Journal of Geophysical Research: Space Physics
RESEARCH ARTICLE
10.1002/2014JA020615
Key Points:
• Electron precipitation models are
developed for global magnetosphere
simulations
• Monoenergetic and diffuse
precipitation exhibit nonlinear
relations with SW driving
• Modeled precipitation power is
consistent with estimations from
UVI images
Correspondence to:
B. Zhang,
[email protected]
Citation:
Zhang, B., W. Lotko, O. Brambles,
M. Wiltberger, and J. Lyon (2015),
Electron precipitation models
in global magnetosphere
simulations, J. Geophys. Res.
Space Physics, 120, 1035–1056,
doi:10.1002/2014JA020615.
Received 19 SEP 2014
Accepted 2 JAN 2015
Accepted article online 7 JAN 2015
Published online 7 FEB 2015
Electron precipitation models in global
magnetosphere simulations
B. Zhang1 , W. Lotko1 , O. Brambles1 , M. Wiltberger2 , and J. Lyon3
1 Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire, USA, 2 High Altitude Observatory, National
Center for Atmospheric Research, Boulder, Colorado, USA, 3 Department of Physics and Astronomy, Dartmouth College,
Hanover, New Hampshire, USA
Abstract General methods for improving the specification of electron precipitation in global simulations
are described and implemented in the Lyon-Fedder-Mobarry (LFM) global simulation model, and the
quality of its predictions for precipitation is assessed. LFM’s existing diffuse and monoenergetic electron
precipitation models are improved, and new models are developed for lower energy, broadband, and
direct-entry cusp precipitation. The LFM simulation results for combined diffuse plus monoenergetic
electron precipitation exhibit a quadratic increase in the hemispheric precipitation power as the intensity
of solar wind driving increases, in contrast with the prediction from the OVATION Prime (OP) 2010 empirical
precipitation model which increases linearly with driving intensity. Broadband precipitation power increases
approximately linearly with driving intensity in both models. Comparisons of LFM and OP predictions with
estimates of precipitating power derived from inversions of Polar satellite UVI images during a double
substorm event (28–29 March 1998) show that the LFM peak precipitating power is > 4× larger when using
the improved precipitation model and most closely tracks the larger of three different inversion estimates.
The OP prediction most closely tracks the double peaks in the intermediate inversion estimate, but it
overestimates the precipitating power between the two substorms by a factor >2 relative to all other
estimates. LFMs polar pattern of precipitating energy flux tracks that of OP for broadband precipitation
exhibits good correlation with duskside region 1 currents for monoenergetic energy flux that OP misses
and fails to produce sufficient diffuse precipitation power in the prenoon quadrant that is present in OP.
The prenoon deficiency is most likely due to the absence of drift kinetic physics in the LFM simulation.
1. Introduction
The flux distributions of electrons precipitating into the high-latitude ionosphere and their integrated
hemispheric precipitation rates and power are key variables of space weather. Physics-based numerical
simulations offer the possibility to provide numerical forecasts of the spatial and temporal characteristics
of electron precipitation, and most global simulations of geospace include either index-based, empirical
precipitation models [Ridley et al., 2006; Codrescu et al., 2012; Qian et al., 2014], or simple first-principles
causal models [Janhunen et al., 1996, 2012; Raeder et al., 1998; Tanaka, 2000; Hu et al., 2007; Wiltberger
et al., 2009]. All of the existing simulation models of electron precipitation exhibit deficiencies either in
causal regulation, neglect of key types of precipitation or accuracy.
Remedying these deficiencies in global simulations is important for several reasons. Global simulations
are driven by time-variable solar wind conditions and using distributed and dynamic physical variables to
regulate precipitation is essential in producing proper causal connections between precipitation patterns
and their drivers. Since precipitation patterns can be imaged at the different wavelengths of light that
precipitating electrons produce upon impacting the atmosphere [Palmroth et al., 2006; Zhang and Paxton,
2008], accurate dynamic images and their inversions for electron energy and energy flux serve as an
important diagnostic of the state of the system. The more energetic precipitating electrons enhance the
electrical conductivity of the ionosphere [Robinson et al., 1987], which influences the electro-magneto-gasdynamic interaction between elements of the system, including the thermosphere which expands with
increased Joule heating and conductivity [e.g., Fuller-Rowell et al., 1996]. Soft (lower energy) precipitation
adds energy to the F-region and topside ionosphere [Liu et al., 1995], which modifies the scale-height of
the ionosphere, the source distribution of outflowing ionospheric ions, and, therefore, the state of both the
ZHANG ET AL.
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Journal of Geophysical Research: Space Physics
10.1002/2014JA020615
ionosphere and magnetosphere. Thus, different types of precipitation have important effects on different
characteristics of the geospace system.
To date, modeling efforts have focused mainly on specification of the more energetic types of
precipitation—diffuse and monoenergetic—while neglecting the less energetic broadband precipitation.
Monoenergetic precipitating electrons, also known as invert-V electrons, are usually accelerated in the
magnetosphere up to several keV by quasi-static parallel potential drops along magnetic field lines
[Hallinan and Davis, 1970; Evans, 1974; Haerendel et al., 1976; Mozer, 1980a, 1980b; Kletzing et al., 1983].
When the pitch angle of trapped electrons in the plasma sheet is reduced to the point that their mirror
points occur at atmospheric altitude (≈ 100 km), the particles will precipitate. This type of electron
precipitation is known as diffuse electron precipitation due to its more or less featureless character.
Broadband electron precipitation is so-named because the electron energy is distributed over a broad
range, typically from zero to several keV [Johnstone and Winningham, 1982], which is believed to be
caused by electron acceleration in dispersive Alfvén waves (DAWs) [Ergun et al., 1998; Chaston et al., 2000,
2003a, 2003b]. Recent efforts to parameterize the observed dependence of precipitation types and their
characteristics on upstream solar wind (SW) and interplanetary magnetic field (IMF) driving have produced
quantitative empirical models for diffuse, monoenergetic and broadband electron precipitation. These
empirical models, collectively termed OVATION Prime by their developers [Newell et al., 2009, 2010, 2014],
provide a useful touchstone for comparing the predictions of numerical simulation models and the impetus
for developing new models of soft precipitation that can be embedded in global simulations.
This paper describes general methods for improving existing monoenergetic and diffuse electron
precipitation models, together with new models for direct-entry cusp and broadband electron precipitation
(section 3). The improved and new models are generally applicable in global magnetohydrodynamic
simulations of the solar wind–magnetosphere–ionosphere interaction, which, when coupled to
ionosphere-thermosphere general circulation models, can provide physical, causal regulation of electron
precipitation. The precipitation models are specifically implemented here in the LFM global simulation to
demonstrate their behavior in a simulation environment. The empirical parameters of the improved and
new models are chosen to produce agreement with the OVATION Prime model for moderate upstream
driving conditions, and their predictions for precipitating energy flux are then compared with OVATION
Prime over a more extensive range of driving conditions (section 4.1). It is emphasized that while OVATION
Prime is an empirical model derived from an extensive data set of DMSP satellite observations spanning
10 years, it is nevertheless a model with biases and limitations of its underlying assumptions. Thus, when
the LFM and OVATION Prime results do not converge to the same prediction in a particular regime, it is not
necessarily clear from the comparisons reported here which prediction is more accurate. We also compare
LFM and OVATION Prime predictions with inversions of Polar satellite UVI images (section 4.2) that provide
estimates of precipitating power during a double substorm event (28–29 March 1998). The three different
methods for converting dual-wavelength UVI image intensities to electron energy fluxes give estimates
of integrated hemispheric precipitation power that vary by more than a factor of 2 among the various
methods. Thus, while comparisons with UVI event estimates help to qualify LFM and OP predictions, they
also do not provide an absolute metric in this study.
2. The LFM Model and Electrostatic M-I Coupling
The LFM global simulation uses an eighth-order finite volume total variation diminishing scheme on a
nonorthogonal structured grid to solve the single-fluid ideal MHD equations describing the evolution of
mass, momentum, and energy for solar wind and magnetospheric plasma. In the Solar Magnetospheric (SM)
coordinates, the magnetospheric simulation domain extends from XSM = 30 Earth radius (RE ) sunward to
XSM = −300 RE anti-sunward and spans 100 RE in both ±YSM and ±ZSM directions. The computational grid
is nonuniform to achieve higher resolution near the bow shock, the magnetopause, in the plasma sheet
and at low altitudes, with lower resolution far from the earth in the solar wind and at the outer boundaries
of the simulation. The low-altitude (inner) computational boundary is approximately a spherical surface at
a geocentric radial distance of 2 RE where the E × B drift velocity derived from electrostatic coupling to a
2-D ionosphere is imposed as a boundary condition on the perpendicular component of the plasma bulk
velocity. Additional details of the LFM model can be found in Lyon et al. [2004].
