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Advances in Space Research xxx (2013) xxx–xxx
www.elsevier.com/locate/asr
Magnetotail current contribution to the Dst Index Using the MT
Index and the WINDMI model
E. Spencer a,⇑, S. Patra a, T. Asikainen b
b
a
Centre for Space Engineering, Utah State University, 4120 Old Main Hill, Logan, UT 84322-4120, USA
Department of Physics, Centre of Excellence in Research, PO Box 3000, FIN-90014, University of Oulu, Finland
Received 15 May 2012; received in revised form 13 August 2013; accepted 17 August 2013
Abstract
In this paper, we have improved the capabilities of a low dimensional nonlinear dynamical model called WINDMI to determine the
state of the global magnetosphere by employing the magnetotail (MT) index as a measurement constraint during large geomagnetic
storms. The MT index is derived from particle precipitation measurements made by the NOAA/POES satellites. This index indicates
the location of the nightside ion isotropic boundary, which is then used as a proxy for the strength of the magnetotail current in the
magnetosphere. In Asikainen et al. (2010), the contribution of the tail current to the Dst index is estimated from an empirical relationship
based on the MT index. Here the WINDMI model is used as a substitute to arrive at the tail current and ring current contribution to the
Dst index, for comparison purposes. We run the WINDMI model on 7 large geomagnetic storms, while optimizing the model state variables against the Dst index, the MT index, and the AL index simultaneously. Our results show that the contribution from the geotail
current produced by the WINDMI model and the MT index are strongly correlated, except during some periods when storm time substorms are observed. The inclusion of the MT index as an optimization constraint in turn increases our confidence that the ring current
contribution to the Dst index calculated by the WINDMI model is correct during large geomagnetic storms.
Ó 2013 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Dst index; Isotropic boundary; Magnetotail current; MT-index
1. Introduction
Geomagnetic storms are typically caused by an increase
in the solar wind Earth directed velocity (600–1000 km/s)
and a strongly southward IMF (10–30 nT), under which
dayside reconnection is enhanced. During such conditions
the Earth’s ring current, geotail current, magnetopause
currents, and field aligned currents are intensified. The rise
and decay of each current system is controlled by the
energy coupled into the magnetosphere by the solar wind
and the subsequent dynamics of the solar wind driven magnetosphere ionosphere system. The Dst index is used as an
indicator of the strength of a geomagnetic storm. After
⇑ Corresponding author. Tel.: +1 435 797 8203; fax: +1 435 797 3054.
E-mail addresses: edmund.spencer@usu.edu (E. Spencer), swadeshp@gmail.com (S. Patra), Timo.Asikainen@oulu.fi (T. Asikainen).
removing the effects of current systems other than ring current from the Dst index it can be used as a measure for the
ring current intensity.
The time development of the ring current during storms
has been studied in the past by different modeling
approaches. Ring current models where the particle motion
is followed in the drift approximation, and the Liouville
theorem is used for particle flux calculations have been
developed (Chen et al., 1993; Ebihara and Ejiri, 2000; Ganushkina et al., 2005a, 2012). Other models like the Comprehensive Ring Current Model (CRCM) (Buzulukova et al.,
2010; Fok et al., 2001) or the Ring current-Atmosphere
interaction Model (RAM) (Liemohn and Kozyra, 2005;
Jordanova et al., 2003) model, solve the time-dependent,
gyration- and bounce-averaged Boltzmann equation for
the phase-space distribution function f ðt; R; u; E; l0 Þ of a
chosen ring current species. Each species is described by
0273-1177/$36.00 Ó 2013 COSPAR. Published by Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.asr.2013.08.016
Please cite this article in press as: Spencer, E., et al. Magnetotail current contribution to the Dst Index Using the MT Index and the WINDMI
model. J. Adv. Space Res. (2013), http://dx.doi.org/10.1016/j.asr.2013.08.016
2
E. Spencer et al. / Advances in Space Research xxx (2013) xxx–xxx
two adiabatic invariants m; K (CRCM) or,equivalently,
energy and equatorial pitch angle (RAM). The anisotropic
pitch angle dependence of distribution function is calculated from the model.
Global energy balance models, like the models proposed
by Burton et al. (1975), O’Brien and McPherron (2000),
and the WINDMI model (Horton and Doxas, 1996,
1998; Mithaiwala and Horton, 2005; Spencer et al.,
2007), use the solar wind parameters as input to the magnetosphere system, which is then translated to the energization of the total energy of the ring current particles. The
Dessler–Parker–Sckopke (DPS) formula (Dessler and Parker, 1959; Sckopke, 1966) is then used to relate the energy
to the Dst index. Empirical models like the models of Temerin and Li (2006, 2002) and Asikainen et al. (2010) have
also been proposed. In addition some predictive models
use neural networks to predict the Dst index (Bala et al.,
2009; Mattinen, 2010).
The Dst index, being computed from measured magnetometer data on the surface of Earth, is also bound to be
affected by other major magnetospheric current systems.
The contributions of other current systems to the Dst
index, have been reported by various authors (Liemohn
et al., 2001; Maltsev, 2004; Tsyganenko and Sitnov, 2005;
Asikainen et al., 2010). In particular the magnetotail
current has been known to contribute significantly to the
Dst index (Alexeev et al., 1996; Maltsev et al., 1996;
Feldstein and Dremukhina, 2000; Kalegaev and Makarenkov,
2008).
