_{exL1}\) than for \(\phi_{exL2}\) from GPS (Global Positioning System), the required \(\phi_{atm}\) calculation may be subject to the additional error induced from the \(\phi_{ext2}\) profile, which can lead to an unsuccessful \(N_{e}\) retrieval. In addition, the relative signal strengths between L1 and L2 transmitters may vary with the GNSS systems. For example, GLONASS (Global Navigation Satellite System) satellites sometimes transmit stronger signals at the \(L2\) frequency than \(L1\). The linear fitting for the \(F\)-region effect removal is similar between this study and one developed by [PERSON] [31], except for slightly different height ranges. In this study, a linear function is fitted to the \(hTEC\) profile at \(h_{t}\) = 30-60 km on a profile-by-profile basis:  
\[hTEC_{fit}=a_{0}+a_{1}\cdot h_{t}\qquad\qquad\text{for $h_{t}$ = 30--60 km} \tag{8}\]  
The derived linear fit is extrapolated to the heights above at \(h_{t}\) > 60 km, as estimated \(F\)-region contributions. By subtracting it from \(hTEC\), we can obtain the \(D\)/\(E\)-region \(\Delta hTEC\) profile (in TECu):  
\[\Delta hTEC=hTEC-hTEC_{fit} \tag{9}\]  
where 1 TECu = 10\({}^{16}\) m\({}^{-3}\). Note that the conversion in Equation (9) neglects higher-order frequency dependence and ionospheric bending effects. In essence, the bottom-up approach uses the difference \(\Delta hTEC(h_{t})\) with respect to the empirical reference (i.e., a linear function derived from \(h_{t}\) = 30-60 km), instead of absolute \(hTEC(h_{t})\) values, for the \(D\)/\(E\)-region \(N_{e}\) retrieval. As shown in the next section, the \(\Delta hTEC(h_{t})\) at the \(D\)/\(E\)-region \(h_{t}\) have much smaller contributions from the \(F\)-region \(N_{e}\) compared to the Abel weighting functions, which allows to yield a more reliable inversion for the \(D\)/\(E\)-region \(N_{e}\).