## 3 Impact of external errors
### Impact of orbit selection  
The Jason-2 orbit, as the ones from Topex/Poseidon and Jason, has been constrained to be non sun-synchronous to cope with the tidal aliasing. However, this kind of orbit requires a strong attitude control onboard so as to keep the solar panels directed toward the Sun, by driving the yaw angle rotation around the axis directed toward the Earth, called yaw steering (see Appendix A). The most constraining angle to look at is the angle between the Sun and its projection on the orbital plane, called \(\beta\) angle; for a repetitive orbit, this angle has strong variations and goes null 6 times per year, corresponding to the best position of the Sun in the orbital plane. It impacts directly the yaw angle and then the geometry of the swath. The width of the swath at a given yaw can be expressed as followed:  
\[L_{\
u}=\sqrt[]{L_{0}^{2}+R_{zz}^{2}}\cos\left[\tan^{-\left[\left(\frac{L_{0}}{ R_{zz}}\right)-\left(\frac{\pi}{2}-\psi\right)\right]}\right. \tag{10}\]  
where  
\[\Psi=-\arctan\left[\frac{\tan\left(\beta\right)}{\sin\left(\
u\right)}\right] \tag{11}\]  
where \(L_{0}\) is the nominal width in the range direction, \(R_{az}\) the azimuth resolution, \(\Psi\) the yaw angle and \(\
u\) the angle between Earth-Sun vector projection on the orbital plane and Earth-Satellite vector. Figure 8 (a) illustrates both the yaw and beta angle evolution onboard the Jason-2 platform over an entire year. The six best periods are 12 days long (green circles in Figure 8). They correspond to no yaw steering when the Sun is within 15\({}^{\text{o}}\) of the orbital plane. Figure 8: (a) Yaw steering onboard Jason-2 over a year (b) WSOA Swath Width over a year. Note the yaw and swath width vary between the minimum and maximum of their envelope within each orbital period. Figure 9 (a) illustrates the daily evolution of the yaw angle versus the latitude. The yaw angle evolves almost periodically with the orbit; it covers a very wide range of values when a steering motion is on, varying in the +/- 90\({}^{\mathrm{o}}\) range twice an orbit; in the worst case, the width of the swath reaches a minimum which corresponds to the azimuth resolution of the instrument. The geographical distribution of the swath width is symmetric with respect to the equator: the minimal width area moves from the equator to the poles when \(\beta\) goes from +/-15\({}^{\mathrm{o}}\) to +/- 90\({}^{\mathrm{o}}\). When \(\beta\) is close to the maximum, the yaw angle remains close to +/- 90\({}^{\mathrm{o}}\) and the width of the swath is always of the order of a few tens of kilometres only (see Figure 9 (b)). Furthermore, these rotated configurations of the resolution cells deteriorate the averaging process and the formation of clean final pixels. If we only consider valid data at zero yaw angle, the global functioning time reduces to _20 %_ of the overall mission lifetime (see Figure 10 (a)). The Doppler centroid, that is the weighted mean of the Doppler shifts within a look direction, is given by Equation (12) and Figure 10(b)), As this is not corrected onboard, it has to be taken into consideration in the ground processing algorithms. Besides, the efficiency of the correction imposes an intrinsic range resolution as short as possible. \[f_{ D}=\frac{2V_{sat}}{\lambda}\frac{d\sin(\Psi)}{\sqrt{H^{ 2}+d^{2}}}\] (12), where \[d\] is the pixel position in the swath  
Finally, this orbital configuration leads to the orientation of the solar panels perpendicular to the satellite velocity. The atmospheric drag has known effects causing the semi major axis to drift and then the ground track to move, as follows (see [20], all variables are defined in Appendix 2):  
\[\Delta track{=}\frac{3\pi_{v}SC_{v}\sqrt{\mu}\rho_{ 0}}{4\sqrt{a_{0}}}(t-t_{0})^{2}\frac{R_{r}\Omega_{r}}{n_{0}} \tag{13}\]  
Figure 9: (a) Evolution of the Swath over 13 orbits at the beginning of yaw steering (b) Width of the swath over 10 days in the worst case (-75\({}^{\mathrm{o}}\)\(<\)\(\beta\)\(<\)-73\({}^{\mathrm{o}}\)).