Surveys in Geophysics

, Volume 39, Issue 1, pp 125–167 | Cite as

Effective Solar Indices for Ionospheric Modeling: A Review and a Proposal for a Real-Time Regional IRI

  • A. Pignalberi
  • M. Pezzopane
  • R. Rizzi
  • I. Galkin


The first part of this paper reviews methods using effective solar indices to update a background ionospheric model focusing on those employing the Kriging method to perform the spatial interpolation. Then, it proposes a method to update the International Reference Ionosphere (IRI) model through the assimilation of data collected by a European ionosonde network. The method, called International Reference Ionosphere UPdate (IRI UP), that can potentially operate in real time, is mathematically described and validated for the period 9–25 March 2015 (a time window including the well-known St. Patrick storm occurred on 17 March), using IRI and IRI Real Time Assimilative Model (IRTAM) models as the reference. It relies on foF2 and M(3000)F2 ionospheric characteristics, recorded routinely by a network of 12 European ionosonde stations, which are used to calculate for each station effective values of IRI indices \(IG_{12}\) and \(R_{12}\) (identified as \(IG_{{12{\text{eff}}}}\) and \(R_{{12{\text{eff}}}}\)); then, starting from this discrete dataset of values, two-dimensional (2D) maps of \(IG_{{12{\text{eff}}}}\) and \(R_{{12{\text{eff}}}}\) are generated through the universal Kriging method. Five variogram models are proposed and tested statistically to select the best performer for each effective index. Then, computed maps of \(IG_{{12{\text{eff}}}}\) and \(R_{{12{\text{eff}}}}\) are used in the IRI model to synthesize updated values of foF2 and hmF2. To evaluate the ability of the proposed method to reproduce rapid local changes that are common under disturbed conditions, quality metrics are calculated for two test stations whose measurements were not assimilated in IRI UP, Fairford (51.7°N, 1.5°W) and San Vito (40.6°N, 17.8°E), for IRI, IRI UP, and IRTAM models. The proposed method turns out to be very effective under highly disturbed conditions, with significant improvements of the foF2 representation and noticeable improvements of the hmF2 one. Important improvements have been verified also for quiet and moderately disturbed conditions. A visual analysis of foF2 and hmF2 maps highlights the ability of the IRI UP method to catch small-scale changes occurring under disturbed conditions which are not seen by IRI.


Ionospheric data assimilation International Reference Ionosphere Universal Kriging St. Patrick storm 



This publication uses data from 14 ionospheric observatories in Europe, made available via the public access portal of the Digital Ionogram Database of the Global Ionosphere Radio Observatory in Lowell, MA. The authors are indebted to observatory directors and ionosonde operators for heavy investments of their time, effort, expertise, and funds needed to acquire and provide measurement data to academic research. GAMBIT Consortium is acknowledged for providing access to IRTAM computations. The IRI team is acknowledged for developing and maintaining the IRI model and for giving access to the corresponding Fortran code via the IRI Web site (


  1. Araujo-Pradere EA, Fuller-Rowell TJ, Codrescu MV (2002) STORM: an empirical storm-time ionospheric correction model 1. Model description. Radio Sci. doi: 10.1029/2001RS002467 Google Scholar
  2. Araujo-Pradere EA, Fuller-Rowell TJ, Bilitza D (2003) Validation of the STORM response in IRI2000. J Geophys Res. doi: 10.1029/2002JA009720 Google Scholar
