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Comparison of full-repeat and sub-cycle solutions in gravity recovery simulations of a GRACE-like missionSiavash Iran Pour, Nico Sneeuw, Matthias Weigelt, Tilo Reubelt

EGU General Assembly, Vienna, Austria, 3 - 8 April 20111

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Sampling the Earth from orbitAliasing of high-frequency geophysical signals to lower frequencies (eventually seen in the recovered gravity eld)

tornado.sfsu.eduwww.ni.comEGU General Assembly, Vienna, Austria, 3 - 8 April 201123

Strategies to mitigate the aliasing problem

Satellite conguration design Alternative recovery strategies (different solutions)How different solutions deal with the problem?

Two different solutions strategies for the gravity eld 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 processingEGU General Assembly, Vienna, Austria, 3 - 8 April 201134

Orbit Design(Choosing the orbital parameters)Orbit Integration(Integrate the satellite parameters in the presence of the gravity field) Inversion(SH coefficients estimation) for different time periodsCalculating positions and velocities of the satellites, as well as range, range rate and range accelerationEGU General Assembly, Vienna, Austria, 3 - 8 April 201145

Orbit design

GRACE like configuration Repeat orbit of 125/8 Near circular, near polar orbit

Differential orbital elementsEGU General Assembly, Vienna, Austria, 3 - 8 April 201156

Orbit integration

Static field egm96Varying 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 201167

Repeat Period Check

EGU General Assembly, Vienna, Austria, 3 - 8 April 201178

Inversion

SH coefficients estimation up to degree 60Comparison of different solutions through maps, coefficients and degree RMS

24 daysInput fieldSolutionEGU General Assembly, Vienna, Austria, 3 - 8 April 201189

8 days (cycle period)3 days (sub-cycle)Input fieldSolutionEGU General Assembly, Vienna, Austria, 3 - 8 April 2011910

Differential SH coefficients Triangle plots24 days8 days (cycle period)3 days (sub-cycle)

EGU General Assembly, Vienna, Austria, 3 - 8 April 20111011

24 days8 days (cycle period)3 days (sub-cycle)

Degree RMS EGU General Assembly, Vienna, Austria, 3 - 8 April 20111112

Spatial aliasing of the higher degrees?Remove the static field which may have the biggest contribution!3 days 46 revolutions => lmax 23

Lin = 60, Lout = 23Lin = 23, Lout = 23EGU General Assembly, Vienna, Austria, 3 - 8 April 20111213

Veryfing the hypothesis

Observe the differential potential (Vtotal V static) at the positions of one of the satellitesEstimate the differential SH coefficients (Klm) from the differential potential observationCould be meaningful!Further investigation: Spatial aliasing by the changing field?

Lin = 60, Lout = 23EGU General Assembly, Vienna, Austria, 3 - 8 April 2011

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Summary

Almost similar results for cycle period (8 days) and the longe time (24 days) solutionsSub-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 degreesThe static field may have the largest contribution for the spatial aliasing effect on the sub-cycle solutionThe remaining aliasing effect may come from the spatial aliasing of the changing field itself (the future work) Thank youEGU General Assembly, Vienna, Austria, 3 - 8 April 201114