The
geomagnetic field in the Brazilian sector is influenced by the South American
Magnetic Anomaly (SAMA) that causes a decrease in the magnitude of the local
geomagnetic field when compared to other regions in the world. Thus, the
magnetometer network and data set of space weather over Brazil led by Embrace
are important tools for promoting the understanding of geomagnetic fields
over Brazil. In this sense, in this work we used the

The use of the magnetosphere time series is important for understanding the important geophysical phenomenon called the South American Magnetic Anomaly (SAMA) and the impact of the perturbations of the coronal mass ejections (CMEs) (Klausner et al., 2016, and references therein). Predictions from models (Bilitza, 2001) provide good agreement with the experimental results. The increase in the sensitivity of these models indicates the necessity of more detailed studies of the intermittent phenomena present in the geomagnetic system (Bolzan et al., 2005, 2009, 2012).

Some works have been carried out in the geomagnetic system in order to obtain characteristics for forecasting. Papa et al. (2006), studying the geomagnetic time series obtained in Brazil, showed that the power-law regime changes are good indications of the incoming disturbance in the geomagnetic system. Also, Papa and Sosman (2008), using data from magnetometers recorded at Vassouras (VSS) and the Dst index time series, have shown the possibility of envisaging a probabilistic forecasting method. These results have shown the possibility of predicting the incoming geomagnetic disturbance. However, several physical factors depend upon a useful predictability, such as the frozen magnetic field inside the CMEs. Over South America other factors become important, such as the presence of the SAMA where the geomagnetic field is the weakest in the world. Thus, the study of the energy transfer process from the CME to inside the coupled magnetosphere–ionosphere system over Brazil is a rich area of research. Besides, it allows us to understand and prevent technological issues like interruption in satellite communications, power-line transmission blackout, and positioning degradations for those GNSS satellite-based positioning systems. One tool for studying such coupling is the wavelet-coherence phase difference.

Locations of the magnetometer stations in South America (source: adapted from Padilha et al., 2017).

Recently, a new magnetometer network in Brazil and Latin America was created,
led by Embrace from the National Institute for Space Research (INPE) along
with the Universidade do Vale do Paraíba (UNIVAP), with several
participants from Latin America. The network covers a range of approximately
50

We have used the

Plots of the Dst, CXP, EUS, RGA, and SLZ time series.

Classical cross-correlation obtained for CXP-EUS, CXP-SLZ, and CXP-RGA.

The same as Fig. 4 but for CXP and SLZ, Brazil.

The same as Fig. 4 but for SLZ and EUS.

The classical cross-correlation was used in order to obtain the time lags
where the time series presented high and/or low correlations. This
mathematical tool is useful for giving us the first insight into both time
series where the 0 value indicates no correlation between time series, the 1
value indicates a perfect correlation, and the

As mentioned before, this classical formalism of the cross-correlation is an important tool for giving us information about the time-lag correlation between two time series. However, this tool is not able to give information about the periodicities where two time series are correlated or not; i.e., it is not possible to infer temporal scales where the correlations are strong or weak. Thus, we used the wavelet cross-correlation, which is a good mathematical tool able to give the information of the correlations by scale. In the next section we present a brief introduction to this subject.

The time series obtained from any natural system are non-stationary; i.e., the statistical moments from superior orders are not constant. Thus, the use of traditional mathematical tools such as fast Fourier transform (FFT) are not appropriate for non-stationary time series. This problem was resolved in the 1980s through the introduction of appropriate mathematical functions able to give the energy temporal variability for each frequency present in the time series. Thus, we present a brief introduction to this robust mathematical tool used in this work.

We used the Morlet wavelet transform to obtain the temporal variability of
the main periodicities and, also, the phase coherence. The Morlet function is
given by

In order to obtain the phase coherence from wavelet transform, we used the
coherence phase suggested by Liu (1994), mentioned by Torrence and Compo
(1998):

The same as Fig. 4 but for CXP and RGA.

