# Polar Cap Patches Scaling Properties: Insights from Swarm Data
## 3 Results
Differently, in this area, under disturbed conditions, values of \(\gamma(1)\) are primarily indicative of antipersistent behavior with \(\gamma(1)<0.5\). At very high latitudes, i.e., larger than approximately 80\({}^{\circ}\), the behavior of \(\gamma(1)\) suggests a decrease in antipersistency when moving from quiet to disturbed geomagnetic conditions. For what concerns \(\gamma(2)\), higher values are observed in the areas characterized by a less antipersistent character. Looking back at the space distribution of PCPs in the Northern hemisphere under quiet and disturbed geomagnetic conditions (left side of Figure 5), we note that the areas with a high number of PCPs are characterized by a less antipersistent character (left side of Figure 7) and by higher values of \(\gamma(2)\) (center of Figure 7). When examining the spatial distribution of intermittency values, interesting observations can be made for periods of quiet geomagnetic conditions: high intermittency values are predominantly found in regions exhibiting a persistent behavior and high values of \(\gamma(2)\). Specifically, these regions are concentrated on the dayside within a latitudinal range between approximately 75\({}^{\circ}\) and 80\({}^{\circ}\). However, when geomagnetic activity increases, it is possible to observe a subtle shift in the spatial distribution of intermittency values. Indeed, high values tend to shift towards lower latitudes. while also extending to high latitudes during nighttime. Figure 7: Northern hemisphere: space distribution of the values of \(\gamma(1)\) (**left side**), \(\gamma(2)\) (**center**), and intermittency (**right side**) corresponding to the presence of PCPs as a function of QD-latitude (\(\lambda_{\text{QD}}\)) and magnetic local time (MLT), for two levels of geomagnetic activity, i.e., quiet (**top**) and disturbed (**bottom**). Circles are drawn at QD-latitudes of 70\({}^{\circ}\), 75\({}^{\circ}\), 80\({}^{\circ}\), and 85\({}^{\circ}\). The analysis presented for the Northern hemisphere has also been repeated for the Southern hemisphere. The corresponding results demonstrate good agreement with those obtained in the Northern Hemisphere, as shown in Figures 8 and 9. In Figure 8, we find again a split between joint probability distributions obtained in the two cases of presence and absence of PCPs, as well as the independence of these distributions from the level of geomagnetic activity. Furthermore, the peak values of the distributions related to the presence and absence of PCPs in the Northern and Southern hemispheres (for both levels of geomagnetic activity and both scaling exponents) are perfectly matching, indicating that the two hemispheres behave, in this regard, in a very similar manner. A slight difference can be observed in the spatial distribution of \(\gamma(1)\), \(\gamma(2)\), and intermittency values, as shown in Figure 9, compared to the findings in the Northern hemisphere. In the Southern hemisphere, the persistent behavior of the first-order scaling exponent occurs within a different MLT range (11:30-15:00) and exhibits slightly higher values than in the Northern hemisphere. Similarly, values of the second-order scaling exponent are slightly higher in the Southern hemisphere, with more localized high values. Moreover, the Southern hemisphere generally shows higher values of intermittency. It is worth specifying here that we are aware that PCPs typically cover space scales from 100 to 1000 km and that the scaling exponents here estimated are capable of accurately describing the physical processes concerning patches with scale sizes up to a maximum of about 400 km. However, we are quite confident in the validity of the obtained results since Figure 3 quite robustly confirms that more than 65% of identified PCPs used in this study have a size--which also includes the edges--smaller than 450 km. To investigate the impact of PCPs on GNSS we conducted an analysis of LoL events recorded by Swarm A during the same 3.5-year interval (from 16 July 2014 to 28 February 2018) used so far.