## 3 Results
### Virtual Height Comparison  
The final comparison performed for each individual site was for the virtual height profiles. Virtual heights are directly measured from the ionosondes, which provides a validating dataset for the RO profiles after they are used to calculate a virtual height. The ionosonde predicted electron density profiles are calculated using assumptions about profile shapes, etc. (e.g., [5; 40]), which adds additional uncertainty into the estimates. However, the virtual height is a direct measurement and, therefore, provides a direct validating dataset. GNSS-RO virtual heights were calculated using the numerical AIRTracer model to estimate ordinary-mode (O-mode) group paths for each plasma frequency in the RO profile above the ionosonde \(fmin\). Virtual heights above 140 km were removed to exclude cusps that result in large virtual heights near \(foE\). Examples of the calculated virtual heights along with the measured virtual heights are displayed in Figure 17. In this figure, only the points used for the comparison are displayed, which removes the virtual heights above 140 km and frequencies below \(fmin\). While some of the \(foE\) estimates in Figure 17 look incorrect (specifically, Gakona and Fortaleza), this is an artifact of the 140 km limit which removes the large virtual heights near the \(foE\) cusp. Further, D-region virtual heights are not calculated for the RO profiles because the ionosonde data are limited to frequencies above \(fmin\). Extending this procedure to all of the EDPs used in this study provides the virtual height scatter plots displayed in Figure 18. From this, a few trends are immediately obvious. First, there is a clustering of data points near the 1:1 line at low altitudes between \(\sim\)100-110 km. This clustering is most obvious for Hermanus, but also present to a smaller extent in I-Cheon and Gakona. As the virtual height is related to the integral of the EDP  
Figure 16: Shifted GNSS-RO\(-\)ionosonde \(N_{e}\) difference histograms showing larger differences at higher altitudes. The color bar represents the number of measurements in each bin. A total of 400 bins were used (\(20\times 20\)) and the color bar represents the number of measurements in each bin. as a function of altitude, this indicates that many of the RO EDP estimates up to \(fmin\) are consistent with the measured virtual heights. However, outlying points also exist for the RO virtual heights within the 100-110 km range of ionosondes, where the RO virtual heights are overestimated by 10 and 30 km. This is most pronounced in the Gakona dataset, but also present at the other sites. Interestingly, Fortaleza only shows the overestimated virtual heights at these lower altitudes and does not show the clustering near the 1:1 line as displayed for the other sites. These outliers are either due to large overestimates of the altitudes for plasma frequencies below \(fmin\), or local peaks (large vertical gradients) in electron density that occurs at these lower altitudes. The second obvious trend is the increased spread in points at higher altitudes. This increased spread is a result of large virtual heights produced near local density peaks (such as \(foE\)), which can occur for both ionosondes and RO profiles. For Gakona and Hermanus, the positive virtual height bias for the RO data indicates that the \(foE\) may be too low compared to the actual \(foE\) measured by ionosondes, or the hmE can be too high. From the small subset of profiles displayed in Figures 10 and 12, it appears the elevated RO \(lnmE\) is the culprit, but this should be re-explored with a larger dataset as it could be a combination of the two factors. For I-Cheon and Fortaleza, the positive bias exists at lower altitudes while it switches to a negative bias (RO virtual heights less than ionosonde) at higher altitudes. Figure 17: Virtual height profiles calculated from GNSS-RO using a numerical ray tracer along with the direct ionosonde measurements showing general agreement in the trends.