Abstract
The global TEC empirical model established with the TEC grid data of IGS as the background has poor prediction accuracy in marine areas, and its ability to describe some ionospheric anomalies is insufficient. In response to the above two problems, we use spherical harmonic (SH) to fuse multi-source TEC data as a modeling dataset and evaluate the accuracy of the fused products. When modeling, we consider three ionospheric anomalies, namely mid-latitude summer nighttime anomaly (MSNA), equatorial ionization anomaly (EIA), and “hysteresis effect,” and establish corresponding model components. We apply the nonlinear least-squares method to establish a global ionospheric TEC empirical model called the TEC model of multi-source fusion (TECM-MF) and verify the model. Results show that: (i) fusion products are valid and reliable modeling data for building global TEC model. (ii) The TECM-MF fits the Fusion TEC input data with a zero bias and a RMS of 3.9 TECU. The model can better show the diurnal, seasonal, and annual variations of the fusion dataset and the “hysteresis effect” of TEC. (iii) In the MSNA area, the prediction ability of the TECM-MF is better, the standard deviation is lower than that of NTCM-GL and Nequick2, close to 1 TECU, and the accuracy is consistent with IRI2016.
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Data availability
The CODE GIMs product data are available at https://cddis.nasa.gov/archive/gnss/products/ionex/. The IRI2016 model data are available at https://ccmc.gsfc.nasa.gov/modelweb/models/iri2016_vitmo.php. The Jason satellite data are provided by the RADS at http://rads.tudelft.nl/rads/data/authentication.cgi. The ionPrf product is provided by the COSMIC Data Analysis and Archive Center at https://data.cosmic.ucar.edu/. The GPS observation data are available at https://cddis.nasa.gov/archive/gnss. The F10.7 data are available at https://omniweb.gsfc.nasa.gov/form/dx4.html.
References
Adolfs M, Hoque MM (2021) A neural network-based tec model capable of reproducing nighttime winter anomaly. Remote Sens 13:4559. https://doi.org/10.3390/rs13224559
Alken P et al (2021) International geomagnetic reference field: the thirteenth generation. Earth, Planets and Space 73:49. https://doi.org/10.1186/s40623-020-01288-x
Bilitza D, Altadill D, Truhlík V, Shubin V, Galkin IA, Reinisch BW, Huang XA (2017) International reference ionosphere 2016: from ionospheric climate to real-time weather predictions. Space Weather 15:418–429. https://doi.org/10.1002/2016SW001593
Bruevich EA, Kazachevskaya TV, Katyushina VV, Nusinov AA, Yakunina GV (2016) Hysteresis of indices of solar and ionospheric activity during 11-year cycles. Geomag Aeron 56:1075–1081. https://doi.org/10.1134/S001679321608003X
Cahuasquí JA, Hoque MM, Jakowski N (2022) Positioning performance of the neustrelitz total electron content model driven by Galileo Az coefficients. GPS Solutions 26:93. https://doi.org/10.1007/s10291-022-01278-4
Chakraborty SK, Hajra R (2008) Solar control of ambient ionization of the ionosphere near the crest of the equatorial anomaly in the Indian zone. Ann Geophys. https://doi.org/10.5194/ANGEO-26-47-2008
Chen P, Yao Y, Yao W (2017) Global ionosphere maps based on GNSS, satellite altimetry, radio occultation and DORIS. GPS Solutions 21:639–650. https://doi.org/10.1007/s10291-016-0554-9
Chen P, Liu H, Ma Y (2020) Empirical orthogonal function analysis and modeling of global ionospheric spherical harmonic coefficients. GPS Solutions 24:71. https://doi.org/10.1007/s10291-020-00984-1
Cherrier, N., Castaings, T., Boulch, A. (2017) Deep sequence-to-sequence neural networks for ionospheric activity map prediction. ICONIP