It has been reported that during the recovery phase of a
magnetic storm, the Dst decay is controlled by the decay of
two different currents: the ring current and the magnetospheric tail current (Alexeev et al., 1996; Feldstein and
Dremukhina, 2000). This decay is in addition to all the different ring current losses that affect the decay of the Dst
index. Recent work of Kalegaev and Makarenkov (2008),
Ganushkina et al. (2004) and Tsyganenko and Sitnov
(2005) indicates that the ring current becomes the dominant Dst source during severe magnetic storms, but during
moderate storms its contribution to Dst is comparable with
the tail current’s contribution. Using magnetic field modeling based on Tsyganenko T89 and T96 magnetic field models, Turner et al. (2000) showed that the tail current
contribution to the Dst index is on an average about
25%. It is important to note that, since their results are
based on the T89/T96 magnetic field models the results
only apply to the small and moderate magnetic storms with
peak Dst > 100 nT where the models are valid.
It has been observed that the Dst decay following a geomagnetic storm shows a two-phase pattern, a period of fast
decay followed by a phase where the Dst returns to its quiet
time value gradually (Takahashi et al., 1990; Feldstein and
Dremukhina, 2000; Kozyra et al., 1998). While the fast decay
of the tail current in the early recovery phase can partly
explain this observation, various ring current loss processes
have also been proposed as an explanation. Liemohn and
Kozyra (2005), used idealized simulations of ring current
decay to show that for realistic plasma boundary conditions,
a two-phase decay can only be created by the transition from
flow-out losses when open drift lines are converted to closed
ones in a weakening convection electric field resulting in the
charge exchange dominance of ring current loss. In a study
by Jordanova et al. (2003) it was shown that the fast initial
ring current decay is controlled not only by the decreased
convection electric field, the dayside outflow through the
magnetopause, and the internal loss processes, but also by
the time-varying nightside inflow of plasma from the magnetotail. Aguado et al. (2010) have proposed that a hyperbolic function describes the decay of Dst index better than
the exponential functions, which are generally preferred.
Other loss processes have also been proposed as contributors
to the storm-time ring current decay: Coulomb collisions
between the hot ring current ions and plasmaspheric particles (Fok et al., 1991, 1993); and ion precipitation into the
upper atmosphere due to the strong pitch angle scattering
of particles into the loss cone by wave-particle interactions
(especially electromagnetic ion cyclotron waves) (Kozyra
et al., 1998; Jordanova et al., 1997, 2001). Walt and Voss
(2001) concluded that wave-particle interactions elevate particle precipitation losses to a level capable of producing a
rapid initial recovery of the ring current.
In a previous work (Patra et al., 2011), we quantified the
effects of ring current decay mechanisms versus the decay
of magnetospheric currents. Geomagnetic storms for which
an abrupt northward turning of the IMF Bz right after the
peak of the Dst index were chosen and modeled. Under this
condition it is expected that the fast flow out losses will be
minimal and the ring current recovery would be mainly due
to charge exchange process. The WINDMI model was used
to model these storms after including contributions from
various magnetospheric currents. In most cases, the tail
field exceeded the contribution due to the ring current during the main phase, but then quickly subsides, leaving the
symmetrical ring current as the dominant source through
the rest of the recovery phase.
In another work (Spencer et al., 2011), we further quantified the effect of using different solar wind magnetosphere
coupling functions on the calculation of the Dst index, and
determined the sensitivity of the relative contribution
between the ring current and the tail current to functions
that employ the IMF By versus the more usual rectified
solar wind input. The inclusion of the IMF By component
in a coupling function slightly overemphasized the ring current contribution and slightly underemphasized the geotail
current contribution.
The Earth’s magnetotail varies in accordance with
changing solar wind conditions. In particular the night side
stretching of the magnetosphere is due to an enhanced tail
current. Correctly estimating the level of tail current provides another means of constraining magnetospheric magnetic field models. The intensity of the tail current can be
monitored by the latitude of the isotropic boundary of
energetic protons which is obtained from energetic particle
observations by low altitude satellites (Sergeev and
Please cite this article in press as: Spencer, E., et al. Magnetotail current contribution to the Dst Index Using the MT Index and the WINDMI
model. J. Adv. Space Res. (2013), http://dx.doi.org/10.1016/j.asr.2013.08.016
E. Spencer et al. / Advances in Space Research xxx (2013) xxx–xxx
Gvozdevsky, 1995; Asikainen et al., 2010). Removing the
systematic MLT variation in the isotropic boundary gives
the MT index which can be used as an indicator of tail current intensity.
In this paper we use the MT index to determine the contribution of the tail current to the Dst index (Dt). The Dt
values inferred are used to impose an additional constraint
on the tail current contribution to the modeling of the Dst
index by the WINDMI model. In the next section we discuss the MT index and Asikainen et al. (2010)’s method
to determine the contribution of the tail current to the
Dst index in detail. Section 3 introduces the WINDMI
model and the modeling of magnetospheric currents are
discussed. In Section 5 we show the Dst, AL and Dt
obtained from the WINDMI model. The Dt values
obtained from the WINDMI model and the MT index
derived Dt values are also compared in this section.
2. MT-index
The extent of nightside stretching of the Earth’s magnetic field has been a subject of interest for many years
Kubyshkina et al. (2009), Sergeev et al. (1994). Several different measurements have been proposed as proxies to estimate the tail stretching, such as the isotropic boundary
(IB). The IB is the latitude which separates the region of
the magnetosphere close to the Earth on quasi dipolar
lines, where protons bounce between mirror points without
(or with a low) scattering (adiabatic motion) and the further tailward region where the pitch angle scattering is efficient enough to keep the loss cone full (non-adiabatic
behavior) (Meurant et al., 2007; Sergeev et al., 1993). The
IB is known to correlate well with the magnetic field inclination at geosynchronous orbit around 00 MLT and therefore provides a way to monitor magnetotail stretching.
