# Perpendicular Electrical Conductivity in the Topside Ionosphere Derived from Swarm Measurements
## 3 Results
### Seasonal Variation of Electrical Conductivity Perpendicular to the Geomagnetic Field  
Given that perpendicular conductivities exhibit similar characteristics to electron density, it is natural to investigate the variation in \(\sigma_{P}\) and \(\sigma_{H}\) with seasons, as electron density demonstrates significant seasonal fluctuations owing to varying sunlit conditions [94]. To accomplish this, we divided the data set based on the seasons, selecting data falling within a three-month long time window centred around: (1) the June solstice to sample summer in the Northern Hemisphere and winter in the Southern Hemisphere; (2) the December solstice to sample winter in the Northern Hemisphere and summer in the Southern Hemisphere; (3) the March equinox to sample spring in the Northern Hemisphere and Autumn in the Southern Hemisphere; (4) the September equinox to sample Autumn in the Northern Hemisphere and spring in the Southern Hemisphere. In Figure 5, we present global maps of \(\sigma_{P}\) in QD-MLT coordinates, from top to bottom: around the December solstice, around the June solstice, around the March equinox, and around September equinox. During the December solstice, the values of \(\sigma_{P}\) span from \(\sim\)4.6 s\({}^{-1}\) to 1.2 \(\times\) 10\({}^{6}\) s\({}^{-1}\), during the June solstice from \(\sim\)0.1 s\({}^{-1}\) to 4.3 \(\times\) 10\({}^{5}\) s\({}^{-1}\), during the March equinox from \(\sim\)15.4 s\({}^{-1}\) to 1.9 \(\times\) 10\({}^{6}\) s\({}^{-1}\) and during the September equinox from \(\sim\)19.9 s\({}^{-1}\) to 1.1 \(\times\) 10\({}^{6}\) s\({}^{-1}\). Associated statistical uncertainties range between \(\sim\)0.7% and \(\sim\)59.4% for the December solstice, between \(\sim\)0.7% and \(\sim\)70.7% for the June solstice, between \(\sim\)0.8% and \(\sim\)70.7% for the March equinox and between \(\sim\)0.4% and \(\sim\)70.7% for the September equinox. In all of these cases, when considering bins with at least 100 counts, the maximum conditioned uncertainty significantly decreases down to 4.7% for the December solstice, 5.2% for the June solstice, 4.9% for the March equinox, and 4.9% for the September equinox. These values are resumed in Table 2.  
Figure 4: Climatological maps in QD-MLT coordinates of Hall electrical conductivity, \(\sigma_{H}\), in polar stereographic projection representations in the Northern (**left panel**) and Southern (**right panel**) Hemisphere. Values within each bin are saturated below 0 and above 2 s\({}^{-1}\). Figure 5: _Cont._  
Similarly to Figure 5, Figure 6 shows global maps of \(\sigma_{H}\) in QD-MLT coordinates, from top to bottom: around the December solstice, around the June solstice, around the March equinox, and around the September equinox. During the December solstice, the values of \(\sigma_{H}\) span from \(\sim\)0.0 s\({}^{-1}\) to 3.1\(\times\)10\({}^{4}\) s\({}^{-1}\), during the June solstice from \(\sim\)0.0 s\({}^{-1}\) to 5.5\(\times\)10\({}^{3}\) s\({}^{-1}\), during the March equinox from \(\sim\)0.0 s\({}^{-1}\) to 6.5\(\times\)10\({}^{4}\) s\({}^{-1}\), and during the September equinox from \(\sim\)0.0 s\({}^{-1}\) to 3.0\(\times\)10\({}^{4}\) s\({}^{-1}\). The associated statistical uncertainties range between \(\sim\)1.0% and \(\sim\)66.7% for the December solstice, between \(\sim\)1.0% and \(\sim\)70.7% for the June solstice, between \(\sim\)1.0% and \(\sim\)70.7% for the March equinox, and between \(\sim\)1.0% and \(\sim\)70.7% for the September equinox. In all of these cases, when considering bins with at least 100 counts, the maximum conditioned uncertainty significantly decreases down to 5.1% for the December solstice, 5.9% for the June solstice, 5.1% for the March equinox, and 5.5% for the September equinox. These values are resumed in Table 3.