# Global GNSS-RO Electron Density in the Lower Ionosphere
## 3 Results
### \(D\)-Region \(H^{\prime}\) and \(\beta\) Parameters  
The \(D\)-region (60-90 km) ionosphere is poorly characterized due to lack of \(N_{\rm e}\) observations. In situ (e.g., sounding rockets) [50; 51], remote sensing from incoherence scattering radar (ISR) [52], and radio wave propagation [53] are the common methods for measuring the \(D\)-region \(N_{\rm e}\)[54], but their locations are sparse and the operation cost can be high. In addition, low electron concentrations in the \(D\)-region requires high power, large-sized antenna radars to obtain useful \(N_{\rm e}\) measurements, which makes such systems unaffordable for wide deployment. On the other hand, high-frequency radio waves, although useful for the \(N_{\rm e}\) sounding in the \(E\)-region and above, tend to pass through the \(D\)-region. At very low  
Figure 8: COMSIC-1 \(N_{e}\) at 60, 80, 100, and 120 km as a function of LST and latitude for March, June, September, and December. The scaling factor for the color bar is indicated by the number in the parenthesis. The solid line denotes solar zenith angle \(\chi=90^{\circ}\).  
frequency (VLF, 3-30 kHz) and extremely low frequency (ELF, 0.3-3 kHz), radio waves are completely reflected by the \(D\)-layer and the ground surface, of which the two conducting boundaries act as an Earth-ionosphere waveguide (EIWG) to allow a low-loss long-range radio propagation. As a result, the VLF/ELF technique has been increasingly used for remote sensing of the \(D\)-region properties, including \(N_{e}\)[55; 56; 57].  
To characterize the \(D\)-region \(N_{e}\), the VLF/ELF observation community often uses a two-parameter \(D\)-region \(N_{e}\) model. As described by [PERSON] [1964], the formula has characteristic reference height \(H^{\prime}\) (km) and exponential growth rate of \(N_{e}\) with height or \(\beta\) (km\({}^{-1}\)), i.e.,  
\[N_{e}(z)=1.43\times 10^{13}e^{-0.15H^{\prime}}e^{[(\beta-0.15)(z-H^{\prime})]} \quad\quad\mathrm{m}^{-3} \tag{14}\]  
The model parameters from fitting to VLF/ELF observations yield a typical \(H^{\prime}\) value of 65-90 km and \(\beta\) of 0.3-0.5 km\({}^{-1}\) with a lower \(H^{\prime}\) value and slightly higher \(\beta\) value during daytime [58; 59; 60; 61; 62; 63; 64]. Recently, an update was proposed to characterize a height split in the \(D\)-region \(N_{e}\) profiles with a four-parameter scheme, which appears to represent the daytime profiles better [65].  
We used the same two-parameter model (Equation (14)) to fit the \(D\)-region \(N_{e}\) retrieved from COSMIC-1 (Figure 9). The \(H^{\prime}\) parameters derived from COSMIC-1 are slightly lower than those derived from the VLF observations [59; 60], showing a daytime variation of 70-73 km, compared to 71-77 km from VLF. The COSMIC-1 \(\beta\) parameters exhibit a little variation around 0.31 km\({}^{-1}\) during the day, compared to 0.25-0.4 km\({}^{-1}\) reported from the VLF observations. For nighttime, the COSMIC-1 \(H^{\prime}\) and \(\beta\) values are also lower, with \(H^{\prime}\) varying between 71 and 76 km compared to 82-86 km from VLF, and \(\beta\) varying between 0.29 and 0.30 km\({}^{-1}\) compared to 0.4-0.6 km\({}^{-1}\) from VLF [61; 62].  
Figure 9: The model parameters (\(H^{\prime}\) and \(\beta\)) for September and December as a function of magnetic latitude and local time from the fitting of COSMIC-1 \(D\)-region (60–80 km) \(N_{e}\) to Equation (14). The solid line is the terminator where the solar zenith angle \(\chi\) at 100 km is equal to 90\({}^{\circ}\).