1. Astronomical Institute University of Bern 1 Astronomical Institute, University of Bern, Switzerland 2 German Research Centre for Geosciences, Potsdam, Germany Swarm Gravity Field Determination using the Celestial Mechanics Approach A. Jäggi 1, C. Dahle 2, D. Arnold 1, U. Meyer 1

2. Slide 2 Astronomical Institute University of Bern Contents Swarm Kinematic Orbit Determination  Recapitulation of ionosphere disturbances Gravity Field Recovery  Presence of systematic errors  Mitigation of systematic errors  Analysis of time-variable solutions Comparison with GRACE Gravity Field Solutions  Availability of kinematic positions  Differences in Swarm and GRACE GPS tracking

3. Slide 3 Astronomical Institute University of Bern Recapitulation of Ionosphere Disturbances Random errors:  Overall RMS is rather high Systematic errors:  Along geomagnetic equator  May be reduced by additional data screening (dL4/dt criterion)  Dominated by polar areas RMS of Swarm-A, 320-365, 2014, descending arcs mm/s RMS of dL3/dt

4. Slide 4 Astronomical Institute University of Bern Bi-Monthly Gravity Field Solutions up to d/o 90 Mar/Apr 2014 Jun/Jul 2014 Nov/Dec 2014 Differences wrt GOCO05S 400 km Gauss smoothing adopted Original GPS Data Screened GPS Data

5. Slide 5 Astronomical Institute University of Bern Bi-Monthly Gravity Field Solutions Mar/Apr 2014 Jun/Jul 2014 Nov/Dec 2014 Impact of screening the raw RINEX GPS data files (dL4/dt criterion): Difference degree amplitudes are significantly improved, especially for periods with strong ionosphere conditions (spring, fall). Very low degrees (n < 15) tend to be weakened due to the very “crude” data screening.

6. Slide 6 Astronomical Institute University of Bern Static Gravity Field Solutions (Differences wrt GOCO05S, 400 km Gauss smoothing adopted) Systematic signatures along the geomagnetic equator may be efficiently reduced for static Swarm gravity field recovery when screening the raw RINEX GPS data files with the dL4/dt criterion. Original GPS Data (13 months) Screened GPS Data (13 months) Screened GPS Data (18 months)

7. Slide 7 Astronomical Institute University of Bern Static Gravity Field solutions (Differences wrt GOCO05S) Systematic signatures along the geomagnetic equator cause the artificial “bumps” and may be reduced for static Swarm gravity field recovery when screening the raw RINEX GPS data files with the dL4/dt criterion. 8 months of screened data 13 months 18 months

8. Slide 8 Astronomical Institute University of Bern Recapitulation from GOCE Systematic effects around the geomagnetic equator were present in the ionosphere-free GPS phase residuals despite modeling of higher order ionosphere (HOI) terms based on global ionosphere models (GIM) Phase observation residuals mapped to the ionosphere piercing point Geoid height differences (-5 cm … 5 cm); Nov-Dec 2011 Degradation of kinematic positions around the geomagnetic equator propagates into gravity field solutions. => affects kinematic positions

9. Slide 9 Astronomical Institute University of Bern Similar experiment for Swarm (Differences wrt GOCO05S, 400 km Gauss smoothing adopted) Systematic signatures along the geomagnetic equator may not be reduced with GPS data including HOI corrections (2nd order), which were kindly provided by Oliver Montenbruck from DLR. DLR GPS Data w/o HOI (Nov/Dec 2014) 13 months) DLR GPS Data with HOI (Nov/Dec 2014)

10. Slide 10 Astronomical Institute University of Bern “True” signal: GFZ-RL05a (DDK5-filtered) “Comparison” signal: GFZ-RL05a (500km Gauss) Swarm signal: 90x90 solutions (Gauss-filtered) Time-Variable Gravity (Amazon) Result: Best agreement for Swarm-C Some outliers to be investigated

11. Slide 11 Astronomical Institute University of Bern “Comparison” signal: GFZ-RL05a (500km Gauss) Swarm signal: 90x90 solutions (Gauss-filtered) Result: Very noisy series, trends are hardly recognized. Not very promising. Time-Variable Gravity (Greenland)

12. Slide 12 Astronomical Institute University of Bern “True” signal: GFZ-RL05a (truncated at 10) Swarm signal: 90x90 solutions (truncated at 10) Nicer, but: It is a point-wise evaluation of the truncated field, expressed in geoid heights instead of EWH. Time-Variable Gravity (Greenland)

