Page - 148 - 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

Time series of RMS ratios Table 9.3 presented the RMSs of several geographically restricted areas for two selected months. The same RMSs were also computed for the remaining months of the time series, again using a 300km Gaussian filter. Then, for both of the improved solutions, a ratio was formed between the RMSs of the improved solutions (blue and pink) and the RMS of the reference solution (old stochastic model, brown). These ratios are displayed in fig. 9.12. The ratio is displayed instead of absolute RMS values for two main reasons: Due to a variety of factors such as observation geometry and gaps in the underlying data, the magnitude of the RMS for one area can vary considerably from month to month. This makes inter-monthly comparisons of absolute differences difficult to interpret, as these in turn also vary from month to month. Further, the differences in EWH RMS between the solutions are small compared to their magnitude, which makes them disappear at these larger scales. When considering the ratios, a value of less than 100% indicates that the RMS of the reprocessed solution is smaller than that of the reference solution. The value for the solution computed using the old model is always 100%, as this is the reference solution. Figure 9.12 shows that for all areas, the RMS of the solution including AOC covariance matrices (blue) is of comparable magnitude as that of the reference solution. Within the scatter of the time series, neither a clear increase nor a distinct decrease of the RMS can be observed. This does not hold for the time series of TLS solutions (pink), where the ratio is below 100% for almost all months. The mean of the RMS reduction for the TLS series is 3.3% globally, 2.3% over land, 4.1% over the oceans, and 5.1% for the pacific patch. This confirms that for the TLS solution the reduction in RMS is higher in areas where noise is expected to be a larger factor of the recovered gravity field, and smaller where signal is expected to be larger. For the solution using AOC covariances only (blue), the mean reductions in RMS are 0.36% globally, 0.25% over land, 0.44% over the oceans, and 0.46% for the pacific patch. Although the patterns in the magnitude of the reductions match those of the TLS solution, the means are small in relation to the scatter of the time series, and caution should be applied when drawing qualitative conclusions from this data. Temporal variability - spectral domain Where observing the temporal variability in the spatial domain allows for insights into the geographical localisation of specific features, the required filtering hides a lot of the variability at small spatial scales. To give a fuller impression of the characteristics of the computed solutions at these scales, the temporal RMS for each solution was also computed in the spectral domain, once for each Stokes coefficient. For the improved solutions, a ratio was again formed with the reference solution using the old stochastic model. Values below 100% again indicate a RMS reduction. These results are shown in fig. 9.13. The ratio for the solution using AOC covariance matrices is shown in fig. 9.13c. The most striking feature here is a reduction of the variability in the zonal and near-zonal coefficients above roughly degree 40. Correspondingly, a small increase in variability Chapter9 Co-Estimation of Orientation Parameters148