GPS Solutions

, 22:2 | Cite as

Influence of spatial gradients on ionospheric mapping using thin layer models

  • Hu Jiang
  • Zemin Wang
  • Jiachun An
  • Jingbin Liu
  • Ningbo Wang
  • Hang Li
Original Article


This study provides information about the influence of various ionospheric spatial gradients on the thin layer ionospheric model (TLIM). Particular attention is paid to the errors caused by the slant total electron content (sTEC) when converted to the vertical total electron content (vTEC) by an elevation-dependent mapping function (MF), ignoring the satellite azimuth. We quantify the influence of the spatial gradient on ionospheric mapping using globally distributed GNSS measurements and the NeQuick2 ionospheric electron density model. The ionospheric mapping errors (IME) were confirmed using GNSS measurements that were observed for different solar activity conditions. It was found that the IME in the low latitudes were significantly higher than those at other latitudes, and the high-latitude region IME were more pronounced than those of the mid-latitude regions. A comprehensive simulation analysis based on the NeQuick2 model was conducted for different azimuth angles and geographical locations. It was found that the vTEC converted by the MF is smaller than the real value of vTEC in different spatial directions. The IME in the north-to-south direction were much higher than those in the east-to-west direction and were symmetrical north–south about the geomagnetic equator. The values of the IME had obviously seasonal variation characteristics: The IME in the spring and autumn were significantly higher than those in the winter and summer; however, in the low latitudes, the IME were abnormal and had larger values. There is an interesting phenomenon wherein the IME were symmetrical about the azimuth of 180°, and the value of the IME was less than 1 TECu when the satellite elevation was up to 50°. From the global perspective, when the thin layer height is at 400 km, the IME were relatively minimal. In addition, the modified single-layer model (MSLM) and Ou (Ou J) segmented mapping functions outperformed other mapping functions at low satellite elevations; however, when the elevation angle was increased to approximately 40°, the differences of the different MFs were small.


Thin layer ionospheric model (TLIM) Total electron content (TEC) Ionosphere mapping error (IME) GPS NeQuick2 model 



The authors would like to acknowledge the Crustal Dynamics Data Information System (CDDIS) of the International GNSS Services (IGS) for providing access to the GPS observation data. We would also like to acknowledge the International Center for Theoretical Physics (ICTP) for providing the NeQuick2 sources. This research was supported by the Natural Science Funds of China (Nos. 41231064, 41776195, 41531069, 41174029 and 41474029) and the National Key Research Development Program of China with project No. 2016YFB0502204.


