# Error Sources of Interferometric Synthetic Aperture Radar Satellites
## 3 Systematic Errors
### Propagation Path (Atmosphere)
#### 3.2.1 Ionospheric Advance  
In contrast with neutral atmosphere (mesosphere, stratosphere, and troposphere), the ionosphere is the portion of the atmosphere where ionization occurs as molecules and atoms absorb strong shortwave solar energy [84]. During the process of ionization, molecules or atoms lose electrons and become positively charged ions and the electrons are released from ionization [84]. Therefore, there are a lot of free electrons in the ionosphere. The number of free electrons is represented by the electron density (electrons/m\({}^{3}\)), and the integral of the electron density along the propagation path within the ionosphere is represented by the total electron content, TEC (\(TECu\) or \(10^{16}\) electrons/m\({}^{2}\)). There are several resulting influences which are dependent on TEC when microwave signals propagate through the ionosphere. The influences include group delay (corresponding to a phase advance with the same magnitude but an opposite sign), Faraday rotation, defocusing of SAR images, and an extra shift between SAR images in the azimuth direction [28; 85]. Scintillation on SAR imaging is an effect which is unrelated to TEC but can also occur within the ionosphere [85]. Unlike the troposphere, there are limited refractions between radar microwaves and the mediums in the ionosphere. This is because radio frequencies exceeding the plasma frequency (typically between 2 and 20 MHz) could directly pass through the ionosphere without significant reflection and refraction [76]. Further, the frequencies of radar microwaves are between 0.4 and 10 GHz from P-band to X-band, which are far higher than the plasma frequency. Though being free from the influence of refraction within the ionosphere, Faraday rotation occurs in this layer and can depolarize the transmitting signals. As Faraday rotation only causes significant influences on applications which are related to the utilization of the polarimetric characteristics of the SAR systems [76], it will not be discussed in this paper. Therefore, group delay (or phase advance) and extra shift in azimuth direction are the main focus in this subsection. As free electrons are a dispersive medium, different frequencies of waves travel at different velocities in the ionosphere [85]. Therefore, a wave-front phase advance, induced by the gradients in the ionospheric electron density, is dependent on the carrier frequencies of the microwave signals. The zenith ionospheric advance (\(\delta^{z}_{iono}\)) in meters is given in Equation (6) [86], where \(TECs_{s}\) represents the total electron content along the propagation path in \(TECu\), \(f\) is radar frequency in GHz, and 40.28 is a constant with the unit m\({}^{3}\)/s\({}^{2}\)[87]. The ionospheric phase advance can be derived as Equation (7). InEquation (6), ionospheric advance is inversely proportional to the square of radar wave frequency due to the dispersive (frequency dependent) nature of the electrons [85]. As a result, L-band SAR systems are severely susceptible to ionospheric distortions owing to their low frequencies [88]. \[\delta^{z}_{iono}=-40.28\times\frac{TEC_{s}}{f^{2}} \tag{6}\]  
\[\phi_{iono}=-\frac{4\pi}{c}\times 40.28\times\frac{TEC_{s}}{f} \tag{7}\]  
The errors resulting from ionospheric effect are determined by the spatiotemporal variations of \(TEC_{s}\) between two acquisitions, thereafter \(\Delta TEC_{s}\)[89; 90; 91; 92; 93; 94]. \(\Delta TEC_{s}\) is strongly related to the ionization process as the stronger the process is, the more free electrons will be created in the ionosphere [95]. Also, when higher \(TEC_{s}\) is associated with stronger spatial variation, \(\Delta TEC_{s}\) will be reasonably larger as well. The ionization level is highest in the equatorial regions due to strong solar radiation resulting from small solar zenith angles and due to the equatorial anomaly resulting from the fountain effect [85; 88; 96].