## 2 Materials and Methods
### Ionospheric Data and Methodologies
#### 2.3.2 Total Electron Content Data Processing  
In order to validate the CSES Ne data and further investigate the ionosphere status above La Palma volcano, the Global Ionospheric Maps (GIM) map of the vertical Total Electron Content (vTEC or simply TEC) has been retrieved. The Total Electron Content is the vertical integral of the electron density Ne. It is measured from Global Navigation Satellite System (GNSS) stations on the ground receiving two frequency signals from GNSS satellites in geostationary orbits of one or more constellations (e.g., Global Position System, GPS; Compassi Baidu, Galileo) operated by several space agencies. As the \"line of sight\" of the satellite is generally inclined with respect to the vertical (defining the zenithal angle distance), the measured quantity is the slant-TEC. By a geometrical correction, the vertical TEC was estimated. In this work, we download the pre-processed GIM-TEC maps that some researchers like [PERSON] et al. [65] compared with other techniques to obtain _TEC_ in a regional context, founding a general good correlation. Despite this, the absolute TEC values were generally overestimated in GIM, especially in high solar activity. For the purpose of this study, the data are used to construct TEC time series, which are irrelevant to an eventual overestimation of TEC and to validate CSES Ne, verifying that the structures are compatible. Therefore, this task is not affected by the TEC absolute value.  
We retrieved the GIM _TEC_ data from International GNSS Service (igns) from 2000 to 2021 from 23 March until 19 September (6 months for each year). In order to construct a time series of the typical value of the year, it was fundamental to remove the solar cycle modulation from the data. As the original data had a 5\({}^{\circ}\) longitude and 2.5\({}^{\circ}\) latitude space resolution and 2 h of time resolution, we interpolate the TEC value above \"La Palma\" volcano at 1:44 LT. The chosen local time is the hour of the night-time passages of CSES-01 at La Palma latitude; in this way, the data will be more reciprocally comparable. To spatially interpolate the data, a two-dimensional cubic interpolation was performed, obtaining the previous and following data after a linear interpolation was performed to estimate the TEC at the selected local time.  
The yearly mean on the values from 23 March to 19 September of TEC above La Palma is shown in Figure 3. The modulation of TEC is evident from the 11 year solar cycle. A sinusoidal fit has been performed, and its period of 11.6 years (2 w) is very close to the theoretical period of 11 years. We note that in the maximum of 2000-2002, the TEC values seem higher than in the maximum of 2013-2015, and better future implementation of this method could include the Sunspot number or another indicator of the solar activity to fit not only the modulation but also the variations of the intensity of each maximum (and minimum). Indeed, for the present work, the fit can be more than sufficient, with adjusted-R\({}^{2}\) equal to 0.889. To obtain a time series that is detrended from the solar modulation, the TEC data were divided for the sinusoidal fit \"Sine\" which estimated the following normalized TEC \"TEC\({}_{\text{NORM}}\)\":  
\[TEC_{\text{NORM}}(day,\ year)=\frac{TEC(day,\ year)}{Sine(year)} \tag{2}\]The historical time series was calculated with the normalized _TEC_ values in analogy with the atmospheric data investigation. The _TEC_ anomalies have also been defined as the value of the 2021 _TEC\({}_{NORM}\)_, which overpassed the two standard deviations of the historical time series based on the years 2000 to 2020.