Introduction
Geomagnetic storms (GSs) are global magnetic disturbances that result from
the interaction between magnetized plasma propagating from the Sun and
magnetic fields in the near-Earth space environment. They are often
accompanied by strong perturbations of the geomagnetic field that can
generate intense disturbances of the terrestrial environments and affect
experimental devices and communications (i.e., high-frequency communications,
GNSS navigation, and so on) . The forecasting of these events (space weather), their
geoeffectiveness, and the associated GSs are then of primary interest.
GS strength is assessed by the disturbance storm time (Dst) index that
reveals the decrease in the horizontal geomagnetic field component and gives
a global measure of midlatitude magnetic disturbance. The Dst index has long
been used as an indirect measure of the ring current that encircles the Earth
at altitudes ranging from about 3 to 7 Earth radii (RE) and increases its
intensity during GSs. Indeed, Dst values are proportional to the total
kinetic energy of the particles that form the ring current according to the
Dessler–Parker–Sckopke relationship . Nowadays, it
is known that this index measures the effects of many terrestrial and
magnetospheric current systems which are enhanced during geomagnetic
disturbed periods. Dst is an hourly index (measured in nanotesla) obtained by
finding the instantaneous average of the deviations from a quiet day in the
horizontal component of the magnetic field at four observatories that are
sufficiently distant from the auroral and equatorial electrojets and
distributed in longitude as evenly as possible . It has
been recently suggested that local geomagnetic indices could represent very
useful tools, complementary to global indices, in defining deviations from
the usual geomagnetic activity. In fact, local geomagnetic disturbances seem
to play a key role in assessing the potential risk factor of extreme events
in specific regions . So, it can be useful to investigate the
time evolution of a baseline of the geomagnetic field defined as the
local geomagnetic activity observed on large scales.
From a theoretical point of view, the separation between a time-dependent
background magnetic field (baseline) and its fluctuations does make sense
under the implicit assumption of a clear timescale separation between the
fluctuations and the background. The validity of this assumption is
questionable due to the nonlinear response of the geomagnetic system to the
complex external forcing provided by the solar wind (SW). It is clear that
neither the scale separation nor the stationarity of the signal are assured
when the geomagnetic field is observed. When a timescale separation is not
present, it is difficult to identify an average magnetic field.
In the present paper, using the empirical mode decomposition (EMD), we
suggest a method to separate the average magnetic field by its variations,
identifying the physical meaning of each contribution.
Empirical mode decomposition
The EMD has been developed to process nonstationary data
and successfully applied in many different contexts , including geophysical
systems . It is an adaptive and a posteriori decomposition method in which
the basis functions are derived from the data. This technique decomposes a
set of observed data X(t) into a finite number m of intrinsic oscillatory
functions Cj(t), named intrinsic mode functions (MFs), so that
X(t)=∑j=1mCj(t)+r(t),
where r(t) is the final residue of the decomposition from which no more MFs
can be extracted. Each mode Cj(t) can be derived by the so-called
sifting process, which represents the core of the decomposition
procedure. This procedure can be summarized by the following steps:
identification of the local extrema of the time series X(t)
interpolation of local minima (maxima) by using a spline function to obtain the local envelope emin(t) emax(t)
computation of the average envelope m1(t)=meanemin(t),emax(t)
evaluation of the detail h1(t)=X(t)-m1(t).
The previous steps are iterated k times until the obtained detail h1k=h1(k-1)-m1k can be identified as an intrinsic MF that must satisfy the
following two properties:
The number of extrema and the number of zero-crossings must either be equal or differ at most by
1.
At any point (locally), the mean value of the envelope defined by the local maxima and by the local minima is 0.
In addition, the number of sifting steps to produce an MF is defined by the
stopping criterion proposed by , similar to the Cauchy
convergence test, which defines a sum of the difference (standard deviation),
σk, between two sifting steps as
σk=∑t=0T|hk-1(t)-hk(t)|2hk-12(t).
