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 Here we provide a secondary data representing regular (daily) variations of the geomagnetic field measured at the ground level for the mid-latitudinal European region and a station located near the latitude of the focus of the ionospheric Sq current vortex.

 Since these Sq and SD data reflect conditions in the ionosphere and magnetosphere both geomagnetic and ionospheric scientific communities can benefit from these datasets.

 These data can be used to study regular daily variations of the geomagnetic field for the midlatitudinal European region, particularly latitudes near the focus of the ionospheric Sq current vortex.

 Since Sq variation is related to the current ionospheric systems, this data set can be used to study the ionospheric Sq current vortex variability.

 These data can be used directly (especially the X and Y components) in studies of the geomagnetic field disturbances at middle latitudes in the European sector: the Sq variation must be removed from the geomagnetic observations data prior to the analysis of any disturbances.

 Due to the proximity of the Coimbra Magnetic Observatory to the ocean coast, a part of these datasets (Z component of the geomagnetic field) can be used to study the coastal effect on the geomagnetic field variations measured at the ground level.

The dataset consists of two main parts: one of the two subsets is the data on the S-type variations of the geomagnetic field obtained using quiet days (see section “Experimental Design, Materials and Methods/Quiet days Sq and SD” for more details); another subset is the modes of the geomagnetic field variation obtaining with the principal component analysis (see section “Experimental Design, Materials and Methods/Principal component analysis “for more details). These two subsets can be found in the folders “IQD Sq and SD" and “PCA modes", respectively. Each of these folders contains subfolders “X", “Y" and “Z" containing the data for the corresponding components of the geomagnetic field. Each of the components’ sub-folders, in turn, contains 12 sub-sub-folders (e.g. “m01 -January") with data related to each calendar months. This structure is shown in Fig. 1.

Organization of the data in folders: left -folders structure in the folder “IQD Sq and SD"; right -folders structure in the folder “PCA modes".

In the case of the “IQD Sq and SD” subset (Fig. 2, top), the “data files" folders have no sub-folders and contain data files named like “COI__Sq.SD.S_m##.dat” where “” is for “X”, “Y” or “Z” and “m##” is for a month (please also see Table 1 for a list of nomination and abbreviations used to name the files). These data files contain Sq, SD and S variations for a certain month (“m##”) and different years (y.20##)

or for all years “y.all” (see Fig. 3). S-type variations are in nT and calculated as described in section “Experimental Design, Materials and Methods/Quiet days Sq and SD”. In the case of the “PCA modes” subset (Fig. 2, bottom) each of the “data files" folders contain three sub-folders “mode 1", “mode 2" and “mode 3". Each of the “mode” sub-folders have data files related to a respective PCA mode, see Fig. 4. These files are names as follow: “COI__EOF#m##.dat” (EOF series for individual years) and “COI_EOF#y_all_m##.dat” (EOF1, EOF2 or EOF3 series for all analyzed years); “COI_PC#m##.dat” (PC1, PC2 or PC3 series for individual years and for the all 11 years together); “COI_mode#m##.dat” and “COI_mode#_m##y_all.dat” (reconstructed mode 1 or mode 2 for individual years and all analyzed years, respectively), “COI_VF#m##.dat” (variance fraction related to this mode for individual years and for the all 11 years together) where “*” is for “X”, “Y” or “Z”, “m##” is for a month, and “VF#” is for a variance fraction for a mode# (please also see Table 1). Please note that reconstructed modes are calculated only for the 1 st and 2 nd modes. All series are either in nT (EOF), in arbitrary units (PC, mode) or non-dimensional (VF) and calculated as described in the section “Experimental Design, Materials and Methods/Principal component analysis” for more details. The internal structure of the “PC.dat”, “EOF.dat”, “mode.dat” and “VF.dat” files are shown in Figs. 5678. Also, the “data files" folders contain two files with daily mean values of a selected component for a particular month: “COImeanField_m##.dat” with data for individual years and “COI_meanField_m##_y_all.dat” with data for all analyzed month. Their internal structure is shown in Fig. 9. For all of time series in this dataset, the time variable is either hours (PCs, S-type series, reconstructed modes) or days (EOFs, daily mean Field series). In all data files, the time variables are integer values. Conventionally, the hourly series of the geomagnetic parameters are centred not to the beginning of an hour but to its middle. Therefore, for the time plot of the series with one-hour time resolution, the correspondence between the integer hour and hour in time format (UTC, HH:MM) shown in Table 2 can be used.

Geomagnetic measurements at Coimbra Magnetic Observatory in Portugal (IAGA code COI) started in 1866 [1,2]. In 2006 a new set of the absolute instruments was installed, providing good quality measurements of geomagnetic field components with 1-hour cadence [2]. Since there were no changes in the instruments or station location from 2006 to the present, the dataset obtained during this time interval can be considered homogeneous [2]. The detailed description of the COI instruments and metadata for the geomagnetic field components’ series can be found in [1,2]. The COI 1h geomagnetic data are regularly submitted to the World Data Centre for Geomagnetism and are available at its Geomagnetism Data Portal [3]. This dataset was used as raw data to obtain datasets for the regular geomagnetic field variations and main modes of the geomagnetic field presented in this paper. The geomagnetic field vector can be measured using a combination of three magnetic elements or components. These components are the total field (F) measured along the geomagnetic field direction at a particular point, horizontal component (H) measured along the magnetic meridian (positive in the direction of the N magnetic pole), declination (D), which is the angle between the magnetic and geographic meridians (positive eastward of true North), inclination (I) which is the angle between the horizontal plane and the F vector (positive downward), vertical component (Z, positive downward), and the north (X) and east (Y) components positive in the direction of the true (geographic) north and East, respectively.