ZHANG ET AL.
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The basic equation of the M-I coupling module in most global simulations, including the LFM model,
combines Ohm’s law with current continuity and the electrostatic approximation in the 2-D ionosphere
to obtain the following elliptic equation for the ionospheric electric potential Φi , given the field-aligned
current J||i at the top of the ionospheric conducting layer and the height-integrated conductance tensor Σ:
∇ ⋅ Σ ⋅ ∇Φi = J||i cos 𝛼.
(1)
The dip factor cos 𝛼 = b̂ ⋅ r̂ where b̂ is a unit vector pointing along the dipole magnetic field at the top of
the ionospheric conducting layer and r̂ is the radial unit vector in spherical polar coordinates. Field-aligned
current J|| is computed near the low-altitude computational boundary at approximately 2.2 RE geocentric
in the magnetosphere and is then mapped along dipole magnetic field lines assuming J|| ∕B = const to
the top of the height-integrated ionospheric conducting layer to give J||i . The height-integrated substrate
is located at 1.02 RE (120 km altitude) geocentric where equation (1) is solved. The ionospheric electric
potential Φi obtained from equation (1) is mapped along dipole field lines to the inner boundary
(2 RE geocentric) assuming the magnetic field lines are equipotential. The electric field at the boundary
is calculated as E = −∇Φi which serves as part of the inner boundary condition for the MHD solver. The
ionospheric potential equation (1) is solved by the Magnetosphere-Ionosphere Coupler/Solver (MIX)
program [Merkin and Lyon, 2010].
The height-integrated ionospheric conductance tensor Σ in equation (1) includes contributions from the
Pedersen (ΣP ) and Hall (ΣH ) conductances. In the stand-alone LFM global simulation, empirical equations
derived by Robinson et al. [1987] are used to specify the spatiotemporal distribution of the auroral
contribution to the ionospheric conductance, using electron precipitation energy flux (FE ) and average
energy Ē calculated from the electron precipitation model:
ΣPAuroral =
40Ē
2
16 + Ē
FE0.5 ,
0.85
ΣHAuroral = 0.45 Ē ΣPAuroral .
(2)
(3)
The ionospheric Pedersen and Hall conductance also includes a contribution from solar EUV ionization,
which varies with solar zenith angle and the observed solar radio flux at 10.7 cm [Wiltberger et al., 2009]. The
total conductance is calculated as
√
ΣP,H = Σ2P,H
+ Σ2P,H .
(4)
Auroral
EUV
When the broadband electron precipitation model is implemented in the stand-alone LFM simulation,
which will be discussed in detail in section 3.3, the Robinson equations (2) and (3) are used to calculate the
Pedersen and Hall conductance induced by broadband electron precipitation. Since the broadband electron
precipitation produces ion density in the bottomside F -region, its contributions to ionospheric conductance
add linearly to the E -region contributions from auroral and EUV production:
√
ΣP,H = Σ2P,H
+ Σ2P,H + ΣP,HBroadband .
(5)
Auroral
EUV
3. Models for Electron Precipitation
The causal electron precipitation model currently included in most global magnetosphere models was
introduced by Fedder et al. [1995] and is based on the linearized kinetic theory of loss-cone precipitation
with allowance for acceleration by magnetic field-aligned, electrostatic potential drops [Knight, 1973;
Fridman and Lemaire, 1980]. The Knight-Fridman-Lemaire (KFL) model describes local features of the precipitation given knowledge of the electron source population and the degree of depletion of its loss cone.
The validity of the basic (KFL) theory has been observationally verified [Lyons et al., 1979; Lu et al., 1991; Frey
et al., 1998; Korth et al., 2014], but upward field-aligned currents are not observed always or everywhere to
be carried by the loss cone of a high-altitude electron population [Sakanoi et al., 1995; Morooka et al., 2004].
Extracting suitable parameters from a global magnetohydrodynamics simulation to regulate the spatial and
temporal properties of loss-cone precipitation, including monoenergetic and diffuse, remains challenging.
ZHANG ET AL.
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Direct-entry cusp electron precipitation has a relatively low average energy compared to typical diffuse
and monoenergetic precipitation, and its characteristics are also described by the KFL theory. It is
distinguished from the latter populations by a velocity distribution with an essentially full (versus depleted)
loss cone of precipitating magnetosheath electrons. Direct-entry cusp precipitation and auroral (diffuse plus
monoenergetic) precipitation respond differently to upstream driving conditions.
Superthermal broadband electron precipitation, with energy distributed over a broad range, typically from
tens of eV up to 1 keV, is believed to be caused by relatively low-altitude electron acceleration in dispersive
Alfvèn waves [Ergun et al., 1998; Chaston, 2003a, 2003b]. Broadband electron precipitation was discovered
in early rocket experiments [Raitt and Sojka, 1977] and was surveyed in ISIS-2 satellite measurements
[Johnstone and Winningham, 1982], but it was mostly ignored until high-resolution particle detectors on
rockets and satellites began to reveal a relationship to intense, small-scale Alfvèn waves [Boehm et al.,
1990, 1995; Chaston et al., 1999; Wygant et al., 2002; Chaston, 2003a, 2007]. It has more recently been
demonstrated to be significant in the coupled magnetosphere-ionosphere (M-I) system due to the fact
that broadband electrons statistically contribute approximately 16% of the total hemispheric power during
active times, which is comparable to that of monoenergetic electrons [Newell et al., 2009]. Broadband
precipitation also has an indirect but pronounced effect on thermospheric upwelling near the dayside and
nightside convection throats in the ionosphere where its intensity is greatest [Zhang et al., 2012a]. Neither
broadband precipitation nor direct-entry cusp precipitation has been included in global simulation models.
(The simulation results reported previously by Zhang et al. [2012a] are actually based on the model
developments described in the following sections.)
3.1. Monoenergetic Electrons
The monoenergetic and diffuse (including direct-entry cusp) electron precipitation can be modeled using
the adiabatic kinetic theory [Knight, 1973; Fridman and Lemaire, 1980]. The electrons in the source region
of the magnetosphere are assumed to be isotropic Maxwellian and may be accelerated by a quasi-static
parallel potential drop V along magnetic field lines. By integrating the first parallel moment of the
source-region electron distribution function over the loss cone, the number flux FN of precipitating electrons
at the ionospheric altitude is given by
[
]
(
)
FN = F0 RM − RM − 1 e−eV∕Te (RM −1)
(6)
where Te is the electron source temperature, e is the electron charge, and RM = Bi ∕Bs is the mirror ratio
based on the magnetic fields at the ionospheric altitude (Bi ) and the source region (Bs ). F0 is the precipitating
electron number flux in the absence of parallel acceleration (V = 0). According to equation (6), the maximum
number flux allowed based on the adiabatic kinetic theory is FNmax = RM F0 as V∕Te → ∞.
In order to use equation (6) in global simulations, the electron temperature Te is calculated from the MHD
fluid temperature TMHD at the low-altitude simulation boundary, assuming the electron temperature is a
portion of the bulk temperature (in keV):
Te = 𝛼TMHD
(7)
The parameter 𝛼 = Te ∕(Te + Ti ) = 1∕6 is determined from an assumed (and typically observed) electron-to-ion
temperature ratio of 1:5 in the magnetospheric source region. Usually, 𝛼 is chosen as a constant without
spatial variations.
The electron thermal flux F0 is given by
1∕2
NT
F0 = 𝛽 √e e ,
2𝜋me
(8)
where Ne is the plasma number density at the low-altitude simulation boundary (assumed source region)
and me is the electron mass. The empirical parameter 𝛽 specifies the degree of loss-cone filling in the
electron source region. The electron-ion temperature ratio is set to be one fifth in this study, and the value
of 𝛽 is determined based on data-model comparisons of the hemispheric precipitating power, which will be
discussed in section 4.
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In the upward field-aligned current region, assuming the currents (J‖ ) are carried entirely by electrons
precipitating in the loss cone:
[
] J‖
(
)
FN = F0 RM − RM − 1 e−eV∕Te (RM −1) = ,
e
(9)
If 1 ≤ J‖ ∕eF0 ≤ RM , the potential drop V can be solved from equation (9) as
eV = Te (RM − 1) ln
RM − 1
.
RM − J‖ ∕eF0
(10)
Combing equations (9) and (10), the precipitating electron number flux FN and energy flux FE in the regions
where 1 ≤ J‖ ∕eF0 ≤ RM can be calculated as
(11)
FN = J‖ ∕e
[
FE = FN 2Te + eV
1 − e−eV∕Te (RM −1)
1 + (1 − 1∕RM ) ⋅ e−eV∕Te (RM −1)
]
(12)
In the regions where J‖ ∕eF0 ≤ 1, a potential drop eV is not needed since the hot magnetospheric source
electron population is sufficient to carry the field-aligned currents, therefore the precipitating electron
number flux FN and energy flux FE in this case are
FN = F0
(13)
FE = 2FN Te .
