# Perpendicular Electrical Conductivity in the Topside Ionosphere Derived from Swarm Measurements
## 3 Results  
### Climatological Behaviour of Electrical Conductivity Perpendicular to the Geomagnetic Field  
Climatological maps of electrical conductivity were obtained using all the LP and ASM measurements selected as described in Section 2. Figure 1 displays the results for \(\sigma_{||}\) using QD-MLT coordinates. In this map, values range between \(\sim\)2.6 \(\times\) 10\({}^{11}\) s\({}^{-1}\) and \(\sim\)9.4 \(\times\) 10\({}^{11}\) s\({}^{-1}\) and are saturated below 3.5 \(\times\) 10\({}^{11}\) s\({}^{-1}\) and above 7.5 \(\times\) 10\({}^{11}\) s\({}^{-1}\). The estimated statistical uncertainties range between \(\sim\)0.1% and \(\sim\)13.8%. However, when considering only bins with at least 100 counts, i.e., excluding the bins around poles, the maximum uncertainty drops to \(\sim\)0.9%. As observed, relative maxima are present at the magnetic equator and around 06:00 MLT, corresponding to the morning overshoot [87] and, at high latitudes in both hemispheres, around 80\({}^{\circ}\) QD magnetic latitude and between 06:00 MLT and 18:00 MLT, corresponding to the polar magnetic cusp [88]. It is noteworthy that the features of \(\sigma_{||}\) align with those of electron temperature, \(T_{e}\), in terms of diurnal, seasonal, and solar activity variations [68; 73]. This alignment is due to \(T_{e}\) being the dominant physical quantity in defining \(\sigma_{||}\). These findings are fully consistent with [PERSON] et al. [55; 56], who extensively studied \(\sigma_{||}\) using a shorter Swarm A data set (up to six years of data, compared to the eight years used in this work). For a comprehensive discussion about \(\sigma_{||}\), the reader can refer to those works. Here, we focus on the perpendicular conductivities, \(\sigma_{p}\) and \(\sigma_{H}\). The top panel of Figure 2 displays the results obtained for \(\sigma_{p}\) in QD-MLT coordinates. In this and all global maps that follow, we represent the values in logarithmic scale, as  
Figure 1: Climatological map in QD-MLT coordinates of electrical conductivity parallel to the geomagnetic field, \(\sigma_{||}\). Values within each bin are saturated below 3.5 \(\times\) 10\({}^{11}\) s\({}^{-1}\) and above 7.5 \(\times\) 10\({}^{11}\) s\({}^{-1}\). they span several orders of magnitude. In the case of Figure 2, values of \(\sigma_{P}\) range between \(\sim\)61 s\({}^{-1}\) and \(\sim\)7 \(\times\) 10\({}^{5}\) s\({}^{-1}\) and are saturated above 10\({}^{6}\) s\({}^{-1}\) and below 10\({}^{2}\) s\({}^{-1}\). The estimated statistical uncertainties range between \(\sim\)0.6% and \(\sim\)25.5%. However, when considering only bins with at least 100 counts, i.e., excluding the poles, the maximum uncertainty drops to \(\sim\)2.4%. The bottom panel of Figure 2 displays the results obtained for \(\sigma_{H}\) in the same coordinates. In this map, values range between \(\sim\)10\({}^{-2}\) s\({}^{-1}\) and \(\sim\)1.3 \(\times\) 10\({}^{4}\) s\({}^{-1}\) and are saturated above 10\({}^{4}\) s\({}^{-1}\) and below 10\({}^{-2}\) s\({}^{-1}\). The estimated statistical uncertainties range between \(\sim\)0.8% and \(\sim\)29.3%. However, when considering only bins with at least 100 counts, i.e., excluding the poles, the maximum conditioned uncertainty drops to \(\sim\)2.6%. These values are summarised in Table 1.  
Figure 2: Climatological maps in QD-MLT coordinates of the following. **Top panel**: Pedersen electrical conductivity, \(\sigma_{P}\). Values within each bin are saturated above 10\({}^{6}\) s\({}^{-1}\) and below 10\({}^{2}\) s\({}^{-1}\). **Bottom panel**: Hall electrical conductivity, \(\sigma_{H}\). Values within each bin are saturated above 10\({}^{4}\) s\({}^{-1}\) and below 10\({}^{-2}\) s\({}^{-1}\). As shown in both panels of Figure 2, relative maxima are observed around the magnetic equator, specifically between \(\sim\)7\({}^{\circ}\) and \(\sim\)13\({}^{\circ}\) QD magnetic latitude, and between 11:00 MLT and 15:00 MLT in both hemispheres.