Space Sci Rev
DOI 10.1007/s11214-009-9494-9
Models of Solar Wind Structures and Their Interaction
with the Earth’s Space Environment
J. Watermann · P. Wintoft · B. Sanahuja · E. Saiz · S. Poedts · M. Palmroth ·
A. Milillo · F.-A. Metallinou · C. Jacobs · N.Y. Ganushkina · I.A. Daglis · C. Cid ·
Y. Cerrato · G. Balasis · A.D. Aylward · A. Aran
Received: 12 November 2008 / Accepted: 19 February 2009
© Springer Science+Business Media B.V. 2009
Abstract The discipline of “Space Weather” is built on the scientific foundation of solarterrestrial physics but with a strong orientation toward applied research. Models describing the solar-terrestrial environment are therefore at the heart of this discipline, for both
physical understanding of the processes involved and establishing predictive capabilities
of the consequences of these processes. Depending on the requirements, purely physical models, semi-empirical or empirical models are considered to be the most appropriate. This review focuses on the interaction of solar wind disturbances with geospace. We
J. Watermann ()
Le Studium and LPC2E/CNRS, 45071 Orléans cedex 2, France
e-mail: jfw@cnrs-orleans.fr
S. Poedts · C. Jacobs
Center for Plasma Astrophysics, Royal University of Leuven, Leuven, Belgium
S. Poedts
e-mail: stefaan.poedts@wis.kuleuven.be
C. Jacobs
e-mail: carla.jacobs@wis.kuleuven.be
A.D. Aylward
Atmospheric Physics Laboratory, University College London, London, UK
e-mail: alan@apl.ucl.ac.uk
I.A. Daglis · G. Balasis · F.-A. Metallinou
Institute for Space Applications and Remote Sensing, NOA, Athens, Greece
I.A. Daglis
e-mail: daglis@space.noa.gr
G. Balasis
e-mail: gbalasis@space.noa.gr
F.-A. Metallinou
e-mail: ametal@space.noa.gr
C. Cid · Y. Cerrato · E. Saiz
Space Research Group, Universidad de Alcala, Alcala de Henares, Spain
J. Watermann et al.
cover interplanetary space, the Earth’s magnetosphere (with the exception of radiation belt
physics), the ionosphere (with the exception of radio science), the neutral atmosphere and
the ground (via electromagnetic induction fields). Space weather relevant state-of-the-art
physical and semi-empirical models of the various regions are reviewed. They include models for interplanetary space, its quiet state and the evolution of recurrent and transient solar perturbations (corotating interaction regions, coronal mass ejections, their interplanetary
remnants, and solar energetic particle fluxes). Models of coupled large-scale solar wind–
magnetosphere–ionosphere processes (global magnetohydrodynamic descriptions) and of
inner magnetosphere processes (ring current dynamics) are discussed. Achievements in
modeling the coupling between magnetospheric processes and the neutral and ionized upper
and middle atmospheres are described. Finally we mention efforts to compile comprehensive and flexible models from selections of existing modules applicable to particular regions
and conditions in interplanetary space and geospace.
Keywords Space weather · Scientific modeling · Solar wind structures · Solar
wind–magnetosphere–ionosphere–atmosphere coupling
1 Introduction
When discussing space weather in a physical context it is worth realizing that the associated discipline has developed into two principal branches, the scientific basis underlying
C. Cid
e-mail: consuelo.cid@uah.es
Y. Cerrato
e-mail: yolanda.cerrato@uah.es
E. Saiz
e-mail: elena.saiz@uah.es
M. Palmroth · N.Y. Ganushkina
Space Research Unit, Finnish Meteorological Institute, Helsinki, Finland
M. Palmroth
e-mail: minna.palmroth@fmi.fi
N.Y. Ganushkina
e-mail: nataly.ganushkina@fmi.fi
A. Milillo
Istituto di Fisica dello Spazio Interplanetario, INAF, Rome, Italy
e-mail: anna.milillo@ifsi-roma.inaf.it
B. Sanahuja · A. Aran
Departament d’Astronomia i Meteorologia, Universitat de Barcelona, Barcelona, Spain
B. Sanahuja
e-mail: blai.sanahuja@ub.edu
A. Aran
e-mail: aaran@am.ub.es
P. Wintoft
Swedish Institute of Space Physics, Lund, Sweden
e-mail: peter@lund.irf.se
Solar Wind–Geospace Modeling
space weather and the development of tools for application which build on and make use of
scientific progress. The two branches are only loosely defined and distinguished. The scientific branch of space weather is often considered as a branch of solar–terrestrial physics, but
viewed in a more comprehensive way this branch applies also to interplanetary space itself,
irrespective of the interaction with the Earth, and to other planetary environments. However,
COST Action 724 (COST—European Cooperation in the field of Scientific and Technical
Research) whose activities provided the basis for this review was intentionally limited to the
study of solar activity and its influence on the solar-terrestrial environment, and we impose
the same restriction on this review.
Space weather research addresses a large number of physical processes in space, ranging from solar activity to its influence on interplanetary space and geospace and its effects
encountered at the surface of the Earth. Physical understanding of this chain is based on a
combination of observations, data analysis and interpretation, and theoretical and empirical
modeling. Seen from an applications point of view, solar activity has a remarkable impact
on the Earth’s environment and may affect technological systems in several ways. Some of
the effects are enjoyable to most people, such as vivid auroral displays (which can reach
mid latitudes under severe storm conditions and in extreme cases even equatorial latitudes).
Others disturb technical operations (with potentially costly consequences) but are not by
themselves dangerous or directly damaging. They include increased air drag on spacecraft
as a result of excessive heating of the upper atmosphere and delays imposed on aeromagnetic
survey flights as a consequence of a highly disturbed geomagnetic field. Still others can be
dangerous and may cause direct damage such as excessive electrical charging of spacecraft
and extremely intense geomagnetically induced currents in electric power networks and
pipeline systems. Radiation effects on technological systems are known consequences of
adverse space weather; see the companion paper on radiation in this issue. Long-range radio
wave propagation and satellite-to-ground radio transmission are areas where space weather
effects can be very annoying and may even play a disastrous role when safety and security
depend on the quality of wireless navigation and communication; see the companion paper
on ionospheric effects in this issue.
Working Group 3 (WG-3) of COST Action 724 focused on the interaction of solar wind
disturbances with geospace, a theme which covers a wide range of domains, namely interplanetary space, the Earth’s magnetosphere (with the exception of radiation belt physics),
the ionosphere (with the exception of radio science), the neutral atmosphere and the ground
(via electromagnetic induction fields). This article represents achievements of WG-3, and in
consequence we restrict our discussion to the domains interplanetary space and the Earth’s
magnetosphere, including the coupling between the interplanetary and magnetospheric plasmas. Collisionless shocks in the heliosphere play an important role in rendering solar activity
geoeffective, but they were not actively represented in COST Action 724. As a consequence
we discuss only models of shock propagation and prediction, but the microphysics of shocks
is not treated in this review. Space weather at other planets is not considered either. The
ionosphere is dealt with only insofar as it is coupled to the magnetosphere on one side and
the neutral atmosphere on the other. Space weather effects on the state of the ionosphere,
very important to the propagation of radio waves, are not treated here, they form the content
of a companion paper in this issue. We deal only to a very limited extent with the initiation of
coronal mass ejections and the acceleration of plasma in the solar corona because the origin
and emergence of solar activity are not a subject of this paper. They are treated elsewhere
in this issue. Very high energy solar particles are only touched upon to the extent that they
play a role for the rapid prediction of fluxes and fluences in the inner heliosphere and for the
J. Watermann et al.
forecast of enhanced levels of geomagnetic activity. Cosmic ray physics and radiation belts
dynamics are not discussed here, they are treated elsewhere in this issue.
Although the impact of space weather on technological systems in space, in the air and on
the ground has been an important motivation for space weather research, it is not discussed
here in detail. We note, however, that effects on spacecraft and ground effects, among others, have received wide attention in the past, and their modeling (from an engineering point
of view) is quite advanced in some areas such as radiation effects on spacecraft and geomagnetically induced currents in powerline and pipeline systems and long-haul telephone
cables. The interested reader may be referred to Valtonen (2005) and Hilgers et al. (2007)
for plasma and radiation effects on space borne technology, Lanzerotti (2007) for effects on
communication technology, and Pirjola (2007) for effects on power grids.
Our objective is to give an overview of modeling efforts which reflect recent advances
in space weather research and which have (or may have in the near future) the potential of
leading to operational schemes for nowcasting and forecasting space weather effects. It is
not our intention to repeat material that has been published within the last few years, such
as the review by Forbes et al. (2006) on theory and modeling of coronal mass ejections,
the review by Forsyth et al. (2006) on observation and modeling of interplanetary coronal
mass ejections, and the review by Lathuillère et al. (2002) on space weather relevant models covering the chain from the solar atmosphere to the Earth’s atmosphere. In this paper
we discuss important models respectively model groups which demonstrate the advance of
physical understanding of solar events as they evolve on their way from the Sun to the Earth.
But we also discuss models which relate cause and effect in a semi-empirical way without
paying detailed attention to the mediating medium.
Some of the models are purely physical but occasionally have the option to assimilate
space or ground based observations as input (if available). They are often research models
which require a substantial degree of understanding of the role of various control parameters
and which tend to be computationally demanding so that they are not fit for implementation
as operational space weather models. Other models are empirical and are often employed
if rapid computation is a requirement, for instance for efficient nowcasting and forecasting
purposes. Some models are hybrids in the sense that they started from plasma physical principles but were subsequently simplified in order to facilitate their integration into nowcasting
and forecasting schemes.
Several solar wind and magnetospheric models have been newly developed while other,
already existing models, were advanced considerably during recent years. They form the
essence of this paper. The content of this review is biased toward the science of space
weather. Consequently, the models discussed here are mostly research models under continuous development.
In the next section we give an introduction to the phenomenology of interplanetary space
and the Earth’s coupled magnetosphere–ionosphere system. This is followed by a brief
overview of physical (in contrast to technological) space weather effects in these regimes.
We then continue with a discussion of models for solar events evolving in interplanetary
space, more precisely, in the inner heliosphere extending from the solar corona to a radial
distance of a few Astronomical Units (AU). Thereafter follows a discussion of space weather
relevant magnetospheric, ionospheric and atmospheric models. The model part is concluded
with an outline of semi-empirical models which can be considered prototype operational
models. A future-oriented section dealing with desired and potentially possible improvements on modeling efforts closes the paper.
Solar Wind–Geospace Modeling
2 The Environment: Interplanetary Space and the Earth’s Magnetosphere
2.1 Interplanetary Space
The existence of a continuous flux of charged particles emerging from the solar surface was
already predicted by Biermann (1951) and theoretically investigated by Parker (1958, 1959)
prior to its confirmation through in-situ observations. A few years earlier Alfvén (1942)
had developed the concept of a magnetic field moving along with the plasma (frozen-in
magnetic field) which is applicable to a plasma having a large magnetic Reynolds number.
This is the case with the solar wind, and it has in fact become a very important concept for
understanding the dynamics of the solar wind and its interaction with obstacles such as the
Earth’s magnetic field.
