eigen-5 activities in gfz and grgs r. biancale , j.-m. lemoine, s. bruinsma, s. loyer*

OSTST Meeting, Hobart, Australia, March 12-15, 2007

EIGEN-5 activities in GFZ and GRGS

R. Biancale, J.-M. Lemoine, S. Bruinsma, S. Loyer*CNES/GRGS Toulouse, France* Noveltis, Ramonville Saint-Agne, France Ch. Förste, F. Flechtner, R. Schmidt GeoForschungsZentrum Potsdam, Germany


EIGEN statistics

Mean Time-variable (monthly solutions)EIGEN-GRACE01S 39 daysEIGEN-GRACE02S 110 days 9 (04/2002-11/2003)EIGEN-GRACE03S 376 days 16 (02/2003-07/2004)EIGEN-GRACE04S 430 days 46 (02/2003-12/2006)EIGEN-GRACE05S not yet 45 (02/2003-11/2006)

Mean Time-variable (10-day solutions)EIGEN-GL04S over 2 full years 86 (07/2002-03/2005)EIGEN-GL05S not yet 146 (07/2002-12/2006)

EIGEN-GL04S1/-GL04C (2006) expanded in s.h. up to 150/360EIGEN-5S/-5C (mid/end 2007) expanded in s.h. up to 150/360


Gain in spectral accuracy of EIGEN models

Further investigations :• adjusting tides (S2,...)• using KBR data• destriping geoid models


EIGEN Standards

Major updates in EIGEN-GRACE05S: Static background gravity model: EIGEN-GL04C (150x150). Updated K2 and included M4 tide in FES2004 ocean tides. Usage of ocean pole tide model (Desai 2002). Usage of new atmospheric/oceanic de-aliasing product AOD1B-RL04 (mass- conserving baroclinic OMCT ocean model). Relativity extended by Lense-Thirring & de Sitter effects (IERS Conventions 2003). IERS 2003 nutation and precession model. Tidal and nutational corrections to EOP (local spline interpolation). Az/El dependent phase center corrections for GPS-SST of GRACE-A/B (JPL)

Major differences of EIGEN-GL04S wrt. EIGEN-GRACE05S : MOG2D (LEGOS/CLS) instead of OMCT Az/El dependent phase center corrections for GPS-SST of GRACE-A/B (GRGS) KBRR data (GRGS’ derivation of Level-1B KBR data) KBRR empirical parameterization


C20 normalized coefficient series

from LAGEOS only (in red), GRACE+LAGEOS (in blue), empirical model (in green)

GGM2C

EIGEN-GL04C .11628 10-10 /y


1. Adjusting bias + drift + annual + semi-annual terms for all coefficients up to degree 40; keeping the static field for higher degrees.

2. Computing « gravitological months » : averaging each month over 4 years.

3. Assimilating GRACE results into hydrological models (i.e. WGHM).

Ways of taking into account time variations


POD Results for GRACE

19 μm12 μm11 μm12 μm

.18 μm/s

.14 μm/s

.14 μm/s

.14 μm/s

7.4 mm7.2 mm7.1 mm6.4 mm

31 mm30 mm29 mm30 mm


POD Results for JASON

54.7 mm54.6 mm54.6 mm54.3 mm

.3219 mm/s

.3185 mm/s

.3185 mm/s

.3181 mm/s

12.7 mm12.2 mm11.9 mm11.5 mm


over 10 days using a 10-day model vs. EIGEN-GL04S

March 2005 – radial rms = 5 mm

Jason radial orbit comparison


Until now degree 1 coefficients were not delivered in the 10-day models (i.e. the origin of EIGEN models is the Earth centre of mass). They are adjusted only through Lageos data.

Nevertheless they could be delivered for altimetric purposes.

Degree 1 coefficients

In summary for the next “satellite” EIGEN-5S model we can propose delivering optional annual and semi-annual sine and cosine terms from degree 1 to 40 (and some drifts as well).


Task Computation of global high-resolution gravity field models in terms of spherical

harmonic coefficients from the combination of satellite data and surface gravity data. At GFZ Potsdam and GRGS Toulouse, such global gravity models are

routinely produced in the framework of the EIGEN* processing activities.

Combined data setsSatellite data: • GRACE GPS/SST and K-Band data• CHAMP GPS/SST data• LAGEOS Satellite Laser Ranging measurements

Ground data:• Gravity anomaly data over land (based on classical and air-born gravimetry)• Ocean geoid height and ocean gravity anomaly data (based on altimetry and

ship gravimetry)

The ground data presently available for GFZ/GRGS allow a global grid coverage of 0.5° x 0.5° resolution, corresponding to a maximum degree of 360 for the spherical harmonic coefficients of a global gravity field model obtained from it.