  3. Astafyeva E, Zakharenkova I, Förster M (2015) Ionospheric response to the 2015 St. Patrick’s Day storm: a global multi-instrumental overview. J Geophys Res 120(10):9023–9037. doi: 10.1002/2015JA0262 CrossRefGoogle Scholar
  4. Barabashov BG, Maltseva O, Pelevin O (2006) Near real time IRI correction by TEC-GPS data. Adv Space Res 37:978–982. doi: 10.1016/j.asr.2006.02.008 CrossRefGoogle Scholar
  5. Belehaki A, Cander L, Zolesi B, Bremer J, Juren C, Stanislawska I, Dialetis D, Hatzopoulos M (2005) DIAS Project: the establishment of a European digital upper atmosphere server. J Atmos Solar Terr Phys 67(12):1092–1099. doi: 10.1016/j.jastp.2005.02.021 CrossRefGoogle Scholar
  6. Bilitza D (1990) International Reference Ionosphere 1990. NSSDC/WDC-A-R&S 90-22Google Scholar
  7. Bilitza D (2003) International Reference Ionosphere 2000: examples of improvements and new features. Adv Space Res 31(3):757–767. doi: 10.1016/S0273-1177(03)00020-6 CrossRefGoogle Scholar
  8. Bilitza D, Sheikh M, Eyfrig R (1979) A global model for the height of the F2-peak using M3000 values from the CCIR numerical map. Telecommun J 46:549–553Google Scholar
  9. Bilitza D, Bhardwaj S, Koblinsky C (1997) Improved IRI predictions for the GEOSAT time period. Adv Space Res 20(9):1755–1760. doi: 10.1016/S0273-1177(97)00585-1 CrossRefGoogle Scholar
  10. Bilitza D, McKinnell LA, Reinisch B, Fuller-Rowell T (2011) The International Reference Ionosphere today and in the future. J Geod 85:909–920. doi: 10.1007/s00190-010-0427-x CrossRefGoogle Scholar
  11. Bilitza D, Altadill D, Zhang Y, Mertens C, Truhlik V, Richards P, McKinnell LA, Reinisch B (2014) The International Reference Ionosphere 2012—a model of international collaboration. J Space Weather Space Clim 4:A07. doi: 10.1051/swsc/2014004 CrossRefGoogle Scholar
  12. Bradley PA, Stanislawska I, Juchnikowski G (2009) Options for mapping foF2. Adv Space Res 43:1776–1779. doi: 10.1016/j.asr.2008.09.028 CrossRefGoogle Scholar
  13. Buonsanto MJ (1999) Ionospheric storms—a review. Space Sci Rev 88:563–601CrossRefGoogle Scholar
  14. Carter BA, Yizengaw E, Pradipta R, Retterer JM, Groves K, Valladares C, Caton R, Bridgwood C, Norman R, Zhang K (2016) Global equatorial plasma bubble occurrence during the 2015 St. Patrick’s Day storm. J Geophys Res 121(1):894–905. doi: 10.1002/2015JA022194 CrossRefGoogle Scholar
  15. Caruana J (1989) The IPS monthly T index. In: Solar-Terrestrial prediction: proceedings of a workshop at Leura, Australia, vol 2. pp 257–261Google Scholar
  16. Chapman S (1930) The absorption and dissociative or ionizing effect of monochromatic radiation in an atmosphere on a rotating earth. Proc Phys Soc 46:26–45Google Scholar
  17. Davis J (1986) Statistics and data analysis in geology. Wiley, HobokenGoogle Scholar
  18. De Michelis P, Consolini G, Tozzi R, Marcucci MF (2016) Observations of high-latitude geomagnetic field fluctuations during St. Patrick’s Day storm: Swarm and SuperDARN measurements. Earth Planets Space 68(105):1–16. doi: 10.1186/s40623-016-0476-3 Google Scholar
  19. Dmitriev AV, Suvorova V, Klimenko MV, Klimenko VV, Ratovsky KG, Rakhmatulin RA, Parkhomov VA (2017) Predictable and unpredictable ionospheric disturbances during St. Patrick’s Day magnetic storms of 2013 and 2015 and on 8–9 March 2008. J Geophys Res Space Phys 122:2398–2423. doi: 10.1002/2016JA023260 Google Scholar
  20. Dudeney JR (1983) The accuracy of simple methods for determining the height of the maximum electron concentration of the F2-layer from scaled ionospheric characteristics. J Atmos Terr Phys 45(8/9):629–640. doi: 10.1016/S0021-9169(83)80080-4 CrossRefGoogle Scholar