Soon after the beginning of the space age the solar wind became a domain of in-situ
probing by spacecraft, and most properties of the solar wind close to the plane of the ecliptic
were established during the early space age. The solar wind can be considered a prototype
large-scale natural plasma laboratory filled with a tenuous fully ionized gas flowing steadily
away from the Sun, and an embedded (frozen-in) magnetic field, both of solar origin. At the
Earth’s orbit (around 1 AU from the Sun) its flow is super-Alfvénic and supersonic with a
Mach number around 6 on the average. In interplanetary space the magnetic field is called
“interplanetary magnetic field (IMF)”, although strictly speaking it remains anchored at the
Sun (except for locally closed loop structures embedded in the solar wind and balanced
temporarily by electric currents) and is therefore still a solar magnetic field.
The solar wind consists primarily of low-energy electrons (10–100 eV), ∼1 keV protons
and a varying percentage of mostly doubly ionized helium. Small traces of heavier ions
were also detected, such as carbon and nitrogen (Gloeckler et al. 1986), oxygen and neon
(Bochsler et al. 1986), iron (Schmid et al. 1988) and silicon (Bochsler 1989). The solar wind
is electrically neutral at scales exceeding the Debye length. It exists at all times but can be
very unevenly distributed. At 1 AU its density has been observed to vary between less than
0.1 protons/cm3 (Usmanov et al. 2000a) and several tens of protons/cm3 in interplanetary
shocks (Hanuise et al. 2006), with a long-term average of 5–10 protons/cm3 .
The solar wind is often—and rather systematically during the declining and minimum
phases of the solar cycle—divided into two separate regimes, a solar equatorial region where
the solar wind is slow, dense and cold, and a high and polar latitude region where the solar
wind is fast, rarefied and hot (McComas et al. 2003). Dense, rarefied, cold and hot are to
be understood relative to the average solar wind parameters and not to magnetospheric or
ionospheric plasma characteristics.
In the inner heliosphere but at some distance from the solar corona the solar wind bulk
speed ranges from slightly below 300 km/s up to more than 1100 km/s, with numbers falling
mostly into the 300–500 km/s range in the slow flow regime and 700–800 km/s in the fast
flow regime during solar minimum (McComas et al. 2000, 2002). The proton and electron
temperatures of the slow solar wind are here typically of the order of 1–2 × 105 K, in the fast
solar wind they tend to be an order of magnitude higher. During solar maximum the solar
wind is much more irregular. The magnetic induction amounts to 2–10 nT most of the time
but can reach several tens of nanoTesla during the passage of a shock. A value as high as
170 nT was measured on 4 August 1972 (Burlaga and King 1979).
Much less is known about the initial stage of the solar wind. Detailed information about
its initiation and acceleration up to some 20–30 solar radii away from the Sun is still missing.
More is known about the evolution and propagation further out, largely due to a series of
spacecraft in-situ measurements in and near the ecliptic plane (HELIOS 1 and 2 missions)
J. Watermann et al.
and over the solar poles (Ulysses mission) and more recently stereoscopic views from the
STEREO mission (Kaiser 2005).
Long-lasting steady-state solar wind conditions are of lesser concern to space weather
research and applications, but they are also not the typical case. The solar wind is as unsteady
as its origin, the Sun. Solar wind perturbations can be divided into two main categories,
quasi-periodic (recurrent) structures and transient events.
Recurrent solar wind structures result from quasi-stationary solar structures which display an apparent return to the position of the Earth after one solar rotation (∼27 days). They
are linked to the boundaries between slow and fast solar wind streams and to the geometry
of the solar equatorial current sheet which separates sectors of different magnetic polarity.
This category includes corotating interaction regions (CIRs) and IMF sector boundaries.
CIRs form when the fast solar wind (i.e., a stream flowing out of coronal holes reaching low
heliographic latitudes) interacts with the slow solar wind by compressing the plasma at their
boundary, thereby enhancing locally the plasma density and heating it up. Occasionally the
boundaries are associated with magnetohydrodynamic shocks. Many in-situ measurements
were made over the past decades. A two-dimensional (2-D) view of CIRs became possible
through remote sensing with the STEREO A (leading) spacecraft (Rouillard et al. 2008).
Transient solar events are associated with bursty solar activity. They include coronal
mass ejections (CMEs), solar flares and solar radio bursts. CMEs occur when solar matter is launched into the heliosphere in a rather violent fashion. Very intense CMEs were
observed to temporarily disrupt cometary tails (Lundstedt and Magnusson 1987). Interplanetary Coronal Mass Ejections (ICMEs) are the interplanetary remnants of CMEs. Magnetic
Clouds (MCs) are frequently detected in association with ICMEs. They are characterized
by a simple magnetic structure and therefore easier to model than many other interplanetary
structures. ICMEs usually propagate with a velocity higher than the background solar wind.
If the velocity difference exceeds the solar wind acoustic velocity the fast ICME builds up
a plasma shock front which, when hitting the Earth’s magnetosphere, can trigger a geomagnetic storm.
The existence of heliospheric structures similar to CMEs (although unmagnetized) was
already hypothesized by Lindemann (1919) who wrote: “The hypothesis to be examined
therefore is that an approximately equal number of positive and negative ions are projected
from the Sun in something of the form of a cloud and that these are the cause of magnetic
storms and aurorae.” He estimated the cloud velocity to be around 800 km/s. CMEs were
discovered only four decades ago by a white light coronagraph on board of the OSO-7
(OSO—Orbiting Solar Observatory) space mission (Tousey 1973), and over the years it
became clear that those impressive solar expulsions are among the most important drivers
of space weather.
A large number of CME observations from space was collected by the Solar Maximum
Mission (SMM) coronagraph/polarimeter and statistically analyzed by Hundhausen (2005).
Many more details of CMEs were identified with the three Large Angle Spectroscopic Coronagraph (LASCO) instruments (Brueckner et al. 1995) onboard the Solar and Heliospheric
Observatory (SOHO) mission (Domingo et al. 1995). Until recently CME observation with
coronagraphs has been possible only up to 32 solar radii around the Sun. With the advent of
STEREO they were observed in a larger part of the heliosphere from an off-Sun–Earth-line
position (Harrison et al. 2008).
2.2 The Earth’s Magnetosphere
The interaction of the solar wind with the geomagnetic field leads to the formation of the
Earth’s magnetosphere. Its characteristic elongated shape is determined by dynamic and
Solar Wind–Geospace Modeling
magnetic pressure balance between the solar wind and the geomagnetic field. Except for
regular geometric variations (due to the rotation and revolution of the Earth and the interplay
between different inclinations between the solar ecliptic and the Earth’s geographic and
geomagnetic axes) only the solar wind can change the shape of the magnetosphere on scales
shorter than about a year. The geomagnetic main field is generated in the Earth’s core, and
the magnetic field at the Earth’s surface varies on timescales rarely less than years, due to
the strong attenuation of short-term core field fluctuations by the Earth’s conducting mantle.
The space influenced by the geomagnetic field is composed of the magnetosphere proper
and its boundary regions: the bow shock with a spatially asymmetric foreshock (where the
supersonic solar wind plasma flow brakes to become a more turbulent subsonic flow), the
magnetopause (the surface where the magnetic pressure of the geomagnetic field balances
the magnetic and dynamic pressure of the solar wind plasma flow) and the magnetosheath
(sandwiched between the magnetopause and the bowshock and characterized by a turbulent
rather than a laminar plasma flow).
Another profound transition occurs at the inner boundary of the magnetosphere, roughly
a thousand kilometers above the surface of the Earth, where the relatively cold, partially
ionized atmospheric gas gives way to the hot, fully ionized magnetospheric plasma. While
the solar wind and the magnetosphere are characterized by large Lundquist numbers and are
therefore usually treated as nearly ideal magnetohydrodynamic (MHD) fluids the ionosphere
does not lend itself to such a treatment. This must be taken into account by models of the
magnetosphere-ionosphere system.
Early magnetosphere models fell into two classes, (a) closed magnetospheres where
the magnetopause current separates interplanetary and geomagnetic field lines and the solar wind influences the magnetospheric electric circuit via viscous interaction (Axford and
Hines 1961), and (b) open magnetospheres where the IMF can merge with the geomagnetic
field to allow the merging electric field enter the magnetosphere (Dungey 1961). Benefitting from a large number of spacecraft measurements starting in the beginning of the 1960’s
(e.g., the Explorer space program in the USA) it has become apparent that each of the two
models applies at certain times, depending on the IMF conditions prevailing at the Earth’s
location in space.
The Earth’s magnetic field and its interaction with the IMF are the most important factors to govern the dynamics of the magnetospheric plasma. Soon after the first Explorer
measurements from the magnetosphere became available it was recognized that the geomagnetic field is an important parameter for ordering plasma physical properties of the magnetosphere, and magnetic field models for the magnetosphere were developed once spacecraft
measurements necessitated it (McIlwain 1961). In consequence, a number of geomagnetic
field models appeared following the beginning of the space age. Some focus solely on the
geomagnetic main and crustal fields and are applicable up to 1–2 Earth radii above the
ground while others emphasize a combination of the internal geomagnetic field and the field
created by magnetospheric currents and are applicable to the inner and outer magnetosphere.
However, magnetic field models are not discussed in this article; they are treated in a companion paper in this issue. A statistical examination of the accuracy of 10 commonly used
magnetospheric magnetic field models was undertaken by McCollough et al. (2008).
A large body of review literature exists on the Earth’s magnetosphere. A recently published overview from a theorist’s point of view (a theoretical treatment of the interaction
between electric fields, magnetic fields and charged particles in the magnetosphere) was
given by Schulz (2007). Otto (2005) discusses the basic structure of the magnetosphere in a
space weather context.
J. Watermann et al.
3 Geophysical Effects of Solar Activity
Solar wind effects on the magnetosphere are manifold. They range from a compression of
the magnetopause caused by elevated solar wind dynamic pressure to frictional heating of
the neutral upper atmosphere caused by enhanced electric field strength and current density
(Joule heating).
The most violent impact of solar wind perturbations on geospace are various sorts of
storms, including geomagnetic storms (large deviations of the magnitude and orientation of
the geomagnetic field), particle storms (enhanced radiation levels in the magnetosphere) and
ionospheric storms (increased and highly variable ionization of the upper atmosphere and
sometimes even the middle atmosphere). The latter two are treated in companion papers in
this issue.
The orientation of the IMF plays a dominant role for the geoeffectiveness of solar wind
disturbances (basically the energy transfer from the solar wind into the magnetosphere).
Echer et al. (2008) determined that all intense (Dst ≤ −100 nT) magnetic storms of solar
cycle 23 occurred under long-lasting southward IMF conditions. The most geoeffective interplanetary structures were identified as MCs driving fast shocks, sheath fields sandwiched
between ICMEs and associated shocks, combined ICME sheath and MC fields, and CIRs
(Echer et al. 2008).
CIRs account for most of the geomagnetic storms during the late declining and minimum phases of the solar cycle while ICMEs are at the origin of the intense storms at the
maximum and early declining phases of the solar cycle (Cid et al. 2004; Denton et al. 2006).
CIR generated storms are mostly moderate but may occasionally be intense (as measured
by the Dst index), in particular if the boundary between slow and fast solar wind is associated with a shock front, see, for instance, Echer et al. (2006) and Denton et al. (2006).
Nearly all severe magnetic storms result from ICME driven shocks interacting with the
Earth’s magnetosphere. Borovsky and Denton (2006) list a number of significant differences between CME-driven and CIR-driven storms, including both physical characteristics
and effects on technological systems. Their study does not only address geomagnetic perturbations but also other manifestations in the magnetosphere such as the influence of storms
on magnetospheric convection and energetic particle fluxes and effects on space-borne and
ground-based technological systems.
