Datasets of the solar quiet (Sq) and solar disturbed (SD) variations of the geomagnetic field from the mid latitudinal Magnetic Observatory of Coimbra (Portugal) obtained by different methods

The datasets of daily variations is obtained from the geomagnetic field raw observations at the Coimbra Magnetic Observatory (COI, Portugal). The data set was obtained for the 01.01.2007-31.12.2017 time interval and covers almost the entire solar cycle 24. The raw data were processed using two methods to extract daily variability. The first method uses the so-called “geomagnetically quiet days” to calculate S-type variations as daily means resulting in the data sub-set named “IQD Sq and SD”. The second method uses the principal component analysis (PCA) to extract main variability modes of the original data. The first three modes produced by PCA and explaining up to 98% of the variability of the raw data are in the data sub-set named “PCA modes”. Both methods allow to extract regular geomagnetic field variations related to daily variations (S-type variations) in the ionospheric dynamo region and some magnetospheric currents (e.g., field-aligned currents). The COI location in middle latitudes near the mean latitude of the ionospheric Sq current vortex's focus allows studying its seasonal and decadal variability using the S-type regular variations of the geomagnetic field measured near the ground. The S-type variations for the X and Y components of the geomagnetic field obtained at the COI observatory can also be re-scaled and used to analyze geomagnetic field variations obtained at other European geomagnetic observatories at close latitudes. The S-type variations for the Z component of the geomagnetic field obtained at the COI observatory can be compared to similar variations observed at more continental regions to study the so-called “coastal effect” in the geomagnetic field variations.


a b s t r a c t
The datasets of daily variations is obtained from the geomagnetic field raw observations at the Coimbra Magnetic Observatory (COI, Portugal). The data set was obtained for the 01.01.2007-31. 12.2017 time interval and covers almost the entire solar cycle 24. The raw data were processed using two methods to extract daily variability. The first method uses the so-called "geomagnetically quiet days" to calculate S-type variations as daily means resulting in the data sub-set named "IQD Sq and SD". The second method uses the principal component analysis (PCA) to extract main variability modes of the original data. The first three modes produced by PCA and explaining up to 98% of the variability of the raw data are in the data sub-set named "PCA modes". Both methods allow to extract regular geomagnetic field variations related to daily variations (S-type variations) in the ionospheric dynamo region and some magnetospheric currents (e.g., field-aligned currents).
The COI location in middle latitudes near the mean latitude of the ionospheric Sq current vortex's focus allows studying its seasonal and decadal variability using the S-type regular variations of the geomagnetic field measured near the ground. The S-type variations for the X and Y components of the geomagnetic field obtained at the COI observatory can also be re-scaled and used to analyze geomagnetic field variations obtained at other European geomagnetic observatories at close latitudes. The S-type variations for the Z component of the geomagnetic field obtained at the COI observatory can be compared to similar variations observed at more continental regions to study the so-called "coastal effect" in the geomagnetic field variations.
© 2021 The Author(s

Value of the Data
• 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 mid-latitudinal 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.

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 \ ".

Fig. 2.
Examples of the data's organization in monthly folders: top -sub-folders structure in the folder "IQD Sq and SD \ X \ m01 -January"; bottom -sub-folders structure in the folder "PCA modes \ X \ m01 -January".

Fig. 3.
Internal structure of the "COI_ * _Sq.SD.S_m##.dat" files. The amplitude of a corresponding PC for a certain day of a month mode 1, mode 2 or mode 3 Reconstructed mode mode1 or mode2 VF1, VF2 or VF3 Variance fraction associated with a certain mode SCF1, SCF2 or SCF3

Fig. 4.
Examples of the data's organization in monthly data folders: left -sub-folders structure in the folder "PCA modes \ X \ m01 -January \ data files"; right -files in the folder "PCA modes \ X \ m01 -January \ data files \ mode 1".
The "plots \ " folders contain two sub-folders named "mode 1" and "mode 2" that contain figures with corresponding plots of the EOFs (files named as

Geomagnetic field components and their measurements
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 h cadence [2] . Since there Fig. 6. Internal structure of the "COI_ * _PC#_m##.dat" files. 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 1 h 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] .

Methods to obtain regular variations of the geomagnetic field
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 1 h 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 for each of the X, Y and Z components separately using two different approaches described below.

Quiet days Sq and SD
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) Fig. 9. Internal structure of the "COI_ * _meanField_m##.dat" (left) and "COI_ * _meanField _m##_y_all.dat" (right) files. Fig. 10. Examples of the data's organization in monthly plots folders: "PCA modes \ X \ m01 -January \ plots". 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, respec-tively. 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
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 1-column 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 × 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 × 308, 24 × 330 or 24 × 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 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 studied 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. The dataset described in this paper is analyzed in a companion paper [14] .

Ethics Statement
Not applicable.