# A Multiscale Approach to Geomagnetic Storm Morphology Analysis Based on DMA Activity Measures
## 4 Conclusions  
The present study displays the new applications of discrete mathematics methods, implying the expert's logic modeling, to physical data analysis. Brief information about the basic concept and development of the methods was provided in the introduction. In the \"Materials and Methods\" section, the methodology was formulated for studying a data record using the analysis of fulfillment of a local property for it at various scales. Two properties of a record were selected as the basic ones: energy (4) (local dispersion \(\equiv\) local deviation of a record from its local mean value) and length (5) (describing local jaggedness of a record). The data related to geomagnetic storms (ground-based observatory geomagnetic measurements, interplanetary magnetic field and solar wind data) were selected as records and analyzed using this approach (\"Results and Discussion\" section). In theoretical terms, the authors see a further continuation of the research in addition to the existing analysis of the regression derivatives recently obtained in the framework of DMA [26; 27]. The main conclusion of the study regards the features of the described methods in the magnetic storm morphological analysis using geomagnetic data. The methods based on straightening reveal the decreases and increases in various durations and intensities during the storm. The general features of the storm, such as its onset and the main phase period, are clearly seen on the activity measure plots. Note that the algorithm based on the \"Energy\" straightening clearly detects even low-amplitude disturbances, such as relatively weak SSC signals or geomagnetic variations during the recovery phase of the storm, while the \"Length\" straightening is more effective in the detection of sequences of disturbed fragments of a time series. With the increase in the vision radius \(\Delta\), the long-term signal fragments can be seen better (such as trends corresponding to the geomagnetic  
Figure 10: Histograms of the activity measure levels for “Energy” (**a**) and “Length” (**b**) indicators built for the \(X\) component of geomagnetic observatory data during the storm on 22–29 June 2015. Figure 9: The \(X\) geomagnetic field component data registered during a storm on 26–28 August 2018 (**a**) and the activity measure plots for these data, based on the “Length” indicator (**b**). storm phases), while at small \(\Delta\) the short sporadic disturbances are better revealed. This provides an opportunity to successfully implement this group of methods into geomagnetic storm studies. In all cases, the SSC signals on geomagnetic data plots are denoted by vertically oriented red zones on the activity measure plot, corresponding to all \(p\) domains and indicating an abrupt increase in the geomagnetic field intensity. The beginnings of the main phase of the storm on horizontal geomagnetic component data are obviously represented by vertical blue zones, marking the horizontal magnetic field suppressed state according to the ground-based magnetic observatory data. Modern geoscience and environmental studies imply the application of advanced mathematical techniques focused on complex dataset analysis [28]. This is mainly due to such data features as nonstationarity, sporadic disturbances, large data sets, etc. Our experience in geophysical data studies makes it possible to conclude that the DMA-based approaches to data analysis have also proven their efficiency and robustness. Another feature of the method is the possibility to perform the combined space weather analysis based on it. For example, the developed techniques can be used in weak SSC signal recognition using a combination of space weather data time series (\(B_{z}\) and \(B_{y}\) IMF components and plasma characteristics, such as flux speed and proton density) and ground-based magnetic observatory data. The use of various mutually complementary space weather data will provide a comprehensive study of extreme phenomena in near-Earth space.