  1. Arikan F, Erol CB, Arikan O (2003) Regularized estimation of vertical total electron content from Global Positioning System data. J Geophys Res 39(2007):867–874Google Scholar
  2. Arslan N, Demirel H (2008) The impact of temporal ionospheric gradients in Northern Europe on relative GPS positioning. J Atmos Sol Terr Phys 70(2008):1382–1400. CrossRefGoogle Scholar
  3. Basu S, Basu S, Valladares C, Yeh HC, Su SY, MacKenzie E, Sultan P, Aarons J, Rich F, Doherty P (2001) Ionospheric effects of major magnetic storms during the International Space Weather Period of September and October 1999: GPS observations, VHF/UHF scintillations, and in situ density structures at middle and equatorial latitudes. J Geophys Res 106(2001):30389–30413CrossRefGoogle Scholar
  4. Bilitza D, Reinisch BW (2008) International reference ionosphere 2007: improvements and new parameters. Adv Space Res 42(4):599–609. CrossRefGoogle Scholar
  5. Birch MJ, Hargreaves JK, Bailey GJ (2002) On the use of an effective ionospheric height in electron content measurement by GPS reception. Radio Sci 37(1015/2002):1–19. Google Scholar
  6. Brunini C, Azpilicueta F (2010) GPS slant total electron content accuracy using the single layer model under different geomagnetic regions and ionospheric conditions. J Geod 84(5):293–304. CrossRefGoogle Scholar
  7. Brunini C, Camilion E, Azpilicueta F (2011) Simulation study of the influence of the ionospheric layer height in the thin layer ionospheric model. J Geod 85(9):637–645. CrossRefGoogle Scholar
  8. Dach R, Brockmann E, Schaer S, Beutler G, Meindl M, Prange L, Bock H, Jaeggi A, Ostini L (2009) GNSS processing at CODE: status report. J Geod 83(3–4):353–365. CrossRefGoogle Scholar
  9. Davies K, Hartmann GK (1997) Studying the ionosphere with the Global Positioning System. Radio Sci 32(4):1695–1703. CrossRefGoogle Scholar
  10. Di Giovanni G, Radicella S (1990) An analytical model of the electron density profile in the ionosphere. Adv Space Res 10(11):27–30CrossRefGoogle Scholar
  11. Dymond K, Thomas R (2001) A technique for using measured ionosphere density gradients and GPS occultations for inferring the nighttime ionospheric electron density. Radio Sci 36:1141–1148CrossRefGoogle Scholar
  12. Feltons J (2003) The international GPS service (IGS) ionosphere working group. Adv Space Sci 31(3):635–644CrossRefGoogle Scholar
  13. Foelsche U, Kirchengast G (2002) A simple “geometric’’ mapping function for the hydrostatic delay at radio frequencies and assessment of its performance. Geophys Res Lett 29:1473. CrossRefGoogle Scholar
  14. Hernández-Pajares M, Juan J, Sanz J, Orus R, Garcia-Rigo A, Feltens J, Komjathy A, Schaer S, Krankowski A (2009) The IGS VTEC maps: a reliable source of ionospheric information since 1998. J Geod 83(3):263–275. CrossRefGoogle Scholar
  15. Hoque MM, Jakwoski N (2013) Mitigation of ionospheric mapping function error. In: Proceedings of the ION GNSS+, Nashville/Tennessee/USA, 16–20 SeptGoogle Scholar
  16. Kashcheyev A, Nava B, Radicella SM (2012) Estimation of higher-order ionospheric errors in GNSS positioning using a realistic 3-D electron density model. Radio Sci 47:RS4008. doi: 10.1029/2011RS004976
  17. Keroub IH (1976) Structure of latitudinal total electron content (TEC) gradients over mid-latitude stations. Ann Geophys 32:227–242Google Scholar
  18. Klobuchar JA (1987) Ionospheric time-delay algorithm for singlefrequency GPS users. IEEE Trans Aero Electron Syst 23(3):325–331CrossRefGoogle Scholar
  19. Komjathy A, Sparks L, Mannucci AJ, Coster A (2005) The ionospheric impact of the October 2003 storm event on wide area augmentation system. GPS Solut 9(1):41–50. CrossRefGoogle Scholar
  20. Konno H, Pullen S, Luo M, Enge P (2005) Analysis of ionosphere gradient using Japan GEONET data. In: Proceedings ION-NTM-2005, Institute of Navigation, San Diego, CA, January, pp 1118–1129Google Scholar
  21. Leitinger R, Zhang M, Radicella MS (2005) An improved bottomside for the ionospheric electron density model Nequick2. Ann Geophys 48(3):525–534Google Scholar
  22. Leong SK, Musa TA, Omar K, Subari MD, Pathy NB, Asillam MF (2015) Assessment of ionosphere models at Banting: performance of IRI-2007, IRI- 2012 and NeQuick2 models during the ascending phase of Solar Cycle 24. Adv Space Res 55(8):1928–1940CrossRefGoogle Scholar
  23. Liu J, Chen R, Wang Z, Zhang H (2011) Spherical cap harmonic model for mapping and predicting regional TEC. GPS Solut 15(2):109–119. CrossRefGoogle Scholar
