Space-wise GOCE products processing

GOCE gravity field products by means of the space-wise approach (release 5)

The processing of the satellite grids and the GOCE-only spherical harmonic model

The space-wise approach is a multi-step collocation procedure, developed in the framework of the GOCE HPF data processing for the estimation of gravity gradient grids at satellite altitude.
By analysing these grids, spherical harmonic coefficients of the Earth gravitational field and their error covariance matrix can be computed.

Processing procedure:

  • SST model:
    • gravitational potential estimation by energy conservation approach applied to kinematic orbits
    • grid interpolation of gravitational potential at mean satellite altitude by least-squares adjustment with local collocation refinement
    • spherical harmonic analysis of the estimated grids by numerical integration.
  • SST+SGG model:
    • orbital filtering of the data reduced by SST model (Wiener filter followed by whitening filter)
    • grid interpolation of gravitational gradients at mean satellite altitude by local collocation, spherical harmonic analysis of the estimated grids by numerical integration.
  • The full error covariance matrices of the estimated grids and spherical harmonic coefficients are derived by Monte Carlo simulations.
  • Grids of standard deviations of each functional are computed from the original Monte Carlo samples.

GOCE input data:

  • Gradients: EGG_GGT_2C, EGG_NOM_2
  • Orbits:
    • SST_PRD_2I (reduced dynamic orbits for geo-locating gravity gradients)
    • SST_PKI_2I (kinematic orbits for long-wavelength gravity field recovery)
    • SST_PCV_2I (variance information of kinematic orbit positions)
    • SST_PRM_2I (rotation between inertial and Earth-fixed reference frames)
  • Attitude: EGG_IAQ_2C
  • Non-conservative accelerations: EGG_CCD_2C
  • Data period: 01/11/2009 – 20/10/2013

A-priori information used:

  • No corrections to any prior gravity field model are computed (GOCE-only model).
  • EIGEN-6C4 and GOCO05C were used for signal covariance modelling.
  • FES2004 was used for ocean tide modelling.


  • The maximum spherical harmonic degree is 330 because this is the maximum degree used for the modelling of the signal covariance functions in the local collocation gridding.
  • The spherical harmonic coefficients with the highest degrees have globally a small signal power, but they could contribute to better model local areas with a high signal-to-noise ratio.
  • Any truncation of the spherical harmonic expansion to a maximum degree lower than 330 could introduce errors due to the correlation of the estimated spherical harmonic coefficients.
  • The variance-covariance error information of the estimated spherical harmonic coefficients is computed by Monte Carlo simulations, also including the signal omission error up to degree and order 330.
  • An error covariance propagation to functionals of the gravitational potential by only using coefficient error variances could be strongly approximated because coefficient error correlations are significant.
  • The use of the full error variance-covariance matrix is therefore recommended.

Grids comparisons

Space-wise grids (SPWG) can be compared with grids synthesised by spherical harmonics models.
We provides different comparisons to show pros and cons of the space-wise solution.
All the syntheses are computed at the maximum degree of 330, when a model is truncated at lower maximum degree coefficients are filled with zeros.


    1. Computation and assessment of the fifth release of the GOCE-only space-wise solution
      A. Gatti, M. Reguzzoni, F. Migliaccio, F. Sansò
      Presented at the 1st Joint Commission 2 and IGFS Meeting, 19-23 September 2016, Thessaloniki, Greece
    2. GOCE-only grids and spherical harmonic models by the space-wise approach from the full-mission dataset
      A. Gatti, M. Reguzzoni, F. Migliaccio, F. Sansò
      – in preparation
    3. Optimal multi-step collocation: application to the space-wise approach for GOCE data analysis
      M. Reguzzoni, N. Tselfes
      Journal of Geodesy, January 2009, Volume 83, Issue 1, pp. 13-29

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Geomatics and Earth Observation laboratory