Page - 114 - 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

0.1 1 10 100 Frequency [mHz] 10−7 10−6 10−5 All residuals Stationary contribution AOCcontribution Figure 8.10: PSDs of the residuals for June 2010. The combined residuals eˆare shown in red. The PSD for the disentangled residuals due to stationary effects eˆsst is shown in green. The PSD for the residuals due to the non-stationary effects eˆAOC is shown in blue. The shaded frequency band has the same bounds as in fig. 8.8. the noise due to the AOC uncertainty must be taken into account when studying these residuals. To capture the variability of the power in the estimated residuals not only in the frequency domain but also with time, a wavelet decomposition is computed for eˆ, eˆsst, and eˆAOC using the Daubechies 5 wavelet (see e.g. Mallat, 2009) . The length of the time series allows for 11 levels of decomposition, where each level corresponds to a specific frequency band. Each of these levels is then re-synthesized individually, giving 11 time series of residuals, each only containing signals at the frequency band corresponding to the decomposition level. These residual series were then divided into 3h intervals. The power of the signal in each frequency band and each interval was then computed as the RMS over the residuals in that bin. Figure 8.11 shows the resulting time-frequency-power diagram for the ll-SST residuals of June 2010. Thetoppaneloffig.8.11showsthepowerof thecombinedresiduals eˆ (red).Duringthe time periods of an increased opening angle (vertical grey lines), a small but consistent increase in power is visible at frequencies above≈3mHz (top horizontal grey line). A further increase in power can be observed on June 2, 2010, where no correspondingly large increase in opening angle is observed (cf. fig. 8.6a). A third, smaller, increase occurs on June 13, 2010. The middle panel of fig. 8.11 shows the power of the residuals due to stationary processes eˆsst (green). The power distribution is mostly homogeneous over time, as would be expected from a stationary process. Several small spikes of power can still be Chapter8 Star Camera Observations and Uncertainties114