The ion precipitating energy flux maxima (b2i), which
generally occurs near the equatorward edge of the main
nightside oval, was shown to be associated with the ion
isotropy boundary (IB) (Newell et al., 1996). Note however
that while the b2i index describes the tail stretching it is not
directly comparable with the MT index which has been
defined differently and is based on particle observations
of different energies.
Two particular situations can complicate the relationship between the precipitation maximum (b2i) and IB
(Newell et al., 1998). First, during the expansion phase of
some substorms the protons can be so strongly accelerated
in the midtail that their maximal energy flux can be
recorded poleward of the true isotropic boundary. Also,
during strong substorm activity, a structure of detached
strong precipitation (corresponding to high-altitude ”nose
events” Konradi et al., 1975) may appear equatorward of
the main body of precipitation (Sanchez et al., 1993).
According to the numerical simulations of trajectories of
small pitch angle particles done by Sergeev et al. (1983) and
Sergeev et al. (1993), the threshold condition for strong
3
pitch angle scattering in the tail current sheet (scattering
to the center of loss cone) is approximately as follows:
Rc =q ¼ B2z ðGdBx =dzÞ
1
68
ð1Þ
where the equality sign corresponds to the isotropic boundary. Here Rc and q are the radius of curvature of the magnetic field line and the particle gyroradius, respectively, and
G ¼ mv=e is the particle rigidity. The boundary between the
regions of adiabatic and nonadiabatic particle motion in
the equatorial current sheet depends only on the equatorial
magnetic field and the particle rigidity. If the ratio Rc =q exceeds 8, then the particles are not scattered and remain
bounding along the field lines.
Donovan et al. (2003) have used ion data from 29 DMSP
overflights of the Canadian Auroral Network for the OPEN
Program Unified Study (CANOPUS) Meridian Scanning
Photometer (MSP) located at Gillam, Canada, to develop
an algorithm to identify the b2i boundary, named as ”optical
b2i” in latitude profiles of proton auroral (486 nm) brightness. Using the algorithm proposed by Donovan et al.
(2003) and Meurant et al. (2007) find the auroral oval’s
Equatorial Limit (EL) and consider it as a potential indicator of field stretching and not as a boundary between two
physically different regions of the tail. Jayachandran et al.
(2002a,b) have shown that the SuperDARN E region backscatter in the dusk-midnight sector is from the region of ion
precipitation/proton aurora and that its equatorward
boundary coincides with the b2i boundary and can be used
as a tracer of the equatorward boundary of the proton auroral oval in the dusk-midnight sector.
Sergeev and Gvozdevsky (1995) used 1 month of data
from the NOAA-6 satellite to determine the MLT dependence of the IB latitude. They defined the IB as the corrected geomagnetic latitude poleward of which the pitch
angle distribution of 80 keV protons becomes isotropic.
The MLT dependence of the IBs was also explored by
Ganushkina et al. (2005b). Sergeev and Gvozdevsky
(1995) constructed a measure of the tail current, the MTindex, by removing the MLT dependence from the measured IB latitudes. Asikainen et al. (2010), have used particle precipitation data from low-altitude polar orbiting
NOAA/POES 15, 16, 17, and 18 satellites during
1:1:1999 31:12:2007, to identify the isotropic boundary.
Using a modified algorithm inspired by Sergeev and Gvozdevsky (1995), and after accounting for radiation damage
in proton detectors on the MEPED instrument onboard
NOAA/POES satellites, the IB values are estimated. The
MLT dependence of the IB latitude was removed using
expressions appropriate for their dataset rather than using
the expressions provided by Sergeev and Gvozdevsky
(1995). The IB location for the northern and the southern
hemispheres were separately determined. Based on local
linear regression techniques, they developed a semi-empirical model to describe the contributions of the ring, tail,
and magnetopause currents to the Dcx index. The Dcx
index is a corrected version of the Dst index (Mursula
Please cite this article in press as: Spencer, E., et al. Magnetotail current contribution to the Dst Index Using the MT Index and the WINDMI
model. J. Adv. Space Res. (2013), http://dx.doi.org/10.1016/j.asr.2013.08.016
4
E. Spencer et al. / Advances in Space Research xxx (2013) xxx–xxx
and Karinen, 2005). The modeled expression for the tail
current contribution (Dt) was chosen so that the Dt = 0
nT when MT = 75.5 (the maximum value of the MT index
in the data corresponding to the quietest state of the tail
current). The expression obtained was:
7:871
1
Dt ¼ 5:495 107
þ
2:633
cos2 MT
when MT 6 75:5 ,
Dt ¼ 0; otherwise
ð2Þ
Because the hourly MT values are typically calculated
only from a few individual measurements within each hour
the MT index has a relatively much larger variance than
the corresponding solar wind parameters and the
Sym H index which are averages computed from 1 min
data. Newell et al. (2002) showed that the location of the
isotropic boundary as measured by the b2i index displays
small seasonal and diurnal variation with a range of a couple of degrees. It is expected that a similar variation is present in the MT index as well. We note that such variations
may introduce small seasonal and diurnal differences
between the Dt computed from the MT index and from
the WINDMI model (which does not include seasonal
effects other than those related to driving solar wind
parameters). However, such differences are expected to be
very small compared to the storm time disturbances in
the Dt.