The same as Fig. 7 but for January 2016.

The classical cross-correlation is used as a first statistical analysis in
order to observe the main temporal scales where two time series are
correlated, anti-correlated, or
non-correlated. Figure 3 shows the results between the following time series:
CXP-EUS, CXP-SLZ, CXP-RGA, where it is possible to see a good correlation
between CXP-EUS and CXP-SLZ at initial time lags with values near to 1 and
other maxima every 1440

Results from the wavelet-coherence phase difference for CXP–EUS and CXP–SLZ have shown that these time series are in phase for any periodicity scales, according to arrows pointing right. This fact corroborates the statement that these three stations are set under the same eastward ionospheric current influence, leading to the good correlation and the same phase coherence as observed in Figs. 3, 4, 5, and 6. We observe low cross-correlation on a 1-day scale even if both time series present the same periodicity. Another interesting point is due to the low cross-correlation in 8-day periodicity between time series from EUS and CXP 5 days (approximately) before the incoming geomagnetic disturbance. The same behavior was also observed between time series from SLZ and CXP, also 5 days before the incoming geomagnetic disturbance and for 8-day periodicity.

In order to analyze the behavior of the two stations close to the equatorial electrojet (EEJ) such as EUS and SLZ, we performed the coherence phase difference for both these stations. Figure 4 shows the results where it is interesting to note that both time series are in phase during all the time and all periodicities, except for semi and diurnal variations. We observe a low cross-correlation between scales 8 to 16 days after the geomagnetic storm and continue for 5 days after this event.

Afterwards, we performed a comparison between CXP and RGA, which are two
stations located really far from each other. Figure 7 shows distinct behavior
when compared to the other cases already analyzed. We note that both time series present a difference phase of
180

It is important to note that the periods found in this work are according to
the Nyquist sampling theorem which states that the sampling frequency should
be at least twice the highest frequency contained in the signal. Thus, the
sample size of our time series (31 days) does not introduce artifacts due to
the processing wavelet software in scales

In summary, the latitudinal extension magnetometer network over South America
led by Embrace allows us to study several physical phenomena such as the
ionospheric current distribution over this region where the SAMA is located.
The classical cross-correlation and cross-wavelet performed between some
chosen stations have shown the following results.

Magnetometers located inside the low-latitude region are very well correlated and are in the same coherence phase.

Magnetometers located in regions where the ionospheric currents are in opposite
directions such as Cachoeira
Paulista and Rio Grande have shown a good correlation but 180

It was very interesting to observe that the presence of strong oscillations, such as a geomagnetic disturbance, put all magnetometer stations in the same phase due to this physical phenomenon.

Another important highlight of this work is the possibility of characterizing the clockwise ionospheric currents in the Southern Hemisphere. Furthermore, it will be possible to study the effect of the geomagnetic substorm effects on these currents in future works. This fact was observed in two distinct geomagnetic storms.

All data used to produce the results of this paper were obtained from EMBRACE/INPE through
the
web site

MJAB designed and analyzed the work, and wrote the paper. CMD also analyzed the work and wrote the paper. AT helped with analysis also.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Space weather
connections to near-Earth space and the atmosphere”. It is a result of the
6

Maurício J. A. Bolzan was supported by CNPq agency contract number 302330/2015-1 and FAPEG agency contract number 2012.1026.7000905. Clezio M. Denardini thanks CNPq/MCTI (grant 03121/2014-9) and FAPESP (grant 2012/08445-9). Alexandre Tardelli was supported by FAPESP (grant 2015/24791-2). The authors thank Embrace/INPE and ISGS for providing the geomagnetic data and the SSC information, respectively. The authors thank editor Alisson Dal Lago and anonymous referees for help in evaluating this paper. The topical editor, Alisson Dal Lago, thanks two anonymous referees for help in evaluating this paper.