Global GRACE-only gravity models with a weekly temporal resolution at GFZ Potsdam

1. Global GRACE-only gravity models with a weekly temporal resolution at GFZ Potsdam SPP-Project JIGOG (Joint Inversion of GPS site displacements, Ocean bottom pressure models and GRACE global gravity models) C. Dahle, F. Flechtner, R. Schmidt, U. Meyer, K.H. Neumayer, R. König, J. Kusche GeoForschungsZentrum Potsdam, Dept. 1 „Geodesy and Remote Sensing“

2. Motivation • Gravity variations in monthly solutions represent: 1) Changes in mass distribution due to unmodelled phenomena (e.g. hydrology, change in polar ice mass, sea level, …) 2) Deficiencies in the background models (AOD, tides) • Time series analysis is needed to separate physical and spurious signals • To this end GRACE gravity model series with a higher than monthly resolution may be helpful • Project JIGOG in the framework of DFG SPP1257: Time-series of 7-daily solutions defined as workpackage

3. Processing Strategies • Based on weekly batches of GRACE normal equation systems (aligned to GPS weeks) the following time series have been generated: 1) Pure weekly subset solutions (no constraint)  30x30 solution: processed for the entire GRACE period (08/2002 - 07/2007)  20x20 solution: processed for the year 2006 2) Pseudo-weeklysubset solutions computed in terms of a moving mean over 5 normal equations systems (= 5 weeks, weighting scheme: [ 0.25 0.5 1 0.5 0.25 ] )  60x60 solution: processed for the year 2006 • Background models and standards identical to GFZ-RL04 models

4. Groundtrack Analysis A full week of data with optimal sampling would allow for a 50x50 solution. However, …

5. Groundtrack Analysis • Based on maximum spacing of ground tracks at 35° N • Spatial resolution limited by 1) orbit configuration 2) data availability

6. Groundtrack Analysis 83% => Nmax ≥ 20 (~ 1000 km)

7. Groundtrack Analysis 66% => Nmax ≥ 30 (~ 670 km)

8. Groundtrack Analysis 66% => Nmax ≥ 30 (~ 670 km)

9. Groundtrack Analysis GPS Week 1400 GPS Week 1407

10. Time Series of Low Degree and Orders • Pure weekly subset solutions in general follow monthly solutions • Some outliers refer to weak solutions due to limited sampling or data coverage, but not all!

11. Time Series of Low Degree and Orders • Not much difference between 20x20 and 30x30 solution • Pseudo-weekly solutions are smoothed version of pure weekly ones – close to GFZ-RL04

12. Time Series of Low Degree and Orders Moving average of pure weekly subset solutions and pseudo-weekly models give very close results => Less computational effort!

13. Comparison to independent solutions GRGS (Toulouse) processed a time series of 10 day solutions (GRACE+LAGEOS, 30x30), also applying a moving average approach. Most coefficients fit nicely (e.g. C40). C20 shows a bias in comparison to solutions from independent SLR data. The reason is still under investigation.

14. Results in the Spatial Domain RMS Variability Surface Mass Anomalies Year 2006, Gaussian Averages 500 km 50 Pseudo-Weekly Models 12 Monthly Models RL04 Series Min. Max. wRMS Pseudo-Weekly Models 1.1 24.4 4.1 Monthly Models RL04 0.7 24.8 4.2 Unit: cm

15. Results in the Spatial Domain RMS Variability Surface Mass Anomalies Year 2006, Gaussian Averages 715 km 50 Pseudo-Weekly Models 50 Weekly Models (30x30) Series Min. Max. wRMS Pseudo-Weekly Models 0.9 19.1 3.3 Weekly Models RL04 1.6 19.9 3.8 WGHM (not shown) 0.0 12.8 1.9 Unit: cm

16. Results in the Time Domain C33 Time series of individual coefficients from the pure weekly subset solutions. Weekly solutions with less than 4 days of data have been removed and replaced by linear interpolation. C44 C31 C50 C42 Some coefficients show clear annual periodic variations proving the plausibility of pure weekly subset solutions. In other coefficients none of such periodicities can be observed. C52

17. Conclusions • Generation of gravity field models from GRACE-data on the basis of 1) Pure weekly subset solutions and 2) Pseudo-weekly solutions in terms of a moving average from weekly normal equations allows for an increased temporal resolution of gravity changes with a clear detection of hydrologically induced variations. • For pure weekly subset solutions the spatial resolution is limited, but still good to resolve features of about 700 km half-wavelength when filtered. • Performance of weekly solutions clearly depends on data gaps & limited ground track coverage.

18. Conclusions • For pseudo-weekly solutions the spatial resolution is even comparable to the standard monthly models. However, the pseudo-weekly models are correlated! • Averaging of pure weekly subset solutions using the same weighting scheme as for pseudo-weekly solutions gives comparable results. • Time-series of selected coefficients show strong annual variations (of hydrological origin), but not all coefficients seem to be sensitive to such mass signal. • For external validation results see poster by Franziska Göttl et al. (Session B): “Comparison of polar motion excitation series from geometric space techniques, geophysical models and weekly GRACE gravity models”

19. Thanks for your attention!

20. Time Series of Low Degree and Orders

23. Results in the Spectral Domain FFT analysis of time series of coefficients from pure weekly subset solutions 1 month processing artefacts (tide models?) 2-yearly atmospheric tide? 2 month hydrological signal 2 year 1 year