(14)
In the regions where J‖ ∕eF0 ≥ RM , the hot magnetospheric source electron population is not sufficient
to carry all of the upward field-aligned current, so a portion of the current must be carried by the colder
or superthermal electrons. Therefore the precipitating number flux of the hot magnetospheric electron
population is limited to RM F0 , which is the maximum number flux calculated from equation (6).
In the above model, both monoenergetic and diffuse electron precipitation number flux are included. When
the parallel potential drop eV = 0, the unaccelerated precipitating electrons may be regarded as diffuse
precipitation. Actually, accelerated electrons are not necessarily characterized as monoenergetic precipitating electrons unless a specific criterion is satisfied. The criterion used in this study for monoenergetic
electron precipitation is derived from Newell et al. [2009] which is based on the property of precipitating
electron energy spectrum. Assuming an isotropic Maxwellian distribution for the source region electrons,
applying Newell et al. [2009]’s criterion suggests that the precipitating electrons may be considered as
quasi-monoenergetic in the global simulation if
eV
≥ 2,
Te
(15)
Although this condition is not rigorous on defining monoenergetic electrons, it does suggest that the
precipitating electrons are approximately considered as monoenergetic electrons only if the electron
energy acquired in parallel potential drop is greater than the average energy of the unaccelerated
source population.
3.2. Diffuse Electrons
The majority of diffuse electron precipitation is modeled by equations (13) and (14), in which the parallel potential drop V→ 0. In the MHD simulation, if the loss cone filling parameter 𝛽 is set to be uniform
in the entire magnetospheric source region, equation (13) can give unrealistically high precipitating flux
at low latitudes where the loss cone of diffuse electron precipitation becomes severely depleted. Therefore, to model diffuse electron precipitation in global simulations, it is necessary and physically reasonable
to introduce spatial variations for the loss cone filling factor 𝛽 which effectively reduces the diffuse precipitation flux at low latitude on the night side. In other words, the spatial distribution of the parameter 𝛽
should be consistent with the low-latitude diffuse electron precipitation boundary (DPB) reported in observations [e.g., Kamide and Winningham, 1977; Gussenhoven et al., 1981; Hardy et al., 1981]. The low-latitude
ZHANG ET AL.
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DPB arises because the loss cone of diffuse precipitation is practically empty earthward of the inner edge
of the plasma sheet. Observations also show that the DPB is regulated by solar wind and IMF conditions
since the diffuse precipitation is closely associated with the large-scale magnetospheric structure of the
Earth’s magnetic field [Hardy et al., 1981; Nikolaenko et al., 1983]. Using ISIS 1 and 2 satellite data, Kamide and
Winningham [1977] obtained the following linear regression between the DPB position in the night sector
(2000–0400 MLT) and the IMF Bz component:
𝜙DPB = 64.5◦ + 0.6◦ Bz .
(16)
Several possible methods may be used to dynamically regulate the DPB in global simulations. One method
might use upstream IMF Bz to regulate DPB, i.e., by using equation (16). This approach would presumably
show good agreement between an empirically specified DPB in global simulations and statistical
observations of DPB. However, under dramatically varying solar wind and IMF conditions, this method may
not be sufficiently dynamic and accurate due to the statistical nature of the empirical relations such as
equation (16).
The Region 2 current boundary is another candidate to regulate the DPB boundary in global simulations.
Ohtani et al. [2010] show that the nightside equatorward diffuse precipitation boundary is located mostly
inside the Region 2 current system in the dusk-to-midnight sector. They also show that it lies near the equatorward boundary of the Region 2 current system, and even further equatorward, in the midnight-to-dawn
sector. Therefore, the Region 2 current distribution could be used in global simulations to define the
nightside DPB. However, in global simulations Region 2 currents are not very well resolved due to the lack
of drift kinetic physics, which results in a relatively weak ring current in the inner magnetosphere and weak
Region 2 currents in the ionosphere. Hence, the Region 2 current boundary method would not be robust in
the stand-alone LFM simulation, although it may give reasonable results in the LFM-RCM coupling version
of the global model with ring current physics included [Pembroke et al., 2012]. Consequently, another
parameter is needed.
The cusp center location Λ is used in this study to dynamically regulate the DPB in global simulations. The
parameter Λ varies in response to the dynamic coupling between the solar wind and the magnetosphere
and to variations in the large-scale structure of the Earth’s magnetic field. The main idea to be pursued here
is to develop a relationship between the dynamic equatorward boundary of the DPB and the cusp latitude.
To first approximation, the DPB is taken to be a circle centered at 85◦ MLAT and 0100 MLT on the nightside.
This offset of the center of the circle from the geomagnetic pole is suggested by observations. The radius of
the circular DPB is determined by the distance between the center of the DPB and the equatorward edge
of the dayside cusp. The equatorial edge of the cusp is assumed to be 3 degrees lower in latitude than the
center of the cusp Λ, which gives reasonable agreement between the latitude of the DPB predicted by
global simulations and the data points from Kamide and Winningham [1977].
Figure 1 shows the geometry of the model for the equatorward edge of the DPB (left) and distribution
of the loss cone filling factor in the ionosphere (right). Inside the DPB, the loss cone filling function 𝛽 is
approximately uniform with a value of 0.5. Near the equatorward edge of the DPB, 𝛽 decreases continuously
from 0.5 to 0 within 3 degrees and outside the DPB, 𝛽 is set to be zero.
Observational results show that diffuse electron precipitation also exhibits significant dawn-dusk asymmetry due to the gradient-curvature drift of electrons towards the dawnside in the inner magnetosphere
[e.g., Newell et al., 2009]. This drift kinetic effect is not included in the MHD description of the inner
magnetospheric plasma on which the LFM and other global simulation models are based. This asymmetry
is introduced heuristically in the diffuse electron fluxes through the function
(
) (
)
D (𝜙) = 1 − a0 sin 𝜙 H 2Te − eV ,
(17)
(
)
where a0 is an asymmetry parameter. The Heaviside function H 2Te − eV differentiates between diffuse
and monoenergetic precipitation according to equation (15). H(x) = 1 when x > 0, and H = 0 otherwise
so (17) is applied only to diffuse electron precipitation. Thus, the loss-cone filling parameter 𝛽 has
a complicated dependence on the cusp center location (Λ), MLT (𝜙), and MLAT (𝜃 ) which may be
represented as
𝛽 = 𝛽0 ⋅ DPB(𝜆, 𝜙, 𝜃) ⋅ D(𝜙),
(18)
where 𝛽0 is the maximum rate of loss cone filling which is set to a constant.
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Figure 1. (left) Geometry of the dynamically regulated circular DPB in the global simulation. (right) An example of
the distribution of the loss cone filling function for cusp center located at 73◦ MLAT and 1200 MLT. The Feldstein oval
[Feldstein and Starkov, 1967] is shown using dashed red line in Figure 1 (left) and dashed black line in Figure 1 (right).
The dashed blue line in Figure 1 (left) is a circle centered at (0100 MLT, 85◦ MLAT) with the radius determined from the
distance between the center of DPB and the equatorial edge of the cusp.
3.3. Direct-Entry Cusp Electrons
The number flux and energy flux of precipitating direct-entry cusp electrons are also modeled using
equations (13). Since the physical origins of direct-entry cusp electron precipitation differ from those of
monoenergetic and diffuse electron precipitation, it is physically reasonable to introduce a different value
of the loss cone filling factor 𝛽 in the cusp region because the source population in the cusp is continuously
refilled by the direct-entry solar wind plasma. As a consequence, 𝛽 is chosen to represent a loss cone filling
factor for a full loss cone (𝛽 = 1.0) inside the cusp region. Outside the cusp region, the precipitating electron
flux calculated from equation (6) is either monoenergetic or diffuse, and the loss cone filling factor 𝛽 is
chosen to be different from the cusp region.
The simulated cusp region is determined dynamically as the mapping to low altitude from a high-altitude
fiducial surface (6 RE for the simulation results here) of the diamagnetic depression of the simulated
magnetic field relative to an earth-centered dipole field. The cusp is defined as the mapped region where
the magnetic depression ΔB satisfies 0.2 ≤ ΔB∕ΔBmax ≤ 1, where ΔBmax is the maximum magnetic depression, corresponding to the cusp centre. Based on the mapped cusp region derived from the MHD simulation,
the precipitating cusp electron number flux and energy flux are calculated using equation (6). The details
about the cusp identification method can be found in Zhang et al. [2013].
