# Ionospheric Remote Sensing with GNSS
## 4 Ionospheric Remote Sensing  
GNSS is not only the ubiquitous modern technology for PNT, but also a versatile remote sensing tool for many areas (e.g., space weather, geodesy, geophysics, and oceanography). For example, GNSS is widely applied to ionospheric remote sensing. Plasma physics describes the basic science of the ionosphere. An important parameter--plasma frequency (\(\omega_{P}\)) can be defined as:  
\[\omega_{P}=q\sqrt{\frac{n_{e}}{\varepsilon_{0}m_{e}}} \tag{7}\]  
where \(q\) is elementary charge (\(\approx\)1.6 \(\times\) 10\({}^{-19}\) C); \(n_{e}\) is electron density; \(\varepsilon_{0}\) is the permittivity of free space; and \(m_{e}\) is the electron rest mass. For radio waves with frequencies below \(\omega_{P}\), typically 10's of MHz, the ionosphere can reflect the RF waves (e.g., amplitude modulated radios) and enables long distance over the horizon radio communications globally. For radio waves frequencies above \(\omega_{P}\), such as GNSS, the signals penetrate through the ionosphere. Due to the difference in index of refraction in the ionosphere compared to a vacuum (free space), the ionosphere can delay, attenuate, disturb or induce Faraday rotation on GNSS signal propagation. The index of refraction depends on electron density and RF wave frequency [17]. These ionospheric effects can dramatically degrade the PNT accuracy, precision, and integrity of GNSS. Conversely, GNSS can be (and has been) utilized to monitor and study the ionosphere. Associated with the ionospheric delay effect, the total electron content (TEC) of the ionosphere can be measured by multi-frequency GNSS receivers on the ground or in space. TEC is defined as the total number of electrons within a cross-sectional volume along the LOS between two points (e.g., a GNSS satellite and a ground-based GNSS receiver): TEC = \(\int_{0}^{R}n_{e}dr\), where \(R\) is the LOS's distance. The TEC is measured in units of number of electrons per m\({}^{2}\), but more often expressed in units of TECU (10\({}^{16}\) electrons/m\({}^{2}\)). The ionospheric delay \(I\) (measured in meters) on a ranging Equation (Equations (4) and (6)) with a specific frequency band can be expressed in terms of TEC as [17]:  
\[I=\frac{40.308}{f^{2}}\times\text{TEC} \tag{8}\]where \(f\) is the GNSS signal frequency. Using the pseudorange from two GNSS different frequency bands (e.g., GPS L1 and L2), the TEC can be measured based on the following formula:  
\[\text{TEC}_{R_{\text{L1}}-R_{\text{L2}}}=\frac{1}{40.308}(\frac{f_{\text{L1}}^{2 }f_{\text{L2}}^{2}}{f_{\text{L1}}^{2}-f_{\text{L2}}^{2}})(P_{\text{L2}}-P_{ \text{L1}}) \tag{9}\]  
where \(f_{\text{L1}}\) is GPS L1 frequency, \(f_{\text{L2}}\) is GPS L2 frequency, \(P_{\text{L1}}\) is GPS L1 pseudorange, and \(P_{\text{L2}}\) is GPS L2 pseudorange. Due to the differential code bias (DCB), an offset caused by different hardware delays on GNSS code/pseudorange observations with different signal frequencies, an additional DCB bias term needs to be accounted for when implementing Equation (10). More details about DCB estimations can be found at [18]. The MIT Madrigal database gathers thousands of multi-frequency GPS/GNSS receiver data to create global TEC maps [19] as shown in Figure 2, which is advantageous for global ionospheric weather monitoring and studies. Note, vertical TEC (VTEC) is an integration of the electron density along the direction perpendicular to the ground standing. There are several other global TEC monitoring systems/institutes, such as NASA Jet Propulsion Laboratory (JPL) [20], International GNSS Service (IGS) [21], and United States' National Oceanic and Atmospheric Administration (NOAA) [22]. Other than ionospheric delay, ionospheric irregularities can cause GNSS scintillations (rapid fluctuations in signal's intensity or/and phase).