# Impact of Groundtrack Pattern of a Single Pair Mission on the Gravity Recovery Quality
## 4 Discussion  
This work aimed to look more closely into the sampling patterns impact on the gravity recovery quality for global and regional studies, as the Colombo-Nyquist and modified Colombo-Nyquist rules apply. We tried to focus on the pure sampling impact in this paper, so no post-processing was considered. In reality, smoothing global or local filter (as one of the filter choices) is implemented. However, higher quality raw solutions (for example, due to denser sampling, and hence less spatial aliasing) can result in using more relaxed filters (e.g., a Gaussian smoothing with smaller radius). That would be then very beneficial in terms of signal-to-noise ratio, although the subject is outside the scope of this paper. In particular, for the regional study, the groundtrack patterns impact of different satellite constellation scenarios have been investigated for a hydrological basin in central Africa. The quality of the gravity products have been assessed by different metrics such as spatial covariance representation. We also tried to investigate the potential meaning of the sub-cycle concept in terms of global and local impacts by different repeat-orbit scenarios with even and odd parities. Furthermore, different recovery scenarios in terms of the original and modified Colombo-Nyquist rules have been discussed. The main points of our results can be summarized as follows:  
In general, for 12 selected mission scenarios of Table 1:  
For the case \(L_{max}=32\), with the increase of the time-pan of the solutions, the recovery error decreases. This is because of more sampling in space, and hence, less spatial aliasing, although the temporal aliasing gradually increases (but not significantly). The same argument applies for the case \(L_{max}=64\) as well. For \(L_{max}=\) CNR and MCNR, it is generally different. That means that for most of the scenarios, the longer the recovery time-span, the bigger the error. But here, it is important to notice that different scenarios have different performances. For some scenarios of the case \(L_{max}=\) CNR, the error increase is significant. The cause of such an increase should be associated with the spatial aliasing which is more predominant for some mission scenarios, most likely because of the geometry of their orbits and therefore their time evolution of their groundtracks. A similar statement also applies for the case MCNR, even though more fluctuations are seen in the recovery error of few scenarios. In terms of global recovery and for the selected inline formation scenarios of Table 2:  
Considering the inline formation missions, for \(L_{max}=32\), the recovery by \(\Omega=132^{\circ}\) after the 5 th day is better than \(\Omega=116^{\circ}\). The recovery by \(\Omega=0^{\circ}\) is the worst. Odd parity usually performs a bit better than the even parity. The 6 th day as sub-cycle period is not significantly important in the global point of view. However, the concept might be more noticeable for \(L_{max}=64\). For this case, the performance of the odd parity is better than the even parity. That is also the case for \(L_{max}=\) CNR. In this case, different impact of odd and even parities on the gravity solutions larger than 7-day are significant. Moreover, the impact of \(\Omega\) can be seen (\(\Omega=132^{\circ}\) usually performs better than \(\Omega=116^{\circ}\), and \(\Omega=0^{\circ}\) is the worst). In terms of global recovery, the 6 th day as sub-cycle period also has a significant influence. After the 6 th day, the error increases with the increase of the recovery time-interval. This effect is mainly assumed to be associated with the impact of temporal aliasing, since the spatial aliasing is tried to be largely avoided, according to CNR (although the spatial aliasing still exits by the impact of orbit geometry). For the MCNR recovery, the odd parity performs better than the even parity above 6-day solutions. Surprisingly, \(\Omega=0^{\circ}\) performs almost equal or even better (for longer time recovery) than the other two cases.