## 3 Results
We note that GPS satellites have orbiting velocities of approximately 3.9 km/s, and thus the corresponding IPP velocity is \(\sim\)60 (80) meter/s at an elevation angle of 90\({}^{\circ}\) (45\({}^{\circ}\)) from the receiver. If we assume a frozen ionosphere, the resulting Fresnel frequencies \(f_{\rm F}\) are between 0.18 and 0.2 Hz. Ref. [11] shows that, using extensive incoherent scatter radar observations from Jicamarca, the daytime westward drifts are significantly smaller than the nighttime eastward drifts, and during solar maximum, the maximum nighttime eastward velocity increases up to about 160 m/s. Even if we include a 160 m/s IPP trace component of plasma irregularity drift velocity, the resulting Fresnel frequencies \(f_{\rm F}\) are approximately 0.66 Hz and are also lower than the 1-Hz sampling rate for the CWB GPS receivers. This means that the derived \(S_{4}\) values from the CWB GPS data are at complete conditions. As a result, Figure 5 shows three developed structures on a two-dimensional \(VS_{4}\) map taken at 13:24, 13:49, and 14:42 UT, which are approximately at the start, middle, and end of the scintillation and ESF event. Referring to Figure 4 and the bottom panel of Figure 5 based on the same CWB GPS data at 14:42 UT, we derive a two-dimensional extended \(VS_{4}\) map deduced through relaxation by applying the red-black smoothing technique [21] on point-distributed \(VS_{4}\) measurements. We execute one pass through the mesh updating the \"red\" cells (like the red squares of a checkerboard) and another pass updating the \"black\" cells (like the black squares) and so forth for two loops. It produces two more cell extents on derived \(VS_{4}\) maps where the cell (latitudinal or longitudinal) resolution is 0.1\({}^{\circ}\), determined approximately by the medium distance between neighboring GPS stations. Figure 4: Geographical geometry of the IPIPs of the simultaneous GPS signal measurements at 14:42 UT on 26 October 2021, and from 133 ground-based receivers located in Taiwan and the surrounding islands. The dots colored in light blue, yellow, and red show the IPP positions at 300 km altitudes for the lines of sights connecting GPS satellite #8, #21, and #27, respectively, which have a minimum elevation angle of 45\({}^{\circ}\) from receivers. The positions of another two software-defined GPS receivers located at Chungli (24.97\({}^{\circ}\)N, 121.19\({}^{\circ}\)E) and Hualien (23.89\({}^{\circ}\)N, 121.55\({}^{\circ}\)E), Taiwan, are shown and labeled by “R1” and “R2”, respectively. Figure 5: Three developed structures in two-dimensional \(VS_{4}\) map taken at 13:24 (**upper panel**), 13:49 (**middle panel**), and 14:42 UT (**lower panel**) on 26 October 2021, and derived by the simultaneous GPS signal measurements from the CWB GPS receiving network. It is now generally accepted that radio scintillation caused by ionospheric plasma irregularities can be characterized by fitting a power-law function with the spectral index \(p\) to the derived signal spectrum [2, 22, 23, 24]. According to the scintillation theory and power spectra analyses [2, 25], the intensity spectrum of weak and moderate scintillations and power-law ionospheric irregularities should have more or less a flat portion at low frequencies and start to roll off around the Fresnel frequency in the form \(f^{1-p}\), where \(p\) is defined as the spectral index and is near 4 in the irregularity power-law relationship. Furthermore, the higher the spectral index, the stronger the scintillation intensity and the smaller the irregularity scale. As described in the last section, we also operate two high-sampling, software-defined GPS receivers located at Chungli and Hualien, Taiwan separately to simultaneously receive GPS signals. The locations of the Chungli and Hualien software-defined GPS receivers are shown in Figures 4 and 5 and labeled by \"R1\" and \"R2\", respectively. In this study, L1-band C/A code signal amplitudes were recorded at a sampling rate of 50 Hz and for a 70-s duration every five minutes.