For the relative instruments (i.e. variographs or variometers), the most widely used combinations are HDZ (cylindrical components) and XYZ (Cartesian). For the absolute, the combinations HDZ, HDI and DIF (spherical) are the most often used. Currently, DIF (absolute) and HDZ (relative) combinations are used at COI [2].

The daily or S-variations of the geomagnetic field are divided into two main classes: the “daily quiet” variation or Sq and the “daily disturbed” variation or SD (the name comes from the similarity of the form between the typical Dst-type and SD-type variations [4]). The datasets described in this paper present the series of S-type variations, Sq and SD, obtained from the 1h raw geomagnetic series for the X, Y and Z components of the geomagnetic field measured at COI during 11 years, from January 1, 2007, to December 31, 2017. The data are in nT. The time is in UTC, but the local time LT = GMT = UTC due to the COI location. The COI data have several gaps that were linearly interpolated in case of PCA. The S-type variations were extracted from the raw data using two different approaches described below for each of the X, Y and Z components separately.

The standard approach to calculate the Sq and SD variations is to use the so-called “geomagnetically quiet days” to select days of a month with the lowest geomagnetic activity level. In most cases, these “quiet days” are defined using the geomagnetic K-indices [5]. When local (obtained at a certain magnetic observatory) K-indices are used for the classification of a day, the resulting “quiet days” are the “local quiet days”. When the planetary K-index (Kp) is used for the classification, the resulting “quiet days” are the “international quiet days” or IQD. In this work, we used IQDs routinely provided by the GFZ German Research Centre for Geosciences at the Helmholtz Centre in Potsdam, Germany [5].

Using the standard procedure, the Sq variation for a specific month is defined as the mean of daily variations of the month’s five quietest days. In turn, the SD variation is calculated as a difference between the mean daily variations obtained using all days of a month (or S variation) and the corresponding Sq. Before the averaging, a baseline was removed from the raw daily series. There are two main ways to define the daily baseline for the geomagnetic field variations: the daily mean level and the night level (since under normal conditions, i.e. with no disturbances, the night is the time period with the lowest influence of the ionospheric currents on the ground measured geomagnetic field values). In this work, we used a baseline defined as a mean calculated for the night hours using the measurements made at 00:30 UTC, 01:30 UTC, 02:03 UTC, 03:30 UTC and 23:30 UTC of each day. Thus, the Sq variation values for the night hours are close to zero, and there are no significant differences between the night values of Sq at the beginning and the end of a day.

Each month was treated separately to take care of the seasonal variability of Sq variation. Thus, for each month of a year, we have one series of Sq and one series of SD variations, each consisting of 24 hourly values, overall 12*11 = 132 series for the Sq and SD variations, respectively. Also, we calculated the average Sq and SD variations for each month using all years of observation: e.g., using all January months from 2007 to 2017, etc., which additionally gives 12 series for the Sq and SD variations, respectively.

Principal component analysis (PCA) is a method allowing to extract main modes of variability of a series without any a priory assumption about the character of those variations (contrary to the widely used Fourier and wavelet analyses). An input data set is used to construct a covariance matrix and calculate corresponding eigenvalues and eigenvectors. The eigenvectors (empirical orthogonal functions, EOF) are used to calculate the principal components (PC). The combination of a PC and the corresponding EOF is called a “mode”. Variations related to a certain mode can be reconstructed as a multiplication of a 1column PC vector and a corresponding 1-row EOF vector. The eigenvalues allow estimation of the explained variances of the extracted modes. PCs are orthogonal and conventionally non-dimensional. The full descriptions of the method can be found in (e.g.) [6,7,8].

Recently, PCA was used to extract modes of the geomagnetic field’s day-to-day variability, which were shown to be related to the S-type variations [9,10,11,12,13]. Here we applied a similar approach to extract modes of the geomagnetic field variations related to the regular variations on the daily time scale.

The PCA input matrices were constructed as follows: 24 rows for 24 hourly values per day and 28 to 31 columns (1 column for a day) depending on a month. All months were treated separately. All February matrices have a size 24 x 28. Individual input matrices (or data sets) were made for each of 12 months and each of 11 years (132 matrices). In addition, 12 matrices were constructed using the data for an individual month but with all years available (matrices with sizes 24 x 308, 24 x 330 or 24 x 341 depending on a month). Using this configuration of the input matrices, the principal components (PCs) correspond to daily variations of a different type that can be matched up with S-type variations calculated using the standard approach. The corresponding EOFs provide the amplitudes of a PC for each of the analyzed days. Also, PCA allows estimation of the “significance” of each of the extracted modes using their eigenvalues, a so-called variance fraction (VF) or squared covariance fraction (SCF) when the singular value decomposition method (SVD) is used to perform PCA, as in our cases. VF can be between 0 and 1 and when multiplied by 100% it shows the per cent of the total variability of the analyzed series related to a particular mode.

Only the three first PCs were selected to form the dataset presented in this paper. Overall, the first 3 PCA modes together explain from >60% to 98% of the COI X, Y and Z series variability depending on the month, year and the component.