Full Resolution Geoid from GOCE Gradients for Ocean Modeling

Matija Herceg & Per KnudsenDepartment of GeodesyDTU Space

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Examples of Scientific Applications

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Gravity field map and improved global geoid models

Improved understanding of ocean circulation and energy distribution

Global unification of height systems

GOCE Products

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GOCE Level 2 products:• EGG_NOM_2_: Gravity Gradients in the Gradiometer

Reference Frame (GRF),• EGG_TRF_2_: Gravity Gradients in Local North-Oriented

reference Frame (LNOF),• SST_PSO_2_: Precise science orbits,• EGG_GOC_2_: Spherical harmonic series

+ derived quantities grids of geoid heights, gravity anomalies and deflections of the vertical are additionally included as well as geoid height errors,

• EGG_GVC_2_: Variance-covariance matrix for the coefficients.

GUT: The GOCE User Toolbox has been developed to facilitate the use of GOCE products for oceanographers and other communities such as Solid Earth physicists.

GOCE Products

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GOCE Level 2 products:• EGG_NOM_2_: Gravity Gradients in GRF,• EGG_TRF_2_: Gravity Gradients in LNOF,• EGG_GOC_2_: Spherical harmonics series to degree and

order 200 + grids.

GOCE gradients contain substantially more gravity related information than the spherical harmonic coefficient set, e.g.:Knudsen and Tscherning (2005) found that the total geoid error (including omission errors) may reduce from about 30 cm to 15 cm when gradients are used regionally.

Simulation

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10-8

10-6

10-4

10-2

10 100 1000

Harm. deg.

Deg

. var

. (m

2 )GOCE Error Degree Variances

Tscherning-Rapp model

Simulated error degree variances

Simulation

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Simulation

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-0.05

0

0.05

0.10

0 0.5 1.0 1.5 2.0

Full: St.dev. = 11 cm, cor.len. = 0.17 deg.200: St.dev. = 31 cm, cor.len. = 0.30 deg.

Lag (degrees)

Cov

. (m

2 )

GOCE Error Covariance Function

This study

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Apply methods for regional gravity field modelling to study potential improvements in the recovery of:

• The gravity field, when using gravity gradients compared instead of the global spherical harmonics to degree and order 200:- Test signal transfer using a simple approximation – dipoles –

to analyse resolution capability,- (Plan to) compare with optimal method (Least squares

collocation).

• The Mean Dynamic Topography:- Use and inter-compare with GOCINA test data.

This study

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We will use synthetic data!- since no Level 2 data was available for this study.

• Delta spikes• GOCINA test data:

– Geoid– MDT

The method

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We apply a simple gravity field approximation method to analyse the use of gravity gradients:

The Dipole method:

Point mass dipoles:

Located on a regular grid:

The method

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Test 1: Resolution capability

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Use a delta spike geoid signal of 0.5 m in a grid of zeros to

Geoid > Gradients > Geoid

Vzz: 16 cm

Test 1: Resolution capability

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Vxx: 14 cm

Vyy: 14 cm

Test 1: Resolution capability

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Vxx:

Vyy:

Test 1: Resolution capability

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Vzz:

Correlations and numerical instabilities cause problems in recovering short wavelength parts of the gravity field.

Success in recovering wavelengths down to about 70-80 km- corresponding to harmonic degree 500-600 roughly.

Test 2: GOCINA MDT

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In the second test the improvements of the geoid and the MDT in the GOCINA region are studied:

• As a first approximation the EGM96 to deg. 200 is used.• Subsequently the geoid is improved using simulated gradients (Vzz

only) derived from the residual gravity field.

Preliminary results:

RMS values

(smoothed quantities)

Ref. 200 This testGeoid 38 cm 19 cmMDT 21 cm 18 cm

Test 2: GOCINA MDT

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Plots of geoid and MDT residuals:

They are very similar.

Results

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The results of the initial tests demonstrate that:1. GOCE gravity gradient data may improve the geoid above harmonic

degree 200 up to about 500-600,2. The improved geoid improves the modelling of the MDT.

Hence, the use of GOCE gradient for regional improvements in the modelling of the MDT will be important for regional ocean circulation modelling.

Much more to do... With real data...