# Impact of Groundtrack Pattern of a Single Pair Mission on the Gravity Recovery Quality
## 3 Results
### Mission Scenarios and the Regional Gravity Recovery
#### 3.2.2 Spatial Covariance  
Another interesting tool to investigate the sampling impact is spatial covariance illustrations [29]. One may expect that denser sampling should result in more symmetric spatial covariance pattern.  
The spatial covariance patterns, centered on the selected points of Figures 19 and 20 (marked by green star at longitude 17\({}^{\circ}\) and latitude 2.5\({}^{\circ}\)) for inline and Pendulum formations are depicted in Figures 21-28 where two different RAAN angles (\(\Omega\) = 0\({}^{\circ}\) and \(\Omega\) = 116\({}^{\circ}\)) and different maximum spherical harmonic coefficient degrees and orders are addressed for 6-day solutions. The calculation of the spatial covariance is based on the work by [29].  
The depicted results of the inline formation show the symmetry of the spatial covariance around the selected points for the cases \(L_{max}\) = 32, 64 and CNR, although in the case of \(L_{max}\) = 64 the spatial covariance graph center is shifted a bit from the center (in this case, the \(\Omega\) = 116\({}^{\circ}\), where sub-cycle happens, shows less affected than \(\Omega\) = 0\({}^{\circ}\)). For the Pendulum formation, the graphs of \(L_{max}\) = 32 and CNR show symmetric feature, but the graph centers are shifted towards left (more predominant for \(L_{max}\) = 32). That is not the case for \(L_{max}\) = 64. Interestingly, for the MCNR, the scenario a significantly outperforms the scenario b in terms of the symmetry.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Inline (GRACE-Like)**} & \multicolumn{3}{c}{**Pendulum**} \\ \cline{2-6}  & \(\Omega\) = 0\({}^{\circ}\) & \(\Omega\) = 116\({}^{\circ}\) & \(\Omega\) = 132\({}^{\circ}\) & \(\Omega\) = 0\({}^{\circ}\) & \(\Omega\) = 116\({}^{\circ}\) & \(\Omega\) = 132\({}^{\circ}\) \\ \hline Global & 0.0721 & 0.0375 & 0.0646 & \(4.2458\times 10^{-4}\) & \(4.5364\times 10^{-4}\) & \(4.0651\times 10^{-4}\) \\ Regional: & 0.0020 & \(4.2256\times 10^{-4}\) & 0.0019 & \(1.8027\times 10^{-5}\) & \(2.8095\times 10^{-5}\) & \(1.4860\times 10^{-5}\) \\ West-Africa & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 10: Error RMS in terms of geoid height for global and regional (West-Africa) 6-day recovery up to \(L_{max}\) = MCNR of the scenario (b) inline and Pendulum formations. The smallest values in global and regional cases for each inline and Pendulum formation are written in blue.  
Figure 19: Groundtrack of the scenario (a) over West-Africa for **left**: \(\Omega\) = 0\({}^{\circ}\), and **right**: \(\Omega\) = 116\({}^{\circ}\) (where sub-cycle happens).  
Inline (GRACE-like) Formation  
Figure 21: Spatial covariance of a selected point in West Africa (from Figures 19 and 20) for 6-day solution of the inline formation up to \(L_{max}=32\), for top: scenario (a), and bottom: scenario (b). **Left** is \(\Omega=0^{\circ}\) and **right** is \(\Omega=116^{\circ}\).  
Figure 20: Groundtrack of the scenario (b) over West-Africa for **left**: \(\Omega=0^{\circ}\), and **right**: \(\Omega=116^{\circ}\) (where sub-cycle happens).  
Figure 23: Spatial covariance of a selected point in West Africa (from Figures 19 and 20) for 6-day solution of the inline formation up to \(L_{max}\) = CNR, for **top**: scenario (a), and **bottom**: scenario (b). **Left** is \(\Omega=0^{\circ}\) and **right** is \(\Omega=116^{\circ}\).  
Figure 22: Spatial covariance of a selected point in West Africa (from Figures 19 and 20) for 6-day solution of the inline formation up to \(L_{max}\) = 64, for **top**: scenario (a), and **