The intensification of the magnetospheric ring current is a characteristic storm phenomenon. Its ground magnetic signature follows largely a standard pattern comprising initial,
main and recovery phases. World-wide magnetic observations of storm-time variations date
back to the early 19th century. Records taken simultaneously at geomagnetic observatories
participating in the Göttingen Magnetic Union (1836–1841) revealed a systematic fast depression and slow recovery of the magnetic north component. This signature is now known
to reflect primarily the growth and decay of the ring current. But ring current dynamics are
still not fully understood. For instance, the relative importance of large-scale magnetospheric
convection and substorm associated electric fields and the quantitative contribution of particle injection from the plasma sheet and the ionosphere are not yet clarified.
The build-up of the ring current is a slow process which takes many hours and may be
preceded by other effects, e.g., an elevated level of ULF wave activity in the magnetosphere
(Khabarova et al. 2006). In contrast, still other effects are delayed such as the enhancement
of the relativistic electron density in the outer radiation belts in the plasmasphere which is
found to roughly coincide with the storm main phase, i.e., the fully developed ring current
(Reeves 1998).
The most important space weather influence on the neutral atmosphere occurs in the
auroral zone where precipitating particles supply energy (via collision) and electric field
Solar Wind–Geospace Modeling
momentum (via plasma convection) to the atmosphere. One of the potential effects is a
modification of the nitric oxide concentration and an enhancement of the temperature of the
neutral upper atmosphere. During intense geomagnetic storms such nitric oxide density increases and temperature enhancements may reach low latitudes within 1–2 days as a result of
strong meridional winds associated with high levels of Joule heating (Dobbin et al. 2006a).
4 Modeling Plasma Structures in Interplanetary Space
4.1 The Solar Wind
The first attempt to numerically model the solar corona was made by Pneuman and Kopp
(1971). Since then considerable progress has been made, not last due to the increment in
computational power which facilitates the usage of three-dimensional (3-D) MHD models
for reconstructing the solar corona and the solar wind. Han et al. (1988) published the first
fully 3-D time-dependent numerical MHD interplanetary global model to simulate the supersonic super-Alfvénic solar wind flow from 18 R (R = solar radius) out to 1 AU.
The availability of more detailed observations makes it possible to produce more realistic
simulations by including observational data through the boundary conditions. Linker et al.
(1999) published the first 3-D MHD coronal model which uses measurements of the lineof-sight magnetic field as boundary conditions. Riley et al. (2002) developed an empirically
driven MHD model for the solar corona and the inner heliosphere and investigated the evolution of the heliospheric current sheet during the course of the solar cycle. Their model is
an extension of the previously mentioned model and employs a polytropic energy equation.
The advantage of using a polytropic pressure-density relation is the simplification of the
set of equations to solve, since the energy equation can be omitted. Although those polytropic models are able to reproduce many qualitative features of the solar corona, they are
not able to reproduce the solar wind in a more quantitative agreement with the observations.
The physics in the algorithm was improved by incorporating thermal conduction along the
magnetic field, radiation losses, and heating into the energy equation (Lionello et al. 2001).
Employing a 3-D MHD model for the solar corona developed by Feng et al. (2007),
Hu et al. (2008) investigated the coronal magnetic structures during 15 Carrington rotations
spanning solar cycle 23. Wilcox solar observatory line-of-sight magnetograms of the solar
photosphere were used as boundary conditions. The large-scale magnetic structure of the
solar corona and the topology of the heliospheric current sheet are then obtained. While good
large-scale agreement with SOHO observations of bright structures is obtained some local
quantitative discrepancies, specifically during solar maximum, remain unresolved. This may
at least in part be due to the fact that transient events such as CMEs were neglected in the
analysis.
A combination of empirical and physical representations of the quasi-steady global solar
wind is the Wang-Sheeley-Arge model (Arge et al. 2004), which is an improved version of
the Wang and Sheeley model (Wang and Sheeley 1990). It relates the magnetic field expansion factor to the solar wind speed. The model has been comprehensively validated with
observations spanning nearly a full solar cycle (Owens et al. 2005). Cohen et al. (2007) use
the WSA model as input to a 3-D MHD code, in which the processes of turbulent heating in
the solar wind are parametrized using a phenomenological, thermodynamical model with a
varied polytropic index, as introduced by Roussev et al. (2003b). They employ the Bernoulli
integral to bridge the observed solar wind speed at 1 AU with the assumed distribution of
the polytropic index on the solar surface. The model results were compared with long-term
J. Watermann et al.
satellite data at 1 AU. Especially for solar minimum conditions this model predicts the magnitude of the magnetohydrodynamical variables rather well (Cohen et al. 2008).
Usmanov and Goldstein (2006) developed a 3-D steady state MHD model of the solar
wind that covers the region from the coronal base to 100 AU and that accounts for the
effect of pickup protons in the distant heliosphere. As initial condition for integrating the
MHD equations from 1 AU to 100 AU they use the 1 AU output from the tilted-dipole
model of Usmanov and Goldstein (2003) which is appropriate for solar minimum conditions.
A kinetic exospheric model of the solar wind was developed by Lamy et al. (2003). The
authors showed that collisionless kinetic theory is able to reproduce the large bulk velocities
observed in the fast solar wind, without ad hoc assumptions about the rate of additional
coronal heating and momentum transfer, as is often the case in the MHD models describing
the solar wind.
Heating and acceleration of the solar wind remain controversial, and no commonly accepted mechanism has yet been established. An interesting mechanism, originally proposed
by Usmanov et al. (2000b) and improved upon by Chen and Hu (2001) calls for lowfrequency Alfvén waves to heat and accelerate the solar wind in the vicinity of the Sun.
The mechanism applies to both fast and slow solar wind regimes, and the numerical results
obtained are in reasonable agreement with observed values.
4.2 CME Initiation
Despite the abundance of CME observations, there is no general consensus about the exact mechanism that drives the eruption. Stressed magnetic fields are often observed before
the onset of the eruption, indicating that the energy needed to drive the eruption must be
provided through the magnetic field. The current CME initiation models can then also be
defined as “storage and release” models (Klimchuk 2001). An important common aspect
of the different CME initiation models is the presence of magnetic flux rope structures, being either present before the eruption takes place (first model group) or created during the
eruption as a consequence of magnetic reconnection (second model group), see Roussev
and Sokolov (2006). The reason for assuming that magnetic flux ropes are a key feature of
CMEs is (i) the link between CMEs and erupting prominences which are believed to possess
some amount of twisted magnetic field, (ii) the appearance of helical structures in images
of erupting prominences and CMEs, and (iii) the correlation between ICMEs and MCs. Reviews of CME initiation mechanisms can be found in papers by Low (2001), Moore and
Sterling (2006) and Forbes et al. (2006).
The first group of models assumes that a flux rope exists prior to the eruption. The analytical flux rope model of Titov and Démoulin (1999), which had been proposed to explain
flares and CMEs, was numerically studied in the context of CME initiation by Roussev et
al. (2003a). The initial flux rope is suspended in the corona by a balance between magnetic pressure and tension forces and a highly twisted field at the surface of the flux rope is
needed in order to produce the eruption. The evolution of a twisted magnetic flux rope from
below the photosphere into the corona was numerically simulated by several authors, e.g.,
Manchester et al. (2004a), Amari et al. (2004) and Fan and Gibson (2007). The evolution
of the flux rope is at first quasi-static and then undergoes a dynamic transition, driven by
reconnection processes.
The second group of models relies on the existence of sheared magnetic arcades, which
become unstable and erupt once some critical state is reached in the solar corona. In contrast
to the previous class of models, a flux rope does not exist prior to the eruption, but is formed
in the course of the eruption by magnetic reconnection. Mikić and Linker (1994) had already
Solar Wind–Geospace Modeling
shown in a 2-D configuration that shearing motions energize the magnetic field and might
cause the formation of a flux rope when the shearing motions continue for a sufficiently long
time. Jacobs et al. (2006) performed a parameter study of the effect of the shear velocity and
the background wind on the evolution of the flux rope formation. The shearing motions are
often combined with a process of flux cancelation (Amari et al. 2003; Linker et al. 2003;
Roussev et al. 2004; Titov et al. 2008). In this class of CME models a flux rope is formed
by reconnecting the opposite polarity feet of a sheared magnetic arcade. In these models the
reconnection takes place at the photosphere or near the base of the solar corona.
Another popular model for explaining solar eruptions is the breakout model (Antiochos
et al. 1999; DeVore and Antiochos 2008; Lynch et al. 2008). In this model the eruption
is again triggered by magnetic reconnection, but here the reconnection process occurs in a
current sheet located above the sheared arcade. The evolution of a breakout CME in the solar
wind was studied by van der Holst et al. (2007) who obtained an eruption of the slow type.
Recently, Amari et al. (2007) combined both the flux cancelation and breakout model. They
concluded that the more complex topology of the magnetic field facilitates the eruption and
a faster CME is obtained than when applying flux cancelation in a simple bipolar topology.
The breakout model asks for a specific multipolar magnetic topology to enable the eruption.
Observational studies of CME source regions (Li and Luhmann 2006; Ugarte-Urra et al.
2007) find both bipolar and quadrupolar topology at the source regions, but the bipolar
topology is more common overall and in each year.
As of today, there is no convincing observational evidence that proves or disproves either class of CME models, and no model is advanced enough to explain real observations.
Numerical simulations are a usefull tool to test different theoretical models. Recently, numerical models coupling the convection zone, photosphere and corona have been developed
(Abbett 2007) and have emerged as a promising tool for studying the initiation of CMEs in
a less idealized setup.
4.3 Interplanetary Shock Propagation
In addition to modeling the background solar wind it became apparent that interplanetary
shock propagation modeling, and specifically forecasting its arrival at 1 AU, is an important
task for space weather research. This observation led to several modeling attempts.
The Hakamada-Akasofu-Fry (HAF) solar wind model was developed jointly by Exploration Physics International, Inc., and the Geophysical Institute, University of Alaska, Fairbanks. It is a time-dependent modified kinematic model which grew out of semi-empirical
numerical simulations and prediction schemes conceived at the Geophysical Institute, Fairbanks, Alaska (Hakamada and Akasofu 1982; Akasofu and Fry 1986). An updated version,
the 3-D HAFv2 code (Fry et al. 2001), is used as an operational forecast tool by the US
Air Force Weather Agency. The model is initialized with observations of the solar magnetic field. Starting at a spherical surface 2.5 solar radii away from the center of the Sun it
kinetically projects solar radial flow from inhomogeneous sources out into the heliosphere
thereby taking care of fast streams overtaking slow streams. The model is semi-empirical.
Its parameters were calibrated by comparison with MHD simulations and observations. It
can be employed to provide ambient solar wind conditions and to simulate transient events.
The HAFv2 model has been extensively compared with other models such as the Interplanetary Shock Propagation Model (ISPM) (Smith and Dryer 1995), the Shock-TimeOf-Arrival (STOA) model (Dryer and Smart 1984; Smart and Shea 1985) and its improved
version, STOA-2 (Moon et al. 2002) and was found to match the performance of ISPM and
STOA (Smith et al. 2000; Fry et al. 2003). It has since been used in various space weather
J. Watermann et al.
application schemes to describe the evolution of the interplanetary medium in the absence of
solar eruptive events, or as a background solar wind model in cases where the evolution of
CMEs has to be modeled under various conditions. The STOA, STOA-2, ISPM and HAFv2
were used in the “fearless forecasts” project to perform real-time shock arrival predictions
during the “Halloween” 2003 storm epoch (Dryer et al. 2004).
