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Learn how GOCE gravity gradients are refined for regional geoid computations in cryospheric research. Explore strategies to cope with noise, improve solution accuracy, and benefit from combining data types. Discover the advantages and challenges of using GOCE gradients, filtering methods, and covariance functions. See how combining GOCE and terrestrial data enhances geoid computation results. Find out about rotation techniques, error propagation, and the impact of noise on gradient stability. Explore the potential of using GOCE data for in-situ observations and improving medium-wavelength solutions.
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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
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)
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)
Gradients for regional Geoid computations • Least Squares Collocation • Prediction • Gravity quantity as functional of disturbing potential T • Covariance function
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
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)
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
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)
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
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
Solution strategies • Noise covariance propagation GRF LORF • GRF: uncorrelated gradient tensor components • LORF: correlation through rotation
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
Geoid computation • Filtering of gradients • Noise PSD Quicklook
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)
Geoid computation • Geoid solution from real Vxx, Vyy and Vzz components Strategy 1 Strategy 2 Difference to reference Standard deviation
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
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
Geoid computation Difference to reference Standard deviation gradients only Dg only combined
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)
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
Thank you for your attention D. Rieser *, R. Pail, A. I. Sharov