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

Contents Introduction Gradients for regional Geoid computations Coping with noise Solution strategies Geoid computation Problems Summary D. Rieser et al., 30.06.2010

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) D. Rieser et al., 30.06.2010

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) D. Rieser et al., 30.06.2010

Gradients for regional Geoid computations Least Squares Collocation Prediction Gravity quantity as functional of disturbing potential T Covariance function D. Rieser et al., 30.06.2010

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 D. Rieser et al., 30.06.2010

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) D. Rieser et al., 30.06.2010

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 D. Rieser et al., 30.06.2010

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) D. Rieser et al., 30.06.2010

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 D. Rieser et al., 30.06.2010

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 D. Rieser et al., 30.06.2010

Solution strategies Noise covariance propagation GRF  LORF GRF: uncorrelated gradient tensor components LORF: correlation through rotation D. Rieser et al., 30.06.2010

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 73° – 78° N D. Rieser et al., 30.06.2010

Geoid computation Filtering of gradients Noise PSD Quicklook D. Rieser et al., 30.06.2010

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 D. Rieser et al., 30.06.2010

Geoid computation Geoid solution from real Vxx, Vyy and Vzz components Strategy 1 Strategy 2 Difference to reference Standard deviation D. Rieser et al., 30.06.2010

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 D. Rieser et al., 30.06.2010

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 D. Rieser et al., 30.06.2010

Geoid computation Difference to reference Standard deviation gradients only Dg only combined D. Rieser et al., 30.06.2010

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) D. Rieser et al., 30.06.2010

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 D. Rieser et al., 30.06.2010

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