1. D. Rieser *, R. Pail, A. I. Sharov
Refining regional gravity field solutions with GOCE gravity gradients for cryospheric investigations
D. Rieser *, R. Pail, A. I. Sharov

2. Contents Introduction Gradients for regional Geoid computations
Coping with noise
Solution strategies
Geoid computation
Problems
Summary
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3. Introduction Background and motivation Project ICEAGE
Arctic snow- and ice cover variations and relations to gravity
Sharov et al.: Variations of the Arctic ice-snow cover in nonhomogenous geopotential (oral, ,11:40)
Gisinger et al.: Ice mass change versus gravity-local models and GOCE's contribution (poster, 30.06, 16:00)
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4. Introduction Contributions of GOCE to regional gravity field
Gradients as in-situ observations
Beneficial dense data distribution
Combination with other data types
terrestrial (gravity anomalies, e.g. ArcGP)
gravity models (EGM2008)
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5. Gradients for regional Geoid computations
Least Squares Collocation
Prediction
Gravity quantity as functional of disturbing potential T
Covariance function
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6. Gradients for regional Geoid computations
Approach following Tscherning (1993)
Covariances as combination of base functions
All covariances up to 2nd order derivatives of the disturbing potential (i.e. gradients)
Advantage:
Covariances can be rotated in arbitrary reference frame
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7. Gradients for regional Geoid computations
Characteristics of GOCE gradients observations
Observations in Gradiometer Reference Frame (GRF)
Assumption of uncorrelated gradients in GRF
Gradients suffering from coloured noise
Vxy and Vyz tensor components badly deteriorated
Error PSD from ESA E2E-simulation (before GOCE launch)
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8. Coping with noise
Filtering of coloured noise by applying Wiener filter method (Migliaccio et al., 2004)
Signal t consisting of signal s + noise n
Wiener filter in spectral domain
Filtered signal in time domain
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9. Coping with noise Covariance function of the filter error
Requirement: stationary signal (valid only in Local Orbit Reference Frame LORF)
Problem: rotation of gradients from GRF to LORF unfavorable (Vxy, Vyz)
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10. Solution strategies Strategy 1 Gradients in GRF Filtering in GRF
not allowed in strict sense
Cll rotated to GRF
Cnn set up in GRF
Csl for signals in Local North Oriented Frame (LNOF) and gradients in GRF
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11. Solution strategies Strategy 2 Rotate gradient tensor to LORF
a-priori replacement of less accurate tensor components with EGM
Filtering in LORF
Set up of Cnn in GRF and rotation to LORF
a-priori covariance propagation for replaced components from EGM
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12. Solution strategies Noise covariance propagation GRF  LORF
GRF: uncorrelated gradient tensor components
LORF: correlation through rotation
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13. Geoid computation GOCE data: 01. November 2009 – 30. November 2009
Reduced up to D/O 49 by EGM2008
5 sec sampling
Region: 53° – 79° E ° – 78° N
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14. Geoid computation Filtering of gradients Noise PSD Quicklook
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15. Geoid computation Noise-free scenario:
Vzz gradients simulated from EGM2008 on real orbit (D/O 50to250)
EGM2008 reference
LSC with Vzz
Difference to EGM2008 reference
Standard deviation
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16. Geoid computation Geoid solution from real Vxx, Vyy and Vzz components
Strategy 1
Strategy 2
Difference to reference
Standard deviation
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17. Geoid computation ‚Terrestrial‘ data
Gravity anomalies simulated from EGM2008 (~ ArcGP)
D/O 50 to 250
s = 3 mgal
0.25° X 0.25° grid
Difference to reference
Standard deviation
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18. Geoid computation Combination of GOCE and terrestrial data
Vxx, Vyy and Vzz gradients (filtered in GRF)
Gravity anomalies (D/O 50 to 250, s = 3 mGal)
Difference to reference
Standard deviation
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19. Geoid computation Difference to reference Standard deviation
gradients only
Dg only
combined
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20. Empirical and EGM2008 model covariance function for Dg (D/O 50 to 250)
Problems
Downward continuation of gradients unstable
Ground data necessary
Global covariance model
Valid for Dg (ground) and gradients (GOCE altitude)
Assumptions
Strategy 1:
Wiener filtering in non-stationary GRF
Strategy 2:
Noise-covariance information from a-priori Wiener filtering in GRF
Replacement of real gradients with EGM information
Empirical and EGM2008 model covariance function for VZZ (D/O 50 to 250) at h=245km
Empirical and EGM2008 model covariance function for Dg (D/O 50 to 250)
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21. Summary GOCE gravity gradients can be used as in-situ observations
Reduction of noise by applying Wiener filtering
Different solution strategies lead to similar results
Assumptions inevitable
Combination of GOCE gradients with terrestrial data improves the solution in medium wavelengths
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22. D. Rieser *, R. Pail, A. I. Sharov
Thank you for your attention
D. Rieser *, R. Pail, A. I. Sharov