Page - 137 - in Contributions to GRACE Gravity Field Recovery - Improvements in Dynamic Orbit Integration, Stochastic Modelling of the Antenna Offset Correction, and Co-Estimation of Satellite Orientations

Table 9.2: Empirical mean and standard deviation of KBR APC estimates computed from complete time series. Values relative to published calibrated APCs. ∆xˆAPC [cm] ∆yˆAPC [mm] ∆zˆAPC [mm] GRACE-A Old model −23.35±15.51 0.74±0.20 −1.12±0.36 Incl. AOC −25.28±12.88 0.72±0.18 −1.15±0.33 With TLS −2.50±20.48 0.50±0.18 −0.86±0.52 GRACE-B Old model −22.96±18.23 −0.46±0.16 −0.37±0.64 Incl. AOC −24.03±15.60 −0.44±0.14 −0.40±0.57 With TLS −4.44±14.22 −0.29±0.19 0.04±0.54 The panels in fig. 9.6 show the difference∆cˆs from the calibrated KBR APC vectors to the estimated APC vectors in the SRF. The top two panels show the differences in the x-coordinate for GRACE-A and GRACE-B. It is immediately obvious that the original estimate for the x-coordinate (brown) has a strong negative bias for both GRACE-A and GRACE-B. This bias is much larger than the formal errors given in table 9.1 would suggest. Introducing the AOC covariance information (blue) does not eliminate this bias but does reduce the spread of the estimates slightly (compare table 9.2). The estimate using TLS (pink) almost completely eliminates this bias. The estimate does however retain a rather large standard deviation. This can to some extent be explained by the unfavourable observation geometry, as the APC vector is better determinable with larger opening anglesβ, which overall are uncommon during science operations. The discrepancy between formal errors and empirical standard deviation is however not fully explained by this circumstance, suggesting the continued presence of some unmodelled systematics. This might still well be due to the systematic errors in the SCA1B data described by Harvey, 2016. The estimated y component on both GRACE-A and GRACE-B shows a clear signal with a roughly annular period. At least for GRACE-A, this is much reduced when employing the TLS estimate. In general, the co-estimation of the APC vectors gives best results in time periods of “good” data quality, roughly from 2006 to 2011. Outside of these periods, the scatter is higher, especially towards the end of the mission lifetime, where the accelerometer on GRACE-B was powered off (not pictured). The estimated APC vectors can also be interpreted as a misalignment of the K-Frame with the SRF (e.g. Horwath et al., 2011). The rotation from the SRF to the K-Frame expressed by the estimated APCs is described by the relationship cˆ=‖cˆ‖·RKFSRF [ 1 0 0 ]T , (9.3.3) withRKFSRF a small angle rotation as in eq. (6.2.5). 9.3 Results 137