3. WINDMI model
The solar WIND Magnetosphere-Ionosphere (WINDMI) interaction model is driven by an equivalent voltage
derived from an appropriate solar wind magnetosphere
coupling function.
The 8 ODEs comprising the WINDMI model are:
L
dI
dI 1
¼ V sw ðtÞ V þ M
dt
dt
ð3Þ
C
dV
¼ I I 1 I ps RV
dt
ð4Þ
3 dp RV 2
pVAeff
3p
1=2
¼
u0 pK k HðuÞ 2 dt Xcps
Xcps Btr Ly 2sE
ð5Þ
dK k
Kk
¼ I ps V dt
sk
ð6Þ
LI
dI 1
dI
¼V VI þM
dt
dt
ð7Þ
CI
dV I
¼ I 1 I 2 RI V I
dt
ð8Þ
L2
dI 2
¼ V I ðRprc þ RA2 ÞI 2
dt
ð9Þ
dW rc
pVAeff W rc
¼ Rprc I 22 þ
dt
Btr Ly
src
ð10Þ
The nonlinear equations of the model trace the flow of electromagnetic and mechanical energy through eight pairs of
transfer terms. The remaining terms describe the loss of energy from the magnetosphere-ionosphere system through
plasma injection, ionospheric losses and ring current energy losses.
In Spencer et al. (2011),we showed that the most reliable
Dst results were obtained when we use the solar wind rectified electric field (VBs ) or the coupling function derived by
Newell et al. (2002). The input coupling function chosen
for this study is the standard rectified vBs formula (Reiff
and Luhmann, 1986), given by:
V y ¼ vsw BIMF
Leff
s
y ðkV Þ
ð11Þ
V Bs
sw ¼ 40ðkV Þ þ V y
ð12Þ
where vsw is the x-directed component of the solar wind
velocity in GSM coordinates, BIMF
is the southward IMF
s
component and Leff
is
an
effective
cross-tail width over
y
which the dynamo voltage is produced. For northward or
zero BIMF
, a base viscous voltage of 40 kV is used to drive
s
the system.
In the differential equations the coefficients are physical
parameters of the magnetosphere-ionosphere system. The
quantities L; C; R; L1 ; C I and RI are the magnetospheric
and ionospheric inductances, capacitances, and conductances respectively. Aeff is an effective aperture for particle
injection into the ring current. The resistances in the partial
ring current and region-2 current, I 2 are Rprc and RA2
respectively, and L2 is the inductance of the region-2 current. The coefficient u0 in Eq. (5) is a heat flux limiting
parameter. The energy confinement times for the central
plasma sheet, parallel kinetic energy and ring current
energy are sE ; sk and src respectively. The effective width
of the magnetosphere is Ly and the transition region magnetic field is given by Btr . The pressure gradient driven current is given by I ps ¼ Lx ðp=l0 Þ1=2 , where Lx is the effective
length of the magnetotail. The outputs of the model are
the AL and Dst indices, in addition to all the magnetospheric field aligned currents. The contributions from the
magnetopause and tail current systems are given by:
pffiffiffiffiffiffiffiffi
ð13Þ
Dstmp ¼ a P dyn
Dstt ¼ aIðtÞ
ð14Þ
where Dstmp is the perturbation due to the magnetopause
currents and Dstt is the magnetic field contribution from
the tail current IðtÞ which is modeled by WINDMI as I.
P dyn is the dynamic pressure exerted by the solar wind on
the Earth’s magnetopause. We used two values 15.5 and
7.26 for a as estimated by Burton et al. (1975) and O’Brien
and McPherron (2000) respectively . Burton’s formula estimates the contribution of Dstmp to be more than twice that
estimated by O’Brien’s formula.
The factor a is an unknown geometrical factor that is
also an optimization parameter. The optimized value of a
is a first order approximation to the actual relationship
between the geotail current and Dt. It is likely that the
Please cite this article in press as: Spencer, E., et al. Magnetotail current contribution to the Dst Index Using the MT Index and the WINDMI
model. J. Adv. Space Res. (2013), http://dx.doi.org/10.1016/j.asr.2013.08.016
E. Spencer et al. / Advances in Space Research xxx (2013) xxx–xxx
factor a is not constant but changes with external conditions (solar wind dynamic/thermal/magnetic pressure
which shapes the tail lobe) and with the I(t) itself (location
of the tail current sheet may correlate with the intensity of
the tail current). Estimates for the value of a can be
inferred from calculations similar to those given in Kamide
and Chian (2007) (pp. 364–365). Kamide and Chian (2007)
estimated that, assuming the PRC and near-earth cross tail
currents are confined within 18 to 06 local time sector in the
nightside, at a distance of 6 RE , each MA of the combined
currents produce a disturbance of 10.4 nT on the Earth’s
surface at low latitudes. Since the effects of the individual
currents are unclear, we leave a comparison of these different methods to find values or functional forms of a for
future work.
The simulated Dst is given by:
Dstwmi ¼ Dstrc þ Dstmp þ Dstt
ð15Þ
Using this expression to calculate the simulated Dst, we
optimized the physical parameters of the WINDMI model
and the geometrical factor a for all the events. Induced currents flowing inside the Earth’s core enhance the measured
magnetic field of each external current approximately by a
factor C IC , which is generally taken to be 1.3 Langel and
Estes (1985) and Tsyganenko and Sitnov (2005).
