M. Dryera, Z. Smitha*
a NOAA/SWPC, Boulder, CO 80303
2. The Models
It has been well known for many years
that appropriate electrodynamic coupling between solar-initiated solar wind disturbances
and the Earth's magnetosphere initiates and sustains geomagnetic storms. In order to
forecast these storms, associated solar events that can be observed in real time have been
sought. It is generally agreed that magnetic energy within confining magnetic topologies
is released during solar flare and helmet streamer blowouts. Energy is then converted into
electromagnetic (X-ray, UV, etc.) emissions, as well as non-thermal energetic particles,
thermal and kinetic forms. If sufficiently energetic, these solar events can initiate
interplanetary (IP) disturbances that are headed by shocks. If these IP disturbances are,
in turn, sufficiently energetic, they can reach 1 AU, or Earth; if not, the leading shocks
decay to (subsonic, sub Alfvenic) waves. The arrival of a shock at Earth is well
correlated to Geomagnetic Sudden Impulses. If the IP conditions are favorable (primarily
Bz turning southward), then a storm usually ensues. The magnitude of the storm is well
correlated with the duration and magnitude of the Bz southward condition. Thus the
observation/prediction of an IP shock at Earth increases the probability of geomagnetic
storm prediction. The Shock Time of Arrival (STOA) model and the Interplanetary Shock
Propagation Model (ISPM) have been developed for the purpose of predicting the time of
arrival and strength of solar-initiated interplanetary shocks.
2. The Models:
The STOA and ISPM models have the same purpose: to
predict whether a solar event will cause an interplanetary shock that will reach Earth
and, if so, the time of arrival and strength of the shock. Although they use almost the
same input data and have similar outputs, the models do have different bases and different
strengths. These properties are outlined here.
2.1 The STOA model (Dryer and Smart,
1984, Smart et al.,1984, 1986, Smart and Shea, 1985, Lewis and Dryer, 1987) is
based on similarity theory of blast waves, modified by the piston-driving concept, that
emanate from point explosions. These ideas (utilized, for example, in supernova and
hydrogen bomb applications) are summarized in the review by Dryer (1974).
The initial explosion (flare) drives a shock. The
shock is assumed to be initially driven at a constant speed, Vs, for a
specified length of time (using GOES X-ray duration as discussed by Smith, Dryer and
Armstrong, 1993) and then allowed to decelerate as a blast wave ( Vs ~ R-1/2
where R is the heliocentric radius) as it expands outward. The magnitude of the total
energy conversion process determines the solid angle of quasi-spherical shock propagation
and how far it would propagate as it "rides over" a uniform background solar
wind. It is assumed that the fastest part of the shock is nearly coincident with the
heliocentric radius vector from the center of the Sun through the flare site. The flanks
of the shock would first decay via viscous and ohmic dissipation to an MHD
(magnetohydrodynamic) wave. The shock speed directly above the flare is calculated from
the Type II radio frequency drift rate (together with an assumed coronal density model)
via the plasma frequency, which is proportional to the square root of the local electron
density. Based on the empirical studies of Lepping and Chao, (1976), STOA uses a cosine
function to account for longitudinal dependence of the shock geometry in the ecliptic
plane. The shock speed is assumed to decrease from the maximum in the direction of the
flare via this cosine function, to give a non-spherical shape in longitude. This
spatially-dependent shock speed is taken to be constant during the piston driven phase.
During the blast wave phase, the longitudinal cosine shape is maintained. .
STOA allows for a radially-variable background solar wind, which is uniform in
heliolongitude. No structures such as stream-stream interactions are considered.
2.2 The ISPM is based on a 2.5 D MHD
parametric study of numerically simulated shocks (Smith and Dryer, 1990). This study
showed that the net energy input into the solar wind is the organizing parameter. If the
net energy ejected into the solar wind by a solar source and its longitude are known, then
the transit time and strength of the shock to 1AU may be computed from algebraic equations
given in that paper. That study also showed that, for drivers longer than ~2hrs, the
properties of the leading shock remain unchanged. Therefore, drivers with durations longer
than 2 hours are truncated to 2 hours in the ISPM. Smith and Dryer (1995) give the details
of this model and the functions in energy-longitude space. Since the energies of solar
ejecta are not available from observations, they describe how the
net input energy is estimated from proxy input data. The ISPM uses the same observational
data as the STOA model.
2.3 The model inputs: The models use
almost the same input parameters. They both require the initial coronal shock velocity,
pulse duration and location close to the Sun. Such measurements are of course not
available, so proxies are used. The shock velocities used are obtained from observations
of metric Type II bursts, which are considered to be the signatures of shocks traveling
outward through the solar corona as described above. For further details, see Section 2.5.
