1. Key Laboratory of Space Weather, National Center for Space Weather China Meteorological Administration Beijing China
2. Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics Chinese Academy of Sciences Beijing China
3. National Space Science Center Chinese Academy of Sciences Beijing China
4. NASA Goddard Space Flight Center Greenbelt Maryland USA
5. Department of Mathematics Eastern Michigan University Ypsilanti Michigan USA
6. Department of Climate and Space Sciences and Engineering University of Michigan Ann Arbor Michigan USA
7. NASA Marshall Space Flight Center Huntsville Alabama USA
8. Institute of Statistical Mathematics Tachikawa Japan