The sifting process stops when σk is smaller than a given value,
typically in the range 0.2–0.3 (in the present work we used 0.3)
An MF is an oscillating function modulated in both amplitude and frequency,
as Cj(t)=Aj(t)cosΦj(t), where Φj(t) is the instantaneous
phase of the jth mode, related to the instantaneous frequency ωj(t)=dΦj(t)/dt . Since other decomposition techniques do
not consider a time-dependent frequency (e.g., Fourier analysis), this concept
of instantaneous frequency is the main point of the EMD technique, allowing
a decomposition of nonstationary time series without any assumption on the
basis of the decomposition. It can be derived by using the so-called
Hilbert–Huang transform , through which for each Cj(t)
we can derive the corresponding Hilbert transform C̃j(t) as
C̃j(t)=1πP∫-∞+∞Cj(t′)t-t′dt′,
where P
denotes Cauchy's principal value. The function defined
by Eq. () exists for all Lp space functions,
allowing us to define an analytical signal Z(t) from the conjugate pair
Cj(t),C̃j(t), such that
Zj(t)=Cj(t)+iC̃j(t)=Aj(t)eiΦj(t),
in which Aj(t) and Φj(t) are the instantaneous amplitude and phase
of the jth mode, respectively, derived as
Aj(t)=Cj(t)2+C̃j(t)2,Φj(t)=arctanC̃j(t)Cj(t).
In this way, the instantaneous frequency can be derived by the instantaneous
phase as ωj(t)=dΦj(t)/dt . Consequently, a
typical average period Tj can be estimated for all the MFs as Tj=2π/<ωj(t)>t (<>t representing the time average). The decomposition
is clearly local and complete, which means that the MFs can reconstruct the
original signal (see Eq. ), while the orthogonality property is
not theoretically ensured. However, it can be verified by evaluating the
orthogonal index (OI) as proposed in by checking the inner
product of each MF with respect to the others. In this case, the EMD can be
used as a filter through partial sums of a subset of modes
. Finally, the statistical significance of each MF with
respect to white noise can be verified through the test developed by
, which allows a comparison of the mean square amplitude of the
MFs with the theoretical spread function of white noise computed for
different confidence levels.
In addition, EMD is capable of overcoming some limitations of other
decomposition analysis techniques. EMD does not require any a priori assumption on the functional form of the basis of the decomposition (as for
Fourier or wavelet analysis). In this way, several misleading results can be
avoided, and this allows us to carry out local nonstationary and nonlinearity
features from each time series, which are usually far from the decomposition
properties obtained with fixed eigenfunctions. However, as for other analysis
techniques we need to outline outstanding open problems with EMD, including
end effects of the EMD or stopping criteria selection. More specifically,
boundary effects occur because there is no point before the first data point
and after the last data point. In most cases, these boundary points are not
the extreme value of the signal; therefore, they can cause the divergence of
the extreme envelope, causing significant errors. These errors can produce
misleading MF waveforms at its endpoints, which can propagate into the
decomposition through the sifting process. To avoid problems due to boundary
effects, various methods have been proposed, including mirror- or data-extending methods . In our case, we used the data-extending method by adding a constant extension to the boundary points of the
maxima and minima vectors, allowing to get a better spline fit at the ends.
Standardized mean test (SMT)
In order to study the physical meaning of the EMD modes and connect them to
the timescales involved in the variations of magnetospheric and geomagnetic
field, we used the method proposed by . They suggest that, if
a clear timescale separation exists in a data set, this can be divided into
two different contributions:
X(t)=δX(t)+X0(t),
where X0(t) is the so-called baseline field and δX(t) are variations around X0(t).
The basic idea is that δX(t)
has a close to zero standardized mean (SM) (defined as the mean divided by the standard deviation)
represents the fluctuating/oscillatory high-frequency contribution to the time series.
Using the orthogonality and completeness properties of EMD, we define δX(t) as the reconstruction of a subset S1 of k<m empirical modes, which satisfies the previous two properties:
δX(t)=∑j=1kCj(t).
The k value represents the last mode index for which the reconstruction
given by Eq. () has an SM close to 0. To investigate if the
k value could be dependent on the length of the considered time series, we
applied the following procedure. First of all, for each j, we evaluate the
SM on the whole time range considered. Then, we consider a set of Ns=1000
time windows, with different lengths, moving within the whole time range; we
evaluate the standardized mean for each partial reconstruction, obtaining a
set of Ns values, and, consequently, we calculate the corresponding
standard deviations at each j. In this way, we associate an error with each
standardized mean evaluated over the whole time range, corresponding to 3 times the standard deviation for the considered partial reconstruction. For
all the considered cases, the k value remains unchanged within the error
band, indicating that the SMT is not significantly dependent on the choice of
the time window length. This implies that the first k modes are able to
reproduce the fluctuating contribution to the time series, while the
remaining m–k modes represent the larger timescale variations. This could
be very useful for research into the framework of turbulent-like processes
where a high-frequency component needs to be properly filtered out. Moreover,
as shown in the next sections, the kth mode characteristic timescale is
also not dependent on the geomagnetic activity of the considered period,
indicating that this separation between high- and low-frequency processes
exists in both quiet and disturbed periods.