Figure 2 shows the 1 h average precipitating number flux and energy flux calculated based on equations (7),
(12), and (13) from the LFM simulation driven by steady upstream SW conditions with velocity (v ), plasma
density (N), and sound speed (cs ) given by vx = 400 km/s, vy = vz = 0, N = 5cm−3 , and cs = 40 km/s
and IMF conditions with Bx = By = 0, Bz = −3 nT. Monoenergetic, diffuse, and direct-entry cusp electron
precipitation are included in the test simulation. The electron-ion temperature ratio is set to be 1:5 and
the loss cone filling factor 𝛽0 is set to be 0.5 inside the dynamic DPB with a0 = 0.5. In the test simulation,
monoenergetic electron precipitation mainly occurs in the upward R1 current region on the duskside while
diffuse electron precipitation dominates the dawnside. Direct-entry cusp electrons dominate the number
flux in the dayside cusp region, but the cusp electron energy flux (< 0.4mW∕m2 ) is relatively small compared
to both monoenergetic (4 mW∕m2 ) and diffuse (2 mW∕m2 ) electron precipitation.
3.4. Broadband Electrons
Figure 3 shows the similar morphologies of electromagnetic power transported earthward by Alfvénic
fluctuations (left) and observed statistical averages of the energy flux of broadband electron precipitation
(right). The comparison in Figure 3 suggests a causal though imperfect correlation. A simple relationship
between the energy flux carried by a dispersive Alfvén wave and its conversion to broadband electron
energy flux is not yet available, primarily because complicated variations in dispersion, refraction, and nonlinear absorption along the wave characteristics are difficult to analyze in the strongly inhomogeneous
ionosphere and low-altitude magnetosphere. The challenges of calculating the energy and number flux
ZHANG ET AL.
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10.1002/2014JA020615
Figure 2. (left) One hour average monoenergetic and diffuse electron precipitation number flux derived from a test
simulation driven by steady SW/IMF conditions with Bx = By = 0, Bz = −3 nT, vx = 400 km/s, vy = vz = 0, N = 5cm−3
and cs = 40 km/s. (right) The corresponding 1 h average energy flux derived from the same test simulation. The
monoenergetic electron fluxes are shown using blue, and the diffuse electron fluxes are shown in red. The hemispheric
electron precipitation rate and power are listed in the top left and right corner of each panel.
of broadband precipitation in a global simulation are also compounded by the subgrid nature of the
acceleration processes.
The lower electron energy flux in Figure 3 relative to Poynting flux in the dayside sector from 9.5 < MLT < 14.5
may be due in part to Newell et al.’s attempt to distinguish weakly energized broadband precipitation
from direct-entry magnetosheath precipitation with the criterion that the broadband precipitation must
reach energies of at least 80 eV in this sector regardless of flux intensity in order to be categorized as
broadband. In any case, while the Poynting flux and broadband precipitation are both known to be much
more persistent in the dayside sector than in the more variable premidnight region, the dayside medians
(versus the means plotted in Figure 3) in peak Poynting flux, peak energy flux, and mean energy of dayside
broadband precipitation are typically lower by about factor of 4 relative to nightside events [Chaston,
2003a]. To make progress in incorporating this important class of precipitation in global simulations, we
Figure 3. (left) Average field-aligned Poynting flux measured at altitudes of 4-6 RE on Polar from 1 January 1997 to
31 December 1997 and mapped to 100 km altitude [Keiling et al., 2003]. (right) Average energy flux in broadband
electron precipitation measured from 1988 to 1998 on DMSP for relatively “high activity” conditions [Newell et al., 2009].
ZHANG ET AL.
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Figure 4. (left) Precipitating electron energy flux FE from FAST electron measurements [Chaston, 2003a] and the inferred
from Polar UVI images [Keiling et al., 2002] versus simultaneously measured downward Poynting flux (S|| ) in the 0.2–20 Hz
passband form FAST at altitudes of 2–4×103 km and in the 6–180 s pass band for Polar at 4–6 RE . All fluxes are mapped
to 100 km reference altitude. Dashed line is FE = S|| and solid line indicates approximate regression.
will initially pursue an empirical approach based on AC Poynting flux guided by observations and simple
theoretical considerations.
The AC Poynting flux (S|| ) is calculated as
S|| =
B
1
𝛿E × 𝛿B ⋅ ,
𝜇0
B
(19)
where 𝜇0 is the permeability of free space and B is mean vector magnetic field calculated from a 180 s
running average of the locally measured magnetic field. 𝛿 E and 𝛿 B are bandpass fluctuating electromagnetic fields calculated by subtracting 180 s running averages <E>, <B> from instantaneous total fields E, B
recorded with 6 s resolution [Keiling et al., 2003]. The resulting Poynting flux values are then separated into
upgoing and downgoing fluxes. The physical origin and global mophology of the downgoing S∥ in global
MHD simulations have been analyzed in detail by Zhang et al. [2012b, 2014]. The downward S∥ is used to
regulate the precipitating broadband electron fluxes.
Given a reasonably faithful distribution and scaled intensity of Alfvénic Poynting flux derived from a global
simulation, the ability to predict broadband precipitation in the simulation still requires a model that relates
the large-scale, bandpass-filtered Poynting flux to basic characteristics of the precipitating electrons. It is
intuitively appealing simply to assume that some fraction of the electromagnetic energy flux flowing to low
altitude is converted to precipitating electron energy flux. The absorption coefficient of downward flowing
Poynting flux determined from Polar and FAST satellite measurements in fact suggests a conversion efficiency of about 40% in the Alfvén-wave frequency band [Dombeck et al., 2005], but results from 2-D regional
simulations [Streltsov and Lotko, 2003; Watt et al., 2005] indicate that the efficiency depends sensitively on
the transverse length scale of the wave.
A closer examination of field and electron data from Polar and FAST reveals a more complicated relation
between EM and particle energy fluxes, as illustrated in Figure 4. The large scatter in FAST data is due in
part to the different local times and altitudes of the measurements and the corresponding difference in
ambient plasma density and Alfvén speed which affect the wave properties (e.g., dispersion and magnitude
of wave-inertial E‖ ) and the relationship between wave energy and momentum fluxes available for
conversion to electron fluxes. Furthermore, the FAST measurements are acquired within or near the lower
boundary of the Alfvénic acceleration region, wherein much of the EM Poynting flux has already been
converted to electron energy flux (most red data points in Figure 4 (left) lie above the FE = S‖ curve). In
contrast, the in situ fields measured by Polar are mainly acquired above the acceleration region before
appreciable conversion of EM to electron power occurs (most black dots lie below the FE = S‖ curve). Thus,
the Polar Alfvénic Poynting fluxes and precipitating electron energy fluxes, which are inferred from UVI
data (magnetically conjugate to within 1◦ of in situ field measurements), should provide a clearer picture
of the relationship between the EM energy source and the electron energy sink. The Polar data exhibit less
ZHANG ET AL.
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scatter with an approximate regression curve for the
relationship between precipitating electron energy flux
(mW∕m2 ) and Poynting flux (mW∕m2 ):
FE = 2S0.5
.
‖
(20)
This somewhat surprising relationship means the
precipitating energy flux is approximately proportional
to wave |E| rather than |E|2 , suggesting acceleration
through a nearly quasi-static field on the transit time of the
electrons throught the wave field.
Figure 5. Relationship between the Alfvénic
Poynting flux and precipitating electron number
density observed by the FAST satellite [Strangeway,
2010].
Strangeway [2010] derived an empirical relationship
between Alfvénic Poynting flux and precipitating electron
number density based on the FAST satellite data. This
relationship is used in this paper to derive an empirical
model for the calculation of broadband electron
precipitation number flux. Figure 5 shows the data points
from the FAST satellite measurements.
The data points in Figure 5 exhibit an approximate linear
regression curve, with fairly large scatter, of the form
Nep = 2.5S0.44
,
‖
(21)
where Nep is the precipitating soft electron number density (cm−3 ). Strangeway et al. [2005] defines Nep in
terms of the fluxes as
3∕2
Nep = 2.134 × 10−14
FN
1∕2
FE
,
(22)
where FN and FE are the number flux and energy flux of soft electron precipitation. Combining the
empirical relations (20) and (21) with definition (22), the number flux of precipitating broadband electrons
at the ionospheric reference altitude (100 km) can be calculated as
( )0.04
BF
FN = 3 × 109 S0.46
≈ 3 × 109 S0.46
[cm−2 s−1 ].
(23)
‖
‖
BI
where S‖ is given in mW∕m2 and BF ∕BI is the ratio of the magnetic field between FAST altitude (4000 km)
(
)1∕2
and ionospheric reference altitude (100 km). The factor 2.134 × 10−14 = me ∕2
is required to obtain the
correct dimensional form of the Nep in cm−3 . Equation (20) and (23) are the empirical relations that can be
used to model broadband electron precipitation in global simulations.