The performance of the STOA, ISPM and HAFv2 models was tested on several cases
and was found to be nearly equal in forecasting shock arrival times (McKenna-Lawlor et al.
2002; Fry et al. 2003; Cho et al. 2003; McKenna-Lawlor et al. 2006).
The HAFv2 algorithm was successfully employed to model interplanetary shock waves
following various C, M and X class solar flares in the years 2000–2002 (Sun et al. 2003).
Other notable events studied so far with the HAFv2 model include the March/April 2001
shock arrivals at the L1 point (Sun et al. 2002), the November 2001 and April 2002 solar
events (Intriligator et al. 2004), the propagation of the October/November 2003 (Halloween)
solar eruptions to more than 90 AU (Intriligator et al. 2005) and the arrival of interplanetary
shocks at the Earth, Mars and Venus following the 5–14 December 2006 sequence of solar
flares (McKenna-Lawlor et al. 2008). Using 421 solar events between February 1997 and
August 2002 McKenna-Lawlor et al. (2006) established a root mean square error of ±11
hours for the prediction of a shock arrival at Earth.
Smith et al. (2008) reexamined the arrival at Earth of the interplanetary shock associated with the 12 May 1997 solar event and simulated it with both the HAFv2 model and
the Hybrid Heliospheric Model System (HHMS) model. Using better estimates of the shock
velocity than those which had been used earlier they demonstrated a shock prediction accuracy of a few hours with both the HAFv2 and the HHMS models. They also note that the
interactions which occur en route to 1 AU cannot be modeled by other models such as the
STOA-2 and the Shock Prediction Model (SPM—not to confuse with the ISPM) developed
by Feng and Zhao (2006). SPM is an analytical model which was tested by Feng and Zhao
(2006) on 165 solar events and shown to perform equally well as the semi-empirical models
chosen for reference.
Performing parametric studies with various initial shock speeds (however constant within
18 R ) with a model based on a code developed by Han et al. (1988), Wu et al. (2005) found
that the time of shock arrival depends on background solar wind speed, the speed of the
solar disturbance, its size and its source location. However, a disturbance with a sufficiently
large momentum is not significantly affected by the pre-existing solar wind speed.
4.4 CME and ICME Evolution
In the past, heliospheric disturbances were often modeled by driving the inner boundary
conditions placed upstream of the critical point of the solar wind (at > 20 R ), e.g., Vandas
et al. (2002). These models provide basic physical insight into how large solar disturbance
propagate and interact with the large-scale solar wind.
Building upon the model developed by Han et al. (1988), Wu et al. (1996) and Wu
and Dryer (1997) studied the relationship between various forms of transient solar activity (simulated through pressure or density pulses near the solar surface) and variations of
the IMF north–south component at 1 AU assuming different heliospheric current sheet configurations. Dryer et al. (1997) performed a 3-D MHD simulation of the propagation of the
April 14, 1994, ICME from 18 R to more than 3.2 AU (the location of the Ulysses spacecraft at the time it detected the ICME). They find reasonable agreement with spacecraft
observations but acknowledge that the inner boundary conditions were essential unknown
and thus ambiguous.
Indeed, there are few or no observable parameters at 20 R or even smaller distances
from the Sun to constrain the boundary conditions. Only recently has the propagation of a
Solar Wind–Geospace Modeling
CME from the inner corona to 1 AU been modeled in 2-D and 3-D geometries. For example,
Jacobs et al. (2006) and Chané et al. (2006) performed parameter studies to investigate the
effect of the background wind and the polarity of the initial flux rope on the CME evolution
in an axi-symmetric set-up.
An example of a 3-D CME propagation model is the theoretical model of Gibson and
Low (1998). This analytical model was used as a CME generation mechanism in numerical
simulations (Manchester et al. 2004b; Lugaz et al. 2005), in which the dynamics of the CME
are followed as it interacts with a bimodal background solar wind. The 12 May 1997 CME
event was numerically simulated by Odstrcil et al. (2004a) and Odstrcil et al. (2005), who
tried to reproduce the plasma parameters near the Earth. The inner boundary in their model
is placed at 0.14 AU, the ambient solar wind is derived from coronal models utilizing photospheric magnetic field data, and the transient disturbances are derived from geometrical and
kinematic fitting of coronagraph observations of CMEs.
The event of 12 May 1997 was also studied by Wu et al. (2007a) who linked the HAFv2
code (Fry et al. 2001) and the 3-D MHD code of Han et al. (1988). In this hybrid model
(named “HAFv2+3DMHD”) solar surface magnetograms are used to specify the solar wind
structure at 2.5 R where it provides the input to the HAFv2 model which then simulates the
solar wind evolution out to 18 R and there feeds the Han et al. (1988) model which is then
used throughout the heliosphere. A velocity pulse serves as initiator for a CME including a
shock but not a flux rope.
The same HAFv2+3DMGD hybrid was employed to model three solar-flare associated
CMEs and interplanetary shocks which occurred during the Halloween storm period, October 2003 (Wu et al. 2007b). Flow velocity pulses were introduced to simulate dynamic
solar wind disturbances, and the collision between two ICMEs and shocks propagating with
different velocities is simulated.
Wu et al. (2006a) studied the detailed nature of interacting CME shocks with a onedimensional (1-D) adaptive grid MHD code. An event study of three interacting CMEs was
done by Lugaz et al. (2007). As model for the background solar wind the varying polytropic
index model of Roussev et al. (2003b) was used. The CMEs were initiated using an outof-equilibrium semi-cylindrical flux rope (Roussev et al. 2003a). The same technique was
applied by Manchester et al. (2008) in order to simulate the well know Halloween events
of 2003. Both event studies showed good agreement with the observations and have lead to
a better insight into the density structure and propagation of CMEs. The shocks generated
by CMEs are important in the production of Solar Energetic Particles (SEPs). Sokolov et
al. (2004) simulated the time-dependent transport and diffusive acceleration of particles at
shock waves driven by CMEs. The geo-effectiveness of a CME event was simulated by
Ridley et al. (2006), who investigated the magnetospheric and ionospheric response to a
very strong interplanetary shock associated with a CME.
Although idealized, these numerical simulations were able to reproduce many generic
features of CMEs seen in observations. In a recent simulation, Lugaz et al. (2008) have
pointed out the need to combine both numerical simulations of CME events with observational data, in order to obtain a correct interpretation of the measurements. Numerical
simulations must be regarded as complementary to the observations and can provide the
missing information which is not directly observable.
4.5 Magnetic Clouds
Magnetic clouds (MCs) are localized regions in interplanetary space with a simple magnetic
field topology as is typical for flux ropes. They are characterized by enhanced magnetic
J. Watermann et al.
field strength, lower proton temperature than the background solar wind and a large-scale
large-angle smooth rotation of the magnetic field vector (Burlaga et al. 1981; Burlaga 1991).
MCs were early on associated with either shocks, stream interfaces, CMEs or disappearing
filaments (Burlaga et al. 1981; Lepping et al. 1990) and are nowadays considered to be contained in ICMEs (Gopalswamy et al. 1998; Lepping et al. 2006). They are a relatively common phenomenon (Klein and Burlaga 1982; Burlaga and Behannon 1982); about 25% of all
ICMEs were reported to fulfill the criteria for MCs (Cane and Richardson 2003). Figure 1
shows a typical example of the observation of an MC preceded by an interplanetary shock.
MCs are distinguished by their chirality (sign of magnetic helicity) (Rust 1994; Burlaga
et al. 1981; Bothmer and Schwenn 1998). This parameter, which is obtained from fitting a
flux rope model to observed data, can be left-handed (negative) or right-handed (positive)
but should always be the same as that of its solar source (solar surface flux rope).
Interaction between MCs, or an MC and the fast solar wind, produces complex ICMEs
which retain the magnetic structure in some cases and are then termed Multi-MCs (Wang et
al. 2003), but not in others and are then called complex ejecta (Burlaga et al. 2002). Because
of their high magnetic field strength and large plasma bulk velocity MCs often (but not
always) drive interplanetary shocks. Extensive analysis of solar and interplanetary sources
of geomagnetic storms (Richardson et al. 2002; Zhao and Webb 2003; Zhang et al. 2003;
Wu et al. 2006b) has indicated that CMEs and MCs frequently trigger major geomagnetic
activity. Echer et al. (2006) determined that combinations of interplanetary structures rather
than isolated structures, and specifically interplanetary shocks driven by MCs, are most
geoeffective.
Ejection of magnetized plasma clouds from the Sun were first proposed by Morrison
(1954) to explain worldwide decreases in cosmic ray intensity. Subsequently various topologies were proposed such as magnetic bottles, tongues or bubbles. Burlaga et al. (1981) were
the first to analyse comprehensively an MC using data from five interplanetary spacecraft.
They proposed a locally cylindrical topology with circular magnetic field lines around a
common cloud axis. Since then different models were developed, all of which face the same
inherent verification problem: a 3-D model topology can only properly be tested if the same
event is observed by different spacecraft separated in solar longitude and latitude, see Fig. 2
for a sketch of the MC shape seen by a single spacecraft. Moreover, only isolated solar events
guarantee that it is the same event which is observed at different locations in interplanetary
space. Such a case occurred in November 2001 when the same MC was observed by ACE
and Ulysses (Rodriguez et al. 2008), with the latter spacecraft being located at 72◦ north of
the ecliptic plane at a distance of 2.3 AU.
The simple flux rope topology of MCs makes them amenable to MHD modeling (Osherovich and Burlaga 1997). As density inside MCs often shows extremely low values, a
force-free configuration was proposed (Goldstein 1983) and solutions of Maxwell’s equations in stationary and low-β plasma conditions and depending on the geometry of the
cloud were obtained. Burlaga (1988) showed that a Lundquist solution, a cylindrical flux
rope (Lundquist 1950), could reproduce the observed magnetic field rotation. Lepping et al.
(1990) developed an algorithm based on that solution and inferred several parameters of the
MC, including its radius, the latitude and longitude of its axis. The results reproduce properly the normalized components of the magnetic field but not the magnetic field strength.
Feng et al. (2006) proposed a new method of identifying the configuration and boundaries
of MCs based on a force-free flux rope configuration. This technique may also be used in
other magnetic field configurations.
Studies based on the time evolution of non-linear cylindrical MHD configurations used
a self-similarity technique in the zero-β limit (Farrugia et al. 1992; Osherovich et al. 1993)
Solar Wind–Geospace Modeling
Fig. 1 Measurements from the MFI and SWE instruments onboard the Wind spacecraft at L1 during three
days in October 1997. A magnetic cloud appears between the second and third vertical dashed lines preceded
by a shock between the first and second vertical dashed lines. From top to bottom: interplanetary magnetic
field strength and GSE components, proton temperature and proton density
or with finite-β plasma (Osherovich et al. 1995) to obtain analytical solutions. These selfsimilar solutions are interesting because of their asymptotic character (Saiz et al. 1992)
which provides information about the evolution of the system on longer time scales.
J. Watermann et al.
Fig. 2 Top: From global to local
topology of magnetic clouds as
cylindrical flux ropes.
Bottom: A sketch of a magnetic
cloud when observed by a
spacecraft
The expansion and distortion of MCs observed farther away from the Sun together with
the asymmetric magnetic field strength profile measured inside MCs (which is in contrast
to the expectations of earlier models) stimulated the development of non-force-free models.
