Low-degree time-variable gravity field (TVG)

1. Possiblecontributionstothe DFG SPP „DynamicEarth“jointlyproposedbyGFZ German Research Centre forGeosciencesandAstronomical Institute ofthe University Bern (AIUB, CH)

2. Low-degree time-variable gravity field (TVG) • AIUB multi-satellite SLR solutions • reduce orbital artefacts of LAGEOS-only TVG solutions • provide TVG information with a quality comparable to GRACE with at least monthly resolution up to degree and order 4x4 • outperform the currently available hl-SST solutions (CHAMP Kalman-filter solutions, essentially restricted to the annual signal) Proposal: AIUB & GFZ GRACE Gap-filling TVG solutions based on a proper combination of normal equations (NEQs) established from Reductionofthedraconiticperiodof LAGEOS-2 (222d) • all LEO satellites observed by GPS hl-SST • all geodetic satellites observed by SLR (very important for lowest degrees) • SLR NEQs should stem from multi-satellite SLR solutions with geometry and gravity simultaneously solved for (C20 and LoDdecorrelation)

3. Swarm specific aspect: POD & ionosphere • First preliminary dynamic orbits at GFZ show 3.62 cm SLR RMS (Swarm-A) • AIUB reduced-dynamic orbits show very good quality of 2.48, 2.34 and 2.34 cm SLR RMS • AIUB kinematic orbits needed for CMA gravity field recovery are “considerably worse” with a quality of 4.06, 3.78, and 3.96cm SLR RMS • This is mainly caused by degraded kinematic positions (from AIUB) over the geomagnetic poles and along the geomagnetic equator => needs to be investigated with high priority as it affects the quality of subsequent field recovery (synergies with ionospheric research ?) Geoid heightswrt ITG-GRACE2010 (300 km Gauss-filtered) Larger noiseofkin. positionsoverthe polar regionsand m alongthe geom. equator

4. Swarm specific aspect: Gravity Field Determination Real results already available based on CMA approach and Swarm/GRACE kinematic orbits. (Presented at 3rd Swarm User Workshop (Poster Dahle et al.)) Swarm GRACE Fig. 5: Difference degree amplitudes wrt EGM2008 in terms of geoid height [m] for individual Swarm and GRACE 2-month solutions. Fig. 6: Difference degree amplitudes wrt EGM2008 in terms of geoid height [m] for a combined Swarm 5- month solution and a combined GRACE 4-month solution. Fig. 7 : Geoid differences [m] wrt EGM2008 (400km Gaussian smoothing ) for a combined Swarm 5-month solution (top) and a combined GRACE 4-month solution (bottom). • Individual Swarm gravity field solutions are of comparable quality, but perform significantly worse than GRACE hl-SST solutions. • Combined Swarm gravity field solutions show quite large improvement for degree 2. • Degradations of kinematic orbits at geomagnetic poles/equator also visible in Swarm gravity field Proposal: Swarm-based gravity field determination using CMA (AIUB) and dynamic (GFZ) approach to be combined with SLR and other HL-GPS LEOs

5. Swarm specific aspect: Gravity and baselines • Experience from GRACE kinematic baselines used for gravity field recovery gained at AIUB • K-band validation shows that ambiguity float baselines have colored noise. Ambiguity- fixed baselines are governed by white noise • Since only long-wavelength excursions are reduced due to ambiguity fixing, but not the measurement noise in the relative positions, no dramatic impact was observed for gravity field determination • Nevertheless, better slopes were observed wrt single-satellite solutions (cancellation of various error sources in baseline formation ) • Exploitation of Swarm baseline determination for gravity field recovery at AIUB • Rigorous combinations of kinematic single-satellite and baseline solutionsusing the corresponding covariance information should be performed and investigated (=> unique aspect of the Swarm constellation) Plot fromJäggi et al. (2009): AIUB istheonlyinstitutionwhicheverused real datatodeterminekinematicambiguity-fixed GRACE spacebaselinesandappliedthemas pseudo-observationsfor subsequent gravityfielddetermination

6. Swarm specific aspect: ACC & Thermosphere • GFZ has already shown that CHAMP and GRACE accelerometer data can be used asgenuine observations: • accelerometer data not needed in all three spatial directions; e.g. along-track only is sufficient; faulty channels (CHAMP radial) can be ignored • meaningful error propagation of accelerometer measurement errors • accelerometer outlier removal during adjustment (instead during L1B preprocessing) possible • Proposed Work: • Contribution to Swarm accelerometer Cal/VAL • Adjusted scaling factors for air drag (either with classical force or genuine observation approach) can be related to atmospheric density values • => CAL/VAL of (a-priori) density models such as DTM or MSIS