Since the transverse scale of dispersive Alfvén waves is subgrid in the LFM simulation, the simulated parallel
Alfvénic Poynting flux S‖ is not exactly the same as the dispersive Alfvénic power measured by FAST and
Polar satellites. However, as discussed in the supplement of [Brambles et al., 2011], the observed Alfvén
waves are part of a continuous Alfvén wavenumber spectrum that extends to the length-scale regime
accessible in global simulation. Therefore, given the uncertainties in both empirical relations and parallel
Alfvénic Poynting flux S‖ , an adjustable parameter A is introduced to scale the simulated S‖ , and the
empirical relations for broadband electron precipitation are given as
( )0.5
FE = 2 AS‖
[mW∕m2 ]
(24)
( )0.47
FN = 3 × 109 AS‖
[cm−2 s−1 ].
(25)
The value of the adjustable parameter A is determined from the data-model comparison discussed in
section 4. The average energy of precipitating broadband electrons can be calculated as
Ē =
ZHANG ET AL.
( )0.03
FE
= 0.41 × AS‖
[keV].
FN
©2015. American Geophysical Union. All Rights Reserved.
(26)
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Table 1. Solar Wind vx and IMF Bz Values Used in Each Test
Simulationa
Runs
1
2
3
4
5
6
7
8
9
10
Bt (nT)
vx (km/s)
𝜃 (deg)
d𝜙MP ∕dt(MWb∕s)
1
2
3
4
5
6
7
8
9
10
400
400
400
400
400
400
400
400
400
400
180◦
180◦
180◦
180◦
180◦
180◦
180◦
180◦
180◦
180◦
0.45
0.71
0.93
1.13
1.31
1.48
1.64
1.80
1.94
2.08
10.1002/2014JA020615
When S‖ varies from 0.001 mW∕m2 to
10 mW∕m2 , the average energy Ē only
increases from 350 eV to 450 eV. The
modelled average energy of precipitating
broadband electrons is a bit higher but
consistent with the statistical distribution
of characteristic energies of downgoing,
Alfvén-wave accelerated electrons shown
in Chaston [2003a, Figure 5] from FAST
measurements.
4. Model Comparisons
4.1. Effects of Empirical Parameters
on Hemispheric Power
To investigate the effects of the empirical
parameters 𝛽 (for monoenergetic and
diffuse electrons) and the scaling factor
A (for broadband electrons), 10 different
sets of ideal upstream driving conditions
are used to drive the LFM global simulation. The electron-ion temperature ratio is fixed to be 1:5, and the
upstream driving solar wind velocity vx and IMF Bz conditions used in the test simulations are listed in
Table 1. The solar wind density N is chosen to be 5 cm−3 , solar wind sound speed cs is set to be 40 km/s,
and the other solar wind velocity (vy , vz ) and magnetic field (Bx , By ) components are set to be zero. In order
to compare the simulated hemispheric power with the OVATION Prime empirical, which is parameterized
4∕3
based on the solar wind coupling function d𝜙MP ∕dt = vsw (B2y + B2z )1∕3 sin8∕3 (𝜃c ) [Newell et al., 2007],
the values of the corresponding solar wind coupling function d𝜙MP ∕dt in units of MWb∕s are also listed
in Table 1 (𝜃c = tan−1 (Bz ∕By ) is the IMF clock angle). In each test simulation, the magnetosphere is
preconditioned for 4 h by first driving with southward IMF with Bz = −5 nT for 2 h, followed by northward
IMF with Bz = +5 nT for 2 h. After the preconditioning of the magnetosphere, the corresponding steady
SW/IMF conditions listed in Table 1 are used to drive the system for 4 h. The simulated electron precipitation
fluxes were calculated as 1 h average values from the last simulation hour (07:00–08:00 ST), in which the
magnetosphere was in a steady magnetospheric convection (SMC) state; that is, the dayside and nightside
reconnection rates are balanced and no substorm activity was observed during the simulation period.
and 𝜃c = tan−1 (Bz ∕By ). Other parameters
are as follows: vy = vz = 0, N = 5cm−3 , and cs = 40 km/s. The
values of the solar wind coupling function d𝜙MP ∕dt in units
of MWb∕s are listed in the fifth column.
aB
2
2 1∕2
t = (By + Bz )
Figure 6a shows the precipitating monoenergetic electron power versus d𝜙MP ∕dt for different values of
the loss cone filling parameter 𝛽 (0.1–0.9) when the electron-ion temperature ratio is fixed at 1:5. The
monoenergetic electron power derived from the OVATION Prime is also shown in Figure 6a (the red
dashed line). In the test simulations, as the solar wind coupling function d𝜙MP ∕dt increases, the simulated
precipitating monoenergetic electron power increases approximately quadratically when the loss cone
filling factor 𝛽0 is fixed, while the OVATION Prime power increases approximately linearly. As will be shown
in the subsequent event study, the simulations exhibit essentially zero monoenergetic precipitation flux on
the dawnside, whereas the OVATION Prime model has a finite flux there. The black dashed curve in Figure 6a
shows the duskside power of monoenergetic electron precipitation derived from the OVATION Prime model.
Figure 6b shows the simulated hemispheric integrated power of precipitating diffuse electrons versus
d𝜙MP ∕dt for different values of the loss cone filling parameter 𝛽0 with a fixed electron-ion temperature
ratio of 1:5, together with the diffuse electron power derived from OVATION Prime. For a given magnitude
of the solar wind coupling function, when the loss-cone filling parameter 𝛽0 increases from 0.1 to 0.9, the
simulated hemispheric diffuse electron power increases approximately linearly since the precipitating
electron number flux is proportional to the loss cone filling. For a given loss cone filling factor, the simulated
hemispheric integrated diffuse electron precipitation power increases approximately quadratically with the
solar wind coupling function. However, the hemispheric precipitating diffuse electron power predicted by
OVATION Prime increases approximately linearly with the solar wind coupling function. One reason for this
difference is because, in the simulation when d𝜙MP ∕dt increases, both the intensity of the diffuse electron
energy flux and the width of the diffuse auroral oval increase. Hence, the hemispheric integrated power of
diffuse electron precipitation exhibits approximately a quadratic relation with d𝜙MP ∕dt rather than linear.
ZHANG ET AL.
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Figure 6. Simulated (a) monoenergetic, (b) diffuse electron hemispheric power with different loss cone filling factor 𝛽 , and (c) broadband electron hemispheric
power with different scaling factor A, together with the electron power predicted by the OVATION Prime empirical model. The simulated hemispheric average
energies from (d) hard and (e) soft electrons.
Other numerical experiments show that in the simulation, when the diffuse precipitation boundary (DPB) is
artificially fixed to 65◦ MLAT on the nightside with constant 𝛼 and 𝛽0 , the diffuse electron power increases
approximately linearly with the solar wind coupling function.
Figure 6c shows the hemispheric integrated power of precipitating broadband electrons versus d𝜙MP ∕dt for
different values of the scaling factor A with Te ∕Ti = 1/5 and 𝛽0 = 0.5 fixed for the monoenergetic and diffuse
electron precipitation for all cases. Note that although Te ∕Ti and 𝛽0 do not directly parameterize broadband
electron precipitation in the model, their values influence the fluxes of broadband electron precipitation
due to the nonlinear nature of the simulation. The results for broadband electron power derived from the
OVATION Prime model are shown as a red dashed line. The test simulation results show that the best fit of
the simulated broadband electron power to the OVATION Prime power occurs for a scaling factor A between
2 and 3. Therefore, in the broadband electron precipitation model, the default value of the scaling factor A is
set to be 2.5.
Figure 6d and 6e shows the simulated hemispheric average energy for the hard and soft electron
populations, respectively. The hemispheric average energy of each precipitating electron population is
calculated as the ratio between the hemispheric integrated energy flux and hemispheric integrated number
flux. Since the average energy is not sensitive to the loss cone filling parameter 𝛽0 which affects the diffuse
electron number flux directly, only the test simulation results derived from 𝛽0 = 50% is shown in Figures 6d
and 6e. Simulation results show that the hemispheric average energies of both monoenergetic and diffuse
electron increase with the solar wind coupling function. The hemispheric average energy of direct-entry
cusp electrons also increases with the coupling function but its magnitude is much lower than the hard
electrons. The hemispheric average energy of broadband electrons remains approximately 400 eV for all
values of the solar wind coupling function and the parameter A, which is consistent with equation (26).
ZHANG ET AL.
©2015. American Geophysical Union. All Rights Reserved.
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Figure 7. Upstream solar wind density (N), velocity (vx , vy , vz ), sound speed (cs ), and IMF (Bx , By , Bz ) for the interval 28
March 1998, 2300 UT, to 29 March 1998, 0600 UT, obtained using the OMNI one minute averaged multispacecraft interplanetary parameter data (NASA Coordinated Data Analysis Web site). The shaded time period is used to initialize the
magnetosphere for the global simulation.
The response of the hemispheric average energy shows that both direct-entry cusp and broadband
electrons are soft electrons (< 500 eV) compared to monoenergetic and diffuse electrons (several keV).