Plasma pressure gradients observed inside MCs provided further reason to study this class of
models. Several geometric approaches were followed. All of them considered a cylindrical
cloud, but cross sections were of circular shape (Cid et al. 2002; Hidalgo et al. 2002a) or of
elliptical shape (Mulligan and Russell 2001; Hidalgo et al. 2002b). This last model proposes
a magnetic topology that provides a proper fit to observed data although it is not a flux rope
topology. An MC observed in January 2005 by Ulysses and ACE, when these spacecraft
were almost radially aligned, allowed Rodriguez et al. (2008) to study the expansion of
MCs by applying this model.
Other elliptical cross section models with force-free configuration were proposed by Vandas et al. (2006). Still other non-cylindrical magnetic field configurations were suggested for
MCs such as spheromaks (Vandas et al. 1993) and toroids (Romashets and Vandas 2001).
Marubashi and Lepping (2007) examined 17 MCs and concluded that spacecraft observations slightly favor a torus over a cylinder shape, but the conclusions were not very definitive.
The Grad-Shafranov reconstruction technique is also used to determine properties of MCs
(Hu and Sonnerup 2002).
An additional problem is the identification of the boundaries of MCs. Different methods
have been used, e.g., examining the plasma characteristics of the MCs (a low-β plasma with
low proton temperature is expected) or the rotation of the magnetic field vector. However,
boundaries established using different methods are not always consistent.
An important yet unsolved question about MCs concerns their connection to the Sun
(Akasofu 2007). They may be rooted in the Sun or disconnected from the solar surface.
Certain observations such as bidirectional electron fluxes favor the root hypothesis (Burlaga
Solar Wind–Geospace Modeling
et al. 1990) while other features, e.g., the huge dimensions of MCs as deduced from Ulysses
measurements, favor disconnection.
4.6 Solar Energetic Particle Events
The most significant sources of Solar Energetic Particle (SEP) fluxes in the interplanetary medium are solar flares and shock waves driven by CMEs, and it is currently
thought that large, gradual SEP events result from acceleration of particles at CME driven
shocks (Gosling 2005; Reames 1999). At the same time, shock compression of magnetic
fields is an important source of a large-magnitude IMF that is a key factor in the generation of magnetic storms. Recent studies (Kahler 2001; Kahler and Vourlidas 2005;
Gopalswamy et al. 2004) demonstrate that pre-existing energetic particles, preceding CMEs
and the density structure of the extended corona all have an influence on the production of
SEPs. SEPs may thus play an important role in predicting the geoeffectiveness of CMEs.
As observed from a heliocentric distance of 1 AU, the energetic particle flux enhancements produced by SEP events may last several days (see the nice example in Fig. 3) and,
in terms of total radiation dose, protons pose the primary hazard. The multiple processes involved in the development of SEP events include acceleration and transport of particles in a
time dependent system formed by the propagating CME-driven shock, the associated evolving magnetic field topology, and the generation of magnetic field fluctuations. Increasingly
detailed models of the evolving shock properties, wave-particle interactions and particle
transport processes were able to reproduce major features of shock-associated SEP events
(Lee 2005; Vainio and Laitinen 2007, 2008; Ng and Reames 2008), see also the companion
paper by Vainio et al. (2009). However, such models include necessary simplifying assumptions that are not always constrained by observations (Lario 2005).
The process of predicting the flux and fluence of large SEP events, days or hours in
advance of their occurrence, must accomplish the following steps: (i) determine where, when
Fig. 3 Intensity–time profiles of the SEP event of 29 October 2000, from 115 keV to 96 MeV. Data from
ACE/EPAM instrument (Gold et al. 1998), except the two higher energy channels that are from IMP-8/CPME
instrument (Sarris et al. 1976). The triggering solar activity is located at heliolongitude W27. The different evolution of these profiles at low and high energy reflects the different contribution to the flux of
shock-accelerated particles. Figure from Aran (2007)
J. Watermann et al.
and how a solar event will occur; (ii) specify the characteristics of the associated CME, such
as location, size, speed, and its ability to drive a shock wave; (iii) determine the efficiency
of the CME-driven shock at accelerating particles, as well as how they will be injected into
the interplanetary medium; and (iv) forecast how these particles and the associated shock
will travel through interplanetary space to reach spacecraft or astronauts. Existing codes for
SEP forecasting are not reliable when predicting basic SEP features such as duration, peak
fluxes, fluences and energy spectra (Baker et al. 2006). The main factor responsible for this
situation is the failure to include the effects of traveling interplanetary shocks as particle
accelerators when propagating out from the solar corona.
The SOLar Particle ENgineering COde (SOLPENCO) by Aran et al. (2006), see also
http://www.spaceweather.eu/es/model_access_interface/, is one of a class of operational
models which aim at predicting solar energetic particle fluxes and fluences in the inner heliosphere (roughly inside the Earth’s orbit). It is based on the combined shock-and-particle
model developed by Lario et al. (1998). This model assumes that the injection of shockaccelerated particles takes place at the point on the front of the shock that magnetically connects with the observer (also known as cobpoint, or Connecting with the OBserver POINT
(Heras et al. 2005)). The cobpoint changes location along the shock front and with that its
properties as the shock expands in interplanetary space. The evolution of the interplanetary
shock is described by means of the 2.5-D magnetohydrodynamic time-dependent model of
Wu et al. (1983).
The key point of the shock-and-particle model is that it allows one to compare the evolution of the MHD variables at the cobpoint with the injection rate of shock-accelerated
particles derived from the transport model. Since both simulations are performed independently, any empirical relation found between the injection rate and the MHD variables is
independent of the mechanism that accelerates particles at the shock. At present, our knowledge of the acceleration mechanisms at the shock and the shock itself are still insufficient to
perform accurate comparisons of theory and observations in individual gradual events.
Most geomagnetic storms occur during the peak and early declining phases of the solar cycle. The vast majority of intense geomagnetic storms (Dst < −100 nT) is generated by halo CMEs (Cid et al. 2004), but many frontside halo CMEs are not followed
by intense storms. Forecasts of magnetic storms solely on the basis of the occurrence
of large, frontside halo CMEs would thus suffer from high rates of false alarms (Cyr
et al. 2000). There is a tendency for the most intense magnetic storms to be generated
by the fastest CMEs, and it has been suggested that CME speed to some extent can
be used as an indicator of CME geoeffectiveness (Srivastava and Venkatakrishnan 2002;
Kim et al. 2005). However, the CME speed derived from observations proved to be unsatisfactory to discriminate between storm effective and ineffective frontside halo CMEs, e.g.,
Cid et al. (2004). Based on the observation that intense magnetic storms are often accompanied by SEP events it was suggested by Valtonen et al. (2005) and Gleisner and Watermann
(2006) that certain characteristics of SEP fluxes may provide for a better discriminator.
Gleisner and Watermann (2006) investigated statistically the relations between CME
speed, SEP flux and intense magnetic storms (defined as periods with Dst exceeding
−100 nT) over the four-year period 2001–2004 and found that enhancements of the >10
MeV SEP flux close to CME onset can be used to indicate whether a frontside full halo
CME will be followed by an intense storm within 18–72 hours. The results suggest that SEP
flux enhancements may provide a more efficient discrimination than CME speed for any
choice of discriminating thresholds. Their results appear to indicate further that a combination of two parameters, namely SEP enhancement and heliographic longitude of the CME
release, may provide for an even better discriminator. But a thorough study on this topic has
yet to be carried out.
Solar Wind–Geospace Modeling
5 Modeling the Solar Wind–Magnetosphere–Ionosphere System
Currently, the only self-consistent method to model the entire solar wind–magnetosphere–
ionosphere system is based on ideal MHD theory where plasma is assumed to be fluid having a common temperature, density and velocity. Therefore, computer simulations based
on ideal MHD are considered the most promising predictive tools for space weather applications. In principle, a computationally efficient code can describe the coupled solar wind–
magnetosphere–ionosphere system in real time, using a point measurement in the solar wind
as input. However, in practice there are several obstacles to overcome when building a fully
operational simulation that can be used for forecasting the space environment. For example,
even the fastest parallelized codes still have to make compromises with spatial resolution in
order to speed up the code execution to the real-time limit.
5.1 Global Magnetohydrodynamic Coupling Models
GUMICS-4 (Grand Unified Magnetosphere–Ionosphere Coupling Simulation) is the latest
model in a sequence of the global MHD simulations developed and operated by the Finnish
Meteorological Institute (Palmroth et al. 2001). GUMICS-4 is a further development of
GUMICS-3 (Janhunen 1996). It consists of two computational domains solving the coupled solar wind-magnetosphere-ionosphere system. Its solar wind–magnetosphere domain
is based on solving the ideal MHD equations conserving energy, mass, and momentum. Its
ionospheric domain is based on solving the electrostatic current continuity equation, with
models for dayside solar UV-dependent conductivities and the response of the thermosphere
to electron precipitation embedded. The two domains are linked by electron precipitation
and field-aligned currents from the magnetosphere which together with the ionospheric
conductivity define the ionospheric potential. This potential is mapped back to the magnetosphere where it is used as a boundary condition for the MHD solution.
The computational volume is a box extending from −224 to +32 Earth radii in GSM
X and from −64 to +64 Earth radii in GSM Y and Z. Advanced numerical methods such
as automatically refined Cartesian octogrid and temporal subcycling are employed to speed
up the computation. The grid size in the magnetosphere depends on the location relative
to the Earth and the steepness of plasma and magnetic field gradients. The ionosphere is
represented by a 3-D grid with 20 height layers in which the grid size is refined to ∼100 km
in the auroral region.
The primary magnetospheric output parameters are plasma density, pressure, velocity,
temperature, and magnetic field in space and time. The ionospheric output parameters include the electric field, height-integrated Pedersen and Hall conductivities, ionospheric electric potential, particle precipitation power, Joule heating rate and field-aligned current density in space and time.
As the MHD equations describe the large-scale behavior of the magnetosphere, quantities such as the location and shape of the bow shock, magnetopause, tail lobes and current sheet are reproduced realistically by the model. Quantities which depend on non-MHD
physics such as overlapping plasma populations with different temperatures and more generally plasma populations characterized by different parallel and perpendicular temperatures
are not reliably reproduced (Janhunen and Palmroth 2001). For instance, the structure and
dynamics of the inner magnetosphere including the ring current and the region-2 current
system are less well reproduced by the model (Palmroth et al. 2003). GUMICS-4 has been
applied successfully to a number of investigations dealing with solar wind energy input, its
magnetospheric transfer and its ionospheric dissipation (Palmroth et al. 2003, 2004, 2006a,
2006b, 2006c).
J. Watermann et al.
Fig. 4 Polar cap potential
difference from GUMICS
simulations (y-axis) and
SuperDARN measurements
(x-axis) from five random events.
Black line gives the one-to-one
correspondence, the red line is
the regression line for the points
In the ionosphere, GUMICS-4 is known to agree, spatially and temporally, with various
measurements, but the magnitude of the ionospheric effects is lower than expected (Palmroth et al. 2005, 2006a). This is illustrated in Fig. 4, although we are looking at small-number
statistics. Five random events are given, with a range of magnetic conditions from quiet to
active. The x-axis gives the SuperDARN radar observations of the cross polar cap potential
during the five events, while the y-axis gives the GUMICS-4 simulation results. The correlation appears quite good as the correlation coefficient of a least-mean-squares fit is 0.75,
though the magnitude of the GUMICS-4 potential is about 50% of the SuperDARN measurements.
