GIMLi: Global Ionospheric total electron content model based on machine learning

Abstract

EXtreme Gradient Boosting over Decision Trees (XGBoost or XGBDT) is a powerful tool to model a wide range of processes. We propose a new approach to create a global total electron content model, using machine-learning-based techniques, in particular, gradient boosting. The model is based on the Global Ionospheric Maps computed by Universitat Politècnica de Catalunya with a tomographic-kriging combined technique (UQRG). To reduce the problem complexity, we used empirical orthogonal functions (EOFs). The created model involves the first 16 spatial EOFs. For training and validation we used the 1998–2016 data sets, and the 2017 data as a test data set. To drive the model, we used the following features: (1) geomagnetic activity indexes (Kp, Ap, AE, AU, AL) and solar activity indexes (R, F10.7); (2) derivative values from these indexes such as the mean value and standard deviations within the last 12 h, last 11 days, and last 40 days; (3) day of the year (DOY); (4) averaged EOFs for given Kp and UT, and those for a given DOY and UT. The validation data set revealed the following hyperparameters for XGBoost learning: number of trees is 100, tree depth is 6, and learning rate is 0.1. Comparisons with the NeQuick2, Klobuchar, and GEMTEC models show that machine learning achieves higher accuracy for the 2017 test data set. The global averaged root-mean-square errors and mean absolute percentage errors were about 2.5 TECU and 19% for the nonlinear GIMLi-XGBDT model, about 4 TECU and 30–40% for NeQuick2, GEMTEC, and the linear model GIMLi-LM, and about 5.2 TECU and 73% for the Klobuchar model. A 4-fully-connected-layer artificial neural network provided a higher error (3.28 TECU and 27.7%) as compared to GIMLi-XGBDT. For all models mentioned, the error peaked in the equatorial anomaly region. The solar activity increase does not affect the error of the nonlinear GIMLi-XGBDT model. However, an increase in geomagnetic activity strongly affects that model.

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Data availability

GIM data is available through ftp://cddis.gsfc.nasa.gov/gps/products/ionex. Indexes of solar and geomagnetic activity are available through OMNI database (https://omniweb.gsfc.nasa.gov/).

References

  1. Bergstra JS, Bardenet R, Bengio Y, Kegl B (2011) Algorithms for hyper-parameter optimization. Advances in neural information processing systems: 2546–2554. https://hal.inria.fr/hal-00642998

  2. Breiman L (2001) Random forests. Mach Learn 45(1):5–32. https://doi.org/10.1023/A:1010933404324

    Article  Google Scholar 

  3. Cander LR, Milosavljevic MM, Stankovic SS, Tomasevic S (1998) Ionospheric forecasting technique by artificial neural network. Electron Lett 34(16):1573–1574. https://doi.org/10.1049/el:19981113

    Article  Google Scholar 

  4. Cesaroni C, Spogli L, Aragon-Angel A, Fiocca M, Dear V, De Franceschi G, Romano V (2020) Neural network based model for global total electron content forecasting. J Space Weather Space Clim 10:11. https://doi.org/10.1051/swsc/2020013

    Article  Google Scholar 

  5. Chen T, Guestrin C (2016) Xgboost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, pp 785–794. https://doi.org/10.1145/2939672.2939785

  6. Cherrier N, Castaings T, Boulch A (2017) Forecasting ionospheric total electron content maps with deep neural networks. Proc Conf Big Data Space (BIDS), ESA workshop, 2017

  7. Feng J, Han B, Zhao Z, Wang Z (2019) Total electron content empirical model. Remote Sens 11(6):706. https://doi.org/10.3390/rs11060706

    Article  Google Scholar 

  8. Friedman JH (2001) Greedy function approximation: a gradient boosting machine. Ann Stat 29(5):1189–1232

    Article  Google Scholar 

  9. Geurts P, Ernst D, Wehenkel L (2006) Extremely randomized trees. Mach Learn 63(1):3–42. https://doi.org/10.1007/s10994-006-6226-1

    Article  Google Scholar 

  10. Golub GH, Van Loan CF (1996) The singular value decomposition and unitary matrices. Matrix Computations. Johns Hopkins University Press, Baltimore, MD, pp 70–71

    Google Scholar 

  11. Habarulema JB, McKinnell L-A, Opperman BDL (2011) Regional GPS TEC modeling; attempted spatial and temporal extrapolation of TEC using neural networks. J Geophys Res Space Phys 116(A4):A04314. https://doi.org/10.1029/2010JA016269

    Article  Google Scholar 

  12. Hernandez-Pajares M, Juan JM, Sanz J, Orus R, Garcia-Rigo A, Feltens J, Komjathy A, Schaer SC, Krankowski A (2009) The IGS VTEC maps: a reliable source of ionospheric information since 1998. J Geod 83(3):263–275. https://doi.org/10.1007/s00190-008-0266-1

    Article  Google Scholar 

  13. Hernandez-Pajares M, Juan JM, Sanz J (1997) Neural network modeling of the ionospheric electron content at global scale using GPS data. Radio Sci 32(3):1081–1089. https://doi.org/10.1029/97RS00431

    Article  Google Scholar 

  14. Hochegger G, Nava B, Radicella S, Leitinger R (2000) A family of ionospheric models for different uses. Phys Chem Earth Part C 25(4):307–310. https://doi.org/10.1016/S1464-1917(00)00022-2

    Article  Google Scholar 

  15. ICD-Galileo (2016) European GNSS (Galileo) open service–ionospheric correction algorithm for Galileo single frequency user. European Commission Tech Rep 1.2, November 2016. https://www.gsc-europa.eu/sites/default/files/sites/all/files/Galileo_Ionospheric_Model.pdf