SSQ, 10–12 October 2003: midlatitude ground observations (AQU:
λg=42.38∘ N and ϕg=13.32∘ E) for the H (left panel) and
D (right panel) components. The time resolution is 1 min.
Magnetospheric and ground observations: EMD approach
In the present paper we show the results obtained when this approach is
applied to a super solar quiet (SSQ) period and to a storm time (ST) event.
In order to distinguish between SSQ and ST, we use the K-index. It quantifies
disturbances in the horizontal (H) and eastward (D) components of the Earth's
magnetic field with an integer in the range of 0–9 with 1 being quiet and 5 or
more indicating a geomagnetic storm. It is derived from the maximum
fluctuations of H or D components observed on a magnetometer during a
3 h interval. According to this scheme, we define an SSQ period when
K < 1, while an ST event is identified when K > 5. We consider, as ST event,
the Halloween super storm that occurred between 28 October and 1 November 2003.
For our analysis, we used 1 min data from the horizontal component of the
geomagnetic field (H) and the eastward component (D) measured at L'Aquila
(AQU: λg= 42.38 ∘ N and ϕg= 13.32∘ E; λg and
ϕg are the geographic latitude and longitude, respectively) permanent
geomagnetic observatory to study the time variations of the geomagnetic
field.
Moreover, we used 1 min geosynchronous satellite observations at
6.6 RE from Geostationary Operational
Environmental Satellites (GOES) (GOES10: LT = UT-9; GOES12: LT = UT-5; both in the Geocentric Solar Ecliptic –
GSE – coordinate system) for the magnetospheric field
(http://cdaweb.gsfc.nasa.gov/). More specifically, we used the BZ,GSE
magnetospheric component and the H ground component. At high and middle
latitudes, their behavior should be comparable because of the 90∘
rotation of the polarization axes through the ionosphere .
Super solar quiet period: 10–12 October 2003
Figure shows the observations of the geomagnetic field at AQU for
the horizontal component of the vector along the local magnetic meridian (H, left
panel) and the eastward component (D, right panel) during the super solar quiet period 10–12 October 2003. During the entire period of interest, the
K-index ranges between 0 and 1 (K being the 3 h long
quasi-logarithmic local index of geomagnetic activity for this observatory:
http://roma2.rm.ingv.it/en/). Both H and D components show the typical
midlatitude solar quiet (Sq) daily variation . Sq is due to two different sources: the current
systems flowing in the so-called ionospheric dynamo region and the induced
telluric currents in the Earth's upper mantle. These currents, in turn,
generate additional magnetic field variations that are almost in phase with
the primary variations. The dynamo currents flowing in the E region of the
Earth's ionosphere are driven by the global thermotidal wind systems and
are dependent upon the local tensor conductivity and the main geomagnetic field
vector. The morphology of the atmospheric tides gives the ionospheric
currents a configuration characterized by two pairs of vortices: two great
vortices in the sunlit hemisphere and the other two in the dark one. The two
vortices in the sunlit hemisphere are the most intense because the
ionospheric conductivity is larger. The pattern of the two current vortices in
the sunlit hemisphere consists of currents circulating about foci at
+30 and -30∘ magnetic latitude. Viewed from the Sun,
circulation is counterclockwise in the Northern Hemisphere and clockwise in
the Southern Hemisphere .
Applying the EMD procedure we found a set of 13 modes and 11 modes for
the H and D component, respectively (see Fig. ), while
characteristic timescales are reported in Table .
SSQ, 10–12 October 2003: empirical modes extracted via EMD from AQU
H component (left panels) and AQU D component (right panels). The modes and
the residue are expressed in nanotesla, and the time resolution is 1 min.
Mean periods of intrinsic modes during the super solar quiet
period (the dash corresponds to the period of the residue r(t) which cannot be
evaluated). G10 and G12 refer to GOES10 and GOES12 satellites, respectively.