4.2. The 28–29 March 1998 Event Simulation
To perform data-model comparisons for actual events, we chose a double-substorm event that occurred
from 23:00 UT 28 March 1998 to 06:00 UT 29 March 1998. The time evolution of hemispheric power during
the event has been studied in detail by Palmroth et al. [2006] using data from Polar UVI images. Figure 7
shows the solar wind and IMF conditions for the 28–29 March 1998 event, which are used as upstream
driving conditions in the LFM global simulation.
In the 28–29 March 1998 event, a southward turning of the IMF at 22:30 UT was observed after several hours
of northward orientation. The IMF Bz rotated from northward to southward (SM coordinate) reaching about
−10 nT at about 00:10 UT, after which the northward orientation was attained at 01:50 UT on 29 March 1998.
Another southward turning of the IMF at 03:00 UT was followed by a northward turning an hour later, at
04:00 UT. The IMF By fluctuated between zero and −5 nT during the two southward orientations. Solar wind
velocity varied between 450 and 500 km/s throughout the time interval of interest, whereas the solar wind
density remained in the range 4–5 cm−3 . The solar wind sound speed fluctuated between 20 and 40 km/s.
The global simulation was started at 20:00 UT on 28 March, 3 h before the start time (2300 UT on March
28) of the 28–29 March 1998 event. The simulation between 20:00 UT and 23:00 UT is thus used to initialize
and precondition the magnetosphere for the global simulation (the shaded area in Figure 7). Between
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20:00 and 23:00 UT, the IMF Bz is mostly
positive and the activity level in the
magnetosphere-ionosphere system
Parameters
Monoenergetic
Diffuse
Cusp
Broadband
is relatively low. Only the simulation
𝛼
1/6
1/6
1/6
—
data from 28 March 23:00 UT to 29
𝛽
0.5
0.5
1.0
—
March 06:00 UT are analyzed and
a0
—
0.5
—
—
compared with observational
A
—
—
—
2.5
results in the following section. The
precipitation parameters used in the
event simulation are listed in Table 2. The parameter 𝛼 in the simulation is chosen to specify an electron-ion
temperature ratio of 1:5 for monoenergetic and diffuse electron precipitation. The loss-cone filling
parameter 𝛽0 is chosen to represent a loss cone filling factor of 0.5 for monoenergetic and nightside diffuse
electron precipitation and 1.0 for the dayside direct-entry cusp electron precipitation. The scaling factor A in
the broadband electron precipitation model is set to be 2.5.
Table 2. The Values of the Empirical Parameters 𝛼 , 𝛽 , a0 and A Used in
the 28–29 March 1998 Event Simulation
Table 3 summarizes the simulated global average precipitation rate, power, and energy for each type of
electron precipitation in the northern hemisphere with the average computed over the full 7 hours of the
event. The hemispheric average global energy of electron precipitation is estimated using the ratio between
the hemispheric electron power to the corresponding hemispheric precipitation rate. Results show that
the simulated hemispheric power of precipitating electrons is dominated by diffuse electrons during the
28–29 March 1998 event. On average, diffuse electrons (including direct-entry cusp electrons) contribute
60.9% of the total precipitating electron power whereas the percentages for monoenergetic and broadband
electrons are 29% and 9%, respectively. The monoenergetic electron precipitation has the highest average
energy of 8.5 keV compared to 2.6 keV for diffuse electron precipitation. Note that the global average energy
for diffuse electron precipitation maybe underestimated since the intense diffuse electron precipitation
only occurs in the auroral oval, while the global average includes all the contributions inside the DPB. Both
broadband and direct-entry cusp electron precipitation have relatively low average energies (0.41 keV and
0.37 keV) and are typically considered as a soft electron precipitation. Note that the hemispheric power of
cusp electron precipitation is at least one order of magnitude less than that of the diffuse, monoenergetic,
and broadband precipitation.
When the energy fluxes of all the precipitating electron populations are added, the total hemispheric
precipitating electron power can be compared with the observational data reported by Palmroth et al.
[2006]. The N2 LBH-long filter used in the Polar UVI technique is insensitive to the characteristic energy of
the precipitating electrons and is mainly dependent on the total energy flux [Doe et al., 1997]. Therefore,
all three types of electron precipitation are combined to compare with Polar UVI data. Figure 8 shows
the simulated northern hemispheric total electron power using both improved and existing electron
precipitation models, together with the observed northern hemispheric electron power derived from
Polar UVI image data from Palmroth et al. [2006]. UVI power was calculated using three different methods
reported by Germany et al. [1998, 2004], Lummerzheim et al. [1991], and Liou et al. [2001, 2003]. Each
method inverts the UVI brightness differently, and it is not clear in literature which inversion method is more
representative of the actual precipitation electron power. Note that the three methods disagree significantly
Table 3. Summary of the Average Electron Precipitation During the 28–29 March 1998
Eventa
Monoenergetic
Diffuse
Cusp
Broadband
Power (GW)
Precipitating Rate (1025 s−1 )
Average Energy (keV)
14.7 (29.5%)
30.4 (60.9%)
0.3 (0.60%)
4.5 (9.0%)
1.1 (7.2%)
7.3 (48.0%)
0.5 (3.3%)
6.8 (41.5%)
8.5
2.6
0.37
0.41
a The global average energy is estimated from the ratio of the hemispheric power (GW)
and precipitating rate (s−1 ).
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Figure 8. Total northern hemispheric precipitation power as computed by the Germany method (red), Lummerzheim
method (green), and Liou method (dark blue), together with the simulated hemispheric electron precipitation power
using the existing Fedder electron precipitation model and the improved electron precipitation model. The prediction
from the OVATION Prime model is shown in black. The data sets shown in the figure are adapted from Palmroth
et al. [2006].
on the magnitude of the power deposited during the period of highest activity (00:00 to 02:00 UT). This
difference must be due to differences in the methods used to convert photon brightnesses to total power.
While these differences are noteworthy, they are not the focus of this study. The three different calculations
provide a range of observationally derived power that can be compared with the global simulation results.
During the most active time period of the 28–29 March event (00:00 UT–02:00 UT), the simulated northern
hemispheric total electron power (light blue curve in Figure 8) rises and falls like the other curves in Figure 8.
Its peak power is most comparable to the Lummerzheim et al. result which gives the largest hemispheric
power derived from UVI image data. During the relatively quiet period from 02:30 UT to 04:00 UT, the
simulated total electron power more closely resembles that of the Germany et al. result, which is greater than
the other two estimates at these time. During the second active period (04:00 UT–06:00 UT), the simulation
result agrees well with the Germany et al. and Lummerzheim et al. estimates. The simulated total electron
power using the existing electron precipitation model is significantly less than any of the UVI inversions
or the predictions using the improved electron precipitation model, except during the least active intervals.
The increase of the hemispheric power using the new electron precipitation models also partially due to
the changes in the electron-ion temerature ratio 𝛼 and the loss cone filling factor 𝛽0 . In the existing electron
precipitation model, the electron temperature Te is calculated as Te = 1.71TMHD , which is nonphysical. As a
consequence, the corresponding optimal 𝛽0 used in the existing model was chosen to be 3% which gives
relative lower hemispheric power. The new diffuse electron precipitation models use an electron-ion
temperature of one fifth which is consistent with observations of plasma properties in the magnetosphere
[e.g., Baumjohann et al., 1989], together with a 50% loss cone filling rate (16 times larger). It is possible that
either of the three inversion method may be the most accurate for this particular event, which suggests
that more diagnostics are needed in order to determine the optimal empirical parameters for model
improvement. Overall, the dynamic response of the simulated hemispheric power during the two substorms
are improved using the new electron precipitation models. The OVATION Prime prediction of the total
hemispheric power during the event are also shown in Figure 8. The empirical model most closely tracks
the double peaks in the intermediate inversion estimate, but it overestimates the total precipitation power
between the two substorms (0200–0400 UT) by approximately a factor of 2 relative to all other estimates
due to the 4 h average algorithm ([Newell et al., 2010]) used in calculating the weighted solar wind coupling
function for this particular event.
Figure 9 shows the comparisons between the simulated distributions of precipitating electron energy
fluxes and the OVATION Prime model prediction for this event. The results for combined distributions of
monoenergetic and diffuse electron precipitation are included in Figures 9a–9c (top). The spatial patterns of
monoenergetic and diffuse precipitation do not overlap appreciably in the simulations whereas significant
overlap does occur in OVATION Prime, particularly in the premidnight region.
