## 2 Materials and Methods
### Ionograms  
The target minimum frequency measured for ionograms, \(fmin\), was 1.2 MHz or less so that the E-region and its peak would be clearly visible during the daytime. A frequency of 1.2 MHz equates to an electron density of \(1.8\times 10^{10}\) m\({}^{-3}\), well under the average density of the daytime E-region peak [27]. Thus, ionosondes with \(fmin\) at or below this level should detect much of the E-region structure. However, for Gakona and I-Cheon, there were a limited number of ionograms that met this \(fmin\) requirement and aligned with an available GNSS-RO profile. As a result, the \(fmin\) threshold was increased to the lowest point which provided enough ionograms to be statistically significant. The \(fmin\) thresholds and corresponding \(N_{e}\) for each site are displayed in Table 1. The typical sounding cadence for Digisondes is every 15 min, which was followed by Hermanus. However, I-Cheonfollowed a 7.5 min sounding cadence, Fortaleza used a 10 min cadence, and Gakona had a variable cadence (all under 15 min). In the event that multiple ionograms met the \(fmin\) threshold and were taken within 30 min of a GNSS-RO measurement, the ionogram closest to the GNSS-RO time was used. Ionograms were retrieved using the SAO Explorer to access data from the Global Ionospheric Radio Observatory (GIRO) [8]. The ionograms were hand-scaled to filter out soundings when the E-region was not measured, or when Sporadic-E (\(E_{s}\)) was present, and to ensure low-quality data were removed. For this comparison, the key interest was the new bottom-up method's performance given a calm ionosphere. Therefore, instances in which \(E_{s}\) was present were excluded. Excluding ionograms that did not have a clear E-region during the hand-scaling process naturally filtered out measurements taken at night. While hand-scaling allows for manual adjustment of the ionogram virtual height traces, the same inversion process used in Automatic Real-Time Ionogram Scaler with True \begin{table}
\begin{tabular}{c c c c c} \hline
**Site** & **Hermanus** & **I-Cheon** & **Gakona** & **Fortaleza** \\ \hline \(fmin\) (MHz) & 1.2 & 2.0 & 1.2 & 1.4 \\ \(N_{e,fmin}\) (m\({}^{-3}\)) & 1.8 \(\times\) 10\({}^{10}\) & 5.0 \(\times\) 10\({}^{10}\) & 1.8 \(\times\) 10\({}^{10}\) & 2.4 \(\times\) 10\({}^{10}\) \\ \hline \end{tabular}
\end{table} 
Table 1: The \(fmin\) threshold and electron density corresponding to the plasma frequency \(fmin\) for each site. The average E-region peak during the daytime is on the order of 10\({}^{11}\) m\({}^{-3}\), thus the daytime E-region is measurable using these thresholds. Figure 1: GNSS-RO uncertainties calculated using the optimal estimation method on 200 profiles from 1 Jan 2023. “Eden’ is the electron density (black) and “Unc’ is the altitude dependent uncertainty (red) with units of 10\({}^{5}\) cm\({}^{-3}\) (10\({}^{11}\) m\({}^{-3}\)). ’Index’ in the lower-right figure corresponds to the phase standard deviation between 50–55 km (black), and ‘Chisq_80 km’ is a quality index used to estimate ionospheric impacts on the neutral atmosphere (red). Height calculation (ARTIST) to calculate real heights from virtual heights [28; 29] is used for the hand-scaled ionograms. As displayed in Figure 2, a non-uniform time distribution is produced for each of the sites, with no ionograms at night, and the majority of ionograms during the morning and evening periods. This time distribution is primarily limited by the low \(fmin\) thresholds (Table 1), which are mostly satisfied during the morning and evening periods. The limited dataset from this non-uniform time distribution may introduce an additional bias into the comparison, as discussed further in Section 4. While the optimal estimation method used for the GNSS-RO bottom-up approach naturally provides an uncertainty, it is more difficult to obtain electron density uncertainties from manually scaled ionogram inversions in SAO Explorer as they are not a direct output.