Super solar quiet periods (h)
TH
TD
TG10
TG12
0.05 ± 0.01
0.05 ± 0.01
0.05 ± 0.02
0.05 ± 0.01
0.10 ± 0.02
0.10 ± 0.02
0.16 ± 0.03
0.17 ± 0.02
0.16 ± 0.02
0.19 ± 0.02
0.28 ± 0.05
0.29 ± 0.04
δH(D)/δBz
0.28 ± 0.04
0.40 ± 0.03
0.46 ± 0.05
0.51 ± 0.06
0.51 ± 0.04
0.73 ± 0.06
2.20 ± 0.4
1.90 ± 0.4
0.92 ± 0.08
1.4 ± 0.2
3.80 ± 0.5
3.0 ± 0.5
1.7 ± 0.2
3.3 ± 0.3
3.7 ± 0.6
3.0 ± 0.4
6.1 ± 0.6
8.2 ± 0.6
H*(D*)
8.7 ± 0.7
12 ± 1
12 ± 1
24 ± 1
24 ± 1
34 ± 2
31 ± 2
24 ± 1
24 ± 1
H0(D0)/Bz0
–
–
30 ± 2
32 ± 3
34 ± 3
–
SSQ, 10–12 October 2003: SMT applied to the EMD reconstruction of
the ground observations for the H (left panel) and D (right panel)
components. The x axis is order in terms of the last mode involved in the
partial sums (see Eq. ).
SSQ, 10–12 October 2003: EMD reconstruction for the H (left panels)
and D (right panels) components at midlatitude ground station (AQU:
λg=42.38∘ N and ϕg=13.32∘ E). The time resolution is 1 min.
Figure shows the SMT applied to the EMD of the H
(left panel) and the D (right panel) components. We found three different sets of
modes: the modes j= 1–8 for H and j= 1–7 for D are identified as
short-timescale reconstructions whose timescale is ≤ 4 h and
for which the SM of the reconstructions is close to 0; the modes j= 9–12
for H and j= 8–10 for D are identified as intermediate-timescale
reconstructions with a timescale in the range of 6–24 h. The mode j= 13
and the residue for H and the mode j=10 and residue for D are identified as
large-timescale reconstructions for which the SM of the
reconstructions departs significantly from 0. For the intermediate
timescales, a significant non-null value is observed when j=9 for H (j=8
for D), while when j=12 (j=10 for D) an SM ∼ 0 is again obtained. The
physical meaning of the intermediate modes will be discussed below. Moreover,
we note the existence of short-timescale modes which are characterized by a
low mean amplitude (j= 1–8 for H, j= 1–7 for D), while modes with
timescales greater than ∼ 4 h are characterized by higher mean
amplitudes. In particular, j=12 for H and j=10 for D show the
characteristic diurnal contribution in the geomagnetic components. According
to the SMT results (Fig. ), AQU data are split into three different
contributions:
H(t)=δH(t)+H*(t)+H0(t),D(t)=δD(t)+D*(t)+D0(t).
Figure shows the EMD reconstructions for the H (left panels) and
D (right panels) components. δH(t) and δD(t) (Fig. , upper panels) represent short-timescale reconstructions; H*(t)
and D*(t) (Fig. , middle panels) are intermediate-timescale
reconstructions; H0(t) and D0(t) (Fig. , lower panels)
represent the large-timescale reconstructions.
SSQ, 10–12 October 2003: magnetospheric observations at
geosynchronous orbit for GOES10 (LT = UT-9; left panel) and GOES12 (LT = UT-5;
right panel) spacecraft. The time resolution is 1 min.
In order to detect if the same timescale separation is found in the magnetosphere, we analyzed magnetospheric observations at a geosynchronous
orbit by applying the same techniques. Figure shows the time
series obtained from GOES10 (left panel) and GOES12 (right panel)
observations with a corresponding color scale related to the magnetic local
time (MLT) of the spacecraft. Both GOES spacecraft show the characteristic
orbital variation (see color scale related to the MLT).
SSQ, 10–12 October 2003: empirical modes extracted via EMD from
GOES10 (left panels) and GOES12 (right panels) Bz components. The modes and
the residues are expressed in nanotesla, with a time resolution of 1 min.
SSQ, 10–12 October 2003: SMT applied to the EMD reconstruction of
the magnetospheric observations for GOES10 (left panel) and GOES12 (right
panel) Bz components. The x axis is order in terms of the last mode involved in the partial sums (see Eq. ).