Other global MHD models include the Block-Adaptive-Tree-Solarwind-Roe-UpwindScheme (BATS-R-US) (Clauer et al. 2000) and the Lyon-Fedder-Mobarry (LFM) codes
(Lyon et al. 2004), which can both be combined with the Rice Convection Model (RCM)
(Wolf 1970; Wolf et al. 1991; Toffoletto et al. 2003). Specific information can be found at
http://ccmc.gsfc.nasa.gov/ and http://cism.hao.ucar.edu/models_lfm.html.
An independent approach to global geospace modeling was taken by Raeder et al.
(2001a). Starting from an early, purely magnetospheric MHD model with crude ionospheric
boundary conditions and subsequently combining it with a more sophisticated inner boundary model, the global multi-fluid CTIM (Coupled Thermosphere–Ionosphere Model) developed by Fuller-Rowell et al. (1996), Raeder et al. (2001a) presented a global, self-consistent,
fully electrically coupled magnetosphere–ionosphere–thermosphere model which became
known as the “OpenGGCM” (see http://openggcm.sr.unh.edu/wiki/index.php/Main_Page).
The magnetospheric model contains a coupling module which maps field-aligned currents
from the magnetosphere to the ionosphere and computes electron precipitation fluxes and
mean energies while in return mapping the ionospheric electric field to the inner boundary
of the magnetospheric regime. The outer boundary conditions are determined by upstream
solar wind parameters. The model was extensively tested against observations and proved
to render realistic results for geomagnetic storm simulations (Raeder et al. 2001a), but some
limitations in substorm modeling were noticed (Raeder et al. 2001b).
5.2 Physical Models of the Inner Magnetosphere
The Rice Convection Model (RCM) is probably the model with the longest history of active
use among the physical models describing the coupling between the inner magnetosphere
Solar Wind–Geospace Modeling
and the ionosphere. Recognizing the different behavior of particles with different energies
and the wide span of energies present in the inner magnetosphere (plasmasphere ∼1 eV, ring
current ∼1–300 keV, radiation belts many MeV) the RCM uses a many-fluid formalism to
describe adiabatically drifting isotropic particle distributions and the flow of electric currents
along magnetic field lines to and from the conducting ionosphere in a self-consistently computed electric field and specified magnetic field. The RCM does not employ ideal MHD theory, but combinations of the RCM with global magnetospheric MHD models (e.g., BATSR-US) have already been implemented.
It is generally accepted that the magnetotail plasma sheet plays a key role as a source
of ring current particles. However, the relative influence of magnetospheric convection and
substorm particle injection on the energization and transport of ions into the storm-time
magnetospheric ring current is one of the areas where full clarification is still awaited and
where modeling has been used to aid clarifying the process.
A possible approach is to examine, through computer simulation, temporal and spatial
variations of ion energy densities in the inner magnetosphere during storms accompanied
by substorms and storms where only convection is at work. For this purpose a 3-D dynamic
ion-tracing model was developed (Delcourt 2002) which uses a test-particle approach to
ion transport and energization. The T89 geomagnetic field model (Tsyganenko 1989) is
employed to provide the average magnetic field configuration for six different levels of geomagnetic activity. The large-scale steady convection electric field in the magnetosphere is
derived from the Volland-Stern model (Volland 1973; Stern 1975). It has been adapted to
fit most of the general features of electric fields observed by polar orbiting satellites. The
electric field induced by a transition of the geomagnetic field from an initial level to a final,
more or less disturbed one, is derived by the vector potential technique proposed by Delcourt
and Sauvaud (1990).
Computer simulations using this approach have demonstrated that the inclusion of
substorm-induced electric fields renders acceleration of the most important ion species (H+
and O+ ) much more efficient (Daglis et al. 2004, 2009). This is demonstrated in Figs. 5
and 6. The difference between these scenarios is more prominent for O+ ions which are
known to be preferentially accelerated by substorm-induced electric fields (Daglis and Axford 1996).
The Inner Magnetosphere Particle Transport and Acceleration Model (IMPTAM), developed by Ganushkina et al. (2001, 2005, 2006), traces ions and electrons with arbitrary
pitch angles in time-dependent magnetic and electric fields. It employs three particle motion
solvers, (1) tracing of a single particle trajectory moving under the Lorentz force, (2) tracing
of a single particle, (3) tracing of a distribution of particles in the drift approximation under
the conservation of the first and second adiabatic invariants. The Liouville theorem is used
to gain information about the entire distribution function. The initial particle distribution
and boundary conditions are set and varied during the modeling process based on observations during specific events. Particle loss processes include charge-exchange with neutral
hydrogen in the upper atmosphere and Coulomb collisions.
The advantage of this model is that it can utilize any magnetic and electric field model. In
the above cited studies, Tsyganenko magnetic field models (Tsyganenko 1995, 2002), which
are empirical average models, were used together with both a time-stationary convection
electric field and pulsed electromagnetic fields. These transient fields, which are associated
with the dipolarization process in the magnetotail during substorm onset, were modeled as
an earthward propagating electromagnetic pulse of localized radial and longitudinal extent
(Sarris et al. 2002). The magnetic field disturbance from this dipolarization process was
obtained from Faraday’s law. Several pulses were launched at substorm onset.
J. Watermann et al.
Fig. 5 Temporal and spatial variations of energy densities of plasma-sheet H+ , in the equatorial plane, under
the influence of (a) a large convection electric field only and (b) a storm-time substorm electric field during
the growth phase. Figure after Daglis et al. (2009)
Fig. 6 Temporal and spatial variations of energy densities of plasma-sheet O+ , in the equatorial plane, under
the influence of (a) a large convection electric field only and (b) a storm-time substorm electric field during
the growth phase. Figure after Daglis et al. (2009)
The IMPTAM model has been tested and used to examine the evolution of the current
systems during magnetic storms, to compute energetic ion drifts in the inner magnetosphere,
and to evaluate the magnetospheric sources of magnetic disturbances recorded on ground
(i.e., the sources of the Dst index). One of the important results is the ability of the model
to reproduce the observed amount of ring current protons with energies >80 keV during the
storm recovery phase (Ganushkina et al. 2005, 2006), which was not possible to obtain with
other models using a dipole magnetic field model and a large-scale convection electric field.
Figure 7 shows the development of a strong ring current in an IMPTAM storm simulation
when substorm pulses are added to a standard convection electric field.
A comparison between three ring current models, the particle tracing scheme described
above (Ganushkina et al. 2005), the empirical ring current model of Milillo et al. (2001)
and the kinetic ring current–atmosphere interaction model (RAM) of Liemohn et al. (2001)
revealed that the choice of initial and boundary conditions has a profound impact on the
intensity and energy spectrum of the modeled ring current (Ganushkina et al. 2006).
Solar Wind–Geospace Modeling
Fig. 7 Calculated energy density maps (from IMPTAM) in the equatorial plane for protons with 80–200 keV
energies when several electromagnetic pulses were activated at substorm onsets during the modeled period
of 2–4 May 1998. Figure from Ganushkina et al. (2005)
J. Watermann et al.
A physics-based ring current model developed in several stages by Fok and Moore (1996)
and Fok et al. (1999, 2001) provides the 1–300 keV proton and electron fluxes in the equatorial plane between dayside magnetopause and a distance of ten Earth radii on the nightside.
It is available for computer runs on request as well as for real-time runs at the Community
Coordinated Modeling Center (CCMC, http://ccmc.gsfc.nasa.gov/).
6 Empirical Models of Solar Wind–Magnetosphere–Ionosphere Coupling
Theoretical models are based on known physical relations, and successful models constitute
a proof of physical understanding of the processes involved. But they are often constrained
by assumptions and approximations such as adiabaticity, electromagnetic configuration, active loss/source processes and boundary conditions, among others (Ebihara and Ejiri 2000;
Jordanova et al. 2001; Fok et al. 2001; Liemohn et al. 2001; Ganushkina et al. 2005). Empirical models start from observations and seek to model the relations between different
observables in an empirical way. For this reason empirical (including statistical) models are
important complements to theoretical models.
The prime goal of empirical models is to make quantitative predictions of the future
given information of the past (Farmer and Sidorowich 1987). The physical understanding
of the problem, the generic form of the empirical model, and the amount and quality of
the data are of importance for the success of the model to predict the true system. The
physical knowledge of the system is usually coded into the model, e.g. through selection of
physical observables, transformations of observables, selection of data, and/or constraints
on the model.
6.1 The Magnetospheric Ring Current
The ring current is the most important large-scale current system in the inner magnetosphere.
It is carried by high-energy (up to several hundred keV) charged particles, primarily positively charged ions. Note, however, that ring current particle energies are at any time still
significantly lower than typical radiation belt populations (the latter are subject of a companion paper in this issue). Protons with medium energies (20–80 keV) are the main contributor
during the storm main phase whereas higher energy protons (80–200 keV) dominate during the storm recovery phase. It is mostly understood that protons (of both, solar wind and
ionospheric origin) are the prime species among ring current ions, and this is probably correct most of the time. But AMPTE/CCE and CRRES spacecraft observations indicated that
during intense magnetic storms single-charged oxygen of ionospheric origin can become the
dominant species (Daglis et al. 1999).
Useful empirical models of the inner magnetospheric ion population appeared once a
large amount of ion data had been collected in a systematic way by the AMPTE-CCE, Polar
and LANL satellites.
Milillo et al. (1999, 2001) devised a stationary model capable of reproducing the inner
magnetosphere distribution of the 90◦ pitch angle proton flux at low geomagnetic activity
(AE < 100 nT) through a functional form which was directly derived from the average ion
fluxes observed by the AMPTE-CCE/CHEM instrument. The functional form of Milillo et
al. (2001), referred to as MODEM (Milillo-Orsini-Daglis-Empirical-Model), is expressed
as a function of L-shell parameter (L), energy (E) and Magnetic Local Time (MLT). One of
the principal outcomes from this model is the relation between the characteristic energy of
the convected/injected population and MLT.
Solar Wind–Geospace Modeling
By varying a certain subset of model parameters according to local measurements, the
general characteristics of the long-term evolution of the proton distribution during quiet as
well as storm times can be reproduced (Orsini et al. 2004; Milillo et al. 2006). This approach
(referred to as dynamic MODEM) proved to be a useful tool for global investigations of
magnetospheric dynamics from local measurements; see also Ganushkina et al. (2006).
The same data set has been used to derive an H+ pitch angle distribution model (De
Benedetti et al. 2005), referred to as PADEM (Pitch-Angle-Distribution-Empirical-Model).
This model describes the pitch angle distribution of the proton flux as a function of geocentric distance, energy and MLT, normalized by the 90◦ pitch angle flux at low geomagnetic
activity.
PADEM consists of a multi-parametric functional form that depends on pitch angle, energy, L-shell and a few independent factors. Different factors are determined for different
MLT hours. The model is capable of accurately reproducing the average proton pitch angle distribution in the whole inner magnetosphere. It reveals interesting statistical features
many of which confirm the results of previous studies related to magnetic field drift shell
splitting (Roederer 1967), electric field drift shell splitting (Korth et al. 1983) and magnetopause shadowing (West et al. 1973). For example, pitch angle anisotropy is higher in the
inner regions than in the outer regions (Fok et al. 1995). Generally, fresh particles, convected
from the plasma sheet, have more isotropic pitch angle distributions than long time resident
particles. which exhibit anisotropic PAD; see, for instance, Fok et al. (1996). By combining
MODEM and PADEM a full description of the ring current proton distribution becomes
available.
