On the Spatial Resolution of Homogeneous Isotropic Filters on the Sphere

Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 142)


Interest in filtering on the sphere was rejuvenated by the necessity to filter GRACE data, which has led to the development of a variety of filters with a multitude of design methods. Nevertheless, a lacuna exists in the understanding of filters and filtered fields, especially signal leakage due to filtering and resolution of the filtered field. In this contribution, we specifically look into the latter aspect, where we take an intuitive and empirical approach instead of a rigorous mathematical approach. The empirical approach is an adaptation of the technique used in optics and photography communities for determining the resolving power of lenses. This resolution analysis is carried out for the most commonly used homogeneous isotropic filters in the GRACE community. The analysis indicates that a concrete number for the filters can only be specified as an ideal number. Nevertheless, resolution as a concept is described in detail by the modulation transfer function, which also provides some insight into the smoothing properties of the filter.


Empirical approach Filters Filtering on the sphere Modulation transfer function Spatial resolution 


  1. Bruinsma SL, Förste C, Abrikosov O, Marty JC, Rio MH, Mulet S, Bonvalot S (2013) The new ESA satellite-only gravity field model via the direct approach. Geophys Res Lett 40:1–6. doi:10.1002/grl.50716CrossRefGoogle Scholar
  2. Freeden W, Schreiner M (2009) Spherical functions of mathematical geosciences: a scalar, vectorial, and tensorial setup. Springer, Berlin/HeidelbergGoogle Scholar
  3. Harris FJ (1978) On the use of windows for harmonic analysis with the discrete Fourier transform. Proc IEEE 66(1):51–93CrossRefGoogle Scholar
  4. Jekeli C (1981) Alternative methods to smooth the Earth’s gravity field. Tech. Rep. 327, Department of Geodetic Science and Surveying, The Ohio State UniversityGoogle Scholar
  5. Kusche J (2007) Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models. J Geod 81:733–749CrossRefGoogle Scholar
  6. Laprise R (1992) The resolution of global spectral models. Bull Am Meteorol Soc 73(9):1453–1454Google Scholar
  7. Lillesand TM, Kiefer RW (1994) Remote sensing and image interpretation, 3rd edn. Wiley, New YorkGoogle Scholar
  8. Longuevergne L, Scanlon BR, Wilson CR (2010) GRACE hydrological estimates for small basins: evaluating processing approaches on the High Plains Aquifer, USA. Water Resour Res. doi:10.1029/2009WR008564Google Scholar
  9. Rummel R, Yi W, Stummer C (2011) GOCE gravitational gradiometry. J Geod 85(11):777–790CrossRefGoogle Scholar
  10. Sardeshmukh PD, Hoskins BJ (1984) Spatial smoothing on the sphere. Mon Weather Rev 112:2524–2529CrossRefGoogle Scholar
  11. Swenson S, Wahr J (2006) Post-processing removal of correlated errors in GRACE data. Geophys Res Lett. doi: 10.1029/2005GL025285Google Scholar
  12. Tapley BD, Bettadpur S, Watkins MM, Reigber C (2004) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett. doi:10.1029/2004GL019920Google Scholar
  13. Werth S, Güntner A, Schmidt R, Kusche J (2009) Evaluation of GRACE filter tools from a hydrological perspective. Geophys J Int 179(3):1499–1515CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of GeodesyUniversity of StuttgartStuttgartGermany

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