SSQ, 10–12 October 2003: EMD reconstruction for GOES10 (left
panels) and GOES12 (right panels) geosynchronous observations. The time
resolution is 1 min.
Halloween super storm, 28 October–1 November 2003: midlatitude
ground observations (AQU: λg=42.38∘ N and ϕg=13.32∘ E)
for the H (left panel) and D (right panel) components. The time resolution is
1 min.
Halloween super storm, 28 October–1 November 2003: empirical modes
extracted via EMD from H (left panels) and D (right panels) components
recorded at AQU observatory. The modes and the residue are expressed in nanotesla,
and the time resolution is 1 min.
Applying the EMD procedure, we obtained a set of nine modes for both GOES
spacecraft, as shown in Fig. . We note that the modes j=7 for
GOES10 and j=8 for GOES12 reproduce the diurnal orbital variation observed
by the spacecraft. Moreover, the SMT results (see Fig. ) reveal
the existence of two timescales of variability, characterized by different
mean amplitudes. For these reasons, both GOES10 (left panels) and GOES12
(right panels) are split into only two different sets of modes: the
short-timescale reconstructions, characterized by a nearly zero mean
contribution to the signal, and the large-timescale reconstructions,
characterized by a non-zero mean contribution to the signal. So, according to
the SMT results, GOES10 and GOES12 EMD results are split into two different
contributions (see Fig. ):
Bz(t)=δBz(t)+Bz0(t),
where δBz(t) represents short-timescale reconstructions (GOES10:
j= 1–6 modes; GOES12: j= 1–7 modes) and Bz0(t) represents the
large-timescale reconstructions (GOES10: j= 7–9 modes and r(t); GOES12:
j= 8–9 modes and r(t)).
Halloween super storm, 28 October–1 November 2003: SMT applied to
the EMD reconstruction of the ground observations for the H (left panel) and
D (right panel) components. The x axis is order in terms of the last mode
involved in the partial sums (see Eq. ).
Halloween super storm, 28 October–1 November 2003: EMD
reconstruction for the H (left panels) and D (right panels) components at
midlatitude ground station (AQU: λg=42.38∘ N and
ϕg=13.32∘ E). The time resolution is 1 min.
Storm time event: 28 October–1 November 2003
On the basis of the result described above, we applied the same approach to
the Halloween super storm (28 October–1 November 2003).
Figure shows the observations at AQU geomagnetic observatory for
the north–south (H, left panel) and the east–west (D, right panel) components
during this time interval. The solar activity at the end of October 2003
produced intense magnetospheric disturbances during three successive deep
reductions in the Dst index (not shown) due to two consecutive coronal mass
ejections (CMEs) which impacted the Earth's magnetosphere . The Halloween super storm, 29–31 October
2003, has received considerable interest and analysis from both ground and
space instrumentation, as it offers a great opportunity of understanding the
response of the magnetosphere–ionosphere system to strong and continuous
driving. At midlatitudes, the H component shows a first storm peak (∼-500 nT at 06:58 UT on 29 October) with an associated short recovery
phase, a second storm peak (∼-250 nT at 20:13 UT on 29 October)
with an irregular recovery phase, and a third peak (∼-280 nT at 22:53 UT
on 30 October) associated with a longer recovery phase.
Halloween super storm, 28 October–1 November 2003: magnetospheric
observations of the Bz component in geosynchronous orbit for GOES10 (LT = UT-9;
left panel) and GOES12 (LT = UT-5; right panel) spacecraft. The time
resolution is 1 min.
Halloween super storm, 28 October–1 November 2003: empirical modes
extracted via EMD from GOES10 (left panels) and GOES12 (right panels) Bz
components. The modes and the residues are expressed in nanotesla, and the time
resolution is 1 min.
Halloween super storm, 28 October–1 November 2003: SMT applied to
the EMD reconstruction of the magnetospheric observations for GOES10 (left
panel) and GOES12 (right panel) Bz components. The x axis is order in terms of
the last mode involved in the partial sums (see Eq. ).
Halloween super storm, 28 October–1 November 2003: EMD
reconstruction for GOES10 (left panels) and GOES12 (right panels)
geosynchronous observations. The time resolution is 1 min.
