There are three main types of geomagnetic field variations on the time scale from hours to several days: regular variations during a calendar or solar day (so-called “daily” or “solar” variations known as S-type variations), regular variations during a lunar month (L-variation) and irregular variations often associated with storms and substorms and called “disturbances” (Dst-variations), see Chapman and Bartels (1940). The S-type variations are divided into two main classes: the “daily (solar) quiet” variation, Sq, which is observed most clearly during the geomagnetically quiet days, and the “daily (solar) disturbed” variation, SD, (Chapman and Bartels, 1940; Yamazaki and Maute, 2017).
The Sq variation of the geomagnetic field results from an electrical current system in the ionospheric E dynamo region. This system consists of two vortices quasi-symmetric to the equator with the anti-clockwise (clockwise) electrical currents in the sunlit Northern (Southern) Hemisphere with foci located in the middle latitudes near 30-40º depending on the longitudinal sector and the hemisphere. Near the equator, they are connected to the equatorial electrojet, and in the high latitudes, they are affected by the current systems of the polar ionosphere. As the day progresses, the position of these vortices on the globe moves westward following the Sun. Thus, for any given location on the planet, the geometry of the system changes along the day returning to a similar condition after one day.
The character of the ground measured Sq variation of the geomagnetic field components X, Y and Z depends on the position of a geomagnetic observatory relative to the vortex. The change of the sign of Sq X takes place around the foci latitudes. The sign of Sq Y and Sq Z changes near the equator (see Chapman and Bartels, 1940; Amory-Mazaudier, 1994 and 2009; Anad et al., 2016; Yamazaki and Maute, 2017). The Sq X and Sq Z variations are symmetric around the local noon, while Sq Y is anti-symmetric. In the real ionosphere, the shape of the current vortex can be far from the ideal circle or oval: the vortex can, e.g., be tilted (resulting in a shift of the daily minimum of Sq X to the afternoon hours, see Amory-Mazaudier, 1994 and 2009; Anad et al., 2016), stretched or compressed. The shape of the vortex affects mostly the Sq X variation, whereas the shapes of the Sq Y and Sq Z variations are almost constant from day to day.
The standard method to obtain Sq from the ground observations of the geomagnetic field consists of the selection of days with the lowest level of geomagnetic field perturbations (so-called "quiet days"), typically, five days per calendar month, and averaging of the daily geomagnetic field variations for a certain component over selected days. These days can be defined using the data of an individual observatory (local quiet days) or using the data from the same set of observatories that are used to calculate the Kp index (international quiet days – IQD), see Chapman and Bartels (1940). Hereafter, the Sq variation obtained using IQD is named "SqIQD”.
Another way to extract regular variations as Sq is to apply a decomposition method to the geomagnetic field data: e.g., the wavelet analysis (Maslova et al., 2010), the empirical mode decomposition (Piersanti et al., 2017) or the principal component analysis, PCA (Xu and Kamide, 2004; Chen et al., 2007; De Michelis et al., 2009, 2010). On the other hand, the shape and position of the vortex can be deduced from the observational data using the spherical harmonic analysis by calculating the equivalent electric field (Takeda, 1982; Haines and Torta, 1994) or it can be reconstructed as equivalent electric current vectors (horizontal component) from the observed horizontal geomagnetic field vector (Stening et al., 2005; Stening, 2008).
First attempts to use PCA (sometimes known as a method of the natural orthogonal component, NOC) to extract regular variations of the geomagnetic field were made in the 1970s-1990s (Golovkov et al., 1978, 1989; Rangarajan and Murty, 1980; Golovkov and Zvereva 1998, 2000) but were not actively supported by the geomagnetic community (Menvielle, 1981). Golovkov et al. (1978, 1989) and Golovkov and Zvereva (1998, 2000) showed that for the H component of the geomagnetic field and for the geomagnetically quiet time intervals, the Sq variation can be associated to the first (or first and third) principal components (PC) and the second PC can be identified as SD variation (Dst-like variation). For the geomagnetically active time intervals the first PC was identified as SD, and the second and third PCs were identified as Sq. Dependence of the order of a PC that can be identified as Sq or SD on the latitude was also shown. Both the existence of the daily variability of the Sq field and the need for studying it was also emphasized in the early works.
Later, Xu and Kamide (2004) and Chen et al. (2007) revived the interest of the geomagnetic community in PCA as a useful tool that allows not only to extract regular variations of the geomagnetic field, as Sq and SD but also to analyze seasonal and geographic variations of the phase and amplitude of the Sq and SD fields and the dependence of their intensity on the level of the solar and geomagnetic activity. Works of Wu et al. (2007), De Michelis et al., (2009, 2010), Bhardwaj et al. (2015, 2016) and others (see also review by Yamazaki and Maute, 2017), generally confirmed the applicability of PCA to the extraction of the regular geomagnetic field variations observed at different latitudes, and for the time intervals of different length and corresponding to different geomagnetic activity levels. However, the results obtained for different regions/time intervals were somewhat different.
In particular, it was found that for the H (X) component for the Asian sector (Xu and Kamide, 2004; Chen et al., 2007; Wu et al., 2007; Bhardwaj et al., 2015, 2016) the Sq variation is filtered to the first PC and the SD variation is filtered to the second PC. On the contrary, for the European sector (De Michelis et al., 2010) PC1 is associated with SD and PC2 is associated with Sq. This difference can be explained both by the different geographic positions of the stations whose data were used for PCA and by the different studied time intervals. Also, for the Y (D) and Z components for the European sector PC1 was identified as Sq and PC2 as SD.
To our knowledge, no systematic study of the applicability of PCA as a tool to extract Sq-type variations was performed yet and no possible explanation for the differences mentioned above was proposed. In this work, we present the results of such an analysis: we test PCA on different components of the geomagnetic field (X, Y and Z), for data obtained in different months and under different levels of solar and geomagnetic activity. We also tested different lengths of the input data sets. We use the geomagnetic field data obtained at a European mid-latitudinal geomagnetic observatory – Coimbra Magnetic Observatory (COI) in Portugal. The peculiarity of COI, and this can be also true for the L’Aquila observatory (De Michelis et al., 2010), is that it is located near the mean latitude of the focus of the Sq ionospheric current vortex. Thus, the shape of the Sq variations for the X component at COI can vary not only due to the intensity of the vortex but also due to the position of its focus: for some days COI is located to the north of the focus, for other days it is located to the south of the focus, and there are days when COI is located very near the focus latitude. These changes of the COI relative position result in different shapes of the Sq X variation. Finally, contrary to all previous studies, we analyzed the data not on the annual or decadal time scale but on the monthly time scale as described in section 2.1 and Morozova et al. (2021a, 2021b).
The paper is organized as follow: Section 1 presents the state of the art and briefly gives an overview of the paper; Section 2 contains the descriptions of the analyzed data sets; Section 3 describes the applied mathematical methods; the results of analyses of the applicability of PCA to extract Sq-type variation from data for different geomagnetic field components, limits of the PCA usage and ways to solve arising ambiguity are presented in Sections 4 (for the Y and Z components) and 5 (for the X component); Section 6 contains main conclusions on the usage of PCA as a tool to extract Sq-type variations from the geomagnetic field measurements.