# Hybrid Electrostatic-Atomic Accelerometer for Future Space Gravity Missions
## 3 Results and Discussions
### Numerical Gravity Performance Simulations
#### 3.1.2 Temporal Variation of the Gravity Field  
A series of simulations was conducted during this study to investigate the hybrid accelerometer's impact when temporal variations of the gravity field due to tidal and non-tidal effects (atmosphere (A), ocean (O), continental hydrology (H), land ice mass (I), and solid earth (S)) are taken into account. For the sake of completeness, we only comment here on the results already presented in detail in [42], since no additional simulation results were obtained. Introducing the different components of the temporal signal induces temporal aliasing, which degrades the gravity retrieval performance. The different components of the temporal signal are introduced subsequently. For the non-tidal signal components, the updated ESA Earth System Model is used, while the ocean tides are introduced by means of the models FES2004 (used as the \"truth\") and EOT08a (used as the a priori model for de-aliasing). In either simulation case, the retrieval error is significantly increased in comparison to a scenario assuming only instrument errors due to the now introduced temporal aliasing. The differences between _Cases 1-4_ were greatly diminished, meaning  
Figure 11: Degree RMS of residual coefficients for a **GRACE-type mission** under consideration of the static gravity field signal and a hybrid accelerometer with a \(1/f^{3}\) EA noise slope for an EA corner frequency (**a**) of 0.3 mHz (**left**), (**b**) of 1 mHz (**center**), and (**c**) of 3 mHz (**right**). The respective formal errors are shown as dashed lines of the corresponding color.  
Figure 12: Degree RMS of residual coefficients for a **Bender-type mission** under consideration of the static gravity field signal and a hybrid accelerometer with a \(1/f^{3}\) EA noise slope for an EA corner frequency (**a**) of 0.3 mHz, (**b**) of 1 mHz, and (**c**) of 3 mHz. The respective formal errors are shown as dashed lines of the corresponding color.  
that the aliasing constitutes the predominant error source for gravity retrieval--especially if the atmosphere and ocean (AO) and ocean tides are considered. Nevertheless, the retrieval errors of _Cases 1-4_ obtained from simulations based on land hydrology, land ice mass, and solid earth (HIS) variations (i.e., where AO and ocean tides are disregarded) still show notable variations primarily in the spectrum below \(n=10\) and, therefore, suggest that the accelerometer performance is not entirely masked by the aliasing errors. In case of additional AO, some variations can still be found in the low-degree spectrum, but they are far less pronounced than in the case of HIS alone. Once the ocean tides are included in the simulations, the accelerometer performance becomes fully subordinate to the temporal aliasing. These findings clearly indicate the need for high-quality de-aliasing models, respectively, techniques to co-estimate AO and ocean tides in order to see the hybrid accelerometer's additional value for gravity field retrieval in the context of a real satellite gravity mission. Consequently, this finding strongly advocates the implementation of a Bender-type mission (or a multi-pair mission in general), as such a configuration enables the co-estimation of high-frequency mass variations for the low-degree coefficients (i.e., reduces the temporal aliasing significantly).