# Polar Cap Patches Scaling Properties: Insights from Swarm Data
## 2 Data and Methods
### The AE Index  
As mentioned in Section 1, our investigation is carried out for two different levels of geomagnetic activity. Because the emphasis is on very high latitudes, we chose the AE index [38] to represent the level of geomagnetic disturbance. We are aware that this index characterizes the auroral electrojet currents, and thus the level of geomagnetic activity away from the polar cap and in the Northern hemisphere only, but it is currently the best available proxy of high-latitude geomagnetic activity. We use 1-min AE index values to divide Swarm-related data into two sets: one corresponding to quiet conditions (AE! 50 nT) and one to disturbed conditions (AE? 300 nT). The AE index has been produced by the World Data Center (WDC) for geomagnetism (Kyoto) until early 2018, when its distribution was stopped. This is why the end of time of our dataset falls right on 28 February 2018. Fortunately, the production of the index has recently resumed.  
Figure 3: Cumulative distribution function (CDF) and probability density function (PDF) of the size \(\Delta\)x of PCPs as identified by Swarm A PCP flag from the period 16 July 2014–28 February 2018. The blue line represents the CDF; red bars represent the PDF.  
Figures 4 and 5 provide information on the distribution in time and space, respectively, of PCPs observed under quiet and disturbed conditions. In detail, time distribution for quiet conditions (i.e., for AE \(<\) 50 nT) is shown in the two top plots of Figure 4, for the Northern (left side) and Southern (right side) hemispheres, respectively. Observing these plots reveals two things: (1) under quiet conditions the number of PCPs in the Southern hemisphere is much lower than that in the Northern hemisphere; (2) peak values in the number of observed PCPs do not seem to depend on the solar cycle (represented in blue in terms of monthly sunspot number). PCPs distribution in space for quiet conditions is shown in the upper plots of Figure 5 for the Northern (left side) and Southern (right side) hemispheres, respectively. In this case, a slight hemispherical asymmetry emerges in the pattern of PCPs distribution in a QD-latitude versus MLT plot. In the Northern hemisphere the distribution shows two peaks (dawn and dusk), in the Southern hemisphere a peak only is visible (post-noon sector).  
Moving to disturbed conditions (i.e., AE \(>\) 300 nT), the corresponding PCP time distribution is shown in the bottom plots of Figure 4. Differently from the case of quiet conditions we find that the total number of PCPs in the analyzed time interval is similar for the two hemispheres but the number of PCPs has a completely different dependence on the solar cycle. Indeed, while in the Northern hemisphere peaks of observed PCPs decrease with decreasing solar activity, in the Southern one peaks do not seem to show a solar cycle dependence. Differently from what found for quiet geomagnetic conditions, for disturbed conditions a clear hemispherical asymmetry emerges in the way PCPs are distributed in a QD-latitude versus MLT plot as shown in the lower plots of Figure 5. Indeed, while in the Northern hemisphere the bulk of PCPs occurs at QD-latitudes higher than 80\({}^{\circ}\) at all MLTs, in the Southern hemisphere PCPs mainly appear at QD-latitudes in the range 75\({}^{\circ}\div\) 80\({}^{\circ}\) at MLTs between 12:00 and 18:00.  
Figure 4: Time distribution of the PCPs identified between 16 July 2014 and 28 February 2018 from Swarm A under different geomagnetic conditions. **Top**: PCPs observed during quiet geomagnetic conditions (AE \(<\) 50 nT); **bottom**, PCPs observed during disturbed geomagnetic conditions (AE \(>\) 300 nT). **Left** side refers to the Northern hemisphere while **right** side to the Southern one. Blue solid line represents the monthly sunspot number.