# Next-Generation Gravity Missions: Sino-European Numerical Simulation Comparison Exercise
## 4 Results and Discussions
It measures mainly in a North-South direction, while the cross-track direction, which is mainly represented by the sectorial coefficients, is determined worse. This general weakness of in-line pairs is also nicely reflected in the estimated formal coefficient standard deviations (Figure 7), representing the main diagonal elements of the variance-covariance matrix. Figure 6: **(a)** Spherical harmonic (SH) coefficients of the AOHIS model, and SH differences to the AOHIS model of the **(b)** TUM; **(c)** IGG-CAS; **(d)** Tongji; **(e)** WHU; **(f)** HUST solutions. Shown is the first 9-day period of Scenario A. Colorbar scale: \(\log_{10}(\mid\dots\mid)\). A typical feature of Bender-type solutions are the error bands forming an inner triangle, which is directly related to the inclination of the second pair, expressing the fact that the near-polar areas are covered only by observations from the polar satellite pair. Since this feature results from the orbit configuration of the double pair, it is also visible in the estimated error standard deviations (Figure 7). In general, these error standard deviations mainly reflect the observation type, the location of the observations, and the stochastic model of observation errors, but they are blind with respect to signal-related temporal aliasing effects, which affect only the right-hand side of the NEQ system. Figure 7: Estimated formal error standard deviations of SH coefficients of the (**a**) TUM; (**b**) IGG-CAS; (**c**) Tongji; (**d**) WHU; (**e**) HUST solutions (empirically scaled). Shown is the first 9-day period of Scenario A. Colorbar scale: \(\log_{10}(\)\(\ldots\)\()\). An exception would be if these systematic effects are included in the stochastic observation model, as it is done in the Tongji solution. Therefore, the coefficient differences to the true solutions (Figure 6) show a higher error level than the formal error estimates and also additional features, because they are affected by temporal aliasing effects. In Figure 7, the formal error estimates were scaled by empirically derived factors to make them comparable among each other. This was necessary because the processing centers followed different strategies regarding stochastic modelling (cf. Table 3). Of course, in principle the scaling (calibration) of the formal errors could have been done also by means of a-posteriori variance estimates from the post-fit residuals. However, on the one hand this information was not available for all processing centers, and on the other hand these variance estimates would be hampered by the systematic errors related to temporal aliasing effects anyway. Analyzing the coefficient differences (Figure 6) and the corresponding scaled statistical error estimates (Figure 7) of the various processing centers in more detail, a striking fact is that the triangular error structure related to the Bender-type constellation of the Tongji solution in Figure 6d is much weaker than for the other processing centers, even though it is clearly visible in the error estimate (Figure 7c). This error triangle of the Tongji solution is hardly visible in the coefficient differences to the true AOHIS model of the Tongji solution and looks generally very different from the other solutions (Figure 7c), with much larger degradation of the sectorial and near-sectorial coefficients. As already addressed above, this could be explained by the fact that the covariance information is derived from the post-fit residuals, which contain also temporal aliasing effects. In the IGG-CAS error estimates (Figure 7b), the contrast between the well-estimated near-zonals of lower SH degrees and worse-estimated near-sectorials of high degree is much larger than in the TUM (Figure 7a), WHU (Figure 7d), and HUST (Figure 7e) solutions.