# Impact of Groundtrack Pattern of a Single Pair Mission on the Gravity Recovery Quality
## 4 Discussion
Spatial aliasing is thought to be the biggest source of the error which increases as time span of the solutions increases (although temporal aliasing also contributes, as it is valid for all the other cases). 6-day (as sub-cycle period) does not show noticeable meaning. Very likely, the domination of spatial aliasing and the distribution of the geophysical signals with different strength over the globe hinder the emergence of any meaningful pattern. Considering the Pendulum formation of the Table 2 scenarios, and in the terms of global recovery, for the \(L_{max}=32\), \(\Omega=132^{\circ}\) performs better than \(\Omega=116^{\circ}\). The recovery by \(\Omega=0^{\circ}\) is the worst and getting even worse over longer periods. One can not see significant difference by the performance of the odd and even parities. The 6 th day as sub-cycle period is not significantly important in this case. For \(L_{max}=64\), the recovery by \(\Omega=132^{\circ}\) is better than \(\Omega=116^{\circ}\). After day 5, recovery by \(\Omega=0^{\circ}\) is the worst and getting even worse at the longer periods. No significant difference is seen by the performance of the odd and even parities, although the even parity performs only a bit better than the odd parity after day 5. In terms of global recovery, the 6 th day as sub-cycle period shows no important feature, although it may depict a very small impact on the recovery by \(\Omega=0^{\circ}\) and \(\Omega=116^{\circ}\). Unlike the case of CNR by inline formation, reduction of errors for \(\Omega=\)116\({}^{\circ}\) and \(\Omega=132^{\circ}\) by the longer period of the solutions are seen (possibly by less spatial aliasing). However, that is not the case for \(\Omega=0^{\circ}\). Therefore, one potential question to be addressed in future works might be the way that combination of isotropy (by Pendulum formation) and sampling plays role. The \(\Omega=132^{\circ}\) case performs better than \(\Omega=116^{\circ}\) which outperforms \(\Omega=0^{\circ}\). The even parity illustrates a slightly better performance than the odd parity. In terms of global recovery, the 6 th day (as sub-cycle period) should not be considered significantly important. For the MCNR case, the error increases for all cases after the 6-day solution. Therefore, it is not clear whether day 6 has meaning in terms of being sub-cycle or not. It is noticeable to see the better performance of the odd parity than the even parity at longer periods of solutions. The case \(\Omega=132^{\circ}\) mostly performs better than the two other cases. This paper also illustrates covariance matrices for 6-day solutions of the scenario (a) inline and Pendulum formations for \(\Omega=116^{\circ}\), where \(L_{max}=32\), \(L_{max}=64\), \(L_{max}=\) CNR and \(L_{max}=\) MCNR. The illustrations show that for the inline formation when the maximum spherical harmonic coefficient degree and order are above the CNR rule for 6-day (i.e., \(L_{max}=64\) and \(L_{max}=\) MCNR), the error level gets significant (assumed to be associated with spatial aliasing). However, for the Pendulum formation, those error patterns are not as noticeable as the inline formation (very likely associated to the more isotropic sampling by Pendulum formation). Interpreting the results above, it should be emphasized that with our starting date choice for recovery simulation (1 January 1996), \(\Omega=0^{\circ}\) corresponds to the groundtrack starting point at Pacific Ocean, east of South America, while \(\Omega=116^{\circ}\) and \(\Omega=132^{\circ}\) respectively stand for starting points at West-Africa and East-Africa. The results of this paper show that the best global performance (the smallest error) usually happens at \(\Omega=132^{\circ}\). This outcome might be expected since, among the three different values of \(\Omega\), the satellite mission track passes over significant hydrological signals when \(\Omega=132^{\circ}\) (i.e., over East-Africa and the corresponding regions in the same longitudes).