## 4 Discussion
Finding the correct weighting balance is critical and is the focus of an ongoing investigation using a larger dataset for comparison that relies on automatically scaled \(foE\) and \(hmE\) instead of the hand-scaling used in current study. Interestingly, while the electron density profiles show an altitude bias at \(fmin\), the virtual height comparison shows an agreement for many profiles near the lower \(fmin\) altitudes (Figure 18). The RO virtual height profiles show a positive bias at lower altitudes due to local density peaks that produce elevated virtual heights, but the mid-latitude sites (Hermannus and I-Cheon) show a clustering near the 1:1 line at the lowest altitudes. Since the ionosonde virtual heights are direct measurements that do not require additional assumptions or processing to interpret, the agreement at lower altitudes suggests that many of the RO profiles are in general agreement with the actual electron density profiles up to \(fmin\). However, this agreement does not match with the persistent altitude bias between ionosonde and RO EDPs at \(fmin\), which motivated us to analyze the ionosonde EDPs using the same AIRTracer used to calculate RO virtual heights. Following the same procedures as described for the RO virtual heights surrounding Figure 18, virtual heights were calculated from the ionosonde EDPs to compare against the direct virtual height measurements from the same ionosondes. The results are displayed in Figure 20, which show a negative altitude bias for the virtual heights calculated using the ionosonde EDPs with a numerical ray tracer. Interestingly, the negative bias observed here at the lower altitudes near \(fmin\) is similar in magnitude and direction as the bias between the RO and ionosonde EDPs discussed in Section 3.1. This altitude bias may be an artifact of the quasi-parabolic shape assumption for the E-layer, which results in a slight altitude difference for the observed virtual heights compared to the idealized electron density profiles derived from the measurements. As the virtual heights are directly proportional to the integral of the altitude gradient with respect to plasma frequency, \(\mathrm{d}z/\mathrm{d}f_{p}\), assumptions on the shape of the E-layer up to \(foE\) will impact the derived altitude gradient, which will in turn impact the virtual heights calculated from the electron density profiles. A comparison between the \(\mathrm{d}z/\mathrm{d}f_{p}\) calculated for the shifted GNSS-RO and ionosonde profiles is displayed in Figure 21. Interestingly, the GNSS-RO profiles have larger \(\mathrm{d}z/\mathrm{d}f_{p}\) for the smaller values, while the ionosonde altitude gradients are larger at elevated values. This indicates that the RO profiles are increasing in altitude more rapidly then the ionosonde profiles at the bottom of the layers near \(fmin\), while the ionosonde profiles increase more rapidly near \(foE\). While the RO profiles cannot be used as a validating dataset here, this difference provides insight into the impacts of the quasi-parabolic shape assumptions that may result in exaggerated \(\mathrm{d}z/\mathrm{d}f_{p}\) near \(foE\)These exaggerated altitude gradients allow for the E-layer to be shifted down in altitude to match the virtual height observations, as the virtual height is dependent on the integral of \(\mathrm{d}z/\mathrm{d}f_{p}\). A reduction in the altitude gradients would require the profiles to be shifted upwards in altitude, which may help to increase agreement between the ray tracer virtual height estimates and the direct ionosonde measurements. This uncertainty in the virtual height to real height inversion has a direct impact on the EDP comparison. The bias observed between the ray tracer virtual heights and ionosonde observations has the same direction and magnitude as the difference between the GNSS-RO and ionosonde EDPs at \(fmin\) (Table 3).