International Symposium on Gravity, Geoid and Height Systems GGHS 2012, Venice, Italy 1 GOCE data...

International Symposium on Gravity, Geoid and Height Systems GGHS 2012, Venice, ItalyInternational Symposium on Gravity, Geoid and Height Systems GGHS 2012, Venice, Italy1

GOCE data for local geoid enhancement

Matija Herceg Per Knudsen

Carl Christian Tscherning


Motivation and objectives

• The success of GOCE depends on adequate methodologies for extracting the gravity field from its observations and on combining the gravity field with information from other sources

• Development of a method for regional gravity field recovery by using GOCE gradients in addition to the global models

• Use enhanced geoid for determination of MDT


The RPM method• The Earth anomalous gravity field at point Q is modeled by a

set of base functions, each obtained as the anomalous gravity potential from each point

• Point mass functions are harmonic functions, which may be used to represent the anomalous gravity potential T


The RPM method• Closed expresions are calculated by:

• For reduction of point masses, the derivative of the sum of a finite Legendre series is used:

• computed using a recursion algorithm (Tscherning and Rapp 1974)

• Reduced point masses

n

ll

ll tPsaS

0

1 )(

2

2

p

R

rVV

5

222

3

)(31

ltrr

lV qpC

RC VVV

International Symposium on Gravity, Geoid and Height Systems GGHS 2012, Venice, Italy5

The RPM method

Fitting the function of different gravity field quantities to the empirical covariance function

All gravity anomalies Marine gravity anomalies

GOCE Tzz gradient anomalies


Local gravity field modelling results

Gravity anomaly in region between Greenland and the United Kingdom (GOCINA)



Reduced geoid in the GOCINA region


Tzz gradient anomaly prediction [E], where the contribution from the EGM2008 up to harmonic degree and order 100 is subtracted

Local gravity field modelling resultsObservations Prediction

Difference


Local gravity field modelling resultsCol prediction RPM prediction

Difference

Gravity anomaly prediction (LSC and RPM) comparison [mGal], where the contribution from the EGM2008 up to harmonic degree and order 100 is subtracted



Geoid height prediction (LSC and RPM) comparison [m], where the contribution from the EGM2008 up to harmonic degree and order 100 is subtracted

Col prediction

Difference

RPM prediction


Power spectrum of the geoid height anomaly prediction when EGM2008 up to harmonic degree and order 100 is subtracted. The prediction is done by the LSC and the RPM

methods with different datasets



Mean Dynamic Topography

GOCE Direct MDT

GOCE Direct enhanced MDT


Mean Dynamic Topography

GOCINA project MDTMaximenko MDTDTU10 MDT

GOCE Direct MDT GOCE Direct enhanced MDT


Current speed

GOCINA project MDT current speed

Maximenko MDT current speed

DTU10 MDT current speed

GOCE Direct MDT current speed

GOCE Direct enhanced MDT current speed


• The GOCE Direct MDT current speeds reveal all the gross features of the general circulation in the region

• Does not show improvement over the GOCE Direct MDT

Power spectrum of different derived MDT

Current speeds


Conclusions• LSC and RPM methods give similar results when the selected GOCE

gradient dataset is used• Using all available GOCE gradients leads to improvement in the

geoid height anomaly prediction• GOCE data provides a better estimation of the MDT in the GOCINA

region than any previously obtained using only satellite observations. It could not be concluded whether the enhanced geoid model contribute to a further improvement of the MDT in the GOCINA area

• GOCE Direct MDT surface geostrophic currents reveal all of the gross features of the general circulation

• GOCINA project shows the smallest scale details, which makes it still the best ocean circulation representation in this region


Future work

• Resolve the issues related to the mean value of the data• Use real error degree variances when computing the RPM

response• Use all GOCE gravity gradients• In the regions with higher gravity anomaly signal oscillations,

i.e. mountain regions, GOCE gradients can possibly provide higher geoid enhancements than the ones shown here

• Removing short wavelength signal from the GOCE gradients


The RPM method regularization

– Adding a diagonal matrix to the normal equations matrix (one, degree dependent factors, or degree variances)

– Diagonal matrix is scaled by a regularization parameter empirically determined, based on a trade-off between the strength of the regularization and the fit to the given observations

– Squared mean error of the input GOCE gradients 0.01 E


Power spectrum of the geoid height anomaly prediction when GOCE Direct r3 model up to harmonic degree and order 240 is subtracted. The prediction is done by the LSC

and the RPM methods with different datasets


International Symposium on Gravity, Geoid and Height Systems GGHS 2012, Venice, Italy 1 GOCE data...

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