Page - 76 - 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

introduced for the daily gravity field solutions. The published ITSG-Grace2016 daily gravity field solutions are determined in a separate adjustment, independently of the monthly solutions. This process is based on Kalman filtering as described by Kurtenbach, 2011, and is not presented here. A more detailed description will be given in the upcoming dissertation of Andreas Kvas, expected to be released in 2019. 6.6.1 High Degree Monthly Gravity Fields To determine a monthly gravity field solution, observation equations are set up for the parameters listed in table 6.2, including all monthly Stokes coefficients up to degree and order 120. This is done for all observation groups, ll-SST KBR observations, and hl-SST POD observations for both GRACE-A and GRACE-B. The observation equations are decorrelated with the stochastic model derived in section 6.5, and then accumulated into a normal equation system. Figure 6.9 illustrates the ordering of the parameters in the normal equation system, and shows the blocks containing correlations between the parameter groups. For the monthly solutions, ultimately only the monthly Stokes coefficients are of interest. To this end, all other parameters are eliminated from the normal equation system before determining its solution, as described in section 2.4. An efficient algorithm to perform this elimination specifically in the context of the ITSG-Grace2016 gravity field solution is described by Kvas (2014). Figure 6.10 shows two gravity field solutions. The lower degree solution, determined up to D/O 60, is the solution determined in the estimation of the stochastic model, as described in section 6.5. The D/O 120 solution is the complete monthly solution as described here. The degree amplitudes of the two solutions are nearly identical up to D/O 30, where short-term temporal variations in the gravity field dominate the recovered signal. Above D/O 40, the lower degree solution shows a lower amplitude. This effect can be observed in all low-degree solutions. It is due to the truncation of the spherical harmonics expansion at too low a degree, which constrains the associated solution space and results in aliasing or leakage of unresolved signal into the solved-for Stokes coefficients (Sneeuw, 2000). 6.6.2 Lower Degree Solutions The normal equation system for the D/O 120 solution, where all parameters but the monthly Stokes coefficients were eliminated, is reused to compute both the final D/O 90 and D/O 60 solution by simple truncation. First, all parameters for Stokes coefficients from degree 91 and order 0 to D/O 120 are cut from the normal equation system, not using the parameter elimination algorithm mentioned in section 6.6.1. The normal equation system is then solved, giving a monthly gravity field up to D/O 90. The process is repeated, truncating the Stokes coefficients from degree 61 and order 0 to D/O 90, then again solving the remaining system to determine a D/O 60 solution. Chapter6 ITSG-Grace201676