The satellite-only gravity field model GOCO06s
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These data are freely available under the Creative Commons Attribution
4.0 International Licence (CC BY 4.0)
When using the data please cite:
Kvas, Andreas; Mayer-Gürr, Torsten; Krauss, Sandro; Brockmann, Jan Martin;
Schubert, Till; Schuh, Wolf-Dieter; Pail, Roland; Gruber, Thomas;
Jäggi, Adrian; Meyer, Ulrich (2019):
The satellite-only gravity field model GOCO06s. GFZ Data Services.
http://doi.org/10.5880/ICGEM.2019.002
GOCO06s is a satellite-only, global gravity field model up to degree and order
300, with constrained secular and annual variations up to degree and order 200.
It was produced by the GOCO Team and is based on more than 1,160,000,000
observations from 19 satellites. The combination of the individual data sources
is performed on the basis of the full systems of normal equations, where the
relative weighting between each constituent is determined by variance component
estimation. In order to account for the polar gap of GOCE, the solution is
Kaula-regularized after degree and order 150. The temporal variations contain
observation information up to degree and order 120 and are regularized with
isotropic noise split by land/ocean masks up to degree and order 200.
GOCO (Gravity Observation Combination) is a project initiative in the frame of
ESA's GOCE Data AO (project no. 4248), with the objective to compute
high-accuracy and high-resolution static global gravity field models.
(Contact: R. Pail, pail@bv.tum.de)
More information can be found on www.goco.eu.
Contributing institutions:
- Technical University of Munich, Institute of Astronomical and Physical
Geodesy
- University of Bonn, Institute of Geodesy and Geoinformation
- Graz University of Technology, Institute of Geodesy
- Austrian Academy of Sciences, Space Research Institute
- University of Bern, Astronomical Institute
To compute a gravity field functional at an arbitrary time t, the expression
V(t) = gfct+trnd*(t-t0)/T+acos*cos(2pi*(t-t0)/T)+asin*sin(2pi*(t-t0)/T)
with t0 as the reference epoch and T as the annual period (365.25 d), has to be
used. The reference epoch is 2010-01-01 (MJD 55197).
This solution is estimated from more than 1,160,000,000 observations from
- GOCE: TIM6 Gradiometer observations (data of the complete mission period)
- GRACE: ITSG-Grace2018s
- Kinematic orbits: Swarm A+B+C, TerraSAR-X, TanDEM-X, CHAMP, GRACE A+B,
GOCE (TIM6 SST)
- SLR: LAGEOS, LAGEOS 2, Starlette, Stella, AJISAI, LARES, LARETS,
Etalon 1/2, BLITS
- Regularization: Kaula degree >150.
Files
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Solution:
- GOCO06s.gfc : Full model with static, trend, and annual signal
System of normal equations, covariance matrix of solution:
For combination purposes, the unconstrained system of normal equations (N, b) with the required metadata (weighted square sum of observation vector, observation count, parameter count)
and the diagonal regularization matrix K are provided. Solving (N+K)*x_hat = b yields the constrained static solution of GOCO06s.
- normals/sinex : system of unconstrained normal equations, Kaula vector and metadata stored in SINEX format (storage format 6b)
- normals/ascii/GOCO06s_normalEquation.**-**.txt.gz : blocked system of unconstrained normal equations (N)
- normals/ascii/GOCO06s_normalEquation.rightHandSide.txt.gz : right hand side of unconstrained normal equations (b)
- normals/ascii/GOCO06s_normalEquation.info.snx : normal equation metadata (observation count, parameter count, square sum of observation vector),
diagonal regularization matrix, right hand side and constrained solution in SINEX format (diag(K), Vector b)
- normals/ascii/GOCO06s_normalEquation.kaula.txt : diagonal regularization matrix (diag(K))
- normals/ascii/GOCO06s_normalEquation.parameterNames.txt : numbering of spherical harmonic coefficients in normal equations
- covariance/ascii/GOCO06s_covarianceMatrix.**-**.txt.gz : upper triangle of variance-covariance matrix of the constrained static solution (blocked)
GOCO06s block matrix file format description
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The coefficients are ordered by degree, within each degree they are sorted by order with c_nm and s_nm alternating:
c20, c21, s21, c22, s22, c30, c31, ... (see also normals/ascii/GOCO06s_normalEquation.parameterNames.txt)
The upper triangle of their covariance matrix is partitioned into blocks of size 2048x2048 in the following way:
------------------------------------------------------------
| *.00-00 | *.00-01 | *.00-02 | *.00-03 | ... | *.00-44 |
| | *.01-01 | *.01-02 | *.01-03 | ... | *.01-44 |
| | | *.02-02 | *.02-03 | ... | *.02-44 |
| | | | *.03-03 | ... | *.03-44 |
| | | | | ... | ... |
| | | | | | *.44-44 |
------------------------------------------------------------
Each block is stored as gzipped ASCII-File using the following file format:
Line 0: file format descriptor
Line 1: Matrix( x )
Size of stored matrix
Line 2 - Line 2+nrows:
Matrix elements as whitespace separated floating point values:
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| a_00 | a_01 | a_02 | a_03 | a_04 | a_05 |
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| a_01 | a_11 | a_12 | a_13 | a_14 | a_15 |
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| a_02 | a_21 | a_22 | a_23 | a_24 | a_25 |
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| a_03 | a_31 | a_32 | a_33 | a_34 | a_35 |
-------------------------------------------