  21. Fuller-Rowell TJ, Codrescu MV, Araujo-Pradere E, Kutiev I (1998) Progress in developing a storm-time ionospheric correction model. Adv Space Res 22(6):821–827. doi: 10.1016/S0273-1177(98)00105-7 CrossRefGoogle Scholar
  22. Galkin IA, Khmyrov GM, Kozlov AV, Reinisch BW, Huang X, Paznukhov VV (2008) The ARTIS 5. Radio sounding and plasma physics. AIP Conf Proc 975:150–159CrossRefGoogle Scholar
  23. Galkin IA, Reinisch BW, Huang X, Bilitza D (2012) Assimilation of GIRO data into a real-time IRI. Radio Sci 47:RS0L07. doi: 10.1029/2011RS004952 CrossRefGoogle Scholar
  24. Grynyshyna-Poliuga O, Stanislawska I, Swiatek A (2014) Regional ionosphere mapping with kriging and B-spline methods. In: Notarpietro R, Dovis F, De Franceschi G, Aquino M (eds) Mitigation of Ionospheric Threats to GNSS: an Appraisal of the Scientific and Technological Outputs of the TRANSMIT Project. INTECH, Rijeka, pp 135–147 (chapter 11) Google Scholar
  25. Habarulema JB, Ssessanga N (2016) Adapting a climatology model to improve estimation of ionosphere parameters and subsequent validation with radio occultation and ionosonde data. Space Weather. doi: 10.1002/2016SW001549 Google Scholar
  26. Hernandez-Pajares M, Juan JM, Sanz J, Bilitza D (2002) Combining GPS measurements and IRI model values for space weather specification. Adv Space Res 29(6):949–958. doi: 10.1016/S0273-1177(02)00051-0 CrossRefGoogle Scholar
  27. Houminer Z, Soicher H (1996) Improved short-term predictions of foF2 using GPS time delay measurements. Radio Sci 31(5):1099–1108. doi: 10.1029/96RS01965 CrossRefGoogle Scholar
  28. ITU-R (2009) ITU-R reference ionospheric characteristics. Recommendation ITU-R P.1239-2Google Scholar
  29. Jones WB, Gallet RM (1962) Representation of diurnal and geographical variations of ionospheric data by numerical methods. Telecommun J 29:129–149Google Scholar
  30. Jones WB, Graham RP, Leftin M (1969) Advances in ionospheric mapping by numerical methods. ESSA Technical Report ERL107-ITS75, US Department of Commerce, Boulder, Colorado, USAGoogle Scholar
  31. Kitanidis PK (1997) Introduction to geostatistics: application to hydrogeology. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  32. Klimenko MV, Klimenko VV, Zakharenkova IE, Cherniak IV (2015) The global morphology of the plasmaspheric electron content during Northern winter 2009 based on GPS/COSMIC observation and GSM TIP model results. Adv Space Res 55:2077–2085. doi: 10.1016/j.asr.2014.06.027 CrossRefGoogle Scholar
  33. Komjathy A, Langley R (1996) Improvement of a global ionospheric model to provide ionospheric range error corrections for single-frequency GPS users. In: Proceedings of the 52nd annual meeting of the institute of navigation, Cambridge, MA, June 1996. pp 557–566Google Scholar
  34. Liu RY, Smith PA, King JW (1983) A new solar index which leads to improved foF2 predictions using the CCIR Atlas. Telecommun J 50:408–414Google Scholar
  35. Liu RY, Quan KH, Dai KL (1994) A corrected method of the International Reference Ionosphere to be used in Chinese region. Chin J Geophys 37(4):422–432 (in Chinese) Google Scholar
  36. Liu RY, Liu GH, Wu J, Zhang BC, Huang JY, Hu HQ, Xu ZH (2008) Ionospheric foF2 reconstruction and its application to the short-term forecasting in China region. Chin J Geophys 51(2):206–213CrossRefGoogle Scholar
  37. Maltseva OA, Zhbankov GA, Trinh Quang T (2010) Improvement of the real time total electron content based on the International Reference Ionosphere model. Adv Space Res 46:1008–1015. doi: 10.1016/j.asr.2010.06.011 CrossRefGoogle Scholar