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Figure 9. (a) The relationship between the hemispheric diffuse and monoenergetic power and the effective solar wind coupling function dΦMP ∕dt with
the corresponding OVATION Prime prediction shown in red, (b) the combined distributions of diffuse and monoenergetic precipitation corresponding to
dΦMP ∕dt = 1MWb∕s derived from LFM, and (c) the combined distributions of diffuse and monoenergetic precipitation corresponding to dΦMP ∕dt = 1MWb∕s
predicted by OVATION Prime. (d) The relationship between the hemispheric broadband power and the effective solar wind coupling function dΦMP ∕dt with the
corresponding OVATION Prime prediction shown in red, 9e) the average distribution of broadband precipitation corresponding to dΦMP ∕dt =1MWb∕s derived
from LFM, and (f ) the distribution of broadband precipitation corresponding to dΦMP ∕dt = 1MWb∕s predicted by OVATION Prime. The averaging range of
dΦMP ∕dt used to calculated the LFM pattern is shown in the shaded band in Figures 9a and 9d. The red contour in Figure 9b shows the region of average upward
field-aligned current for dΦMP ∕dt =1MWb∕s.
Figure 9a shows the relationship between the hemispheric diffuse plus monoenergetic power versus the
effective solar wind coupling function dΦMP ∕dt. The hemispheric power predicted by the OVATION Prime
empirical model at seven discrete values of dΦMP ∕dt is indicated by the red dots which are connected
in the plot by straight lines. In order to compare the simulated patterns and hemispheric power with the
OVATION Prime model, the effective dΦMP ∕dt for the simulation data in Figure 9a is derived from the SW/IMF
conditions at the bow shock using exactly the same weighting method described by Newell et al. [2010].
The values of dΦMP ∕dt and the hemispheric precipitation power are calculated on a one-minute cadence
in the simulation, and the corresponding values are shown as plus symbols in Figure 9a. The hemispheric
power predicted by OVATION Prime exhibits an approximately linear relation with dΦMP ∕dt, while the
hemispheric diffuse plus monoenergetic power in LFM exhibits an approximately quadratic variation with
the weighted dΦMP ∕dt. In other words, the OVATION Prime empirical model gives higher hemispheric
power for quiet driving and lower hemispheric power for high driving compared to the LFM simulation. The
overestimation of precipitating power during quiet time is also evident in the comparisons shown in
Figure 8 between the two substorms during the 28–29 March 1998 event. The quadratic relationship in LFM
is due to the expansion of the DPB together with the increase of the intensity of diffuse electron energy flux
as dΦMP ∕dt increases, which is consistent with the test simulations discussed in section 4.1.
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To compare the simulated patterns of diffuse plus monoenergetic electron precipitation with the OVATION empirical model for moderate driving conditions (dΦMP ∕dt = 1 MWb∕s), we average the simulated
precipitation patterns with 0.75<dΦMP ∕dt<1.25 MWb∕s (the shaded band in Figure 9a) and consider the
averaged pattern as the representation for dΦMP ∕dt =1 MWb∕s for this event. Figures 9b and 9c show the
spatial distributions of diffuse plus monoenergetic precipitation corresponding to dΦMP ∕dt = 1 MWb∕s
derived from LFM and OVATION Prime, respectively. In the event simulation, the diffuse electron precipitation is mainly located in the midnight-dawn sector between 62 and 70 MLAT, with a peak energy flux of
2.6 mW∕m2 . The simulated diffuse electron precipitation exhibits significant dawn-dusk asymmetry which
is a consequence of the drift function introduced in section 3.2. The diffuse electron precipitation predicted
by the OVATION Prime model is located between 60 and 68 MLAT, with a a peak energy flux of 2.5 mW∕m2 .
An especially noteworthy difference between the LFM and OVATION Prime diffuse electron precipitation
pattern is the low intensity of simulated precipitating energy flux in the dawn-noon sector between 60 and
70 MLAT, relative to that of OVATION Prime. The noticeable enhancement in energy flux in OVATION Prime
between 0600 and 0900 MLT is probably due to the gradient-curvature drift of relatively energetic electrons
that are scattered into the loss cone along drift paths. Statistical patterns of the energy of precipitating
electrons are consistent with this interpretation [Hardy et al., 1985]. The causative kinetic effects are absent
in the LFM simulation. The paucity of diffuse electron precipitation within ±2 h of local noon in the
simulation is a shadowing effect of the inner boundary at r = 2 RE in the MHD simulation. In the global
simulation, E × B drifting fluid from the nightside plasmasheet is largely excluded from this local time
segment, and the thermal electron flux is consequently low in this region.
In the event simulation, for moderate driving conditions (dΦMP ∕dt =1 MWb∕s), the monoenergetic
electron precipitation is mainly located on the duskside between 70 and 80 MLAT where upward R1 current
occurs. It achieves a peak energy flux of 4.6 mW∕m2 in this region as shown in Figure 9b. The monoenergetic
electron energy flux predicted by the OVATION Prime model is less intense than in the LFM simulation, and
it has a peak energy flux of 1.9 mW∕m2 located approximately 5°–10° lower in MLAT compared to the LFM
simulation, as shown in Figure 9c. The field-aligned current in the MHD simulation may be several degrees
higher in latitude than is typically observed [Zhang et al., 2011] due to the fact that the magnetotail is not as
stretched in the simulation as in the actual system. The magnitudes of monoenergetic plus diffuse electron
energy flux are similar for LFM (21.3 GW) and OVATION Prime (24.1 GW), but a greater portion of this energy
flux is deposited by monoenergetic precipitation in LFM than in OVATION Prime. It is worth mentioning that
the monoenergetic electron precipitation pattern in LFM is consistent with the statistic results presented
by Korth et al. [2014] in contrast with those of OVATION Prime. The strong correlation between duskside R1
currents and intense monoenergetic electron energy flux and the weaker correlation between dawnside
R2 currents and precipitation energy flux is manifest in both the LFM patterns (Figure 9b) and the statistical
results of Korth et al. [2014] for IMF Bz < 0 (their Figure 7).
Figure 9d shows the relationship between the hemispheric broadband electron power and the effective
dΦMP ∕dt, together with the hemispheric power predicted by the OVATION Prime empirical model. The
hemispheric broadband electron power predicted by OVATION Prime increases approximately linearly
with the coupling function dΦMP ∕dt. The simulated hemispheric broadband power increases similarly
with dΦMP ∕dt but with relatively large scatter. The large scatter in the simulated broadband power may
be related to a significant IMF By in the driving condition [Zhang et al., 2014]. Overall, the linear fit of the
scattered data points is approximately consistent with the OVATION Prime model as suggested also by the
ideal test simulations discussed in section 4.1.
Figures 9e and 9f show the distributions of broadband electron precipitation corresponding to
dΦMP ∕dt = 1 MWb∕s derived from LFM and OVATION Prime, respectively. The main enhancement in the
intensity of the simulated broadband electron precipitation occurs on the nightside, in the pre-midnight
sector between 70◦ –78◦ MLAT and 2100–2400 MLT with a peak energy flux of 0.4 mW∕m2 . Another
enhancement in the intensity of the simulated broadband electron energy flux occurs on the dayside
between 72◦ –76◦ MLAT and 0900–1500 MLT with a peak energy flux of 0.3 mW∕m2 . The dayside broadband
electron flux is due to the fact that during the event simulation, the dayside magnetic field lines are
continuously perturbed by the upstream solar wind, which generates significant amount of downward
Alfvenic Poynting flux. This dayside enhancement of broadband electron flux (Alfvenic Poynting flux) does
not exist when the system is in an SMC state [e.g., Brambles et al., 2011; Zhang et al., 2014]. Note that the
distribution of the simulated broadband electron precipitation exhibits a significant dawn-dusk asymmetry
ZHANG ET AL.
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Journal of Geophysical Research: Space Physics
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and approximately 70% of the broadband precipitation occurs in the premidnight sector. This dawn-dusk
asymmetry also exists for other values of dΦMP ∕dt and is a consequence of the nonuniform ionospheric
conductance regulated by the electron precipitation model in the simulation [Zhang et al., 2012b;
Lotko et al., 2014]
The spatial distribution of the OVATION Prime broadband electron precipitation energy flux also has two
main intensity enhancements. On the dayside, the broadband electron precipitation energy flux intensifies
in the region between 70◦ –76◦ MLAT and 0600–1600 MLT with a peak energy flux of 0.19 mW∕m2 in the
prenoon sector near 0800 MLT. On the nightside, the OVATION Prime broadband electron precipitation
energy flux is mainly located between 64◦ and 74◦ MLAT with a peak energy flux of 0.69 mW∕m2 near
2230 MLT. The simulated broadband electron precipitation exhibits the same dawn-dusk asymmetry
compared with the OVATION Prime results, with magnitudes of number flux and energy flux similar to those
of OVATION Prime. Both simulation and OVATION Prime suggest that the broadband electron precipitation
is relatively soft compared with monoenergetic and diffuse electron precipitation. On the nightside, the
simulated broadband electron precipitation patterns are located approximately 4◦ MLAT higher that the
OVATION Prime patterns. This difference may be due in part to the fact that the simple dipole magnetic field
used in the global simulation is not accurate at low altitude.
