# Ionospheric Global and Regional Electron Contents in Solar Cycles 23–25

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{i}, in each cell (over the set of GIM cells), multiplied by the GIM cell area, S

_{i}

_{00}, given the proper normalization, and thus it is possible to estimate GEC from C

_{00}using a simple relation:

_{E}+ H)

^{2}C

_{00},

_{E}is the Earth’s radius and H is the shell height used in the GIM model.

_{E}+ H)

^{2}/R

_{E}

^{2}. This is one of the reasons why GEC computed according to [7,10] is typically underestimated, which was noted by Gulyaeva and Veselovsky [11]. Gulyaeva et al. [12] used 450 km altitude; this altitude is indicated in GIM and should correspond to the model involved.

_{E}+ H)

^{2}/R

_{E}

^{2}is common for all GIM cells, it contributes the same in the mean TEC value for different regions. This also allows direct comparison of the ionospheric dynamics in different regions—in this way, the region size does not influence the values. To calculate the global mean TEC, one can use different approaches. The first is to average TEC in GIM

^{16}m

^{−2}).

_{i}/S (S

_{i}is the area of a cell, $S={\displaystyle \sum}_{i}{S}_{i}$): the area of a GIM cell S

_{i}is the biggest at the equator and decays towards higher latitudes. Introducing the weighting factor allowed us to compare different regions taking into account different areas covered by the same number of GIM cells.

_{00}for GIM based on SH expansion (see above).

**Figure 2.**Comparison between the mean and weighted mean TEC: (

**a**) the weighted mean (red dots) and mean (blue dots) TEC throughout the world; (

**b**) the weighted mean TEC in Siberia (red dots); (

**c**) the difference between the weighted mean and the mean TEC throughout the world (black dots) and in Siberia (orange dots).

**we used the weighted mean (4) to calculate GEC and REC**(we preserved these names keeping in mind the simple transformation between the number of electrons and mean TEC).

## 3. GEC and REC in Solar Cycles 23–25

_{13}, I

_{1}were REC at 12–13 LT and 0–1 LT, respectively.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of REC calculation. Left column shows TEC distribution for 06:00 UT, 1 January 2003; 10:00 UT, 1 January 2008; 14:00 UT, 1 January 2015; 18:00 UT, 1 January 2020. The region for REC is shown by light violet rectangle. On the right panel, the bold dots show corresponding REC, while black dots show general REC dynamics.

**Figure 3.**Dynamics of REC in Siberia (blue curve), Europe (thin black curve), Japan (thick gray curve), Canada (red curve), Australia (green curve), and GEC (thick black curve) from 1998 to 2023. In panels (

**a**,

**b**), the series are smoothed with a 10-day window; in panels (

**c**,

**d**) with an 81-day window and a 365-day window, respectively. Light blue dots on the background of panel (

**d**) represent the F10.7 index.

**Figure 4.**Annual (

**a**,

**b**) and semi-annual (

**c**,

**d**) REC variations in Siberia, Japan, Europe, Australia, Canada, and GEC variations.

**Figure 5.**Envelope of 27-day variations. (

**a**) 27-day variations (black line) and their envelope (gray lines) for Siberia; (

**b**) upper envelope of 27-day REC variations in Siberia (blue curve) and Europe (gray curve); (

**c**) upper envelope of 27-day REC variations in Australia (green curve) and of REC variations throughout the world (black curve), and envelope of the F10.7 index variations (magenta); (

**d**) upper envelope of 27-day REC variations in Japan (gray curve) and Canada (red curve).

**Figure 6.**The amplitude of diurnal TEC variations in Siberia (panel (

**a**), blue dots), Europe (panel (

**a**), black dots), Japan (panel (

**b**), blue dots), Canada (panel (

**c**), red dots), Australia (panel (

**c**), green dots), and throughout the world (panel (

**b**), black dots).

**Figure 7.**Daytime (

**a**) and nighttime (

**b**) REC in Siberia (black curve) and Europe (blue dots). Panels (

**c**–

**e**) show the ratio of daytime to nighttime REC in Europe ((

**c**), blue dots), Japan ((

**d**), blue dots) and Siberia ((

**c**,

**d**), black curves), Canada ((

**e**), blue dots), and Australia ((

**e**), black curve).

**Figure 8.**Dependence of GEC (

**b**) and REC in Siberia (

**a**), Europe (

**c**), Canada (

**d**), Japan (

**e**), and Australia (

**f**) on the F10.7 index. Red lines show second-order polynomial fit for the rise of SC23/SC24 (3.5 years from the cycle beginning) and 95% confidence intervals (dashed red lines). The green dots and the blue lines are data and the fits for SC25.

**Figure 9.**The Morlet wavelets for F10.7 index, GEC, REC in Europe, Siberia, Canada, Japan, and Australia (from top to bottom).

**Figure 10.**Wavelet coherence for F10.7 index and GEC spectra for 50–500 days (

**upper**panel) and 1–65 days (

**bottom**panel). Solid black contour lines show 5% significance level against noise. Arrows present relative phase with in-phase pointing up, and anti-phase pointing down.

**Figure 11.**Wavelet coherence for GEC and REC in Siberia (

**upper**panel) and Australia (

**bottom**panel). Solid black contour lines show 5% significance level against noise. Arrows present relative phase with in-phase pointing up, and anti-phase pointing down.

**Figure 12.**Periods of 27-day variations

**.**Maxima of GEC spectrums within 22.5–37 vs. those of F10.7 index. Slanted gray lines show a 45° slope shifted by T = 2 days.

**Figure 13.**GEC modeling based on neural networks. Black dots show experimental GEC, red dots the neural network model involving the F10.7 index, blue dots the neural network without the F10.7 index, gray dots the F10.7 index.

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**MDPI and ACS Style**

Yasyukevich, Y.; Padokhin, A.; Vesnin, A.; Bykov, A.; Kiselev, A.; Ivanov, A.; Yasyukevich, A.
Ionospheric Global and Regional Electron Contents in Solar Cycles 23–25. *Symmetry* **2023**, *15*, 1940.
https://doi.org/10.3390/sym15101940

**AMA Style**

Yasyukevich Y, Padokhin A, Vesnin A, Bykov A, Kiselev A, Ivanov A, Yasyukevich A.
Ionospheric Global and Regional Electron Contents in Solar Cycles 23–25. *Symmetry*. 2023; 15(10):1940.
https://doi.org/10.3390/sym15101940

**Chicago/Turabian Style**

Yasyukevich, Yury, Artem Padokhin, Artem Vesnin, Alexei Bykov, Alexander Kiselev, Alexander Ivanov, and Anna Yasyukevich.
2023. "Ionospheric Global and Regional Electron Contents in Solar Cycles 23–25" *Symmetry* 15, no. 10: 1940.
https://doi.org/10.3390/sym15101940