  38. Matheron G (1963) Principles of geostatistics. Econ Geol 58:1246–1266CrossRefGoogle Scholar
  39. McBratney AB, Webster R (1986) Choosing functions for semi-variograms of soil properties and fitting them to sampling estimates. J Soil Sci 37:617–639CrossRefGoogle Scholar
  40. Migoya-Orué Y, Nava B, Radicella S, Alazo-Cuartas K (2015) GNSS derived TEC data ingestion into IRI 2012. Adv Space Res 55(8):1994–2002. doi: 10.1016/j.asr.2014.12.033 CrossRefGoogle Scholar
  41. Mikhailov AV, Mikhailov VV (1995) A new ionospheric index MF2. Adv Space Res 15(2):93–97. doi: 10.1016/S0273-1177(99)80050-7 CrossRefGoogle Scholar
  42. Minnis CM (1955) A new index of solar activity based on ionospheric measurements. J Atmos Terr Phys 7:310–321. doi: 10.1016/0021-9169(55)90136-7 CrossRefGoogle Scholar
  43. Mirò Amarante G, Cueto Santamarìa M, Alazo K, Radicella SM (2007) Validation of the STORM model used in IRI with ionosonde data. Adv Space Res 39:681–686. doi: 10.1016/j.asr.2007.01.072 CrossRefGoogle Scholar
  44. Nava B, Coisson P, Amarante GM, Azpiliculeta F, Radicella SM (2005) A model assisted ionospheric electron density reconstruction method based on vertical TEC data ingestion. Ann Geophys 48(2):313–320. doi: 10.4401/ag-3203 Google Scholar
  45. Nava B, Radicella SM, Leitinger R, Coisson P (2006) A near-real-time model-assisted ionosphere electron density retrieval method. Radio Sci 41:RS6S16. doi: 10.1029/2005RS003386 CrossRefGoogle Scholar
  46. Nava B, Coisson P, Radicella SM (2008) A new version of the NeQuick ionosphere electron density model. J Atmos Sol Terr Phys 70:1856–1862. doi: 10.1016/j.jastp.2008.01.015 CrossRefGoogle Scholar
  47. Nava B, Radicella SM, Azpiliculeta F (2011) Data ingestion into NeQuick 2. Radio Sci 46:RS0D17. doi: 10.1029/2010RS004635 CrossRefGoogle Scholar
  48. Nava B, Rodríguez-Zuluaga J, Alazo-Cuartas K, Kashcheyev A, Migoya-Orué Y, Radicella SM, Amory-Mazaudier C, Fleury R (2016) Middle-and low-latitude ionosphere response to 2015 St. Patrick’s Day geomagnetic storm. J Geophys Res 121(4):3421–3438. doi: 10.1002/2015JA022299 CrossRefGoogle Scholar
  49. Olea RA (1974) Optimal contour mapping using universal kriging. J Geophys Res 79(5):695–702CrossRefGoogle Scholar
  50. Oliver MA, Webster R (1990) Kriging: a method of interpolation for geographical information systems. Int J Geogr Inf Syst 4(3):313–332CrossRefGoogle Scholar
  51. Olwendo OJ, Cesaroni C (2016) Validation of NeQuick 2 model over the Kenyan region through data ingestion and the model application in ionospheric studies. J Atmos Sol Terr Phys 145:143–153. doi: 10.1016/j.jastp.2016.04.011 CrossRefGoogle Scholar
  52. Orus R, Hernandez-Pajares M, Juan JM, Sanz J (2005) Improvement of global ionospheric VTEC maps by using kriging interpolation technique. J Atmos Sol Terr Phys 67(16):1598–1609. doi: 10.1016/j.jastp.2005.07.017 CrossRefGoogle Scholar
  53. Ovodenko VB, Trekin VV, Korenkova NA, Klimenko MV (2015) Investigating range error compensation in UHF radar through IRI-2007 real-time updating: preliminary results. Adv Space Res 56(5):900–906. doi: 10.1016/j.asr.2015.05.017 CrossRefGoogle Scholar
  54. Pezzopane M, Scotto C (2005) The INGV software for the automatic scaling of foF2 and MUF(3000)F2 from ionograms: a performance comparison with ARTIST 4.01 from Rome data. J Atmos Sol Terr Phys 67(12):1063–1073. doi: 10.1016/j.jastp.2005.02.022 CrossRefGoogle Scholar
