Combination of GRACE monthly gravity fields on the normal equation level

Ulrich Meyer, Yoomin Jean, Andreas Kvas, Christoph Dahle, Jean-Michel Lemoine, Adrian Jäggi

Research output: Contribution to journalArticlepeer-review


A large number of time-series of monthly gravity fields derived from GRACE data provide users with a wealth of informationon mass transport processes in the system Earth. The users are, however, left alone with the decision which time-series toanalyze. Following the example of other well-known combination services provided by the geodetic community, the prototypeof a combination service has been developed within the frame of the project EGSIEM (2015–2017) to combine the differenttime-series with the goal to provide a unique and superior product to the user community. Four associated analysis centers(ACs) of EGSIEM, namely AIUB, GFZ, GRGS and IfG, generated monthly gravity fields which were then combined usingthe different normal equations (NEQs). But the relative weights determined by variance component estimation (VCE) on theNEQ level do not lead to an optimal combined product due to the different processing strategies applied by the individualACs. We therefore resort to VCE on the solution level to derive relative weights that are representative of the noise levels ofthe individual solutions. These weights are then applied in the combination on the NEQ level. Prior to combination, empiricalscaling factors that are based on pairwise combinations of NEQs are derived to balance the impact of the NEQs on thecombined solution. We compare the processing approaches of the different ACs and introduce quality measures derived eitherfrom the differences w.r.t. the monthly means of the individual gravity fields or w.r.t. a deterministic signal model. Aftercombination, the gravity fields are validated by comparison to the official GRACE SDS RL05 time-series and the individualcontributions of the associated ACs in the spectral and the spatial domain. While the combined gravity fields are comparablein signal strength to the individual time-series, they stand out by their low noise level. In terms of noise, they are in 90% of allmonths as good or better than the best individual contribution from IfG and significantly less noisy than the official GRACESDS RL05 time-series
Original languageEnglish
Pages (from-to)1645-1658
JournalJournal of Geodesy
Issue number9
Publication statusPublished - 1 Sept 2019


  • Satellite gravimetry
  • Time-variable gravity
  • Combination service

ASJC Scopus subject areas

  • General Earth and Planetary Sciences

Fields of Expertise

  • Sustainable Systems


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