The Dst index is calculated after removing the baseline
H and quiet time (Sq) from the H value measured at each
station. The quiet time magnetic field is calculated from
measurements made during the five quietest days in a
month. This magnetic field contains effects of all the
large-scale current systems (Chapman–Ferraro currents
as well). The input to the WINDMI model includes a base
viscous voltage in addition to the rectified solar wind V y as
given in Eq. (12). This additional viscous voltage generates
the quiet time values for the various magnetospheric currents (other than the magnetopause currents) for the
WINDMI model. The quiet time contributions from each
current system are less than 20 nT. The Dt values obtained
with this model include the quiet time values when IMF Bz
was northward.
In order to compare these results directly with the DtMT
values, the quiet time values were subtracted from the
WINDMI Dt (Dtwmi ) values. In the rest of the paper, the
contribution of the tail current as estimated from the
WINDMI model and the MT index will be mentioned as
Dtwmi and DtMT respectively. The base viscous voltage of
40 KV drives the WINDMI model, when IMF Bz is northward. This value also accounts for any viscous coupling
during southward IMF Bz conditions. The results obtained
are discussed in Section 5.
4. Optimization of the WINDMI model
The variable coefficients in the WINDMI model are L, M,
C, R, Xcps , u0 , I c , Aeff , Btr , Ly , sE , sjj , LI , C I , RI , L2 , Rprc , RA2 , src ,
and a. These parameters are constrained to a maximum and
a minimum physically realizable and allowable values and
5
combined to form a 18-dimensional search space S R18
over which optimization is performed.
To optimize the WINDMI model, we use one form of the
genetic algorithm (Coley, 2003) to search the physical
parameter space in order to minimize the error between
the model output and the measured geomagnetic indices.
The optimization scheme was used to select a parameter
set for which the outputs from the WINDMI model most
closely matches the AL index and the Dst index
simultaneously.
For this work we are primarily interested in the features
of the Dst index, so we have chosen a higher bias of 0.5 for
the Dst index. The contribution of the tail current is an
important parameter in the modeling of the Dst index,
while the fit against AL index is important as the physical
parameters in Eqs. (3)–(9) are dependent on it. The weighting for the AL index and Dt values were set to 0.3 and 0.2,
in order of relative importance. There is a strong direct correlation between solar wind parameters and the AL index
during geomagnetic activity over hour time scales, and
the Dst matches of the model are more believable if the
additional data is represented well too.
The performance of the algorithm is evaluated by how
well the average relative variance (ARV) compares with
the measured indices. The average relative variance gives
a good measure of how well the optimized model tracks
the geomagnetic activity in a normalized mean square
sense. The ARV is given by:
ARV ¼
Ri ðxi y i Þ2
Ri ðy y i Þ
2
ð16Þ
where xi are model values, y i are the data values and y is the
mean of the data values. In order that the model output
and the measured data are closely matched, ARV should
be closer to zero. A model giving ARV ¼ 1 is equivalent
to using the average of the data for the prediction. If
ARV ¼ 0 then every xi ¼ y i . ARV values for the AL index
above 0.8 are considered poor for our purposes. ARV below 0.5 is considered very good, and between 0.5 and 0.7
it is evaluated based upon feature recovery. For the Dst index, an ARV of 0.25 is considered good.
The ARV values for all the three constraints are calculated
over the period when the most geomagnetic activity occurs.
When these criteria are observed to be acceptable, the optimization process is assumed to have reached convergence.
In previous works, the WINDMI model has been used to
model isolated substorms Horton and Doxas (1996, 1998),
and classify them in some cases as being driven by a northward turning of the IMF Bz Horton et al. (2003). During
storm time, periodic substorms have been analyzed by Spencer et al. (2007, 2009). In the first part of the results section
below we have turned off the substorm effect in the WINDMI model by setting the critical geotail current parameter Ic
at a level such as to preclude a substorm trigger. The nature
of this trigger and the effect of including substorms on the
modeled Dt values will be detailed later in Section 5.1.
Please cite this article in press as: Spencer, E., et al. Magnetotail current contribution to the Dst Index Using the MT Index and the WINDMI
model. J. Adv. Space Res. (2013), http://dx.doi.org/10.1016/j.asr.2013.08.016
E. Spencer et al. / Advances in Space Research xxx (2013) xxx–xxx
A set of thirteen events were selected by Patra et al.
(2011) where the IMF Bz turned northward abruptly after
the peak in Dst index was observed. Under these conditions
it is assumed that the flow out losses will be less dominant
and the recovery would be governed by the contributions
from the tail current and ring current.
Later in Spencer et al. (2011), we chose six events out of
the initial thirteen events. In addition to the 6 out of 13
events, we also selected the October 2000 and April 2002
storm events used previously in Spencer et al. (2009). For
this work, we have analyzed the same 6 events chosen from
the previous group of 13. These are (1) days 158–166, 2000,
(2) days 258–266, 2000, (3) days 225–235, 2001, (4) days
325–335, 2001, (5) days 80–88, 2002, and (6) days 245–
260, 2002. In addition we also analyzed the April 2002
storm. However, in what follows we will discuss four out
of the seven events. This is in order to determine the relative contribution of the geotail current to the observed
Dst index.
The MT index for the seven storms analyzed were
obtained from particle precipitation data from low-altitude
polar orbiting NOAA/POES 15, 16, 17, and 18 satellites.
The isotropic boundary (IB) was identified from the particle precipitation measurements. The MT index was derived
after removing the MLT dependence of the IB latitude
derived Asikainen et al. (2010). These seven storms were
found to fall into two categories in Spencer et al. (2011).
