# Error Source Analysis and Correction of GF-3 Polarimetric Data
## 3 Influence Analysis of Error Source
### Ionosphere Effect  
The orbit height of the GF-3 satellite is about 755 km, hence a large number of free electrons in the ionosphere will affect the transmission of the electromagnetic wave, as shown in Figure 7. When a linearly polarized wave traverses the ionosphere, it is split into two circularly polarized waves, rotating in opposite senses. When leaving the ionosphere, these waves recombine, but the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **HH (dB)** & **HV (dB)** & **VH (dB)** & **VV (dB)** & **HH-VV (dB)** \\ \hline \(1\) & \(-43.8\) & \(-74.0\) & \(0\) & \(-43.6\) & \(-75.5\) \\ \(2\) & \(-43.4\) & \(-77.1\) & \(0\) & \(-45.1\) & \(-58.4\) \\ \(3\) & \(-41.4\) & \(-68.3\) & \(0\) & \(-40.1\) & \(-57.2\) \\ \(4\) & \(-45.8\) & \(-71.0\) & \(0\) & \(-44.5\) & \(-61.7\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Amplitude of the PARC scattering matrix. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **1** & **2** & **3** & **4** \\ \hline Mode & Q9 & Q15 & Q17 & Q25 \\ Look angle (deg) & 29.36 & 35.5 & 36.41 & 41.18 \\ \(\varphi\) (deg) & \(-0.003\) & \(0.005\) & \(-0.001\) & \(-0.001\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Theoretical polarization orientation angles (POAs) of 4 scene data with polarimetric active radar calibrator (PARC). resulting linear polarization is rotated relative to the original, a phenomenon known as Faraday rotation. [PERSON] et al. pointed out that a one-way Faraday rotation (FR) of more than 5\({}^{\circ}\) to 8\({}^{\circ}\) adversely affects the retrieval accuracy of geophysical parameters [15]. [PERSON] also argued that the one-way FR within 5\({}^{\circ}\) is acceptable for most land applications [28]. Therefore, in this study, if the one-way FA is within 5\({}^{\circ}\), the correction for FR is considered to be unnecessary. The FR can be predicted utilizing the beam parameters and the ionospheric total electron content (TEC) [15] by Equation (8). \[\Omega\approx\left(K/f^{2}\right)B\cos(\theta)\sec(\phi)TEC \tag{8}\]  
where \(\Omega\) is the one-way FR, \(B\) is the local geomagnetic field, \(f\) is the radio center frequency, \(\theta\) is the angle between the magnetic field and the satellite pointing vector, \(\phi\) is the view angle, \(K\) is a composite constant. According to TEC values available at Center for Orbit Determination in Europe, TEC typically ranges from 5 to 20, emerges at a maximum of about 50 at weak solar activity and at a 100 during periods of intense solar activity. And the mean and the maximum of global geomagnetic fields near a year are obtained from the National Geographic Data Center. Under different TEC and geomagnetic field, C-band (5.6 cm wavelength) FR is calculated and shown in Table 5. As shown in Table 5, under normal conditions, FR is less than 0.18\({}^{\circ}\), and the worst value is 0.6\({}^{\circ}\). When intense solar activity happens, the extreme value reaches 1.21\({}^{\circ}\). It can be seen that all of them are far smaller than 5\({}^{\circ}\), and can be left uncorrected. The FR also can be detected from the actual data [29]. There are several common FR estimation methods, of which the Bickel and Bates [5] method is less affected by noise, residual crosstalk and channel imbalance [15; 30], and has a good estimation result, so we apply this method to five groups of GF-3 measured data with different latitudes. Data information and FR estimation are shown in Table 6. The estimated FR angles of these real data are less than 0.1\({}^{\circ}\), which is smaller than the estimation precision of this method [31]. Thus, these results cannot stand for the exact value of FR, but can confirm that the FR dose is very small. Generally, the predicted and estimated values of FR both suggest that the influence of ionosphere on GF-3 polarization observation is negligible.