# Global GNSS-RO Electron Density in the Lower Ionosphere
## 2 Data and Methods
### \(N_{e}\) Retrievals
#### 2.3.4 TEC and Vertical Gradient of \(hTEC(h_{t})\)  
The vertical gradient of \(hTEC(h_{t})\) profiles at the lower ionospheric \(h_{t}\) contains quantitative information on \(TEC\) and can be used to retrieve \(TEC\) without requiring absolute calibration of \(hTEC(h_{t})\). In this section we further analyzed the \(TEC\) information using the synthetic data from the January 2008 IRI-2016 \(N_{e}\) profiles for different geolocation and solar local time conditions. We compute \(TEC\) and \(hTEC(h_{t})\) from these \(N_{e}\) profiles and applied the same retrieval algorithm as in Equation (8) to the modeled \(hTEC(h_{t})\) and coefficient \(a_{1}\). As illustrated in Figure 7a, the coefficient \(a_{1}\) from the synthetic data and \(TEC\) are highly correlated. There is a clear difference between the daytime and nighttime \(a_{1}\)-\(TEC\) relationships, showing a smaller slope from the daytime profiles. On the other hand, \(TEC\) appears to correlate well the \(hTEC\) difference or \(\Delta hTEC\) between \(h_{t}=200\) and \(h_{t}=60\) km. These sensitivities have an important application for the \(TEC\) remote sensing, because the \(hTEC\) differencing (\(\Delta hTEC\)) approach does not require absolute calibration about \(hTEC\) measurements. It can be simply achieved by using the \(\Delta hTEC\) with respect to the value at a reference \(h_{t}\). In a broader sense, it is a similar technique to the measurement vector as formulated in Equations (7) and (8). Figure 6: Zonal mean \(N_{e}\) profile from MetOp-A (top panels) and Spire (bottom panels) as a function of magnetic latitude for October 2021. The model simulation shows that _TEC_ can be retrieved from the lower-ionospheric \(\Delta hTEC\) measurements with the reference at \(h_{t}\) = 60 km. The technique appears to work best for the \(\Delta hTEC\) measurements with the top reaching \(h_{t}\) = 200 km, the altitude slightly below the \(F\)2 peak. Assuming a measurement uncertainty of 1 TECu, we test this idea with the synthetic IRI-2016 data and derive a set of regression coefficients for the _TEC_ retrieval. The synthetic \(\Delta hTEC\) and _TEC_ data represent all variabilities from 2008, and the linear regression is used to develop the retrieval coefficients for \(\Delta hTEC\). Figure 7c,d show two _TEC_ retrieval methods from different five-level \(\Delta hTEC\) data. The regressed coefficients for the five-level \(\Delta hTEC\) data are given by Equations (12) and (13) for the RO top reaching 220 km and 180 km, respectively,  
\[ \begin{split} TEC^{\prime}&=0.319\cdot\Delta hTEC_{140 }+0.103\cdot\Delta hTEC_{160}-0.071\cdot\Delta hTEC_{180}\\ &\qquad\qquad-0.226\cdot\Delta hTEC_{200}+0.327\cdot\Delta hTEC_{ 220}\end{split}  \tag{12}\]  
\[ \begin{split} TEC^{\prime}&=0.077\cdot\Delta hTEC_{100 }+0.069\cdot\Delta hTEC_{120}+0.015\cdot\Delta hTEC_{140}\\ &\qquad\qquad-0.086\cdot\Delta hTEC_{160}+0.368\cdot\Delta hTEC_{ 180}\end{split}  \tag{13}\]  
where _TEC_' is the _TEC_ retrieval from the five-level \(\Delta hTEC\) measurements. Figure 7c produces a mean standard deviation of 1.03 TECu of the retrieved _TEC_ from five \(h_{t}\) levels at 140, 160, 180, 200, and 220 km, whereas in Figure 7d the retrieved _TEC_ error increases to 1.75 TECu if the lower levels (100, 120, 140, 160, and 180 km) are used. The \(\Delta hTEC\) measurements near the \(F\)2 peak (\(h_{t}\) = 180-220 km) are generally weighted more than those from other heights, as indicated by the regression coefficients in the simulated data. The  
Figure 7: Simulated _TEC_ relationships with (**a**) coefficient \(a_{1}\) in Equation (8), (**b**) _HTEC_ difference between \(h_{t}\) = 200 km and \(h_{t}\) = 60 km, (**c**) _TEC_ values regressed from the _HTEC_ differences at five levels between 140–220 km, and (**d**) _TEC_ values regressed from five levels between 100–180 km. weight coefficient decreases for the \(\Delta hTEC\) measurements at \(h_{t}\) above the \(F2\) peak (not shown), as expected for the measurements not going through the bulk of the ionosphere.