In the first category (category I) were storm events where
the coupling functions look qualitatively slightly different
from each other, but using any solar wind magnetosphere
coupling function resulted in a good fit to the measured
Dst data. In these events, the relative contributions from
each current system due to the different inputs remained
roughly the same through the optimization process. These
storm events were characterized also by their classical nature in that the onset, main phase and decay phase are distinct. In another category (category II), the storms are
much more dependent on the input coupling function used.
For coupling functions that are significantly different from
each other, the output Dst curves were different, and each
Dst curve predicted a different level of geomagnetic activity
over 6–8 h time scales. Here we have chosen to just use the
standard rectified solar wind input for our analysis.
Fig. 1 shows the comparison of Kyoto Dst and the Dst
generated by the WINDMI model for the storm on days
261–267 in the year 2000. This storm fell into category II
from our previous work. The optimized result shown was
obtained after using DtMT as an additional matching criteria. The solar wind velocity vx , IMF Bz , and the proton density N p , are shown in the top three panels. Contributions
from the magnetopause current, the ring current and the
tail current are shown in the fourth panel of Fig. 1. In
Fig. 2 the modeled westward Auroral Electrojet (AL) index
and the magnetotail contribution Dt are shown. The top
panel compares the hourly averaged Kyoto AL index with
the AL calculated by the WINDMI model from the region
1 current. The bottom panel of Fig. 2 plots the Dtwmi and
DtMT values.
The degree of correspondence between the modeled and
measured Dst, AL and Dt values is very similar for the 4
other storms (days 159–167 in 2000, days 229–236 in
2001, days 326–336 in 2001, and days 247–261 in 2002)
as for the storm shown in Figs. 1 and 2. The fact that the
dynamics of the tail current contribution are similar in
Year −2000
800
600
z
B (nT)
400
20
0
−20
50
40
30
20
10
Velocitysw[Km/s]
5. Results and discussion
Proton density
6
50
Dst(nT)
0
Dst
−50
data
−100
Dmp
Dst
−150
Dsttail
windmi
Dstrc
−200
261.4
262.2
263
263.8
264.6
265.4
266.2
267
Days
Fig. 1. The top three rows of the figure show the solar wind velocity,Bz , and proton density respectively during the storm starting on day 261, 2000. The
fourth row shows the best fit obtained by the WINDMI model. The contributions from other magnetospheric currents are also shown.
Please cite this article in press as: Spencer, E., et al. Magnetotail current contribution to the Dst Index Using the MT Index and the WINDMI
model. J. Adv. Space Res. (2013), http://dx.doi.org/10.1016/j.asr.2013.08.016
E. Spencer et al. / Advances in Space Research xxx (2013) xxx–xxx
7
AL and Dt Comparison, Year 2000
1000
AL
windmi
ALdata
AL [nT]
800
ARV AL = 0.66
600
400
200
0
262
263
264
265
266
Dt
windmi
Dt [nT]
−50
DtMT
−100
−150
261
262
263
264
265
266
267
Time [Days]
Fig. 2. The top panel shows the comparison of the AL index and the modeled values. The bottom panel of this figure shows the comparison between the
DtMT values derived from the MT index and the Dtwmi for the storm starting on day 261, 2000.
are shown in Figs. 3 and 4. The Dt matches are good in the
initial phase of the storms as well as during the entire
recovery period. However, during the main phase on days
83 and 84 (Fig. 4), a sequence of sawtooth events were
found to occur Cai (2007). During this time, soon after
the substorm onset in the beginning of day 83, the Dtwmi significantly overestimates the tail current intensity being
about 2 times larger than DtMT .
Another event for which the Dt fits obtained by the
model were not corresponding well with the DtMT values
was during the sequence of sawtooth events between days
Year −2002
600
400
10
0
−10
60
40
20
Dst(nT)
50
Proton density
Bz(nT)
20
Velocitysw[Km/s]
the two very different modeling approaches (MT and
WINDMI based) corroborates that the tail current and
its dynamics can be robustly monitored by the MT index
and that the WINDMI model is able to represent the overall variation in the tail current as well. However, it seems
that the good agreement between DtMT and Dtwmi is sometimes broken during storm time substorms. We will next
discuss two such events.
The first is the storm on days 81–89, 2002, which was
categorized as a Category-II storm Patra et al. (2011),
Spencer et al. (2011). The Dst, AL and Dt fits for this storm
0
Dstdata
Dmp
Dst
−50
windmi
Dsttail
Dst
rc
−100
81
82
83
84
85
Days
86
87
88
89
Fig. 3. The top three rows of the figure show the solar wind velocity,Bz , and proton density respectively during the storm starting on day 81, 2002. The
fourth row shows the best fit obtained by the WINDMI model. The contributions from other magnetospheric currents are also shown.