  24. Liu J, Hernandez-Pajares M, Liang X, An J, Wang Z, Chen R, Sun W, Hyyppä J (2016) Temporal and spatial variations of global ionospheric total electron content under various solar conditions. J Geod 91(5):485–502. CrossRefGoogle Scholar
  25. Luo M, Pullen S, Walter T, Enge P (2004) Ionosphere spatial gradient threat for LAAS: mitigation and tolerable threat space. In: Proceedings of the 2004 national technical meeting of the institute of navigation, pp 490–501Google Scholar
  26. Mannucci AJ, Wilson BD, Yuan DN, Ho CH, Lindqwister UJ, Runge TF (1998) A global mapping technique for GPS-derived ionospheric total electron content measurements. Radio Sci 33(3):565–582. CrossRefGoogle Scholar
  27. Mannucci AJ, Iijima BA, Lindqwister UJ, Pi X, Sparks L, Wilson BD (1999) GPS and ionosphere, review of Radio Science 1996–1999. Oxford University Press, New YorkGoogle Scholar
  28. Memarzadeh Y (2009) Ionospheric modeling for precise GNSS applications. Doctoral dissertation, Delft Institute of Earth Observation and Space Systems, Delft University of Technology, NetherlandsGoogle Scholar
  29. Nava B, Radicella SM, Leitinger R, Cöisson P (2007) Use of total electron content data to analyze ionosphere electron density gradients. J Adv Space Res 39(8):1292–1297CrossRefGoogle Scholar
  30. Nava B, Coïsson P, Radicella SM (2008) A new version of the NeQuick ionosphere electron density model. J Atmos Sol Terr Phys 70(15):1856–1862CrossRefGoogle Scholar
  31. Orús R, Hernández-Pajares M, Juan J, Sanz J, Garcı́a-Fernández M (2002) Performance of different TEC models to provide GPS ionospheric corrections. J Atmos Sol Terr Phys 64(18):2055–2062CrossRefGoogle Scholar
  32. Ou J (1996) Atmosphere and its effects on GPS surveying. LGR-Series 14. Delft Geodetic Computing Center, DelftGoogle Scholar
  33. Radicella SM (2009) The NeQuick model genesis, uses and evolution. Ann Geophys 52(3/4):417–422Google Scholar
  34. Rama Rao PVSK, Niranjan DSVVD Prasad, Gopi Krishna S, Uma G (2006) On the validity of the ionospheric pierce point (IPP) altitude of 350 km in the Indian equatorial and low-latitude sector. Ann Geophys 24(2006):2159–2168CrossRefGoogle Scholar
  35. Schaer S (1999) Mapping and predicting the earth’s ionosphere using the global positioning system. Doctoral dissertation, Univ. Bern, SwitzerlandGoogle Scholar
  36. Tao A-L, Jan S-S (2016) Wide-area ionospheric delay model for GNSS users in middle- and low-magnetic-latitude regions. GPS Solut 20(1):9–21CrossRefGoogle Scholar
  37. Venkatesh K, Fagundes PR, de Jesus R, de Abreu AJ, Pillat VG, Sumod SG (2014) Assessment of IRI-2012 profile parameters by comparison with the ones inferred using NeQuick2, ionosonde and FORMOSAT-1 data during the high solar activity over Brazilian equatorial and low latitude sector. J Atmos Sol Terr Phys 121:10–23CrossRefGoogle Scholar
  38. Vo H, Foster J (2001) A quantitative study of ionospheric density gradients at midlatitudes. J Geophys Res 106(2001):21555–21563CrossRefGoogle Scholar
  39. Wang N (2016) Study on GNSS differential code biases and global broadcast ionospheric models of GPS, Galileo and BDS. Doctoral dissertation, University of Chinese Academy of Sciences, ChinaGoogle Scholar
  40. Wang N, Yuan Y, Li Z, Huo X (2016) Improvement of Klobuchar model for GNSS single-frequency ionospheric delay corrections. Adv Space Res 57(7):1555–1569CrossRefGoogle Scholar
  41. Wang N, Yuan Y, Li Z, Li Y, Huo X, Li M (2017) An examination of the Galileo NeQuick model: comparison with GPS and JASON TEC. GPS Solut 21(2):605–615CrossRefGoogle Scholar
  42. Zus F, Deng Z, Heise S, Wickert J (2017) Ionospheric mapping functions based on electron density fields. GPS Solut 21(3):873–885. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Chinese Antarctic Center of Surveying and MappingWuhan UniversityWuhanChina
  2. 2.Collaborative Innovation Center for Territorial Sovereignty and Maritime RightsWuhan UniversityWuhanChina
  3. 3.State Key Laboratory of Information Engineering in Surveying, Mapping and Remote SensingWuhan UniversityWuhanChina
  4. 4.Collaborative Innovation Center of Geospatial TechnologyWuhan UniversityWuhanChina
  5. 5.Department of Remote Sensing and PhotogrammetryFinnish Geospatial Research InstituteMasalaFinland
  6. 6.Academy of Opto-ElectronicsChinese Academy of SciencesBeijingChina

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