The empirical models can be used to formulate initial and/or boundary conditions for
theoretical models (Ebihara et al. 2002). Furthermore, macroscopic quantities such as energy
density, total energy, perpendicular current density and so forth which characterize the inner
magnetosphere can be derived and compared to the results of theoretical models (Milillo et
al. 2003; Ganushkina et al. 2006). For instance, Milillo et al. (2003) derived from MODEM
an electric field model that can be used as input for theoretical particle circulation models.
6.2 The High-Latitude Ionospheric Electric Potential
The high-latitude ionospheric electric field can be considered the effect of the magnetohydrodynamic interaction between the solar wind and the magnetosphere mapped down to the
ionosphere. This electric field drives, together with neutral thermospheric winds, the highlatitude plasma convection and is partially responsible for the large-scale energy transfer
between magnetosphere and ionosphere. The recognized significance of the high-latitude
plasma convection for magnetosphere–ionosphere coupling led to several attempts to build
models of the ionospheric electric potential.
One of the earliest quantitative high-latitude electric field models was developed by Heppner (1977). It is an empirical model based on OGO-6 (OGO—Orbiting Geophysical Observatories) measurements which were limited in space by the dawn-dusk orbit of the satellite.
After measurements became available from the Dynamics Explorer 2 (DE-2) satellite which
covered all local times the model was extended by Heppner and Maynard (1987). The model
is in principle a set of representations of the electric field under various IMF-By and negative Bz conditions during moderate geomagnetic activity. The model was improved upon by
Rich and Maynard (1989) who fitted a spherical harmonic representation to a digitized version of the Heppner-Maynard patterns and included a dependence on geomagnetic activity
for the case of southward IMF.
J. Watermann et al.
In recent years the Weimer empirical model (Weimer 2005a, 2005b) became a popular
alternative to the Heppner-Maynard-Rich model. It includes representations of the highlatitude electric field and field-aligned currents (FACs). The model is represented as a spherical harmonic expansion at very high latitudes combined with a Fourier series expansion
at auroral and subauroral latitudes, the low-latitude boundary being defined by the cut-off
of significant magnetic and electric field perturbations in polar orbiting satellite data. The
required input variables are solar wind density and velocity and the IMF component perpendicular to the Sun–Earth line. The model delivers electric potential and FAC patterns
directly and the Poynting flux and thermospheric Joule heating rate indirectly. Another empirical high-latitude ionospheric electric potential model was developed based on a large
collection of Millstone Hill incoherent scatter radar observations.
A different approach was taken at IZMIRAN (Pushkov Institute of Earth Magnetism,
Ionosphere and Radiowave Propagation) where a season-dependent model of high-latitude
electric field and FAC distributions (known as IZMEM) was derived from high-latitude
ground-based magnetometer observations (Levitin et al. 1982; Feldstein and Levitin 1986;
Papitashvili et al. 1994). Linear regression coefficients between IZMEM maps and IMF
parameters were established so that IZMEM provides electric field distributions for any
given IMF and season without the need for actually collecting and inverting ground-based
magnetic field data. IZMEM was subsequentially recalibrated using DMSP (Defense Meteorological Satellites Program) electrostatic potential maps (Papitashvili et al. 1999). In two
recent attempts the linear regression approach was applied to empirical DMSP electrostatic
potential maps in order to construct a new ionospheric convection model (Papitashvili and
Rich 2002) and to empirical Oersted/Magsat FAC maps in order to construct a FAC model
(Papitashvili et al. 2002), all ordered by season and IMF parameters.
More complex models such as AMIE (Assimilative Mapping of Ionospheric Electrodynamics) developed at the High Altitude Observatory (HAO), Boulder, CO, by Richmond and Kamide (1988) and Richmond (1992), make use of the most comprehensive data set available. The AMIE procedure is an optimally constrained, weighted
least-squares fit of the electric potential distribution to diverse types of atmospheric
observations including those from magnetometers, radars and low altitude satellites,
see http://www.hao.ucar.edu/modeling/amie/AMIE_head.php. One-min dual-hemisphere
AMIE patterns using ground magnetometer data only were prepared by A. Ridley at the
University of Michigan, see http://amie.engin.umich.edu/~amie.
6.3 Prediction of Magnetic Indices
The prediction lead time is an important parameter to be considered when constructing a
model. The physics of the system sets an upper limit to the lead time. Going past the physical
limit will lead to a purely statistical prediction. That may be useful, but it requires the process
to be stationary at those time scales.
An index is used to summarize phenomena and is often derived from a single quantity.
Empirical models are well suited to predict indices as many different underlying physical
processes may be at play that are not easily modeled from first principles. However, once an
empirical model has been shown to accurately map from an input space to an output space
the model is available for further analysis to explore the input-output relation.
In Table 1 publicly available empirical models are listed which forecast certain magnetospheric or ionospheric parameters and which run in real time operation. There are of
course many more models described in the literature but only those models that provide online forecasts are included. The list contains only models which are semi-empirical, i.e. the
Solar Wind–Geospace Modeling
Table 1 Online empirical models. The Physics column indicates the reason for the lead time: “L1-Earth”
means the solar wind advection time from L1 to Earth; “ring current” refers to ring current dynamics;
“mag.sph.” is general magnetospheric dynamics; “statist.” means that it is a purely statistical model. The
Model column indicates either the model name or the provider of the forecast
Parameter
Lead time
Physics
Model
RWC-Sweden (Wintoft 2005)
rms dB/dt
30 min
L1-Earth
AE
1 hr
L1-Earth
EDDA (Pallocchia et al. 2006)
Dst
1 hr
L1
ACSE-Sheffield (Boaghe et al. 2001)
Dst
1–2 hr
L1 + ring current
RWC-Sweden (Lundstedt et al. 2002)
Dst
1–2 hr
L1 + ring current
EDDA (Pallocchia et al. 2006)
Dst
1–2 hr
L1 + ring current
LASP (Temerin and Li 2006)
Dst
1–6 hr
L1 + statist.
ACSE-Sheffield (Wei et al. 2004)
Kp
0–6 hr
L1 + mag.sph. + statist.
RWC-Sweden (Boberg et al. 2000)
Kp
30–90 min
L1 + mag.sph.
SEC (Costello 1997)
Kp
1, 4 hr, 4 d
L1 + mag.sph. + statist.
UPOS (Wing et al. 2005)
models are derived empirically but are governed by a physical connection between observed
data and predicted data. In some cases lead times extend beyond the known physical process
time, and a statistical element is added. Purely statistical models are not included.
The first model in the list (Wintoft 2005) predicts the 10-minute root-mean-square of the
one-minute difference horizontal geomagnetic field components (Bx,y (t) = Bx,y (t + 1) −
Bx,y (t)). This is not an index in the sense that it is derived to capture a physical phenomena, it is instead derived from the technological point that geomagnetically induced currents
(GIC) (Pirjola 2002) have a close relationship to the time derivative dB/dt of the magnetic
field through Faraday’s law of induction. However, predicting dB/dt at minute resolution or
higher is a too complex task, therefore the 10-min RMS Bx,y was derived as it captures the
main phenomena at a suitable level of detail. It was found that the lead time is completely
determined by the L1-Earth solar wind advection time of about 30 minutes. Trying to increase the lead time will seemingly only reduce the prediction accuracy by a small amount,
however, studying the predictions in detail will show a shift in the predictions.
The AE index captures the global auroral electrojet activity (Mayaud 1980) and is derived
from the horizontal geomagnetic field from a chain of auroral zone stations. Apart from
being a fundamental index when studying geomagnetic storms and substorms the AE index
can be used to predict ionospheric storms several hours in advance (Wintoft and Cander
2000) due to travelling atmospheric disturbances that are triggered at high latitudes and
move equatorward (Prölss 1993). The EDDA model (Pallocchia et al. 2006) predicts the AE
index up to an hour in advance using solar wind data from ACE.
Models predicting the Dst index have received considerable attention over the years starting with the empirical relation suggested by Burton et al. (1975). The Dst index was developed to capture the ring current and is derived from the horizontal geomagnetic field from
four low-latitude observatories (Sugiura and Kamei 1991). The five models listed in Table 1
rely on real time ACE solar wind data. The prediction lead time is governed by the L1Earth solar wind advection time plus about one hour for the development of the ring current
(manifested in the storm main phase). The key parameter to these models is the IMF Bz component. When Bz turns southward reconnection takes place at the magnetopause enabling
solar wind energy to enter the magnetosphere. However, the velocity is also important as it
controls the rate at which the energy enters. It can be estimated from the solar wind electric
field E = V × B.
J. Watermann et al.
The LASP model (Temerin and Li 2006) uses an ARMA-type filter with non-linear terms
and is quite complex. Dst is calculated from a sum of six terms:
Dst = dst1 + dst2 + dst3 + pressure term + direct IMF Bz term + offset term
where the dstn terms, n = 1, 2, 3, contain a driver term that depends on the solar wind, and a
decay term. Except for the offset term all terms are modulated by a function which depends
on season. The model contains about 150 coefficients which are determined such that the
RMS error between predicted and observed Dst is minimized.
The Dst model at the RWC-Lund (RWC—Regional Warning Center) uses an Elman
neural network (Lundstedt et al. 2002). This is a recurrent neural network (RNN) that contains feed-back connections which add memory and complex behaviour. The EDDA model
(Pallocchia et al. 2006) is very similar to the RWC-Lund model but uses only solar wind IMF
data as input. The model has also three inputs (x1 = Bz , x2 = B2, and x3 = By 2) and four
context units. Specifically in operational applications the use of IMF only is suggested by
the observation that enhanced proton fluxes (which tend to occur prior to intense magnetic
storms) disturb the ACE plasma instruments more often than the magnetometers.
Several models were proposed by the Department of Automatic Control and Systems
Engineering (ACSE) of Sheffield University (Boaghe et al. 2001; Wei et al. 2004). They represent mathematical models based on nonlinear system identification schemes (e.g., NARMAX, NARX, wavelet). Solar wind data (the product of velocity v and southward magnetic
field Bs ) form the input, and the output is a prediction of Dst up to six hours ahead.
A range of successful models to forecast different space weather parameters exist. However, the demand on a model for real time operation is different from that of a model for
studying solar-terrestrial relations. It is very difficult to decide which model is the optimal
one among all available when only overall measures like RMS error or correlation is used.
The forecast lead time must be thoroughly analyzed in order to judge the usefulness of a
model.
7 Simulating Atmospheric Effects of Space Weather
The need for developing coupled atmosphere-thermosphere-ionosphere-plasmasphere models has long been recognized by the atmospheric science community. As a consequence,
global circulation models of the terrestrial upper atmosphere have evolved and are now able
to simulate to a certain degree observed physical effects of the penetration of space weather
effects into and through the thermosphere. But not all the details can yet be predicted—or
even reproduced—at even medium resolution (50–100 km) because the effects are complex and result from spatially and temporally variable inputs for which there is insufficient
density of measurements.