By applying the EMD procedure we found a set of 15 modes and 14 modes for
the H and D components, respectively (see Fig. ). We note an
enhancement of the amplitude of short-timescale modes due to the arrival of
the CMEs. Moreover, the characteristic diurnal contribution related to the SQ
is also present (j=14 for H; j=12 for D). Figure shows the
SMT applied to the EMD of the H (left panel) and the D (right
panel) components. Also for this event, we found three different sets of modes
which we reconstructed as shown in Fig. (H (left panels) and D (right panels)
components). According to the SMT results, AQU data are split into
three different contributions: δH(t) and δD(t) (Fig. , upper panels) with timescales ≤4 h, H*(t) and
D*(t) (Fig. , middle panels) with timescales in the range of 6–24 h, and H0(t) and D0(t) (Fig. , lower panels)
with timescales greater than 24 h.
Mean periods of intrinsic modes during the Halloween storm (the
dash corresponds to the period of the residue r(t) which cannot be
evaluated).
Halloween super storm periods (h)
TH
TD
TG10
TG12
0.06 ± 0.01
0.06 ± 0.01
0.06 ± 0.02
0.06 ± 0.01
0.12 ± 0.03
0.12 ± 0.02
0.11 ± 0.03
0.11 ± 0.02
0.23 ± 0.04
0.22 ± 0.02
0.19 ± 0.03
0.29 ± 0.03
δH(D)/δBz
0.41 ± 0.07
0.45 ± 0.03
0.32 ± 0.05
0.49 ± 0.04
0.75 ± 0.08
0.71 ± 0.06
0.57 ± 0.05
0.87 ± 0.05
1.3 ± 0.2
1.1 ± 0.2
0.96 ± 0.08
1.3 ± 0.2
2.4 ± 0.2
1.8 ± 0.3
1.4 ± 0.2
2.2 ± 0.3
3.4 ± 0.5
2.8 ± 0.5
2.3 ± 0.3
2.9 ± 0.5
3.0 ± 0.4
3.7 ± 0.6
3.9 ± 0.4
5.6 ± 0.6
5.8 ± 0.6
H*(D*)
8.6 ± 0.7
12 ± 1
12 ± 1
16 ± 1
24 ± 1
24 ± 1
30 ± 2
43 ± 4
18 ± 1
20 ± 1
H0(D0)/Bz0
38 ± 3
–
24 ± 1
24 ± 1
48 ± 6
34 ± 3
33 ± 2
–
41 ± 3
38 ± 3
48 ± 4
47 ± 5
–
–
Percentage of each contribution to the total signal (%) during both
SSQ and ST periods.
Percentage of each contribution
to the total signal (%)
Contribution
SSQ
ST
δBz
1
28
Bz0
99
72
δH
2
33
H*
95
62
H0
3
5
δD
1
28
D*
97
63
D0
2
9
As for the SSQ case, we analyzed the magnetospheric observations which are
shown in Fig. by using a color scale for the MLT. In this
case, a superposition of current systems can be seen at noon, related to the
magnetopause current, and at midnight, due to tail current contribution.
Figure shows the empirical modes extracted from GOES
observations during the Halloween storm. In this case, we also note the
enhancements of amplitudes due to the impact of the CMEs and their effects on
the orbital variation (see j= 12–13 for GOES10, j= 11–12 for GOES12). At
a geosynchronous orbit (Fig. ), the SMT analysis shows only two different sets of
modes for both GOES10 (left panels) and GOES12 (right panels). As a consequence, GOES10 and GOES12 are split into two different
contributions: δBz(t) (GOES10: j= 1–10 modes; GOES12: j= 1–9 modes)
and Bz0(t) (GOES10: j= 11–15 modes and r(t); GOES12: j= 10–14 modes
and r(t)). Figure shows the results of the EMD reconstructions
for GOES10 (left panels) and GOES12 (right panels). As expected, δBz(t) in both GOES spacecraft orbits (Fig. , upper panels)
increases during the main phase of the geomagnetic storm as a consequence of
the magnetospheric response to the CME arrival and comes back close to its
initial values at the end of the storm time. Concerning the GOES baseline
Bz0(t) (Fig. , lower panels), it is evident that
before the storm it is characterized by the typical diurnal variation
during the storm it is characterized by a huge decrease due to the increase
in the intensities of the magnetospheric currents (the main phase of the
geomagnetic storm)
after the storm it comes back to its original diurnal variation.
Moreover, Bz0(t) behavior is influenced by the ring and magnetopause
current activity at noon, while at midnight the superimposed effect of the
ring and tail currents can be seen, with a greater contribution related to
the tail current activity.
