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Combination of GRACE and GOCE in situ data for high resolution regional gravity

field modeling

M. Schmeer1, C. Gruber1, M. Schmidt2, F. Flechtner1

1 German Research Centre for Geosciences, Helmoltz Centre Potsdam (GFZ), Germany

2 German Geodetic Research Institut (DGFI), Germnay

schmeer@gfz-potsdam.de

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Outline

• GRACE in situ observationsNew method using calibrated K-Band observations

• Multi-resolution representation

• Combination of GRACE and GOCE observations for regional application (simulation).

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Motivation

In situ observations Representations

Regional Gravity field Modeling

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GRACE in situ observations

Transformation of residual K-Band range rate observations relative to adjusted K-Band range rates from GFZ GRACE L2 processing into residual potential differences by simplified relation (Jekeli 1999):

AAB rV

Residual K-Band observations from GFZ processing-chain (EPOS-OC) for monthly GRACE solutions by applying reductions for:

• static gravity field (EIGEN-4C/EIGEN-5C)

• ocean and atmospheric mass variations (AOD)

• third body attractions

• ocean and solid earth tides

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GRACE in situ observations

GRACE L2 solution

Using calibrated K-Band observations

Disturbing potential differences [m2/s2] across Africa and Europe relative to EIGEN-4C

Correlation between GRACE L2 and method using calibrated K-Band observations > 0.80

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Theory of Multi-resolution Representation (MRR)

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Multi-resolution Representation

Multi-resolution representation (MRR) splits an input signal into detail signals related to specific resolution levels, i.e., frequency bands: the higher the level the finer the spatial-temporal structures.

Modeling the spatial behavior of the gravity field by means of spherical scaling and wavelet functions, i.e., maintaining relation to spherical harmonics.

Example based on Blackman scaling function.

(Schmidt et al., 2007)

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Results from MRR

Mass distributions [EWH] from regional gravity modeling using calibrated K-Band observations due to EIGEN-4C for Jan. 2008

MRR up to detail level i = 4 → spatial resolution comparable to spherical harmonics d/o = 60

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January 2008 March 2008

Results from MRR

Differences between GRACE L2 solution and method using calibrated K-Band observations.• characteristic patterns (stripes)• residual signal level decreasing (RL04 → RL05)• spherical scaling function = optimal filter

Mass differences [EWH] between GRACE L2 solution (left: GRACE RL04 standards; right: GRACE RL05 standards) and method using calibrated K-Band observations.

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Inversion of observations into discrete values of geopotential

dKfTVTf ii ),()(4

1,)( yxyxx

Integral inversion based on scalar-valued integral kernels (locally extended) allows for evaluation of discrete values of gravitational functionals at a geocentric sphere.

Integral inversion of GRACE data (Novák 2007)

KeKeKeRrrH rrBBBAAA ),,,,,,(

GRACE: scalar-valued Abel-Poisson kernel function

GOCE: second order Abel-Poisson kernel function (non-scalar)

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Integral Inversion

Axl

Mutltivariate Gauss-Markov model

Numerical simulation

• computation of residual observations from L2 models (EIGEN5C – EGM96)• introduction of spherical cap • definition of different zones (far and near zones) • calculation of normal equations, regularization• superposition of GRACE and GOCE equation system, inversion

With observation vector I for combined observations from GRACE and GOCE For real data: variance components estimation, high-pass filtering

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Results: GRACE and GOCE-only

Simulated gravity field recovery (geoid height residuals) for GRACE (left) and GOCE (right) surrounded by low-resolution FAR-zone in [m]

Regional gravity field recovery from GRACE and GOCE separately due to their spectral behaviour.

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Results: Combination GRACE and GOCE

Reproduction of residual signal by combination of GRACE and GOCE

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Conclusion

• GRACE: Regional gravity field modeling using calibrated K-Band observations (residuals).

• Differences between GRACE L2 und regional gravity field modeling reflecting in characteristic patterns (stripes).

• Optimal filtering due to application of spherical scaling functions (MRR).

• Validation with external data outstanding.

• Combination of GRACE and GOCE: Integral inversion.

• GRACE and GOCE spectral complementary.

• Complementary coverage (e.g. Antarctica)