One of the models developed in Europe is the Coupled Middle Atmosphere and Thermosphere model (CMAT) which is derived ultimately from the time-dependent 3-D Coupled Thermosphere Ionosphere Plasmasphere (CTIP) model (Fuller-Rowell et al. 1996;
Millward et al. 1996). This was extended down to 30 km by Harris (2001) as CMAT(1), and
subsequently down to 15 km altitude as CMAT2 (Dobbin 2005). The extensions to CTIP
mean that lower atmosphere dynamic effects such as gravity waves can be included, and
conversely the effects of ionospheric inputs such as auroral precipitation on the middle and
lower atmosphere can be examined. CMAT2 incorporates a complex ion and neutral chemical scheme, high-resolution solar flux data and variable auroral energy inputs. It solves the
Solar Wind–Geospace Modeling
Fig. 8 CMAT calculated nitric oxide number density (×10−14 m−3 ) at ∼110 km altitude as a function of
latitude and time at 0◦ (a) and 180◦ (b) longitude. The time axis covers the period from 12:00 UT 23 October to 12:00 UT 3 November 2003 which includes the Halloween storm. Intervals between contours are
1.5 × 1014 m−3 . Figure from Dobbin et al. (2006b)
non-linear coupled equations of energy, momentum, and continuity. The model grid has variable resolution grid-spacing and can be run with virtually any useful latitude-longitude and
height spacing (within the possible resolution), so that one can trade off resolution against
system usage. Figure 8 gives an example of the effect major geomagnetic storms (in this
case the Halloween storm) may exert on the neutral atmosphere.
J. Watermann et al.
CMAT2 is modularized and allows different combinations of sub-systems. If, for example, only a simple, non-coupled ionosphere is required the model can be run with a parameterized ionosphere, e.g., the Chiu ionosphere (Chiu 1975) or the Parameterized Ionosphere
Model (PIM). If a coupled ionosphere-neutral atmosphere is needed then the self-consistent
Global Ionosphere Plasmasphere (GIP) model is used. The magnetic field configuration used
in GIP is an “Apex” system, that is one that traces the field lines from the equatorial apex to
ground, rather than approximating them analytically.
CMAT2 covers atmospheric regions from the exosphere (from 10,000 km for the
ionospheric flux tubes) down to a lower boundary of 15 km altitude. It allows for a variety
of lower boundary conditions—e.g., specified by MSIS (Mass Spectrometer and Incoherent Scatter), NCEP (National Centers for Environmental Prediction) or fixed—and can be
used with four different parameterizations for atmospheric gravity waves (AGWs), including one that demonstrates penetration of gravity wave momentum deposition to the middle
thermosphere (Yiğit et al. 2008). Parameterizations are necessary because individual AGWs
are too small to resolve on the model grid.
The most obvious space weather input to the neutral atmosphere occurs in the auroral
zone. The auroral input comprises an energy effect (particle precipitation and heating) and
a momentum effect (plasma convection). To simulate it properly high-latitude convection
and particle precipitation patterns are required as input variables. They may be continually
changed and can thus simulate dynamic coupling.
8 From the Solar Corona to the Earth’s Atmosphere—Comprehensive Modular
Schemes
At present only two groups have developed comprehensive predictive physics-based 3D models for the coupled solar corona–solar wind–magnetosphere–ionosphere–upper atmosphere system, the Center for Space Environment Modeling (CSEM) at the University
of Michigan (http://butch.engin.umich.edu/), and the Center for Integrated Space Weather
Modeling (CISM), a USA-wide research consortium headquartered at Boston University
(http://www.bu.edu/cism/). Their models are modularized schemes which draw on existing
components (which are, however, under continuous development) and newly devised integration schemes.
The CSEM-developed Space Weather Modeling Framework (SWMF) modularized
scheme (Tóth et al. 2005) comprises, in its various versions and combinations, modules
for the solar corona (SC), eruptive events (EE), the inner heliosphere (IH), solar energetic
particles (SP), the global magnetosphere (GM), the inner magnetosphere (IM), the radiation
belts (RB), the ionosphere (IE) and the upper atmosphere (UA). Several of the modules are
implemented in different versions of the 3-D BATS-R-US code. The user has the choice between different models and model combinations. Some modules feed parameters into other
modules while others deliver end results. A brief description is also available at the Community Coordinated Modeling Center (CCMC) web site, http://ccmc.gsfc.nasa.gov/ where
also model runs can be requested. Using reasonable spatial resolutions in all of the coupled
components, the SWMF model runs significantly faster than real time on massively parallel
supercomputers.
The CISM model is being built around existing state-of-the-art cores including the MAS
(Magnetohydrodynamics outside A Sphere) code (Linker et al. 2003) and the 3-D ENLIL
heliospheric MHD code (Odstrcil 2003), the LFM (Lyon-Fedder-Mobarry) MHD code for
the global magnetosphere–ionosphere system (Lyon et al. 2004), the TING (Thermosphere
Solar Wind–Geospace Modeling
Ionosphere Nested Grid) code (Wang et al. 2004) which is based on the NCAR-TIGCM
model, and the RCM (Rice Convection Model). The former two form the CORHEL module,
the latter three the CMIT/LTR module. More information is given at the CISM model web
site, http://www.bu.edu/cism/CISM_Thrusts/modelsandcoupling.htm
9 Venues for Future Development
In the last couple of years, the modeling of the solar wind and of CMEs superposed on this
wind has advanced to a stage where individual events can be simulated rather realistically
and then compared with observations. The current state-of-the-art 3-D MHD models are beginning to apply magnetogram data as input boundary conditions and are starting to include
non-MHD effects, such as solar particle acceleration and kinetic effects. Still, very few of
them are sufficiently developed to explain the real events in detail, and most of them only
consider one of the sub-problems involved in space weather modeling.
Future models should aim to model the entire process from CME initiation to CME
evolution. However, this is a difficult task as considerable variations of physical conditions
in the solar photosphere, corona, and interplanetary space involve many physical processes
occurring on vastly different spatial and temporal scales. One way to deal with this problem
is to decouple the solar corona model from a model solving the inner heliosphere and to use
the output of the coronal model as a boundary condition for the heliospheric model (Odstrcil
et al. 2004b). Coronal models need to simulate more complex physical processes while
heliospheric models can use simpler approximations over a much larger spatial domain. It
is also more efficient computationally to advance the heliospheric portion of the simulation
independently of the coronal time step. Another way to deal with the varying spatial scales
is the use of adaptive mesh refinement techniques as done in the BATS-R-US code (Powell
et al. 1999) or in the AMR-VAC code (van der Holst and Keppens 2007).
It has been demonstrated that substorm-associated magnetospheric electric fields are effective in the storm-time particle transport and energization. There is a great need to find
more realistic models for the electric field. Likewise, there is an equal need for better and
more comprehensive electric field observations that can be used to constrain such models
both for the large-scale convection and smaller-scale temporally evolving structures. The
present state of our understanding of magnetospheric dynamics is quite advanced. Gaining
even better understanding will necessarily require complex models of the electromagnetic
fields and particle motions. This will require combination and coupling of multiple sources
as well as large-scale and small scale processes. The relative significance of these is still an
open issue and calls for detailed as well as synoptic observations, preferably simultaneously.
Models of the Earth’s upper atmosphere have become increasingly complex and more
tightly coupled to the regions above and below. There is a move to more flexibility in the
resolution and increasing modularity which allows code-sharing between models. The lower
boundary can be as low as the ground, with a choice of boundary models. Such models are
already useful for a range of studies of the coupling between atmospheric layers, and are
being used increasingly to couple to other models in the Sun–Earth chain. Developments
continue, but some elements are still unclear, in particular, how to extend the representation
of electric fields to include the global electric circuit.
Models are most valuable if they enhance our understanding of the physical processes
which the models attempt to simulate or if they improve our predictive capabilities or both.
A problem common to the vast majority of scientific models is the lack of proper quantitative validation in terms of objective measures. To validate a model or to compare the
J. Watermann et al.
performance of different competing models a certain metric has to be established. A typical
metric contains a reference model, a set of model parameters selected for comparison and
a scheme to assess quantitatively the difference between test model and reference model
output. Metric studies have so far mainly (but not only) been carried out by the US-based
Community Coordinated Modeling Center (http://ccmc.gsfc.nasa.gov/) where a selection
of reports and presentations published up to the year 2005 can be examined at the CCMC
metrics web site, http://ccmc.gsfc.nasa.gov/metrics/.
An example of a recent study to investigate the performance of various CISM solar
corona and heliospheric models, ranging from empirical over semi-empirical to physical
models, was performed by Owens et al. (2008). Their comparison between results obtained
from several models and one-hour resolution solar wind measurements taken at the L1 point
revealed that their empirical coronal-heliosphere model currently gives the best forecast of
solar wind parameters at 1 AU. However, the authors also note that physics-based models
accurately capture dynamic effects at solar wind stream interaction regions, such as magnetic field compression, flow deflection, and density buildup, which the empirical scheme
cannot.
The ionospheric output from SWMF models was tested and validated by Wang et al.
(2008). The authors found that the accuracy of modeling the ionospheric potential and fieldaligned currents varies with local time, season and geomagnetic activity (where periods of
higher activity are less accurately modeled).
Model validation has also been carried out in a handful of studies on the performance
of magnetic indices and specifically Dst, see Lundstedt et al. (2002), Wei et al. (2004),
Pallocchia et al. (2006), Temerin and Li (2006) and Amata et al. (2008). However, much
work has yet to be done to meet the space weather prediction requirements where much
emphasis is put on numerical accuracy.
10 Conclusions
The success of physical models is an indicator of physical understanding of the model mechanism. That means that the value of models does not simply derive from their shear existence and sophistication. It is rather the synergy of theoretical modeling, numerical simulation and data analysis which results in better understanding of solar wind–magnetosphere–
ionosphere coupling processes. Space weather research has, because of its practical applications, the responsibility to address practical problems, and there are cases where this can and
should be done through modeling efforts even if only limited physical understanding exists.
It is thus obvious that the Space Weather research community is well advised to continue, at
least for the time being, to work in all of the three model categories, physical, semi-empirical
and empirical modeling.
A modern venue of studying solar-terrestrial relations adopts a system science approach,
i.e., an approach which views the Sun–heliosphere–Earth complex as a single integrated
system whose behavior results from interactions between various drivers and moderators
which cannot be considered independent or self-confined entities. The system science approach has led to the development of comprehensive Sun–Earth models, favoring modularized schemes for greater flexibility. Such an approach is already quite advanced in the United
States. A number of excellent models for specific space regimes and scales were developed
in Europe, but we are still awaiting a comprehensive European approach. The establishment
of a European space weather research community has progressed substantially, largely because of support from the European Space Agency (ESA) and the European Union through
Solar Wind–Geospace Modeling
the “Cooperation in the field of Scientific and Technical Research” (COST) program. The
newly established COST Action ES0803 “Developing space weather products and services
in Europe” is expected to build on the success of COST 724 and further advance a systems
science approach.
Acknowledgements We gratefully acknowledge the financial support provided by the EU COST office to
COST Action 724 which helped to create a stimulating working atmosphere for the European Space Weather
science community and eventually led to this review. We thank the International Space Science Institute
(ISSI), Berne, Switzerland, for generously hosting us during part of our effort. Thanks are due to one referee
for providing constructive comments which helped to enrich this paper. During the preparation of this paper
JW benefited from a grant provided by Le Studium, agence régionale de recherche et d’accueil international
de chercheurs associés en région Centre, France. BS acknowledges partial support from PN AYA2007-60724
of the Ministerio of Educación y Ciencia (Spain). CC, ES and YC received support from the Comisión Interministerial de Ciencia y Tecnología (CICYT) of Spain under the projects ESP 2005-07290-C02-01 and
ESP 2006-08459. MP received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC Starting Grant agreement number 200141QuESpace and support from the Academy of Finland. The research of NG was supported by the Academy of
Finland. FAM was supported by a Heraclitus research grant through the EPEAEK framework of the Greek
Ministry of Education.
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