4.3. Discussion
The main difference between the LFM and OVATION Prime diffuse precipitating electron power is that the
LFM simulation exhibits a quadratic relationship between the hemispheric power and the SW coupling
function dΦMP ∕dt while OVATION Prime exhibits a linear relationship. Although the comparisons shown
in Figure 9 suggest that the LFM electron precipitation agrees reasonably well with OVATION Prime
for moderate driving (dΦMP ∕dt = 1 MWb∕s), the LFM simulation gives lower power for weak driving
(dΦMP ∕dt < 0.5 MWb∕s) and higher power for strong driving (dΦMP ∕dt >1.5 MWb∕s). The linear regression
in OVATION Prime is based on the large amount of satellite data, but it is not clear if the precipitating diffuse
electron power should exhibit an exactly linear relation with intensity of driving in the actual M-I system.
It is possible that the OVATION Prime model is limited in predicting precipitating power during active
periods. The most recent version of OVATION Prime (OP-13) developed by Newell et al. [2014] uses data from
TIMED GUVI to improve the prediction of total precipitation power during active times. In the OP-13 model,
for example when Kp ≈ 8, the equatorial boundary of the empirical precipitation pattern moves below
60◦ MLAT, and the total precipitation power increases by almost 50% compare to the original OVATION
Prime model. The improved OP-13 model is believed to be more realistic, especially expanding to lower
latitudes than the original OP, which suggests that the expansion of the DPB during active periods in the
LFM simulation is reasonably well modeled.
Compared with the OVATION Prime empirical model, the simulated monoenergetic, diffuse, and broadband
electron precipitation results agree reasonably well for select values of the parameters Te ∕Ti ≈ 1∕5, 𝛽0 ≈ 0.5,
and A ≈ 2.5. Additional simulations of events with separate global estimates of precipitating power are
needed to evaluate the accuracy of the new electron precipitation model and the robustness of these model
parameter choices. The properties of monoenergetic and diffuse electron precipitation in the simulation
depend on the magnetospheric conditions near the low-altitude boundary, in particular, the field-aligned
current, fluid density, and sound speed. Therefore, some memory of initial conditions may persist in these
simulations. Validation of simulations that demonstrate the robustness of optimal values of 𝛼 , 𝛽 , and A
requires comprehensive statistical studies, such as the LFM “Long Run” [Guild et al., 2008a, 2008b; Zhang
et al., 2011]. In addition, to further calibrate the empirical parameters used in the electron precipitation
models, global observations such as UVI images, which not only provide estimates of hemispheric
precipitating power but also give possible validations on the spatial distributions of the simulated electron
precipitation fluxes, may be useful.
Note that the empirical ionospheric conductance model used in the stand-alone LFM simulation is
essentially derived for an incident Maxwellian distribution of precipitating electrons, which is not accurate
for precipitating electrons especially for broadband electrons. Given the fact that the distributions of ionospheric condcutance are crucial in regulating the coupling between the magnetosphere and ionosphere
[e.g., Lotko et al., 2014], a more sophisticated calculation of the ionospheric conductance [e.g., Fang et al.,
2010] will be important for further improving the empirical parameters used in the electron precipitation
models. However, this type of model improvement is beyond the scope of this study and is more suitable
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for a follow-up study using the coupled magnetosphere-ionosphere-thermosphere (CMIT) model, which
couples the LFM magnetosphere model to the NCAR-Thermosphere-Ionosphere Electrodynamics General
Circulation Model [Wiltberger et al., 2004; Wang et al., 2004].
The grid resolution of the simulation also affects the results. The resolution of the LFM global model used in
this study is 53 × 48 × 64 (the 48 × 64 grid cells corresponds to the resolution in the ionosphere which is
approximately 2◦ × 2◦ in the polar cap), which is relatively low but also the most popular resolution in the
LFM simulation community. Numerical experiments show that when the resolution of the global simulation
increases, the location of field-aligned current, the open/close field line boundary, MHD state variables near
the inner computational boundary, and the magnitude of the Alfvénic Poynting flux can change. Therefore,
the electron precipitation models give different results, and the values of 𝛼 , 𝛽 and A will need to be
optimized for agreement with data for each grid resolution of the code. These values of the empirical
parameters will also need to be tuned when nonideal MHD physics are incorporated in the global simulation
such as coupling to a ring current model or extending the global simulation to be multi-ion fluid.
5. Summary
In this paper, the existing models for monoenergetic, diffuse, and direct-entry cusp electron precipitation
were improved in the single-fluid Lyon-Fedder-Mobarry (LFM) global magnetosphere simulation. An
empirical model of broadband electron precipitation was also implemented in the LFM simulation.
The monoenergetic, diffuse, and direct-entry cusp electron precipitation are all calculated from the
Fridman and Lemaire [1980] kinetic model. The inconsistent causality of the existing monoenergetic electron
precipitation model is addressed by solving the potential drop from the full nonlinear F-L relation instead
of the linear Knight potential drop relation. The existing diffuse electron precipitation model is improved
by introducing a dynamically regulated diffuse precipitation boundary (DPB). The DPB is regulated by the
simulated latitude of the polar cusp which is controlled by the dayside solar wind–magnetosphere
interaction and large-scale structure of the magnetic field. The unrealistically high fluxes of diffuse electron
precipitation at low latitude in the existing precipitation model are effectively eliminated by the DPB in the
LFM simulation.
The direct-entry cusp electron precipitation is implemented in the LFM simulation based on a cusp
identification algorithm. This algorithm uses diamagnetic depression properties of the simulated magnetic
field at high altitude (6 RE or less if the magnetopause is pushed inside 6 RE by the solar wind). The
high-altitude cusp region is mapped along magnetic field lines to low altitude (1.02 RE ). The mapped cusp
region is used to calculate direct-entry cusp electron fluxes using the Fridman and Lemaire [1980] model
with a loss cone filling factor that represents a full loss. The cusp loss cone is full because cusp flux tubes are
assumed to be continuously refilled by solar wind plasma.
The broadband electron precipitation is regulated by simulated field-aligned Alfvénic Poynting flux (S‖ ).
The number flux and energy flux of broadband electron precipitation are specified using empirical relations
derived from data measured by the FAST and Polar satellites. The nightside Alfvénic Poynting flux in the
LFM simulation is generated in the plasmasheet through the braking process of earthward fast flows, with a
significant dawn-dusk asymmetry. The asymmetric distribution of S‖ and broadband electron precipitation
are also observed by satellites. Global simulation shows that this dawn-dusk asymmetry is caused by the
nonuniform distribution of ionospheric conductance.
The simulated four types of electron precipitation flux from the improved and new electron precipitation
models have been compared to the OVATION Prime empirical model. Ideal simulation results show that the
hemispheric electron power of diffuse and monoenergetic electron precipitation increases approximately
quadratically with the solar wind coupling function dΦMP ∕dt, while the OVATION Prime empirical model
shows a linear relationship with the same coupling function. The simulated broadband electron power
exhibits approximately a linear relationship with the solar wind coupling function which agrees well with
the empirical model. Comparisons of LFM and OVATION Prime predictions with estimates of hemispheric
precipitating power derived from inversions of Polar satellite UVI images during the 28–29 March 1998
event (a double-substorm event) show that the LFM peak precipitating power is > 4× larger than the
existing model prediction when using the improved precipitation model and most closely tracks the larger
of three different inversion estimates. On the other hand, the OVATION Prime prediction most closely tracks
ZHANG ET AL.
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Journal of Geophysical Research: Space Physics
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the double peaks in the intermediate inversion estimate, but it overestimates the precipitating power
between the two substorms by approximately a factor 2 relative to all other estimates. LFMs polar pattern of
precipitating energy flux tracks that of OVATION Prime for broadband precipitation exhibits good correlation
with duskside region 1 currents for monoenergetic energy flux that OVATION Prime misses and fails to
produce sufficient diffuse precipitation power in the prenoon quadrant that is present in OVATION Prime.
The prenoon deficiency in the LFM simulation is most likely due to the absence of drift kinetic physics.
Acknowledgments
The research was supported by the
following projects: NASA grants
NNX11AO59G and NNX11AJ10G,
NSF grant AGS-1023346 (NSWP), and
ATM-0120950 (CISM-STC). Computing
resources were provided by the CISL
at the National Center for Atmospheric
Research (NCAR) under Projects
36761008, 3761009, and UDRT0001.
B. Zhang and W. Lotko would like
to acknowledge the hospitality of
the UCAR Advanced Study Program.
The NCAR is sponsored by the NSF.
Simulation data are available from B.
Zhang ([email protected]).
Michael Liemohn thanks the reviewers
for their assistance in evaluating
this paper.
ZHANG ET AL.
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