Please cite this article in press as: Spencer, E., et al. Magnetotail current contribution to the Dst Index Using the MT Index and the WINDMI
model. J. Adv. Space Res. (2013), http://dx.doi.org/10.1016/j.asr.2013.08.016
8
E. Spencer et al. / Advances in Space Research xxx (2013) xxx–xxx
AL and Dt Comparison, Year 2002
800
AL
windmi
AL
data
AL [nT]
600
ARV AL = 0.23
400
200
0
82
83
84
85
86
87
88
Dtwindmi
Dt [nT]
−10
DtMT
−20
−30
−40
81
82
83
84
85
Time [Days]
86
87
88
89
Fig. 4. The top panel shows the comparison of the AL index and the modeled values. The bottom panel of this figure shows the comparison between the
DtMT values derived from the MT index and the Dtwmi for the storm starting on day 81, 2002.
the work we have turned the switch off. The reason for this
is that in order to correctly optimize the model to capture
substorm activity, we will have to perform optimizations
over intervals in the order of hours, and not over a storm
period of many days. We do not expect the substorm
switch to be accurate over long periods of time, since the
state of the magnetosphere may change considerably over
a day. For predicting and analyzing the Dst index over a
multiple day period the model has been found to be more
consistent and reliable when the substorm effect is
excluded. In the following section, we will discuss some
Year −2002
600
500
400
0
−20
60
40
20
Proton density
Bz(nT)
20
Velocitysw[Km/s]
108 and 109, 2002 (Figs. 5 and 6). Here, again the Dt
matches are good everywhere, except during the time when
periodic substorms occur (Fig. 6). From Fig. 6 we observe
that during days 108-109, even though the DtMT values are
smaller, the corresponding values of the Kyoto AL are elevated which corresponds to substorms.
Note that the WINDMI model has the capability to
produce substorm phenomena through the HðuÞ switching
function in Eq. (5), which switches a pressure relieving
energy unloading component when the geotail current
reaches a certain critical value. However, for this part of
Dst(nT)
50
0
Dst
−50
data
Dmp
Dstwindmi
−100
Dsttail
Dst
105.4
106.6
107.8
109
110.2
Days
111.4
112.6
113.8
rc
115
Fig. 5. The top three rows of the figure show the solar wind velocity,Bz , and proton density respectively during the storm starting on day 105, 2002. The
fourth row shows the best fit obtained by the WINDMI model. The contributions from other magnetospheric currents are also shown.
Please cite this article in press as: Spencer, E., et al. Magnetotail current contribution to the Dst Index Using the MT Index and the WINDMI
model. J. Adv. Space Res. (2013), http://dx.doi.org/10.1016/j.asr.2013.08.016
E. Spencer et al. / Advances in Space Research xxx (2013) xxx–xxx
9
AL and Dt Comparison, Year 2002
1200
AL [nT]
1000
AL
windmi
ARV AL = 0.34
AL
data
800
600
400
200
0
106
107
108
109
110
111
112
113
114
Dt [nT]
−20
Dt
−40
windmi
DtMT
−60
−80
105
106
107
108
109
110
111
112
113
114
115
Time [Days]
Fig. 6. The top panel shows the comparison of the AL index and the modeled values. The bottom panel of this figure shows the comparison between the
DtMT values derived from the MT index and the Dtwmi for the storm starting on day 105, 2002.
results from the WINDMI model with the substorms
turned on to illustrate the difference in model behavior.
During substorms the particle distribution may become
more isotropic equatorward of the original IB due to
increased precipitation. However, it is expected that the
region of precipitation penetrates closer to Earth (to lower
latitudes) which would lead to the IB (MT index), being
closer to the Earth than it should be (Newell et al., 1998).
This would lead to larger values of DtMT . The observations
are to the contrary. The DtMT values during substorms are
smaller in magnitude than the Dtwmi values. When the substorm mechanism in WINDMI is turned off, Dtwmi overestimates the Dt because the model will not unload magnetic
and plasma thermal energy into the ionosphere through the
field aligned currents or the earthward parallel flow of
plasma.
The MT index is mostly defined at any time by only a
couple of (sometimes even just one) point observation
within the hour. This may lead to the fact that small scale
local disturbances in the IB are misinterpreted as global
changes in the Dt. In Asikainen et al. (2010) to avoid this
effect, a 3 h running mean of the MT time series was taken,
before determining the DtMT values. This would decrease
the small scale local variations in the tail current/IB and
emphasize the smoother time evolution of the global tail
current.
In this work we have used the unsmoothed MT index.
This was done in order to retain some of the information that
can be obtained with the higher resolution data. The MT
index values show more variation in the hourly time scale,
in the tail current, some of which may be due to local effects.
However, the differences in the Dts during the storms are
rather large and long lived which suggests that the main differences are probably not due to local effects but due to the
substorm effects.
5.1. Substorm effects
In order to account for the difference between Dtwmi and
DtMT during the periods where substorm activity was
reported, we repeated the optimization procedure for the
storms on days 81–89, 2002 and 105–114, 2002 with the
substorm trigger allowed to activate. All other parameters
were allowed the same flexibility as before, but the critical
geotail current Ic was allowed to take low enough values so
that a substorm could be triggered. Ic appears in the HðuÞ
switching function in Eq. (5), which is given by,
1
I Ic
HðuÞ ¼ 1 þ tanh
ð17Þ
2
DI
The values of I c and the interval DI in Eq. (17) represent
the rate at which a transition to loss of plasma along newly
opened magnetic field lines occurs. The function HðuÞ
changes from zero to unity as a function of the geotail current I compared to I c . The unloading function follows from
current gradient driven tearing modes or cross-field current
instabilities, see for example Yoon et al. (2002).
In the WINDMI model, ring current energization is produced by two mechanisms (Eq. (10)), the flow of plasma
thermal energy from the near earth plasma sheet, and the
current I 2 (region 2 current), that leaves the ionosphere
on the dawnside, closes in the ring current and returns to
the ionosphere on the duskside. This secondary loop of
current has a self inductance L2 and drives a current
through the partial ring current resistance Rprc as well as
the resistance of the region 2 current loop footprint RA2 .
