GPS Solutions

, Volume 15, Issue 2, pp 109–119 | Cite as

Spherical cap harmonic model for mapping and predicting regional TEC

  • Jingbin LiuEmail author
  • Ruizhi Chen
  • Zemin Wang
  • Hongping Zhang
Original Article


An approach to modeling the regional ionospheric total electron content (TEC) based on spherical cap harmonic analysis is presented. This approach not only provides a better regional TEC mapping accuracy, but also the capability for ionospheric model prediction based on spectrum analysis and least squares collocation. Unlike conventional approaches, which predict the immediate TEC with models using current observations, the spherical cap harmonic approach utilizes models using past observations to predict a model which will provide future TEC values. A significant advantage in comparison with conventional approaches is that the spherical cap harmonic approach can be used to predict the long-term TEC with reasonable accuracy. This study processes a set of GPS data with an observation time span of 1 year from two GPS networks in China. The TEC mapping accuracy of the spherical cap harmonic model is compared with the polynomial model and the global ionosphere model from IGS. The results show that the spherical cap harmonic model has a better TEC mapping accuracy with smoother residual distributions in both temporal and spatial domains. The TEC prediction with the spherical cap harmonic model has been investigated for both short- and long-term intervals. For the short-term interval, the prediction accuracies for the latencies of 1-day, 2-days, and 3-days are 2.5 TECU, 3.5 TECU, and 4.5 TECU, respectively. For the long-term interval, the prediction accuracy is 4.5 TECU for a 2-month latency.


GPS Ionosphere TEC mapping Regional ionosphere model Ionosphere TEC prediction Spherical cap harmonic analysis 



This work was supported from Chinese National Key Basic Research and Development Program funding (973 Program, 2009CB724002).


  1. Georgiadou Y (1994) Modeling the ionosphere for an active control network of GPS station. LGR-series (7), Delft Geodetic Computing Centre, DelftGoogle Scholar
  2. Georgiadou Y, Kleusberg A (1988) On the effect of ionospheric delay on geodetic relative GPS positioning. Manuscripta Geodaetia 13:1–8Google Scholar
  3. Haines GV (1985) Spherical cap harmonic analysis. J Geophys Res 90(B3):2583–2591CrossRefGoogle Scholar
  4. Haines GV (1988) Computer programs for spherical cap harmonic analysis of potential and general fields. Comput Geosci 14(4):413–447CrossRefGoogle Scholar
  5. Komjathy A (1997) Global ionospheric total electron content mapping using the global positioning system. Dissertation, University of New BrunswickGoogle Scholar
  6. Li J (1993) The spectral methods in physical geodesy. Dissertation, Wuhan Technical University of Surveying and MappingGoogle Scholar
  7. Liu J (2008) SCHA analysis and predication of regional ionospheric TEC using ground-based GPS measurements. Dissertation, Wuhan UniversityGoogle Scholar
  8. Liu Z, Gao Y (2004) Ionospheric TEC predictions over a local area GPS reference network. GPS Solut 8(1):23–29CrossRefGoogle Scholar
  9. Liu J, Wang Z, Zhang H, Zhu W (2008a) Comparison and consistency research of regional ionospheric TEC models based on GPS measurements. Geomat and Inf Sci of Wuhan University 33(5):479–483Google Scholar
  10. Liu J, Wang Z, Wang H, Zhang H (2008b) Modeling regional ionosphere using GPS measurements over China by spherical cap harmonic analysis methodology. Geomat and Inf Sci of Wuhan University 33(8):792–795Google Scholar
  11. Parkinson BW, Spilker JJ (1996) Global positioning system: theory and applications, vol I and II. American Institute of Aeronautics and Astronautics, Washington DCGoogle Scholar
  12. Sardon E, Rius A, Zarraoa N (1994) Estimation of the transmitter and receiver differential biases and the ionospheric total electron content from Global Positioning System observations. Radio Sci 29(3):577–586CrossRefGoogle Scholar
  13. Schaer S (1999) Mapping and predicting the earth’s ionosphere using the global positioning system. Dissertation, University of BernGoogle Scholar
  14. Schaer S, Gurtner W, Feltens J, Feltens J (1998) IONEX: The IONosphere map Exchange format version 1. Astronomical Institute, University of Berne, Switzerland and Darmstadt, Germany. Available via DIALOG. Accessed 19 June 2009
  15. Skone S (1998) Wide area ionosphere grid modeling in the auroral region. Dissertation, University of CalgaryGoogle Scholar
  16. Wilson BD, Mannucci AJ, Edwards CD (1995) Subdaily northern hemisphere ionospheric maps using an extensive network of GPS receivers. Radio Sci 30:639–648CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Jingbin Liu
    • 1
    Email author
  • Ruizhi Chen
    • 1
  • Zemin Wang
    • 2
  • Hongping Zhang
    • 3
  1. 1.Department of Navigation and PositioningFinnish Geodetic InstituteMasalaFinland
  2. 2.Chinese Antarctic Center of Surveying and MappingWuhan UniversityWuhanChina
  3. 3.State Key laboratory Information Engineering in Surveying, Mapping and Remote SensingWuhan UniversityWuhanChina

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