Combination of grace and goce in situ data for high resolution regional gravity field modeling
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Combination of GRACE and GOCE in situ data for high resolution regional gravity field modeling. M. Schmeer 1 , C. Gruber 1 , M. Schmidt 2 , F. Flechtner 1 1 German Research Centre for Geosciences, Helmoltz Centre Potsdam (GFZ), Germany 2 German Geodetic Research Institut (DGFI), Germnay

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

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Combination of grace and goce in situ data for high resolution regional gravity field modeling

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

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

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

2German Geodetic Research Institut (DGFI), Germnay

[email protected]


Outline

Outline

  • GRACE in situ observations

  • New method using calibrated K-Band observations

  • Multi-resolution representation

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


Motivation

Motivation

Regional Gravity field Modeling

In situ observations

Representations


Grace in situ observations

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):

  • 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


Grace in situ observations1

GRACE in situ observations

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

GRACE L2 solution

Using calibrated K-Band observations

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


Combination of grace and goce in situ data for high resolution regional gravity field modeling

Theory of Multi-resolution Representation (MRR)


Multi resolution representation

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)


Combination of grace and goce in situ data for high resolution regional gravity field modeling

Results from MRR

MRR up to detail level i = 4

→spatial resolution comparable to spherical harmonics d/o = 60

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


Combination of grace and goce in situ data for high resolution regional gravity field modeling

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

March 2008

January 2008

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


Inversion of observations into discrete values of geopotential

Inversion of observations into discrete values of geopotential

Integral inversion of GRACE data (Novák 2007)

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

GRACE: scalar-valued Abel-Poisson kernel function

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


Integral inversion

Integral Inversion

  • 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

Mutltivariate Gauss-Markov model

With observation vector Ifor combined observations from GRACE and GOCE

For real data: variance components estimation, high-pass filtering


Results grace and goce only

Results: GRACE and GOCE-only

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

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


Results combination grace and goce

Results: Combination GRACE and GOCE

Reproduction of residual signal by combination of GRACE and GOCE


Conclusion

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)


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