Full Resolution Geoid from GOCE Gradients for Ocean Modeling
Matija Herceg & Per KnudsenDepartment of GeodesyDTU Space
living planet symposium 28 June – 2 July, Bergen, Norway
Examples of Scientific Applications
2living planet symposium 28 June – 2 July, Bergen, Norway
Gravity field map and improved global geoid models
Improved understanding of ocean circulation and energy distribution
Global unification of height systems
GOCE Products
3living planet symposium 28 June – 2 July, Bergen, Norway
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
4living planet symposium 28 June – 2 July, Bergen, Norway
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
5living planet symposium 28 June – 2 July, Bergen, Norway
10-8
10-6
10-4
10-2
10 100 1000
Harm. deg.
De
g.
var.
(m
2 )GOCE Error Degree Variances
Tscherning-Rapp model
Simulated error degree variances
Simulation
6living planet symposium 28 June – 2 July, Bergen, Norway
Simulation
7living planet symposium 28 June – 2 July, Bergen, Norway
-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)
Co
v. (
m2 )
GOCE Error Covariance Function
This study
8living planet symposium 28 June – 2 July, Bergen, Norway
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
9living planet symposium 28 June – 2 July, Bergen, Norway
We will use synthetic data!- since no Level 2 data was available for this study.
• Delta spikes• GOCINA test data:
– Geoid– MDT
The method
10living planet symposium 28 June – 2 July, Bergen, Norway
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
11living planet symposium 28 June – 2 July, Bergen, Norway
Test 1: Resolution capability
12living planet symposium 28 June – 2 July, Bergen, Norway
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
13living planet symposium 28 June – 2 July, Bergen, Norway
Vxx: 14 cm
Vyy: 14 cm
Test 1: Resolution capability
14living planet symposium 28 June – 2 July, Bergen, Norway
Vxx:
Vyy:
Test 1: Resolution capability
15living planet symposium 28 June – 2 July, Bergen, Norway
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
16living planet symposium 28 June – 2 July, Bergen, Norway
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 test
Geoid 38 cm 19 cm
MDT 21 cm 18 cm
Test 2: GOCINA MDT
17living planet symposium 28 June – 2 July, Bergen, Norway
Plots of geoid and MDT residuals:
They are very similar.
Results
18living planet symposium 28 June – 2 July, Bergen, Norway
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...