# Perpendicular Electrical Conductivity in the Topside Ionosphere Derived from Swarm Measurements
## 3 Results
### Electrical Conductivity Variation Perpendicular to the Geomagnetic Field Due to Solar Activity
In the third biennium, which corresponds to a period of low solar activity, \(\sigma_{P}\) values range between 0.6 s\({}^{-1}\) and 3.7 \(\times\) 10\({}^{5}\) s\({}^{-1}\). The estimated statistical uncertainties range between \(\sim\)0.5% and 70.5%. When considering only bins with at least 100 counts, excluding the magnetic poles, the maximum conditioned uncertainty decreases to 5.0%. These values are resumed in Table 4.  
Figure 9: Daily solar radio flux at 10.7 cm (F10.7, blue solid line) as a proxy of solar activity from 1 April 2014 to 31 March 2022. Flux is expressed in solar flux units (sfu): 1 sfu = \(10^{-19}\) erg\(\cdot\)s\({}^{-1}\cdot\)cm\({}^{-2}\cdot\)Hz\({}^{-1}\) in cgs units. The shaded area in orange between the red dashed lines marks a two-year period of moderate solar activity. The shaded area in green between the black dashed lines marks a two-year period of low solar activity. Compared to the climatological case shown in the top panel of Figure 2, during moderate-high solar conditions, \(\sigma_{P}\) increases and its characteristic features around the magnetic equator expand up to \(\pm 25^{\circ}\) QD magnetic latitude. Moreover, these structures persist until nearly midnight MLT. Conversely, during low-solar-activity conditions, the features typical of \(\sigma_{P}\) become visibly weaker and less extended compared to the climatological case. Indeed, the most intense features of \(\sigma_{P}\) do not exceed a \(12^{\circ}\) QD magnetic latitude and are confined within 15:00 MLT and 16:00 MLT. A similar behaviour is observed for \(\sigma_{H}\), as illustrated in Figure 11. During the first biennium, under moderate-high solar activity conditions, \(\sigma_{H}\) values range from 0.0 s\({}^{-1}\) to 1.1 \(\times\)\(10^{5}\) s\({}^{-1}\). The estimated statistical uncertainties range between \(\sim\)1.1% and 99.7%. However, when considering only bins with \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Minimum** & **Maximum** & **Minimum** & **Maximum** & **Maximum Conditioned** \\  & **Value (s\({}^{-1}\))** & **Value (s\({}^{-1}\))** & **Uncertainty (\%)** & **Uncertainty (\%)** & **Uncertainty (\%)** \\ \hline First Biennium & 10.7 & \(2.8\times 10^{6}\) & 0.9 & 70.6 & 4.7 \\ Third Biennium & 0.6 & \(3.7\times 10^{5}\) & 0.5 & 70.5 & 5.0 \\ \hline \end{tabular}
\end{table} 
Table 4: Values of \(\sigma_{P}\) for the first and third biennia, respectively representing, medium–high and low solar activity. Figure 10: Maps in QD-MLT coordinates of Pedersen electrical conductivity, \(\sigma_{P}\), during the first (**top panel**) and third (**bottom panel**) biennia as selected in Figure 9. Values within each bin are saturated above \(10^{6}\) s\({}^{-1}\) and below \(10^{2}\) s\({}^{-1}\). at least 100 counts, i.e., excluding the magnetic poles, the maximum uncertainty falls to 4.9%. In the third biennium, under low-solar-activity conditions, \(\sigma_{P}\) values range between 0.0 s\({}^{-1}\) and 5.3 \(\times\) 10\({}^{3}\) s\({}^{-1}\). The estimated statistical uncertainties cover the widest range between \(\sim\)0.8% and 109.4%. Again, when considering only bins with at least 100 counts, i.e., excluding the magnetic poles, the maximum conditioned uncertainty collapses to 5.2%. These values are resumed in Table 5.  
The structures of \(\sigma_{H}\) closely mirror those of \(\sigma_{P}\), exhibiting similar behaviour in response to solar activity. During periods of increased solar activity, both \(\sigma_{P}\) and \(\sigma_{H}\) intensify and expand in QD latitude, extending toward midnight MLT. Conversely, during periods of low solar activity, their features become more subdued and confined. Similarly to the case of seasonal maps, at high latitudes, biennial maps of \(\sigma_{P}\) (Figure 12) and \(\sigma_{H}\) (Figure 13) spread over a wide range of values in the transition from the first to the third biennia. This makes it impossible to compare maps of \(\sigma_{P}\) and \(\sigma_{H}\) setting the same level of saturation for different solar activity conditions.