# 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  
We studied also the dependence of perpendicular conductivities, \(\sigma_{P}\) and \(\sigma_{H}\), on solar activity during the eight years of Swarm observations considered here. To this aim, we evaluated the level of solar activity by taking advantage of the daily solar radio flux at a 10.7 cm wavelength (F10.7) as a proxy [104]. The F10.7 time series was downloaded from the Space Physics Data Facility of the NASA Goddard Space Flight Center. Figure 9 reports F10.7 (blue line) from 1 April 2014 to 31 March 2022 in solar flux units (sfu). We recall that 1 sfu = 10\({}^{-19}\) erg\(\cdot\)s\({}^{-1}\).cm\({}^{-2}\).Hz\({}^{-1}\) in cgs units. F10.7 spans the range between 63.4 sfu, at the minimum of the current solar cycle reached in December 2019, and 255.0 sfu, which was reached in June 2015. During the period considered in this study, the solar activity started near the maximum of the 24 th solar cycle and then descended to the minimum that started in the 25 th solar cycle. After the minimum, the Swarm measurements used in this work sampled part of the new cycle's rise, which is expected to peak between 2024 and 2025. We examined the cumulative distribution function (CDF, not shown in this work) of the F10.7 time series. We found that the flux values at the 25 th percentile and 75 th percentile are, respectively, 70.3 sfu and 100.0 sfu. This means that 25% of F10.7 values are below 70.3 sfu and, likewise, 25% of F10.7 values are above 100.0 sfu. Thus, these values could be used as thresholds to select periods with low and moderate/high solar activity. However, a selection based only on CDF values could lead to an oversampling of one season over another, and thus mix the seasonal variation of \(\sigma_{P}\) and \(\sigma_{H}\) with that associated with the different levels of solar activity. On the other hand, inspecting biennial changes of \(\sigma_{P}\) and \(\sigma_{H}\) may be an optimum compromise between the two: (1) two years of Swarm A observations provide a statistical data coverage robust enough to sample Swarm A measurements in  
Figure 8: Seasonal maps (from top to bottom: winter, summer, spring, autumn) in QD-MLT coordinates of Hall electrical conductivity, \(\sigma_{H}\), in polar stereographic projection representation in the Northern (left column) and Southern (right column) Hemispheres. bins of QD magnetic latitude versus MLT \(1^{\circ}\times 1^{\circ}\) wide; (2) two years of data ensure even sampling of the seasons so that they have the same effect on each biennium. On this basis, we have identified two biennia in our data set as representative of low and medium-high solar activity: the third biennium (between 1 April 2018 and 31 March 2020) and the first biennium (between 1 April 2014 and 31 March 2016), respectively. These two-year periods are highlighted with shaded regions in Figure 9. The orange-shaded area between the red dashed lines indicates a period of medium-high solar activity, while the green-shaded area between the black dashed lines denotes a period of low solar activity. This selection aligns with the 25 th and 75 th percentiles of the CDF for selecting solar activity levels. Specifically, nearly all F10.7 values in the orange region exceed 100.0 sfu, and almost all F10.7 values in the green region fall below 70.3 sfu. In Figure 10 we present a global map of \(\sigma_{P}\) in QD-MLT coordinates for the first (top panel) and third (bottom panel) biennia of the entire selected time window used in this study. During the first biennium, which represents a period of moderate-high solar activity, \(\sigma_{P}\) values range from 10.7 s\({}^{-1}\) to 2.8 \(\times\) 10\({}^{6}\) s\({}^{-1}\). The estimated statistical uncertainties range between \(\sim\)0.9% and 70.6%. However, when considering only bins with at least 100 counts, excluding the magnetic poles, the maximum uncertainty decreases to 4.7%.