13. Slide 13 Astronomical Institute University of Bern Comparison with GRACE hl-SST Solutions Processed data: Dec 2013 – Nov 2014 Swarm-A/C (screened) GRACE-A/B (GPS-only) (original L1B data) Worse performance for higher degrees cannot be explained by higher orbital altitude. It is probably caused by the higher noise of the Swarm GPS data. Worse performance for short wavelengths Results: Similar performance for long wavelengths

14. Slide 14 Astronomical Institute University of Bern Comparison with GRACE hl-SST Solutions (Differences wrt GOCO05S, 400 km Gauss smoothing adopted) Original GPS Data (Swarm) Original GPS Data (GRACE) Systematic signatures along the geomagnetic equator are not visible when using original L1B RINEX GPS data files from the GRACE mission.

15. Slide 15 Astronomical Institute University of Bern Number of available Kinematic Positions Swarm-A, doy 060-090, 2014 (ascending arcs) For the selected period descending arcs are predominantly affected by ionosphere disturbances. Swarm-A, doy 060-090, 2014 (descending arcs) Missing kinematic positions are found over the geomagnetic poles, but not along the geomagnetic equator.

16. Slide 16 Astronomical Institute University of Bern Number of available Kinematic Positions GRACE-B, doy 060-090, 2014 (ascending arcs) GRACE-B, doy 060-090, 2014 (descending arcs) For the selected period ascending arcs are predominantly affected by ionosphere disturbances (nodes happen to be separated by ~180°). Missing kinematic positions are found along the geomagnetic equator => problematic signatures cannot be present in the gravity field.

17. Slide 17 Astronomical Institute University of Bern Number of missing Observations in RINEX files GRACE-B, doy 060-090, 2014 (all arcs) Significant amounts of data are missing in GRACE L1B RINEX files => problematic signatures cannot propagate into gravity field. Swarm-A, doy 060-090, 2014 (all arcs) Swarm RINEX files are more complete (gaps only over the poles) => problematic signatures do propagate into the gravity field. L1A

18. Slide 18 Astronomical Institute University of Bern Number of missing Observations in RINEX files SWMB FEB 2014 Swarm-B Jan. 2014 Equatorial data losses only present during commissioning phase. This has already been found by Buchert et al. (2015), GRL. Swarm-B Feb. 2014 Swarm-B Mar. 2014 Swarm-B Apr. 2014

19. Slide 19 Astronomical Institute University of Bern Number of missing Observations in RINEX files Swarm-C, before 6. May 2015 Swarm-C, after 6 May 2015 Change of Swarm-C tracking loops possibly yields more data over the polar regions and some additional losses over other regions. Impact is currently difficult to assess due to the “quiet” summer period. Needs to be assessed for the upcoming months.

20. Slide 20 Astronomical Institute University of Bern Summary Ionosphere disturbances affect orbit and gravity field solutions. GPS data screening for large ionosphere changes helps to reduce the geomagnetic signatures, but also weakens low degrees. “Free-preview” on largest time-variable signals is encouraging despite the still very short time series. Very low degree coefficients are of similar quality as from GRACE GPS hl-SST. Different behavior of GRACE solutions is related to missing GPS data along the geomagnetic equator (related to bad quadratic fits of BlackJack receiver?).

21. Slide 21 Astronomical Institute University of Bern Outlook and Questions Outlook:  HOI modeling based on STEC product.  Further tracking-loop experiments (next slide) Questions and points for discussion:  Are GPS data collected at critical equator passes okay? Or are they rather corrupted by receiver tracking limitations, e.g., caused by real STEC variations on small regional scales?  What is actually causing the double (triple) bands around the geomagnetic equator? Could ionosphere or magnetic field experts somehow help to find an explanation?

22. Slide 22 Astronomical Institute University of Bern Further tracking-loop experiments Suggestions from Oliver Montenbruck, DLR:  a) Go back to old P(Y) code DLL bandwidth (to reduce code noise) on SWARM-C  b) Implement current SWARM-C settings (except P(Y) DLL) on SWARM-A  c) Try another slight increase of the L2 P(Y) PLL bandwidth on SWARM-C Remarks:  To a): DLL adjustments were unnecessary, but just done by RUAG  To b): Baseline applications would profit if the implementation is done on Swarm-A, as well