The durations of X-ray flares associated with the metric Type IIs are taken as a proxy for
the event duration, and an optical flare identification is used for the source location.
In addition, STOA requires the ambient solar wind velocity at 1 AU. This value is obtained
from real-time L1 satellite data or, if unavailable, a default value of 400 km/s may be
selected. The ISPM is based on a single background solar wind model, but this model asks
the user whether there was a prior event within the previous 24 hours. If yes,
a cautionary note is given, because both STOA and ISPM models are based on the assumption
that the solar-initiated shocks travel independently (i.e. that they do not interact) en
route to 1 AU.
2.4 The model outputs are very
similar. Both models predict whether a shock will arrive at Earth and if so, when. They
also give a measure of the shock strength. STOA gives the shock magnetoacoustic Mach
number, Ma, The ISPM gives a shock strength index, SSI (log10
of the ratio of dynamic pressure jump at shock to the background value). The SSI index is
used to discriminate between the shocks that are too weak to be significant by the time
they reach 1 AU. The value of SSI = 0 is used here as the threshold value, equivalent to
the limit of Ma = 1.0 below which shocks decay to MHD waves
2.5 Metric Type II radio bursts,
signatures of coronal shock waves, are usually associated with solar flares. Accordingly,
the United States Air Force (USAF) established a world-wide network of sweep frequency
recorders from which, given a coronal density model, estimates of the shock speed in the
corona can be made. This network, called the Radio Solar Telescope Network (RSTN), uses a
bandwidth from 25 MHz to 85 MHz. It is complemented in this real-time capability by a
radio telescope operated from 25 MHz (the ionospheric cutoff) to 1800 MHz by the
Ionospheric Prediction Service in Culgoora, Australia. The USAF/RSTN system is currently
being upgraded in frequency to a bandwidth from 25 MHz to 180 MHz by the Solar Radio
Spectrometer (SRS) system at Palehua, Hawaii; San Vito, Italy; Sagamore Hill,
Massachusetts; and Learmonth, Australia. The Sagamore Hill site will be moved to Holloman
AFB, New Mexico. Finally, real time statistical studies have been initiated for STOA and
ISPM by Smith et al., (2000). These authors propose that these results be used as
reference metrics for future modeling studies of this kind.
Dryer, M., 1974. Interplanetary shock waves
generated by solar flares, Space Sci. Rev., 15, 403-468.
Dryer, M., and D.F. Smart, 1984. Dynamical models of
coronal transients and interplanetary disturbances, Adv. Space Res., 4, 291-301.
Lepping, R.P. and J.-K. Chao, 1976. A shock surface
geometry: the February 15-16 February 1967 event, J. Geophys. Res., 81, 60 - 64.
Lewis, D. and M. Dryer, 1987. Shock-Time-of-Arrival
Model (STOA-87), NOAA/SEL Contract Report (Systems Documentation) to USAF Air Weather
Smart, D.F. and M.A. Shea, 1985. A simplified model
for timing the arrival of solar-flare-initiated shocks, J. Geophys. Res., 90, 183 - 190.
Smart, D.F., M.A. Shea, W.R. Barron, and M. Dryer,
1984. A simplified technique for estimating the arrival time of solar flare-initiated
shocks, in Proceedings of STIP Workshop on Solar/Interplanetary Intervals, (M.A. Shea,
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Gentile, and A.A. Bathurst, 1986. Estimating the arrival time of solar flare-initiated
shocks by considering them to be blast waves riding over the solar wind, in Proceedings of
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and spatial evolution of simulated interplanetary shocks in the ecliptic plane within 1
AU, Solar Phys., 129, 387 - 405.
Smith, Z.K. and M. Dryer, 1995. The Interplanetary
Shock Propagation Model: A model for predicting solar-flare-caused geomagnetic sudden
impulses based on the 2-1/2D MHD numerical simulation results from the Interplanetary
Global Model (2D IGM), NOAA Technical Memorandum, ERL/SEL - 89.
Smith, Z.K., M. Dryer, and M. Armstrong, 1993. Can
soft X-rays be used as a proxy for total energy injected by a flare into the
interplanetary medium? in IAU Colloquium 144 on Solar Coronal Structures, (V. Rusin, P.
Heinsel, and J.-C. Vial, Eds), Kluwer Acad. Publ., Dordrecht, pp. 267-270.
Smith, Z., M. Dryer, E. Ort, and W. Murtagh,
Real-time performance of the STOA and ISPM models, J. Atm. Solar-Terr. Phys., submitted,