In Table we report the percentage of each contribution
to the total signal for both SSQ and ST periods. During the SSQ period the
ground signal (H and D components) variations are principally due to
H*(t) and D*(t) (∼ 95 %), while for geostationary observations
they are mostly reproduced by using the baseline Bz0(t) (∼ 99 %).
Conversely, during the ST period, the short-timescale reconstructions (δH(t) and δD(t) for ground measurements and δBz(t)
for magnetospheric observations) contribute more significantly to the signals
(∼ 30 %).
Results and discussion
In this work we applied the EMD to satellite and ground-based
observations of the Earth's magnetic field during both quiet and disturbed
periods in order to detect a timescale separation between the baseline and the
time variations of the magnetospheric and ground magnetic field.
SSQ contributions
In ground-based observations we found three different contributions: the
short-timescale contribution that can be associated with the internal
dynamics of the magnetosphere, the intermediate-timescale contribution which
can be related to ionospheric processes, and the large-timescale contribution
related to the local time-dependent geomagnetic field. The associations of
intermediate-timescale (H*(t) and D*(t)) contributions with ionospheric
physical processes has been made by looking at their characteristic
timescales (Table ) and
taking into account that the time behavior of H*(t) and D*(t) is in
agreement with the solar quiet daily variation observed in October at
L'Aquila, as determined by . So, our findings seem to suggest
that the H*(t) and the D*(t) fields are of ionospheric origin.
This hypothesis is confirmed by analyzing the magnetospheric observations
from which only two contributions are detected. It can easily be seen (Fig. , lower panels) that Bz0(t) represents the diurnal
magnetospheric field variation due to the geosynchronous orbit
, while δBz(t) (Fig. , upper panels) is
related to its fluctuations (1 order of magnitude lower than Bz0(t)).
Interestingly, since Bz0(t) by definition represents the baseline field
observed by GOES and it is completely free of any magnetospheric field
fluctuations, it can be used for the calibration of the International Geomagnetic Reference Field/Definitive Geomagnetic Reference Field (IGRF/DGRF). In
fact, by a direct comparison between an IGRF model, such as the Geomag 7.0C
, and Bz0(t), the IGRF degree coefficients can be tuned
and better evaluated.
Since the only difference between ground and magnetospheric data during an SSQ
period is the ionospheric contribution, we can reasonably assert that
H*(t) and D*(t) are of ionospheric origin. Moreover, the characteristic
periods of the modes involved in the δH(t) and δD(t)
reconstructions are consistent with the relative characteristic periods
involved in the δBz(t) reconstruction for both GOES spacecraft (Table ). This indicates that they might be of magnetospheric
origin.
ST contributions
As for the SSQ case, both H and D components can be split into three
different contributions. Both δH(t) and δD(t) (Fig. , upper panels) show two increases in the fluctuation amplitudes as a consequence of the magnetospheric response to two consecutive CME
impacts on the Earth's magnetosphere .
H0(t) (Fig. lower left panel) gives a representation of the
geomagnetic disturbance associated with the Halloween super storm
, characterized by three storm peaks and the relative
recovery phases, while D0(t) (Fig. , lower right panel)
shows only a slight modulation around 0. H*(t) and D*(t) (Fig. , middle panels), which are of ionospheric origin, show variations
between 6–24 h which increase in amplitude during the storm time, with
amplitude peaks of ∼-250 and ∼-200 nT, respectively, during the
first main phase. Moreover, D*(t) shows two huge increases (∼220
and ∼270 nT) during the second and the third main phase of the storm.
Summary
Our results can be summarized as reported below.
Magnetosphere
Both in the quiet (Fig. ) and storm time periods (Fig. ), the SMT applied to the EMD shows two different
contributions:
Short-timescale δBz(t): this gives a representation
of the magnetospheric field variations probably due to the dynamic of the
ring current system. In fact, in the SSQ (Fig. , upper panels)
and in the GS (Fig. , upper panels) periods, both GOES
spacecraft orbit in the ring current .
