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Geocenter motion and surface loading coefficients from a joint inversion of GPS, GRACE and Ocean Bottom Pressure from a model

22nd of June 2011: the series is now extended including 2009


The exerted pressure due to the movement of water, air and ice in the thin layer consisting of the atmosphere, ocean and the terrestrial hydrosphere is called 'surface loading'. The term 'loading' is used because the pressure differences essentially load the crust of the Earth.

Over the ocean this pressure effect can be modelled by general circulation models forced by atmospheric models. Furthermore, the crust will deform under the load which can in its turn be measured by a GPS network. Due to the redistribution of water, air, ice and the associated deformation of the solid Earth, small perturbations in the gravity field will be induced as well. The latter effect is measured on a global scale by the satellite twin mission GRACE (gravity recovery and climate experiment).

Conversely, using observations of gravity, crustal deformations and ocean bottom pressure we are able to infer estimates of surface loading. Estimates for surface loading from a specific implementation of this so-called 'Inverse Problem' are provided on this site.

Surface loading coefficients


Used data:

  1. GPS reprocessing solutions (TU Dresden), using full error-covariance
  2. GRACE-GFZ rl04, with calibrated full covariance
  3. Pseudo observations of Ocean bottom pressure from the FESOM model. Diagonal error-covariance based on 2 model runs with different atmospheric forcing (ECMWF vs. NCEP).
  • Time period:Jan. 2003- Dec. 2009
  • Space resolution: Spherical harmonic degree and order 30
  • Units 'm' of equivalent water height
  • weekly ascii files in the ICGEM format (but with a different row tag 'slc' and product_type)
  • Time resolution: weekly, aligned to GPS weeks. (Note: long term trends derived from the data are currently inaccurate)
  • The time-variable Ocean/Atmosphere models are restored! (The signal therefore contains atmosphere+ocean+hydrology)
  • Detrended

The coefficients can be mapped to equivalent water in meters at a geographical location by applying the following formula:

h=sum(n=1..nmax)sum(m=0..n) [Cnm cos(m*longitude) + Snm sin(m*longitude)] Pnm[cos (colatitude)]

Where Pnm[..] are the 4 pi normalized associated Legendre functions (no Condon-Shortley phase applied).


Geocenter motion

The use of GPS data in the inversion allows the estimation of the geocenter motion, while this is not possible for GRACE-only data (the degree 1 coefficients are set to zero per definition). The geocenter motion describes the relative motion of the center of figure of the Earth wrt to the center of mass of the Earth system (Earth+Ocean+atmosphere+ terrestrial water storage). Due to the time variable distribution of water over the Earth's surface, the geocenter motion mostly notably varies on seasonal scales.

A correction for the geocenter motion is required when comparing GRACE when with observations/models which are provided wrt. the Earth's crust:

In situ bottom pressure

Superconducting gravimeter

The detrended geocenter motion can be  downloaded as seen from the center of figure frame (link) or from the center of solid Earth frame (link). The files are formatted as 7 columns: time in years, X,Y,Z in meters and standard deviations of X,Y,Z in meters. The geocenter motion is defined as the difference CM-CF/CE: the origin of the center of common mass frame minus the origin of the center of figure frame or center of solid Earth frame.

When using these data please cite:

Rietbroek, R., Fritsche, M., Dahle, C., Brunnabend, S.-E., Behnisch, M., Kusche, J., Flechtner, F., Schröter, J., Dietrich, R. (2014) Can GPS-Derived Surface Loading Bridge a GRACE Mission Gap?, Surveys in Geophysics, 1–17, doi:10.1007/s10712-013-9276-5.

The data from the previous release can be downloaded here: coefficients and geocenter motion. More details on that release can be found in the following paper:

Rietbroek, R, Brunnabend, SE, Dahle, C, Kusche, J, Flechtner, F, Schröter, J, & Timmermann, R. 2009. Changes in total ocean mass derived from GRACE, GPS, and ocean modeling with weekly resolution. Journal Of Geophysical Research-Oceans, 114(C11004), C11004.

General project info can be found on the SPP 1257 massentransporte website

For more information please contact roelof(at)

last updated: 29th October 2012 (correct time tag for geocenter motion)

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