Fig. 3
![Fig. 3](http://media.springernature.com/full/springer-static/image/art%3A10.1186%2Fs40623-022-01616-3/MediaObjects/40623_2022_1616_Fig3_HTML.png)
Cross-correlation analysis (i.e., time lag analysis) of the HFD and GPS-TEC data. a The amplitude of reflected radio waves obtained from the three HFD receivers (Sugito, Fujisawa, and Sugadaira) on August 22, 2014, 00:00–02:00 JST. b Vertical GPS-TEC data above the HFD sensing area (i.e., mid-points between Tx and Rx stations at Sugito, Fujisawa, and Sugadaira) during the same interval. The black dots are the original data and the red dots are the time-shifted data with the highest correlation coefficient relative to the data at the mid-point of Sugito