Baseline Bz0(t): this describes the magnetospheric field
observed by the spacecraft during its diurnal orbit (Fig. , lower panels). It has a periodicity of 24 h and an average value of ∼90 nT at 6.6 RE
(http://www.ngdc.noaa.gov/IAGA/vmod/igrfhw.html),
during both SSQ and the pre-storm period. For this reason, during SSQ conditions,
it could be used for a local calibration of the IGRF model in the
magnetosphere. Moreover, its time evolution can be used as a measure of the
local magnetospheric current activity, especially during storm time periods
when fluctuations increase and the evaluation of an average magnetic field is
not straightforward (Fig. , lower panels). In fact, Bz0(t)
shows large variations during the different phases of the storm and a smooth
recovery to its diurnal variation after the storm.
Ground
Both in the SSQ (Fig. ) and in the storm period (Fig. ),
the SMT applied to the EMD shows three different
contributions:
Short-timescale δH(t) and δD(t): they
represent the geomagnetic field variations due to the magnetospheric field
fluctuations. The similar temporal scales of δH(t) and δBz(t) (Table and Table ) seem to
confirm this hypothesis. A visual inspection of the interplanetary magnetic
field (Bz,IMF, not shown) seems to suggest that any coherent increase
(decrease) in δH(t) is correlated with the northward (southward)
switching of the Bz,IMF.
Intermediate-timescale H*(t) and D*(t): they represent
the geomagnetic field variations of ionospheric origin, as confirmed by their
absence in the magnetospheric EMD reconstructions and by their characteristic
timescales (Table and Table ). In
both SSQ and storm conditions, both H*(t) and D*(t) show periods in the range of 6–24 h (Fig. , middle panels). In addition,
during a GS, H*(t) increases in amplitude, with higher values in the main
phase. By contrast, D*(t) shows a decrease in the first main phase and two
huge increases of ∼220 and ∼270 nT in the second and in the third
main phase of the storm (Fig. , middle panels), respectively.
Baseline H0(t) and D0(t): they represent the local
average deviation of the geomagnetic field. During the SSQ (Fig. , lower panels), their mean value is set around 0, as a
consequence of the lack of a baseline value from AQU ground measurements
(we used the relative measurements of the geomagnetic field variations
recorded by a triaxial fluxgate magnetometer). On the other hand, during the
storm time period (Fig. , lower panels), H0(t) shows the
typical behavior of a geomagnetic storm, characterized by huge decreases
(main phases) followed by a smooth increase in the magnetic field (recovery
phases).
Conclusions
We provide a method to easily discriminate between the average magnetic field
and its time variations in both magnetospheric and ground observations. The
SMT applied to the EMD is capable of identifying the physical
meaning of each evaluated contribution. In the magnetosphere, we associated the
large-timescale variation (baseline) to the magnetic field observed by the
spacecraft during its diurnal orbit . During a GS, this
baseline shows large amplitude variations, and it could be used as a measure
of the local magnetospheric current activity by a comparison between
Bz0(t) and the TS04 magnetospheric field model . In fact,
since the TS04 model is modular, it can be used to evaluate the magnetospheric
current that best fits the Bz0(t) variations
.
Moreover, during an SSQ period, the same baseline could be used to efficiently
calibrate the IGRF model. On the other hand, the short-timescale variations
could be related to the magnetospheric field fluctuations that can
tentatively be associated with the symmetric and partial ring current dynamics
. On the ground, we associated the short-timescale
reconstructions with the variations of the geomagnetic field driven by the
different magnetospheric current system dynamics. This is confirmed by the
similar timescales between δH(t) and δBz(t) (Tables and ). In addition, we found
intermediate-timescale variations that we associated with an ionospheric origin
contribution. This is confirmed by their absence in the magnetospheric
reconstructions and by their characteristic time periods in the range of 6–24 h.
Moreover, we connected the large-timescale variations to the local
average of the geomagnetic field. In fact, for SSQ, the local average shows a mean value set
around 0, while during active magnetic conditions, the baseline (H0(t))
presents the typical GS feature, characterized by sudden impulse, main phase, and recovery. Thus, H0(t) might be used for the evaluation of the
local intensity of a GS on the ground because it is not necessary to
calculate and subtract any average value for its evaluation (including the SQ
field) and it is free of any magnetospheric fluctuations and ionospheric
origin contributions. Since it is easily evaluated at any ground and
magnetospheric observatory, it can be used as a local geomagnetic disturbance
index.
Interestingly, on the ground we explicitly separated the ionospheric and
magnetospheric fluctuations from the observations. This could be very useful in evaluating the local ionospheric and magnetospheric responses to the solar
wind conditions. Further investigation on several other storm events are in
progress.