* EIGEN = European Improved Gravity model of the Earth by New techniques

GFZ/GRGS activities on combined gravity field models


contribution to the solution, full normal matrix:

kept separately and bound together with the surface data using constraints**):

kept separately (reduced from the full normal matrix):

not used:

contribution to the solution, block diagonal matrix:

contribution to the solution, numerical integration:

70

GRACE

degree/order 359 360

Integration

overlapping

surface, full

70

GRACE

155

surface, block diagonal

degree/order 359

30 LAGEOS

150 200

2 90

24.6

90l10 e10 0.8696=σwith

**) constraints (pseudo observations), applied between degree 90 and 150 :

σ±0=S/CS/C LAG. GRACEm,n,Surfacem,n,

Combination scheme of EIGEN-GL05Cp


EIGEN-GL05Cp gravity anomaly

Resolution:0.5° x 0.5°

[mgal]


Δζ, 0.5° x 0.5°

Geoid height differences vs. a global ground data only solution

EIGEN-CG03C

-2.0 0.0 2.0

[meter]

EIGEN-GL04C

-1.0 0.0 1.0

[meter]

EIGEN-GL05Cp

-1.0 0.0 1.0

[meter]

Improvement of combined EIGEN-models (1)

→ Reduction of the meridional stripes !


EIGEN-CG03C

EIGEN-GL04C [meter]

EIGEN-GL05Cp

→ Reduction of the meridional stripes !

Improvement of combined EIGEN-models (2)

Δζ, 0.5° x 0.5°

Geoid height differences vs. a global ground data only solution


EIGEN-GL05Cp: Geoid Degree Amplitudes (1)

yellow: yellow: EIGEN-CG01C vs. GGM02CEIGEN-CG01C vs. GGM02Clight blue:light blue: EIGEN-CG03C vs. GGM02CEIGEN-CG03C vs. GGM02Cbrown:brown: EIGEN-GL04C vs. GGM02CEIGEN-GL04C vs. GGM02Cgreengreen EIGEN-GL05Cp vs. GGM02CEIGEN-GL05Cp vs. GGM02C

EGM 96EGM 96


EIGEN-GL05Cp: Geoid Degree Amplitudes

EIGEN-GL04C

EGM96EIGEN-GL05Cp

EIGEN-CG01C vs. GGM02CEIGEN-CG03C vs. GGM02CEIGEN-GL04C vs. GGM02CEIGEN-GL05Cp vs. GGM02C


Comparison with independent ocean gravity data

Latitude-weighted root mean square of geoid- and gravity anomaly differences between gravity field models and altimetry based data sets,

formed on 1° x 1° grids of the compared data sets, after filtering with different filter lengths.

Altimetry based data sets for comparison*) NIMA altimetric gravity anomalies over the ocean (Kenyon, Pavlis 1997) **) Geoid undulations over the oceans derived from CLS01 altimetric Sea Surface Heights (Hernandez et al., 2001) and ECCO simulated sea surface topography (Stammer et al., 2002)

0.1170.1170.1190.1160.1170.11510°

0.1280.1290.1330.1330.1290.1315°

0.1690.1740.1830.1820.1710.1763°CLS-ECCO **)

[m]

0.3130.3130.3130.3130.31310°

1.0001.0271.1051.1071.0085°

4.1094.1914.2614.2564.1653°NIMA *)

[mgal]

EIGEN-GL05Cp

EIGEN-GL04C

EIGEN-CG03C

EIGEN-CG01C

GGM02CEGM96Filter- length

gravity field model

altimetrybased data set


Status and Future plans:

The current published combined model is EIGEN-GL04C. It’s coefficient set is available for download at the ICGEM* data base at GFZ Potsdam:

http://icgem.gfz-potsdam.de/ICGEM/ICGEM.html

Further improvements of the preliminary EIGEN-GL05Cp model are planned for the upcoming EIGEN-05C gravity field model:

- based on EIGEN-GRACE05S (GFZ) and EIGEN-GL05S (GRGS) models- inclusion of CHAMP data- extension of the full ground data based normal equations to

higher degrees (n,m=250 or more)- usage of new/updated ground data sets

*ICGEM = The International Center of Global Earth Models at GFZ Potsdam is one of the six datacenters of the International Gravity Field Service (IGFS) of the IAG

GFZ/GRGS activities on combined gravity field models

eigen-5 activities in gfz and grgs r. biancale , j.-m. lemoine, s. bruinsma, s. loyer*

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