# Unveiling the Core Patterns of High-Latitude Electron Density Distribution at Swarm Altitude
## 4 Results  
We begin our investigation by applying the MEMD method to the electron density distribution during the equinox period when geomagnetic activity is low. Figure 2 presents the results of the decomposition. We obtained a total of eight modes plus the residue. These are represented on polar maps by plotting their average electron density value using QD latitude and MLT. The top of the map corresponds to noon and the bottom to midnight; the MLT equal to 06:00 (on the right) and 18:00 (on the left) is indicated in order to better visualize the morning and evening sectors, and a \(1^{\circ}\times 1^{\circ}\) binning grid is used. Figure 2: Polar view of the eight modes and the residue obtained from the MEMD of electron density distribution during the equinoctial period, in the Northern Hemisphere, when geomagnetic activity is low. Maps are represented using the QD-magnetic latitude (MLat) and MLT reference system. The concentric circles are plotted in 10\({}^{\circ}\) intervals, with the outermost circle corresponding to 50\({}^{\circ}\). In Figure 3, the left side shows the average period obtained through the latitudinal averaged frequency analysis associated with each mode and right side shows the energy distribution in terms of the normalized variance of each mode with respect to the total variance of the signal. Observing the energy trend of each mode, the first six exhibit extremely low energy levels, with a normalized variance value lower than that of the first mode; as a result, because the EMD acts as a dyadic filter [32] and the first mode is usually associated with the noise content of the signals [33], when the normalized variance is less than that of the first mode it cannot be physically meaningful in the statistical sense. As a result of analyzing the energy contribution of each mode to the original signal, it is clear that the last two modes and the residue contribute significantly to the description of the initial distribution. By examining the time periods associated with each mode, however, three distinct trends emerge, allowing the obtained modes to be classified into three classes. The first class includes the first two modes, the second class includes the four following modes (from the third to the sixth mode), and the third class includes the seventh and eighth modes. We examined any variations with the latitude in the average period value for each of these four modes by conducting a comprehensive analysis of the periodicities of the modes in MLT belonging to the second class. The periodogram for a given magnetic latitude value was computed by taking into account the series of density values corresponding to different MLTs. This entailed analyzing 40 distinct periodograms for each mode obtained from a series of 360 data points, with a resolution of 1\({}^{\circ}\) for both magnetic latitude and MLT. The fundamental frequency value was calculated from each periodogram based on the peak position. The average period was then calculated using the frequency values in MLT, with the period found to be practically constant with the latitude for all four analyzed modes. The average periods obtained for each one of the four modes are (\(41\pm 4\)), (\(81\pm 9\)), (\(130\pm 10\)), and (\(235\pm 25\)) min. These periodicities are in good agreement with the harmonics and subharmonics of the satellite's orbital period (\(\sim\)94 min). In other words, the spatial structure of the electron density distribution associated with these modes closely resembles the satellite traces, implying a possible link to the data acquisition process. However, we note that these modes do not contribute significantly to the overall decomposition, because their energy remains lower than that of the first one. As a result, we combine this second class of modes together and consider a smaller number of modes for further analysis. Figure 4 illustrates the grouped modes that effectively describe the fundamental modes present in the spatial distribution of electron density in the Northern Hemisphere.