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The STOA and ISPM Models

M. Dryera, Z. Smitha*

a NOAA/SWPC, Boulder, CO 80303

1. Introduction

2. The Models



1. Introduction

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 Service.

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, D.F. Smart, and S. McKenna-Lawlor, Eds.), Maynooth, Ireland, 4-6 August 1982, Book Crafters, Inc., Chelsea, MI, pp. 139 - 156.

Smart, D.F., M.A. Shea, M. Dryer, A. Quintana, L.C. 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 the Symposium on Solar-Terrestrial Predictions, (P. Simon, G.R. Heckman, and M.A. Shea, Eds.), Meudon, France, 18-22 June 1984, U.S. Government Printing Office, Washington, D.C., pp. 471-481.

Smith, Z. and M. Dryer, 1990. MHD study of temporal 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, 2000.



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