# Gravity Field Recovery Using High-Precision, High-Low Inter-Satellite Links
## 4 Results
### Temporal Gravity Field Retrieval  
The retrieval of the temporal gravity field is dominated by temporal aliasing errors due to the undersampling of high frequency geophysical signals and imperfect de-aliasing models, which has already been shown by, e.g., References [47; 48; 49] for the GRACE mission. In order to analyze the impact of different time-varying mass signals on gravity field retrieval, we performed simulations by using signals that were subdivided into non-tidal AOHIS, HIS, and tidal signals, including the instrument errors described in Section 2.2. Figure 8 displays the corresponding retrieval errors for both satellite concepts. The results indicate that the errors with the highest signal amplitudes were related to AOHIS signals (Figure 8, red curves), and in particular to atmospheric and oceanic signals. Tidal aliasing effects played a key role in the total error budget as well (Figure 8, blue curves) by representing the highest aliasing errors next to non-tidal atmosphere and ocean aliasing errors. In this context it is important to mention that errors in ocean tide models are considered as one of the major sources of error in the determination of temporal gravity field models from GRACE data [50; 51]. Our simulations show that the MOBILE configuration can reduce non-tidal aliasing errors (\(\approx\)45%) as well as tidal aliasing errors (\(\approx\)30%) over the whole spectrum significantly (see also Table 3, part: temporal aliasing errors). Despite the fact that for the high-low tracking concept the assumed arrangement of satellites causes incomplete data time series, the multi-directional observation geometry enables the sampling of time varying signals with reduced aliasing errors compared to the low-low pair configuration. Figure 7: Spatial covariance functions in m\({}^{2}\) for the equator (**a**,**c**), and for 45\({}^{\circ}\) latitude (**b**,**d**), for the low–low pair formation (**a**,**b**), and the MOBILE constellation (**c**,**d**). Usually high-frequency mass signals are a priori reduced based on atmosphere and ocean de-aliasing (AOD) products [52], and ocean tide de-aliasing models. The resulting temporal gravity field models thus contain mainly information on sub-seasonal, seasonal, and secular continental hydrological mass variations and ice mass variations on Earth [53; 54], and solid Earth signals related to glacial isostatic adjustment (GIA), and co- and post-seismic gravity changes of big earthquakes. For the analysis of such mass flux signals we performed simulations by using only the HIS signal. The resulting gravity field retrieval errors (Figure 8, green curves) again revealed smaller aliasing effects for the MOBILE concept (\(\approx\)60%), which is even better visible when looking at the spatial domain, shown in Figure 9. As already suggested by Figure 7, the retrieved HIS fields demonstrate, that the error pattern of MOBILE was much more homogeneous, and the typical striping of a low-low along-track ranging system is significantly reduced, particularly in the equatorial regions where the orbit ground tracks were less dense. This resulted in a clearly improved free representation of hydrological and ice mass signals for the MOBILE concept. Figure 8: Degree (error) standard deviations after 1 month of full AOHIS signal (black), low–low pair formation (dashed curves), and MOBILE constellation (continuous curves), when including only AOHIS signals + instrument errors (red), ocean tide signals + instrument errors (blue), HIS signals + instrument errors (green), and HIS signals + instrument errors using the extended processing method (magenta). The high quality of multi-directional observations of the high-low tracking concept allows the application of an extended alternative processing method first proposed by [PERSON] et al. 2011 [23], which enables the mitigation of temporal aliasing effects due to non-tidal time varying signals, as it was stated in Section 1. [PERSON] et al.