The Joule heating through the resistance Rprc energizes
the ring current particles. Aeff is an effective aperture for
particle injection into the ring current, that on the duskside
merges with what is known as the Alfven layer Doxas et al.
(2004). The Alfven layer is defined to be the separatrix
Please cite this article in press as: Spencer, E., et al. Magnetotail current contribution to the Dst Index Using the MT Index and the WINDMI
model. J. Adv. Space Res. (2013), http://dx.doi.org/10.1016/j.asr.2013.08.016
10
E. Spencer et al. / Advances in Space Research xxx (2013) xxx–xxx
AL and Dt Comparison, Year 2002
ALwindmi
1200
AL
data
AL [nT]
1000
800
ARV AL = 0.52
600
400
200
0
Time [Days]
Dt [nT]
−5
−10
Dt
−15
Dtwindmi−opt
windmi
Dt
−20
MT
−25
−30
−35
81
82
83
84
85
Time [Days]
86
87
88
89
Fig. 7. The best fits of AL and Dts for the storm on days 81–89,2002. The AL is estimated every minute. Optimization was performed over days 82.5–84.
between two sets of drift trajectories, one comprising open
drift paths extending from the magnetospheric tail to the
dayside magnetopause and another, nearer set consisting
of closed drift paths, encircling the Earth Wolf et al. (2007).
The model was optimized over the main phase for the
two storms, which were chosen to be from days 82.5–85,
2002, and 108–110, 2002. Sym H and minute resolution
AL were used in addition to DtMT as the constraining
parameters. The resulting Dt plots are shown in Figs. 7,
and 8. These results should be compared with the plots
shown in Figs. 4 and 6.
The results indicate that during the main phase of the
storms the disruption of the tail current leads to reduction
in the strength of the crosstail current. This reduction is
reflected well in the DtMT values. The decrease in the Dt
intensity is compensated by energization of the ring current
particles due to increased particle injection during a substorm. The effect of substorms on Dst index has been
reported earlier as small decreases in its magnitude Ohtani
et al. (2001). The sudden enhancement in the nightside ion
fluxes is a consequence of particle energization during substorm expansion. The energy (or momentum) of a particle
gyrating along a stretched field line will increase when the
field line relaxes to more dipole-like, in order to conserve
the first and second adiabatic invariants (Fok and Moore,
1997).
AL and Dt Comparison, Year 2002
AL
2000
windmi
ALdata
AL [nT]
1500
ARV AL = 0.83
1000
500
0
0
106
107
108
109
110
Time [Days]
111
112
113
114
t
D [nT]
−20
−40
Dt
windmi
Dtwindmi−opt
−60
105
DtMT
106
107
108
109
110
Time [Days]
111
112
113
114
115
Fig. 8. The best fits of AL and Dts for the storm on days 105–115,2002. The AL is estimated every minute. Optimization was performed over days 108–
110.
Please cite this article in press as: Spencer, E., et al. Magnetotail current contribution to the Dst Index Using the MT Index and the WINDMI
model. J. Adv. Space Res. (2013), http://dx.doi.org/10.1016/j.asr.2013.08.016
E. Spencer et al. / Advances in Space Research xxx (2013) xxx–xxx
But the enhanced inductive electric field during a substorm alone is not completely effective in energizing the
ring current. Sanchez et al. (1993) propose that, dipolarization and accompanying current disruption cause ions
within the reconfiguration region to be prevented from further earthward penetration, thus creating a temporary void
of plasma sheet particles in the inner edge of the plasma
sheet. This could lead to lower enhancement of the ring
current particles during a substorm.
In our simulations, the optimization procedure makes
the energy input due to I 22 Rprc into the ring current during
substorms become dominant. The pVAeff energy input
becomes small because the thermal pressure decreases substantially in the plasma sheet when a substorm is triggered
(Eq. (10)). Whether this is accurate can only be determined
by means of another measurement constraint imposed on
the model. We will address this issue in future modeling
work.
6. Conclusion
In this work we have used the MT-index, which is an
indicator of the ion-isotropic boundary location, to constrain the WINDMI model geotail current. The best fit
WINDMI values were compared with the magnetic disturbance estimated on the surface of the Earth due to the
strength of the tail current. The magnetotail current contribution to the Dst index as calculated by the WINDMI
model has a very good correlation with the values calculated from the empirical expression relating the MT index
to the ground perturbation due to geotail current.
The addition of this additional constraint on the
WINDMI model makes the calculated magnetospheric
currents more reliable. We observed that for most storms,
the relative contribution from the geotail current and ring
current to the Dst index obtained from our earlier studies
are consistent with the present work. The most significant
difference was observed for the storms where periodic substorms were observed during the storm. During such
storms the MT index and the resulting Dt values show a
significant drop in magnitude that is attributed to the current disruption during a substorm, leading to lower
strength of the geotail current.
The WINDMI model is able to confirm this observation
when the substorms are triggered in the model. The corresponding drop in contribution to the Dst/Sym H indices
is compensated by the enhancement in the energization of
the ring current due to the increased inductive E-field during a substorm dipolarization. The observed Sym H correlates favorably with these substorm dynamics. This work
suggests that the contribution from tail current to ground
perturbation is important.
More work needs to be done to confirm the exact mechanism for the energization of the ring current during a substorm. The conditions that trigger a substorm in the
magnetosphere is still an open question and further studies
are required. The combination of the right trigger condi-
11
tion as well as the correct energization mechanism for the
ring current will enable the WINDMI model to reproduce
the Dst index more realistically.
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