Siavash Iran Pour, Nico Sneeuw, Matthias Weigelt, Tilo Reubelt

1. Comparison of full-repeat and sub-cycle solutions in gravity recovery simulations of a GRACE-like mission Siavash Iran Pour, Nico Sneeuw, Matthias Weigelt, Tilo Reubelt EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

2. Aliasing of high-frequency geophysical signals to lower frequencies (eventually seen in the recovered gravity field) Sampling the Earth from orbit tornado.sfsu.edu www.ni.com EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

3. Strategies to mitigate the aliasing problem • Satellite configuration design • Alternative recovery strategies (different solutions) • How different solutions deal with the problem? • Two different solutions strategies for the gravity field recovery: • - Repeat period of a repeat orbit scenario - Sub-cycle of the scenario • Investigation of the aliasing behavior of different solution strategies • The possibility of sub-cycle solution for further processing EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

4. Orbit Design (Choosing the orbital parameters) Orbit Integration (Integrate the satellite parameters in the presence of the gravity field) Calculating positions and velocities of the satellites, as well as range, range rate and range acceleration Inversion (SH coefficients estimation) for different time periods EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

5. Orbit design • GRACE like configuration • Repeat orbit of 125/8 • Near circular, near polar orbit • Differential orbital elements EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

6. Orbit integration • Static field egm96 • Varying fields: 6 hourly time series of gravity potential spherical harmonic coefficient series • - Atmosphere: ECMWF ERA-40 • - Ocean: OMCT • - Hydrology: PCR-GLOBWB driven with ECMWF meteorological data • - Ice: ECMWF • - Solid Earth: DEOS University of Luxembourg • - Models reprocessed by Mass Transport Study – ESA Contract 20403 • January 2005 • Up to degree 60 (avoiding spatial aliasing by ) EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

7. Repeat Period Check EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

8. Inversion • SH coefficients estimation up to degree 60 • Comparison of different solutions through maps, coefficients and degree RMS Input field Solution 24 days EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

9. Input field Solution 8 days (cycle period) 3 days (sub-cycle) EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

10. Differential SH coefficients – Triangle plots 24 days 8 days (cycle period) 3 days (sub-cycle) EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

11. Degree RMS 3 days (sub-cycle) 24 days 8 days (cycle period) EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

12. 3 days ≈ 46 revolutions => lmax ≈ 23 Lin = 60, Lout = 23 Lin = 23, Lout = 23 Spatial aliasing of the higher degrees? Remove the static field which may have the biggest contribution! EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

13. Veryfing the hypothesis • Observe the differential potential (Vtotal – V static)at the positions of one of the satellites • Estimate the differential SH coefficients (∆Klm) from the differential potential observation Lin = 60, Lout = 23 Could be meaningful! Further investigation: Spatial aliasing by the changing field? EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

14. Summary • Almost similar results for cycle period (8 days) and the longe time (24 days) solutions • Sub-cycle soltion does not provid good results for the degrees up to half of the revolutions in the period when the orbit is integrated by higher degrees • The static field may have the largest contribution for the spatial aliasing effect on the sub-cycle solution • The remaining aliasing effect may come from the spatial aliasing of the changing field itself (the future work) Thank you EGU General Assembly, Vienna, Austria, 3 - 8 April 2011