# Impact of Satellite Attitude on Altimetry Calibration with Microwave Transponders
## 4 Results  
### Jason-3 Attitude Determination  
The Jason-3 attitude angles are evaluated at the TCA over CDN1 and GVD1 transponder sites for each cycle using the methodology of Section 3.1. The files containing the Jason-3 quaternion data for the construction of matrix \(\mathbf{R}_{\mathrm{IRS\to SAT}}\) are acquired from NASA's Crustal Dynamics Data Information System (CDDIS). Each quaternion file covers a time period of 28 h with a temporal resolution of 30 s. The data stored in consecutive quaternion files have a two-hour overlap. The quaternions at a specific TCA are estimated using spherical linear interpolation. Daily values of mass and CoG displacements for Jason-3 are obtained from the International DORIS Service (IDS). The estimation of CoG displacements at TCA is performed using linear interpolation. The estimated CoG displacements are then used for the calculation of \(\delta\mathbf{V}_{\mathrm{SAT}}\) parameter. The attitude angles are presented in Figure 7 for the entire duration of the Jason-3 operational phase (February 2016-April 2022) before transitioning to an interleaved orbit (after the end of Sentinel-6A MF tandem phase). The temporal resolution of all time series in Figure 7 is 9.915 days, which corresponds to the repeat period of Jason-3. Each sample represents a different cycle, with the entire time series spanning 226 cycles. The presence of an attitude angle for a specific cycle does not necessarily denote an operation of the corresponding transponder. For example, the calculation of attitude angles for the GVD1 transponder location is performed for the entire duration of Jason-3 altimetric phase, although operation of the GVD1 transponder commenced in October 2021. Therefore, all attitude angles for the GVD1 D018 and GVD1 A109 times series before October 2021 are referred to the Jason-3 TCA over the \"apparent\" GVD1 transponder location. Obtaining a complete time series for the GVD1 site increases the confidence of spectral analysis on attitude angles. Due to the relatively short time period (11 s; see Figure 3) it takes Jason-3 to travel from the CDN1 Cal/Val site in Crete to the GVD1 Cal/Val site in Gavdos, the attitude angles remain almost unchanged, and thus the CDN1 D018 and GVD1 D018 time series overlap (Figure 7). From the results of Figure 7, an incident of abnormal roll (\(\theta_{r}=7.25^{\circ}\)) and pitch (\(\theta_{p}=19.58^{\circ}\)) angles is evident in both CDN1 D018 and GVD1 D018 time series at 2020.67 (9 September 2020 22:32:43, cycle 169). These extreme angles are caused by the on-board gyro calibration, which occurred on 9 September 2020 from 22:13:36 to 23:04:55 [46]. It is worth noting that for this date, the returned waveform did not correspond to a typical point target response. Consequently, the calibration of Jason-3 could not be performed. Prior to the examination of the satellite attitude, this strange behavior of the returned waveform  
Figure 6: Jason-3 mass and CoG (x-component) history since deployment. could not be explained; therefore, the reason for this unsuccessful calibration was not clear to the PFAC Cal/Val team. This highlights the importance of always examining the satellite attitude and not taking for granted nominal attitude in the context of Cal/Val activities. There are sporadic gaps in the time series of Jason-3 attitude angles in Figure 7, e.g., on26 February 2019 (cycle 112), 8 February 2020 (cycle 147) and 16 June 2020 (cycle 160), because the satellite was set on safe hold mode [46]; thus, quaternions are not available. The general behavior of the roll angle \(\theta_{r}\) is approximately the same for all time series, with values fluctuating from \(\theta_{r}=-0.12^{\circ}\) to \(-0.03^{\circ}\). The pitch angle \(\theta_{p}\) is positive for the descending pass D018 from \(\theta_{p}=+0.08^{\circ}\) to \(+0.17^{\circ}\) and negative for the ascending pass A109 from \(\theta_{p}=-0.17^{\circ}\) to \(-0.08^{\circ}\); hence, the pitch angle is also in agreement in terms of absolute magnitude for all time series.