## 5 Results and Discussion
This constellation has been selected due to its high temporal resolution in \(I_{0t}\), as seen in Figure 8:3 The logarithm of the actual error resulting from the simulations using constellation six is shown in Figure 8:4 Here, we see a significant error in C20, as is common in GRACE-like missions. In GRACE and GRACE-like designs, it is common to express the disturbing gravitational potential in equivalent water height units. To do this, changes in surface mass density  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**id (-)** & \(i_{\mathbf{1}}\) (\({}^{\circ}\)) & \(\Omega_{\mathbf{1}}\) (\({}^{\circ}\)) & \(M_{\mathbf{1}}\) (\({}^{\circ}\)) & \(i_{\mathbf{2}}\) (\({}^{\circ}\)) & \(\Omega_{\mathbf{2}}\) (\({}^{\circ}\)) & \(M_{\mathbf{2}}\) (\({}^{\circ}\)) & \(i_{\mathbf{3}}\) (\({}^{\circ}\)) & \(\Omega_{\mathbf{3}}\) (\({}^{\circ}\)) & \(M_{\mathbf{3}}\) (\({}^{\circ}\)) \\ \hline c01 & 87.13 & 78.55 & 236.16 & 99.52 & 168.61 & 269.94 & 116.55 & 33.52 & 134.84 \\ c02 & 23.97 & 258.68 & 224.9 & 139.26 & 146.1 & 157.35 & 102.35 & 157.35 & 67.29 \\ c03 & 81.39 & 179.87 & 67.29 & 66.29 & 112.32 & 191.13 & 116.55 & 292.45 & 348.74 \\ c04 & 58.42 & 134.84 & 202.39 & 89.0 & 44.77 & 247.42 & 91.0 & 360.0 & 33.52 \\ c05 & 144.55 & 112.32 & 326.23 & 133.58 & 247.42 & 33.52 & 96.68 & 112.32 & 292.45 \\ c06 & 92.87 & 269.94 & 112.32 & 102.35 & 360.0 & 44.77 & 116.55 & 337.48 & 247.42 \\ c07 & 98.61 & 236.16 & 157.35 & 108.03 & 44.77 & 33.52 & 86.16 & 360.0 & 314.97 \\ c08 & 64.16 & 292.45 & 326.23 & 89.0 & 337.48 & 67.29 & 83.32 & 146.1 & 56.03 \\ c09 & 87.13 & 269.94 & 224.9 & 54.94 & 157.35 & 202.39 & 77.65 & 179.87 & 56.03 \\ c10 & 35.45 & 247.42 & 269.94 & 110.87 & 281.19 & 101.06 & 89.0 & 134.84 & 112.32 \\ \hline
**id (-)** & \(i_{\mathbf{4}}\) (\({}^{\circ}\)) & \(\Omega_{\mathbf{4}}\) (\({}^{\circ}\)) & \(M_{\mathbf{4}}\) (\({}^{\circ}\)) & \(i_{\mathbf{5}}\) (\({}^{\circ}\)) & \(\Omega_{\mathbf{5}}\) (\({}^{\circ}\)) & \(M_{\mathbf{5}}\) (\({}^{\circ}\)) & \(i_{\mathbfare defined using the same set of spherical harmonics coefficients previously characterized in Equation (12). The variation in surface mass density is expressed in Equation (13), where \(\rho_{\oplus}\) is the mean density of Earth and \(k\) stands for the Earth's Love number [61]. Figure 8:5  
To convert the surface mass density in equivalent water height (EWH), it is divided by the density of water \(\rho_{H_{2}O}\). Figure 16 shows the spatial representation of the truth hydrology and ice signals along with the recovered signals truncated at degree and order 30 and the corresponding errors. In Figure 16, we see the mean of the daily signal over a period of 29 days of the truth models (top), recovered best estimate (center), and errors in the recovered signal by constellation six (bottom). The C20 pattern dominates over the ocean; so, it is removed for visual comparisons. Due to the size of the constellation and variety of the inclinations present in a six-pair constellation, these solutions have neither been destriped nor smoothed since it was not a necessary step to reduce correlated errors. Figure 8:6 Mean daily signal over a period of 29 days of the truth signal (**top**), the recovered best estimate by constellation six (**center**), and errors in the recovered signal by constellation six (**bottom**). Units are in cm of equivalent water height (EWH) and truncated at degree 30.