## 4 Discussion  
The most obvious difference between the GNSS-RO and ionosonde-derived profiles is the shape of the D- to E-transition region. While the ionosonde EDPs show a sharp decrease from \(fmin\) to an electron density of zero, the GNSS-RO shows a smooth transition to the D-region with a greatly reduced but non-zero electron density. This smooth transition is in good agreement with the FIRI profile shapes, which were derived from rocket measurements [35]. Ionosondes do not measure below \(fmin\) and make the assumption of a quasi-parabolic shape for the bottomside E-region, thus the \(N_{e}\) rapidly decreases to zero at an altitude close to the \(fmin\) altitude [41]. FIRI, however, includes D-region \(N_{e}\) estimates [35] such that \(N_{e}\) is zero at approximately 60 km and slowly increases with altitude up to the E-region where it rapidly increases up to \(hme\). The GNSS-RO profile has a strong similarity to the FIRI profile shape at these low altitudes, indicating that it is properly measuring the D- to E-region transition and is characterizing the lower ionosphere at electron densities that cannot be measured by ionosondes. The process used by ARTIST to calculate the real height has uncertainty as to the starting height of the profile [32]. Error can be introduced into the ionogram profiles in several ways, such as non-representative auto-scaling, uncertainty in the region between the E- and F- layers, and the fact that ionosondes are unable to measure below \(fmin\)[40]. Additionally, ionosondes calculate real height from the measured virtual height using Chebyshev polynomials, which require some knowledge of the starting height of each layer, and an assumption of a parabolic E-region below \(fmin\)[41]. The authors of [42] provide a method for estimating the starting height for the inversion process using the solar zenith angle, a seasonal term, sunspot number, and time after sunset. An in-depth discussion on calculation strategies used by ionograms is provided in [5]. Further, it must be noted that alternative ionogram inversion models, such as POLynomial ANalysis program (POLAN),  
Figure 19: GNSS-RO—ionosonde virtual height difference histograms and CDFs which show a positive bias for all sites except Fortaleza. The Frequency on the right corresponds to the number of datapoints within each bin. do not make the same assumptions about the profile shape below \(fmin\)[5; 43], which may be helpful for studies of the D- to E- transition region. While there are uncertainties in ionosonde derived EDPs, uncertainties also exist for the GNSS-RO profile altitudes due to ray bending/separation [13] and ionospheric inhomogeneities [17; 44; 45]. The E-region EDP retrieval from the bottom-up method has the highest data quality at 90-100 km. At lower altitudes it is limited by measurement noise because it removes the F-region contribution using the GNSS-RO profile itself and the E-region EDP contribution decreases exponentially with height. At higher altitudes \(>\)100 km, F-region bending and sporadic-E effects are neglected by the bottom-up method. Therefore, the EDP retrieval error is expected to increase at higher altitudes. Additionally, the optimal estimation method [25] used to invert the GNSS-RO measurements [22; 23] is optimized to minimize oscillations in the EDP which may induce biases in \(foE/hmE\) estimates. The typical top-down onion peeling method used for RO inversion [46] is known to produce negative electron densities from oscillations near the bottom of the profile [17; 47], and the optimal estimation method is able to significantly reduce these negative oscillations through an E-region focused retrieval design and the effective removal of the majority of the F-region contribution (see discussion in [22; 23]). However, this places fewer constraints on the densities predicted for the top of the profiles near and above 120 km, which may smooth out the E-layer peak such that the \(foE\) and \(hmE\) estimates are negatively impacted.