Ercha A, Zhang D, Ridley AJ, Xiao Z, Hao Y (2012) A global model: Empirical orthogonal function analysis of total electron content 1999–2009 data. J Geophys Res. https://doi.org/10.1029/2011JA017238
Feng J, Wang Z, Jiang W, Zhao Z, Zhang B (2016) A new regional total electron content empirical model in northeast China. Adv Space Res 58:1155–1167. https://doi.org/10.1016/j.asr.2016.06.001
Feng J, Jiang W, Wang Z, Zhao Z, Nie L (2017a) Regional TEC model under quiet geomagnetic conditions and low-to-moderate solar activity based on CODE GIMs. J Atmos Solar Terr Phys 161:88–97. https://doi.org/10.1016/J.JASTP.2017.05.013
Feng J, Wang Z, Jiang W, Zhao Z, Zhang B (2017b) A single station empirical model for TEC over the Antarctic Peninsula using GPS TEC data. Radio Sci 52:196–214. https://doi.org/10.1002/2016RS006171
Feng J, Han B, Zhao Z, Wang Z (2019) A new global total electron content empirical model. Remote Sens 11:706. https://doi.org/10.3390/rs11060706
Feng J, Zhang T, Han B, Zhao Z (2021) Analysis of spatiotemporal characteristics of internal coincidence accuracy in global TEC grid data. Adv Space Res 68:3365–3380. https://doi.org/10.1016/j.asr.2021.06.002
Hernández-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 Geodesy 83:263–275. https://doi.org/10.1007/s00190-008-0266-1
Hoque M, Jakowski N (2012) A new global model for the ionospheric F2 peak height for radio wave propagation. Ann Geophys 30:797–809. https://doi.org/10.5194/ANGEO-30-797-2012
Hoque MM, Jakowski N (2015) An alternative ionospheric correction model for global navigation satellite systems. J Geodesy 89:391–406. https://doi.org/10.1007/s00190-014-0783-z
Hoque MM, Jakowski N, Orús-Pérez R (2019) Fast ionospheric correction using Galileo Az coefficients and the NTCM model. GPS Solut 23:41. https://doi.org/10.1007/s10291-019-0833-3
Horvath I, Lovell BC (2009) An investigation of the northern hemisphere midlatitude nighttime plasma density enhancements and their relations to the midlatitude nighttime trough during summer. J Geophys Res. https://doi.org/10.1029/2009JA014094
Huang J, Hao Y, Zhang D, Xiao Z (2020) The use of monthly mean average for investigating the presence of hysteresis and long-term trends in ionospheric. J Geophys Res 125:e2019JA026905. https://doi.org/10.1029/2019JA026905
Jakowski N, Hoque M, Mayer C (2011) A new global TEC model for estimating transionospheric radio wave propagation errors. J Geodesy 85:965–974. https://doi.org/10.1007/S00190-011-0455-1
Krankowski, A., Wielgosz, P., Hernándeš Pajares, M., García-Rigo, A. (2010) Present and future IGS ionospheric products. EGU general assembly conference abstracts
Li Z, Wang N, Liu A, Yuan Y, Wang L, Hernándeš Pajares M, Krankowski A, Yuan H (2021) Status of CAS global ionospheric maps after the maximum of solar cycle 24. Satell Navig 2:19. https://doi.org/10.1186/s43020-021-00050-2
Lin CH, Liu CH, Liu JY, Chen CH, Burns AG, Wang W (2010) Midlatitude summer nighttime anomaly of the ionospheric electron density observed by FORMOSAt 3/COSMIC. J Geophys Res. https://doi.org/10.1029/2009JA014084
Liu H, Thampi SV, Yamamoto M (2010) Phase reversal of the diurnal cycle in the midlatitude ionosphere. J Geophys Res. https://doi.org/10.1029/2009JA014689
Mannucci AJ, Wilson BD, Yuan DN, Ho C, Lindqwister UJ, Runge TF (1998) A global mapping technique for GPS derived ionospheric total electron content measurements. Radio Sci 33:565–582. https://doi.org/10.1029/97RS02707
Mikhailov AV, Mikhailov VV (1995) Solar cycle variations of annual mean noon foF2. Adv Space Res 15:79–82. https://doi.org/10.1016/S0273-1177(99)80026-X
Mukhtarov P, Andonov B, Pancheva DV (2013a) Global empirical model of TEC response to geomagnetic activity. J Geophys Res 118:6666–6685. https://doi.org/10.1002/jgra.50576
