Enhancing Cryospheric Investigations with GOCE Gravity Gradients Solutions

1. 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

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, 30.06.,11:40) • Gisinger et al.: Ice mass change versus gravity-local models and GOCE's contribution (poster, 30.06, 16:00)

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)

5. Gradients for regional Geoid computations • Least Squares Collocation • Prediction • Gravity quantity as functional of disturbing potential T • Covariance function

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

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)

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

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)

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 • Cslfor signals in Local North Oriented Frame (LNOF) and gradientsin GRF

11. Solution strategies • Strategy 2 • Rotate gradient tensor toLORF • a-priori replacement ofless accurate tensor components with EGM • Filtering in LORF • Set up of Cnn in GRF and rotation to LORF • a-priori covariance propagation for replacedcomponents from EGM

12. Solution strategies • Noise covariance propagation GRF  LORF • GRF: uncorrelated gradient tensor components • LORF: correlation through rotation

13. Geoid computation • GOCE data: • 01. November 2009 – 30. November 2009 • Reduced up to D/O 49by EGM2008 • 5 sec sampling • Region: 53° – 79° E 73° – 78° N

14. Geoid computation • Filtering of gradients • Noise PSD Quicklook

15. EGM2008 reference LSC with Vzz Difference to EGM2008 reference Standard deviation Geoid computation • Noise-free scenario: • Vzz gradients simulated from EGM2008 on real orbit (D/O 50to250)

16. Geoid computation • Geoid solution from real Vxx, Vyy and Vzz components Strategy 1 Strategy 2 Difference to reference Standard deviation

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

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

19. Geoid computation Difference to reference Standard deviation gradients only Dg only combined

20. 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)

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

22. Thank you for your attention D. Rieser *, R. Pail, A. I. Sharov