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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. - PowerPoint PPT Presentation
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Refining regional gravity field solutions with GOCE gravity gradients for cryospheric
investigations
D. Rieser *, R. Pail, A. I. Sharov
D. Rieser et al., 30.06.2010 2
Contents
• Introduction
• Gradients for regional Geoid computations
• Coping with noise
• Solution strategies
• Geoid computation
• Problems
• Summary
D. Rieser et al., 30.06.2010 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)
D. Rieser et al., 30.06.2010 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)
D. Rieser et al., 30.06.2010 5
• Least Squares Collocation
– Prediction
– Gravity quantity as functional of disturbing potential T
– Covariance function
Gradients for regional Geoid computations
D. Rieser et al., 30.06.2010 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
D. Rieser et al., 30.06.2010 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)
D. Rieser et al., 30.06.2010 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
D. Rieser et al., 30.06.2010 9
• 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)
Coping with noise
D. Rieser et al., 30.06.2010 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 gradientsin GRF
D. Rieser et al., 30.06.2010 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
D. Rieser et al., 30.06.2010 12
Solution strategies
• Noise covariance propagation GRF LORF
– GRF: uncorrelated gradient tensor components
– LORF: correlation through rotation
D. Rieser et al., 30.06.2010 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
D. Rieser et al., 30.06.2010 14
Geoid computation
• Filtering of gradients
– Noise PSD Quicklook
D. Rieser et al., 30.06.2010 15
Geoid computation
• Noise-free scenario:
– Vzz gradients simulated from EGM2008 on real orbit (D/O 50to250)
EGM2008 reference LSC with VzzDifference to EGM2008 reference Standard deviation
D. Rieser et al., 30.06.2010 16
Geoid computation
• Geoid solution from real Vxx, Vyy and Vzz components
Strategy 1 Strategy 2
Sta
nda
rd
devi
atio
nD
iffer
enc
e t
o re
fere
nce
D. Rieser et al., 30.06.2010 17
Geoid computation
• ‚Terrestrial‘ data
– Gravity anomalies simulated from EGM2008 (~ ArcGP)
– D/O 50 to 250
– = 3 mgal
– 0.25° X 0.25° grid
Standard deviation
Difference to reference
D. Rieser et al., 30.06.2010 18
Geoid computation
• Combination of GOCE and terrestrial data
– Vxx, Vyy and Vzz gradients (filtered in GRF)
– Gravity anomalies (D/O 50 to 250, = 3 mGal)
Standard deviation
Difference to reference
D. Rieser et al., 30.06.2010 19
Geoid computation
Standard deviation
Difference to reference
com
bine
dg
on
ly
grad
ient
s on
ly
D. Rieser et al., 30.06.2010 20
Problems
• Downward continuation of gradients unstable
– Ground data necessary
• Global covariance model
– Valid for g (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 g (D/O 50 to
250)
Empirical and EGM2008 model covariance function for V ZZ (D/O 50 to 250) at
h=245km
D. Rieser et al., 30.06.2010 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
D. Rieser *, R. Pail, A. I. Sharov
Thank you for your attention