  16. ICD-GLONASS (2016) GLONASS. Interface control document. General description of code division multiple access signal system. Russian space systems, Tech. Rep., 2016. https://russianspacesystems.ru/wp-content/uploads/2016/08/ICD-GLONASS-CDMA-General.-Edition-1.0-2016.pdf

  17. Ivanov V, Gefan G, Gorbachev O (2011) Global empirical modelling of the total electron content of the ionosphere for satellite radio navigation systems. J Atmos Sol-Terr Phys 73(13):1703–1707. https://doi.org/10.1016/j.jastp.2011.03.010

    Article  Google Scholar 

  18. Jakowski N, Mayer C, Hoque MM, Wilken V (2011) Total electron content models and their use in ionosphere monitoring. Radio Sci. https://doi.org/10.1029/2010RS004620

    Article  Google Scholar 

  19. Kingma D, Ba J (2015) Adam: a method for stochastic optimization. https://arxiv.org/abs/1412.6980

  20. Klobuchar JA (1987) Ionospheric time-delay algorithm for single-frequency GPS users. IEEE T Aero Elec Sys AES 23(3):325–331. https://doi.org/10.1109/TAES.1987.310829

    Article  Google Scholar 

  21. Li W, Zhao D, He C, Hu A, Zhang K (2020) Advanced machine learning optimized by the genetic algorithm in ionospheric models using long-term multi-instrument observations. Remote Sens 12(5):866. https://doi.org/10.3390/rs12050866

    Article  Google Scholar 

  22. Llewellyn SK, Bent RB (1973) Documentation and description of the Bent ionospheric model. Technical report AFCRL-TR-73–0657, July 1973, AD. 772733

  23. Miikkulainen R (2017) Topology of a neural network. In: Sammut C, Webb GI (eds) Encyclopedia of machine learning and data mining. Springer, Boston. https://doi.org/10.1007/978-1-4899-7687-1_843

    Google Scholar 

  24. Montenbruck O, Gonzalez Rodriguez B (2019) Nequick-G performance assessment for space applications. GPS Solut 24:13. https://doi.org/10.1007/s10291-019-0931-2

    Article  Google Scholar 

  25. Nava B, Coisson P, Radicella SM (2008) A new version of the NeQuick ionosphere electron density model. J Atmos Sol-Ter Phys 70(15):1856–1862. https://doi.org/10.1016/j.jastp.2008.01.015

    Article  Google Scholar 

  26. Orus-Perez R (2019) Using TensorFlow-based neural network to estimate GNSS single frequency ionospheric delay (IONONet). Adv Space Res 63(5):1607–1618. https://doi.org/10.1016/j.asr.2018.11.011

    Article  Google Scholar 

  27. Orus-Perez R, Hernandez-Pajares M, Juan J, Sanz J (2005) Improvement of global ionospheric VTEC maps by using kriging interpolation technique. J Atmos Sol-Terr Phys 67(16):1598–1609. https://doi.org/10.1016/j.jastp.2005.07.017

    Article  Google Scholar 

  28. Srivani I, Siva Vara Prasad G, Venkata Ratnam D (2019) A deep learning-based approach to forecast ionospheric delays for GPS signals. IEEE Geosci Remote S Lett 16(8):1180–1184. https://doi.org/10.1109/LGRS.2019.2895112

    Article  Google Scholar 

  29. Wang N, Yuan Y, Li Z, Huo X (2016a) Improvement of Klobuchar model for GNSS single-frequency ionospheric delay corrections. Adv Space Res 57(7):1555–1569. https://doi.org/10.1016/j.asr.2016.01.010

    Article  Google Scholar 

  30. Wang Y, Yao H, Zhao S (2016b) Auto-encoder based dimensionality reduction. Neurocomputing 184:232–242. https://doi.org/10.1016/j.neucom.2015.08.104

    Article  Google Scholar 

  31. Yuan Y, Wang N, Li Z, Huo X (2019) The BeiDou global broadcast ionospheric delay correction model (BDGIM) and its preliminary performance evaluation results. Navigation 66(1):55–69. https://doi.org/10.1002/navi.292

    Article  Google Scholar 

  32. Zhang Z, Pan S, Gao C, Zhao T, Gao W (2019) Support vector machine for regional ionospheric delay modeling. Sensors 19(13):2947. https://doi.org/10.3390/s19132947

    Article  Google Scholar 

  33. Zhukov AV, Sidorov DN, Mylnikova AA, Yasyukevich YV (2018) Machine learning methodology for ionosphere total electron content nowcasting. Artif Intell 16(1):144–157

    Google Scholar 

Download references

Acknowledgement

The authors thank D.A. Zatolokin for his help in preparing the GEMTEC and Klobuchar model data, and Dr. B. Nava for making the source code of NeQuick2 available. We acknowledge the Universitat Politècnica de Catalunya and the International GNSS Service for the GIM data and OMNI database on solar and geomagnetic activities. The study is supported by the Russian Foundation for Basic Research Grant No. 18-35-20038 and partly by the Ministry of Education and Science (Basic Research program II.16).

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Correspondence to Yury V. Yasyukevich.

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Zhukov, A.V., Yasyukevich, Y.V. & Bykov, A.E. GIMLi: Global Ionospheric total electron content model based on machine learning. GPS Solut 25, 19 (2021). https://doi.org/10.1007/s10291-020-01055-1

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Keywords

  • Ionosphere
  • Machine learning
  • Global model
  • Total electron content
  • Global ionospheric maps
  • Gradient boosting