GRACE Monthly Solutions

Monthly gravity field solutions are calculated with our own evaluation strategy as normalized spherical harmonic coeffients and made available to the scientific community. Calculations are done with the software GRACE-SIGMA, which was developed at the institute.

The monthly gravity field solutions in terms of normalized spherical harmonic coefficients up to degree and order n = 80 are computed at IfE and provided here. The solutions are obtained using the GRACE-SIGMA software which is designed and developed at the Institute of Geodesy.

The GRACE-SIGMA is a completely MATLAB-based programme and estimates the orbit and gravity field parameters using the direct method or the classical variational approach. More details of the processing chain can be found in our EGU 2018 presentation.

The LUH-GRACE solutions are unconstrained monthly gravity field models and are based on the analysis of the K-band range rate observations on board GRACE and span the time period between January 2003 until December 2009 (The solution set will be updated soon for the whole GRACE mission time). The models are individually validated and compared and show full agreement with the solutions provided by the three official centers, CSR, JPL and the GFZ.


© IfE / I. Koch
Degree standard deviations of different solutions for March 2006. As mean field GIF48 was subtracted.
  1. First, the initial state vector as well as the accelerometer bias parameters are adjusted. For every 3 hourly arc 9 parameters are estimated. In this step reduced-dynamic GNV1B orbits serve as observations. The iterative estimation converges usually after two to three iterations.
  2. During the second step the gravity field parameters up to degree and order 80 are added as unknown quantities. Altogether the gravity field is modelled by 6557 normalized spherical harmonic coefficients. In addition, 8 geometric-empirical KBRR parameters per arc and satellite pair are solved. During this step KBRR measurements and reduced-dynamic positions are combined with a relative weight of 1×1010. For the determination of the gravity field coefficients no regularization is applied.

The LUH-GRACE2018 solutions agree well with the solutions of other analysis centres (see figure above). For dynamic satellite orbit modelling the following force models were used:

EffectModel / Parameter
Earth Gravity Field GIF48, max. d/o 300
Direct tides Mond und Sonne, Ephemeriden: DE405
Solid Earth tides IERS Conventions 2010
Ocean tides EOT11a, max. d/o 80
Pole tides of solid Earth IERS Conventions 2010
Ocean pole tides IERS Conventions 2010, max. d/o 60
Relativistic effects IERS Conventions 2010
De-aliasing AOD1B RL05, max. d/o 100
Data and additional information


  • Naeimi M., Koch I., Khami A. and Flury J. (2018): IfE monthly gravity field solutions using the variational equationsPresentation, EGU 2018, 8-13 April 2018, Vienna, Austria More Info
    DOI: 10.15488/4452
  • Koch I., Flury J., Naeimi M., Shabanloui A. (2020): LUH-GRACE2018: A New Time Series of Monthly Gravity Field Solutions from GRACEIn: International Association of Geodesy Symposia. Springer, Berlin, Heidelberg
    DOI: 10.1007/1345_2020_92
  • Koch I., Flury J., Naemi M., Shabanloui A. (2019): LUH-GRACE2018: a new time series of monthly gravity field solutions from GRACE27th IUGG General Assembly, July 8.-18., Presentation, Montreal, Canada
    DOI: 10.1007/1345_2020_92
  • Koch I., Naeimi M., Flury J., Shabanloui A. (2018): LUH-GRACE2018: a new time series of monthly gravity field solutions from GRACEPoster, GRACE/GRACE-FO Science Team Meeting 2018 Helmholtz-Zentrum Potsdam – Deutsches GeoForschungsZentrum GFZ, October 9-11, Potsdam, Germany More Info
    DOI: 10.15488/4461
  • Koch I., Flury J., Shabanloui A. (2019): GFR processing standards at IfEFirst COST-G International Team Meeting (ISSI), January 14-18, Bern, Switzerland More Info
    DOI: 10.15488/4465


Igor Koch, M. Sc.
Research Staff
Schneiderberg 50
30167 Hannover
Schneiderberg 50
30167 Hannover