Mukhtarov P, Pancheva DV, Andonov B, Pashova L (2013b) Global TEC maps based on GNNS data: 2. Model evaluation. J Geophys Res 118:4609–4617. https://doi.org/10.1002/jgra.50412
Mukhtarov P, Pancheva DV, Andonov B, Pashova L (2013c) Global TEC maps based on GNSS data: 1. Empirical background TEC model. J Geophys Res 118:4594–4608. https://doi.org/10.1002/jgra.50413
Orus R, Hernándeš Pajares M, Juan JM, Sanz J (2005) Improvement of global ionospheric VTEC maps by using kriging interpolation technique. J Atmos Solar Terr Phys 67:1598–1609. https://doi.org/10.1016/J.JASTP.2005.07.017
Orus Pérez R (2019) Using TensorFlow-based Neural Network to estimate GNSS single frequency ionospheric delay (IONONet). Adv Space Res 63:1607–1618. https://doi.org/10.1016/J.ASR.2018.11.011
Schaer S (1999) Mapping and predicting the Earth’s ionosphere using the Global Positioning System. Institut für Geodäsie und Photogrammetrie, Eidg, Technische Hochschule Zürich
Sebera GAF, Wild CJ (1989) Computational methods for nonlinear least squares. In: Regression N (ed) SEBER, G.A.F & WILD, C. J. Wiley, New Jersey, pp 619–660
Sezen U, Arikan F, Arikan O, Ugurlu O, Sadeghimorad A (2013) Online, automatic, near-real time estimation of GPS-TEC: IONOLAB-TEC. Space Weather 11:297–305. https://doi.org/10.1002/swe.20054
Thampi SV, Lin C, Liu H, Yamamoto M (2009) First tomographic observations of the Midlatitude Summer Nighttime Anomaly over Japan. J Geophys Res Space Phys. https://doi.org/10.1029/2009JA014439
Trísková L, Chum J (1996) Hysteresis in dependence of foF2 on solar indices. Adv Space Res 18:145–148. https://doi.org/10.1016/0273-1177(95)00915-9
Wan W, Ding F, Ren Z, Zhang ML, Liu L, Ning B (2012) Modeling the global ionospheric total electron content with empirical orthogonal function analysis. Sci China Technol Sci 55:1161–1168. https://doi.org/10.1007/S11431-012-4823-8
Wang C, Xin S, Liu X, Shi C, Fan L (2018) Prediction of global ionospheric VTEC maps using an adaptive autoregressive model. Earth, Planets and Space 70:1–14. https://doi.org/10.1186/s40623-017-0762-8
Yuan Y, Ou J (2004) A generalized trigonometric series function model for determining ionospheric delay. Prog Nat Sci 14:1010–1014. https://doi.org/10.1080/10020070412331344711
Yuan Y, Huo X, Ou J, Zhang K, Chai Y, Wen D, Grenfell R (2008) Refining the Klobuchar ionospheric coefficients based on GPS observations. IEEE Trans Aerosp Electron Syst 44:1498–1510. https://doi.org/10.1109/TAES.2008.4667725
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 66:55–69. https://doi.org/10.1002/navi.292
Zhukov AV, Yasyukevich YV, Bykov AE (2020) GIMLi: Global Ionospheric total electron content model based on machine learning. GPS Solut 25:19. https://doi.org/10.1007/s10291-020-01055-1
Yuan Y (2002) Study on theories and methods of correcting ionospheric delay and monitoring ionosphere based on GPS. Institute of Geodesy and Geophysics, Chinese Academy of Science, Wuhan
Yuan Y, Tscherning CC, Knudsen P, Xu G, Ou J (2008) The ionospheric eclipse factor method (IEFM) and its application to determining the ionospheric delay for GPS. J Geodesy 82(1):1–8. https://doi.org/10.1007/s00190-007-0152-2
Acknowledgements
We are grateful for the GIM products provided by the CODE. This work is supported in part by the National Natural Science Foundation of China under Grant NO. 42274040, 42204030 and Funded by State Key Laboratory of Geo-Information Engineering, NO.SKLGIE2021-M-3-2.
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Feng, J., Zhang, T., Li, W. et al. A new global TEC empirical model based on fusing multi-source data. GPS Solut 27, 20 (2023). https://doi.org/10.1007/s10291-022-01355-8
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DOI: https://doi.org/10.1007/s10291-022-01355-8