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Empirical orthogonal function analysis and modeling of global ionospheric spherical harmonic coefficients

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Abstract

We developed a global empirical model for computing spherical harmonic (SH) coefficients based on the empirical orthogonal function (EOF) method and periodic functions by utilizing global ionospheric SH coefficients data provided by Center for Orbit Determination in Europe (CODE) during the years 2005–2016. Results show that the first four-order base functions and corresponding associated coefficients can represent 97.15% of the basic characteristics of the original data. The first four-order associated coefficients have noticeable periodic variations, and the correlation between these coefficients and the solar activity intensity is high. By fitting the associated coefficients with the periodic function that takes into account the influence of solar activity, it is possible to establish an EOF model to characterize the variations of the ionospheric SH coefficients with few model parameters and further calculate the global vertical total electron content (VTEC). Relative to the existing global VTEC EOF models, this EOF method can achieve high-accuracy modeling of global VTEC with a smaller number of model coefficients. By comparing the SH coefficients and the global VTEC between the EOF model and CODE, results demonstrate that the EOF model can achieve high accuracy and reliability under different solar activities. The difference between the EOF model and CODE is basically at the same level as that between the individual ionospheric analysis centers and CODE. In the extreme event of magnetic storms, the EOF model can also present higher accuracy than the international reference ionosphere (IRI) model.

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Data availability

The final GIMs products corresponding to different IAACs are collected by the Chinese Academy of Sciences and can available via the FTP server: ftp://ftp.gipp.org.cn/product/ionex/. The Dst, AE, and Kp indexes are available via NASA Goddard Space Flight Center (https://omniweb.gsfc.nasa.gov/form/dx1.html).

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Acknowledgements

The authors are grateful to the IGS Ionosphere Associate Analysis Centers (IAACs), including the Center for Orbit Determination in Europe (CODE), the European Space Operations Center of European Space Agency (ESA), the Jet Propulsion Laboratory (JPL), and the Universitat Politècnica de Catalunya (UPC) for providing the data. We also gratefully acknowledged the use of Generic Mapping Tool (GMT) and MATrix LABoratory (MATLAB) software. This study was funded by the National Natural Science Foundation of China (41404031) and Outstanding Youth Science Fund of Xi’an University of Science and Technology (2018YQ2-10). The CSC scholarship also supported this study.

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Authors and Affiliations

  1. College of Geomatics, Xi’an University of Science and Technology, Xi’an, 710054, China

    Peng Chen, Hang Liu & Yongchao Ma

  2. Deutsches Geodätisches Forschungsinstitut der Technischen Universität München (DGFI-TUM), Arcisstraße 21, 80333, München, Germany

    Peng Chen

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  1. Peng Chen
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  2. Hang Liu
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Correspondence to Peng Chen.

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Chen, P., Liu, H. & Ma, Y. Empirical orthogonal function analysis and modeling of global ionospheric spherical harmonic coefficients. GPS Solut 24, 71 (2020). https://doi.org/10.1007/s10291-020-00984-1

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