## 2 Materials and Methods
### GNSS-RO Bottom-Up Approach  
GNSS-RO profiles were calculated using the COSMIC Data Analysis and Archive Center's (CDAAC) 50 Hz atmPhs files [24]. Following [23], the first step of the bottom-up approach is the calculation of the horizontal total electron content (hTEC) using both the L\({}_{1}\) and L\({}_{2}\) excess phase. The inclusion of both L\({}_{1}\) and L\({}_{2}\) allows for the removal of the neutral atmosphere contribution to the phase, which follows an exponential relationship with respect to altitude. After the hTEC is calculated, a linear fit to the hTEC as a function of altitude is performed over the altitude range of 30-60 km. The linear phase profile in this altitude range corresponds to the F-region hTEC contribution, as the local electron density is essentially zero at these low altitudes.  
Removing this F-region contribution provides \(\Delta\)hTEC, which allows for estimates of D- and E-region electron densities by effectively reducing the F-region \"noise\" in the phase profiles. Weighting functions for this \(\Delta\)hTEC have a much smaller reliance on higher altitudes than the Abel functions, providing a more localized dependence [22; 23]. The \(\Delta\)hTEC profiles are subsequently inverted to provide electron densities as a function of altitude (EDPs). For this inversion, the optimal estimation method [25] is implemented with a reference electron density profile composed of the 2008 annual mean from IRI-2016 [26] for the F-region and FIRI using solar minimum conditions for the E- and D-regions. While the bottom-up approach is helpful for removing the F-region contributions in the lower ionosphere, the extrapolated linear fit can produce large uncertainties at F-region altitudes. Therefore, this method is generally recommended for use at altitudes below 150 km.  
The optimal estimation method provides an altitude dependent uncertainty, as displayed in Figure 1. Here, we see the electron density uncertainty increases with altitude from \(\sim\)\(1\times 10^{9}\) m\({}^{-3}\) at 70 km to \(\sim\)\(6\times 10^{9}\) m\({}^{-3}\) at 100 km. Additional quality indices are also used to help remove poor profiles, such as the standard deviation of the phase noise in the altitude range of 50-55 km. As displayed in the bottom-right of Figure 1, a phase noise threshold of 0.005 m is used to eliminate poor profiles. Another quality index is based on the electron density \(\chi^{2}\) at an altitude of 80 km, which can estimate ionospheric impacts to the neutral atmosphere at lower altitudes (the so-called residual ionospheric effect, RIE). However, this \(\chi^{2}\) index does not strongly correlate with poor electron density profiles in the E-region.  
GNSS-RO derived EDPs were compared against ionosonde derived EDPs when the occultation was within 2\({}^{\circ}\) of the ionosonde location and within 30 min of the ionogram time. Before matching the RO crossings with ionograms satisfying the comparison criteria (outlined in the next section), the total number of occultations within the 2\({}^{\circ}\) regions during the periods of interest for each site were: 2162 for Fortaleza, 1402 for I-Cheon, 1739 for Hermanus, and 1403 for Gakona.