## 3 Results
In this study, we operated the Hualien VIPIR, a modern ionosonde, and observed spread-F features from the ionograms recorded between 13:19-15:04 UT, i.e., 21:19-23:04 LT, on 26 October 2021. The observed ESF event lasted for approximately one hour and forty-five minutes. In Figure 3, the upper ionogram shows two traces of one-hop F-layer echoes, where the upper trace is weaker than the main trace and has higher altitudes with approximately 25 km differences at the start (13:19 UT) of the ESF event. Furthermore, the lower ionogram shows a weak range spread-F, which was recorded during the middle (13:49 UT) of the ESF event. We note that the spread-F frequencies ranged from \(\sim\)1.7 MHz up to 11.5 MHz, which presents the top frequency of ordinary ionospheric echoes, i.e., _fol_. It is usually difficult to retrieve a critical plasma frequency _foF2_ from ionograms with ESF, but not difficult to retrieve _fol_. Multi-trace echoes could be interpreted as being due to the large-scale plasma depletion that happened before an ESF event. Meanwhile, the range-type spread-F indicates the existence of small-scale irregularities on the whole bottom side ionosphere. Figure 2: Results of F57/COSMIC2 RO scintillation observations #1 (**left panel**) and #4 (**right panel**) as in Figure 1. Both figures show the limb-viewing L1-band SNR amplitude profiles at the occulting (calibrating) side in black (grey) and the resulting undersampling \(S_{4}\) profiles in cyan. The retrieved \(N_{e}\) profiles are shown in red. Figure 4 shows the geographical geometry of the ionospheric pierce points (IPP) of the simultaneous GPS signal measurements at 14:42 UT on 26 October 2021, using the CWB GPS receiving network. The IPP altitudes were designed to be 300 km in accordance with the statistical peak scintillation or irregularity altitude retrieved from the FS7/COSMIC2 limb-viewing \(S_{4}\) and/or \(N_{e}\) profiles, as shown in Figure 2. Furthermore, the IPPs were obtained at and limited by a minimum elevation angle of 45\({}^{\circ}\) from receivers to avoid multi-path signals. In this study, we define the vertical scintillation index \(VS_{4}\) as the vertical component of the normalized variance of the signal power intensity \(I\) as follows:  
\[VS_{4}\,=\,\sin(\theta)\,\times sqrt\left(\frac{\left\langle\left(I-\left\langle I \right\rangle\right)^{2}\right\rangle}{\left\langle I\right\rangle^{2}}\right)\,, \tag{1}\]  
where \(\theta\) is the line-of-sight elevation angle from the receiver. We calculate \(VS_{4}\) values by applying (1) and a 30-s duration window to 1-Hz L1-band signal amplitudes from the CWB GPS data archives. We note that the use of \(VS_{4}\) to represent a vertical scintillation index is based on an assumption in which irregular \(N_{e}\) distribution is a function of altitude only along a transionospheric radio path. However, equatorial plasma bubbles are plume-like structures from low altitudes [4], and the shapes of bubbles are extended vertically upward and also stretched in the north-south direction along the magnetic field lines. Ref. [20] shows  
Figure 3: Two typical ionograms showing multi-trace echoes (**upper panel**) and weak range spread-F (**lower panel**) observed at the start (13:19 UT) and mid (13:49 UT) of an ESF event by the Hualien VIPIR on 26 October 2021. Note that the signals throughout all virtual ranges are radio frequency interferences from other radio sources. that GPS RO observations with high \(S_{4}\) values are much more likely to occur when the ray paths are distributed in certain bubbles and more nearly aligned with the magnetic field. The details of two-dimensional and even three-dimensional irregular \(N_{e}\) structures should be figured out in future studies. Meanwhile, we can assume the observing irregularities located at altitudes around 300 km to be the IPP altitude, and the corresponding FFZ scale sizes (\(D_{\rm F}\)) of L1-band signals are between 239 and 275 m for elevation angles from 90\({}^{\circ}\) to 45\({}^{\circ}\).