  55. Pignalberi A, Pezzopane M, Tozzi R, De Michelis P, Coco I (2016) Comparison between IRI and preliminary Swarm Langmuir probe measurements during the St. Patrick storm period. Earth Planets Space. doi: 10.1186/s40623-016-0466-5 Google Scholar
  56. Radicella SM, Leitinger R (2001) The evolution of the DGR approach to model electron density profiles. Adv Space Res 27(1):35–40. doi: 10.1016/S0273-1177(00)00138-1 CrossRefGoogle Scholar
  57. Reinisch BW, Galkin IA (2011) Global Ionospheric Radio Observatory (GIRO). Earth Planets Space 63:377–381. doi: 10.5047/eps.2011.03.001 CrossRefGoogle Scholar
  58. Rush CM, Fox M, Bilitza D, Davies K, McNamara L, Stewart FG, PoKempner M (1989) Ionospheric mapping—an update of foF2 coefficients. Telecommun J 56:179–182Google Scholar
  59. Samardjiev T, Bradley PA, Cander L, Dick MI (1993) Ionospheric mapping by computer contouring techniques. Electron Lett 29(20):1794–1795CrossRefGoogle Scholar
  60. Secan JA, Wilkinson PJ (1997) Statistical studies of an effective sunspot number. Radio Sci 32(4):1717–1724. doi: 10.1029/97RS01350 CrossRefGoogle Scholar
  61. Spogli L, Cesaroni C, Di Mauro D, Pezzopane M, Alfonsi L, Musicò E, Povero G, Pini M, Dovis F, Romero R, Linty N, Abadi P, Nuraeni F, Husin A, Minh LH, Tran TL, The VL, Pillat VG, Floury N (2016) Formation of ionospheric irregularities over Southeast Asia during the 2015 St. Patrick’s Day storm. J Geophys Res 121(12):12211–12233. doi: 10.1002/2016JA023222 CrossRefGoogle Scholar
  62. Stanislawska I, Juchnikowski G, Cander L (1996a) The kriging method of ionospheric parameter foF2 instantaneous mapping. Ann Geophys 39(4):845–852. doi: 10.4401/ag-4007 Google Scholar
  63. Stanislawska I, Juchnikowski G, Cander L (1996b) Kriging method for instantaneous mapping at low and equatorial latitudes. Adv Space Res 18(6):217–220. doi: 10.1016/0273-1177(95)00927-2 CrossRefGoogle Scholar
  64. Stanislawska I, Juchnikowski G, Cander L, Ciraolo L, Bradley PA, Zbyszynski Z, Swiatek A (2002) The kriging method of TEC instantaneous mapping. Adv Space Res 29(6):945–948. doi: 10.1016/S0273-1177(02)00050-9 CrossRefGoogle Scholar
  65. Tsagouri I, Zolesi B, Belehaki A, Cander L (2005) Evaluation of the performance of the real-time updated simplified ionospheric regional model for the European area. J Atmos Sol Terr Phys 67:1137–1146. doi: 10.1016/j.jastp.2005 CrossRefGoogle Scholar
  66. Wang S, Liu W, Jiao P, Kong Q (2010) A study on the ionospheric parameter foF2 instantaneous mapping based on equivalent sunspot number. In: IEEE conference publications. pp 407–410Google Scholar
  67. Zhong J, Wang W, Yue X, Burns AG, Dou X, Lei J (2016) Long-duration depletion in the topside ionospheric total electron content during the recovery phase of the March 2015 strong storm. J Geophys Res 121(5):4733–4747. doi: 10.1002/2016JA022469 CrossRefGoogle Scholar
  68. Zolesi B, Cander L (2014) Ionospheric prediction and forecasting. Springer, BerlinCrossRefGoogle Scholar
  69. Zolesi B, Cander L, De Franceschi G (1993) Simplified Ionospheric Regional Model for telecommunication applications. Radio Sci 28(4):603–612. doi: 10.1029/93RS00276 CrossRefGoogle Scholar
  70. Zolesi B, Belehaki A, Tsagouri I, Cander L (2004) Real-time updating of the simplified ionospheric regional model for operational applications. Radio Sci 39:RS2011. doi: 10.1029/2003RS002936 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Dipartimento di Fisica e AstronomiaUniversità di Bologna “Alma Mater Studiorum”BolognaItaly
  2. 2.Istituto Nazionale di Geofisica e VulcanologiaRomeItaly
  3. 3.Space Science LaboratoryUniversity of MassachusettsLowellUSA

Personalised recommendations