Surveys in Geophysics

, Volume 39, Issue 2, pp 289–309 | Cite as

Reconstructing Regional Ionospheric Electron Density: A Combined Spherical Slepian Function and Empirical Orthogonal Function Approach



The computerized ionospheric tomography is a method for imaging the Earth’s ionosphere using a sounding technique and computing the slant total electron content (STEC) values from data of the global positioning system (GPS). The most common approach for ionospheric tomography is the voxel-based model, in which (1) the ionosphere is divided into voxels, (2) the STEC is then measured along (many) satellite signal paths, and finally (3) an inversion procedure is applied to reconstruct the electron density distribution of the ionosphere. In this study, a computationally efficient approach is introduced, which improves the inversion procedure of step 3. Our proposed method combines the empirical orthogonal function and the spherical Slepian base functions to describe the vertical and horizontal distribution of electron density, respectively. Thus, it can be applied on regional and global case studies. Numerical application is demonstrated using the ground-based GPS data over South America. Our results are validated against ionospheric tomography obtained from the constellation observing system for meteorology, ionosphere, and climate (COSMIC) observations and the global ionosphere map estimated by international centers, as well as by comparison with STEC derived from independent GPS stations. Using the proposed approach, we find that while using 30 GPS measurements in South America, one can achieve comparable accuracy with those from COSMIC data within the reported accuracy (1 × 1011 el/cm3) of the product. Comparisons with real observations of two GPS stations indicate an absolute difference is less than 2 TECU (where 1 total electron content unit, TECU, is 1016 electrons/m2).


Computerized ionospheric tomography Slant total electron content (STEC) Slepian base function Empirical orthogonal function (EOF) 



The authors are grateful to Professor M. Rycroft and two reviewers for their comments, which helped us to improve this manuscript. We would like to acknowledge (1) the NASA’s Archive of Space Geodesy Data (CDDIS, and Instituto Brasileiro de Geografia e Estatística (IBGE, for the RINEX data, and (2) the NPSO (Taiwan’s National Space Organization) and UCAR (University Center for Atmospheric Research) for access to the COSMIC RO data (


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Authors and Affiliations

  1. 1.School of Surveying and Geospatial Engineering, College of EngineeringUniversity of TehranTehranIran
  2. 2.School of Earth and Ocean SciencesCardiff UniversityCardiffUK

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