A large geomagnetic storm can cause widespread auroral displays. It can also adversely affect many aspects of our technological society. It can wipe out high frequency communications, render over-the-horizon radar systems useless, interfere with navigation systems, affect satellite communication and cause increased drag on satellites in low-Earth orbit. It it thus very useful to be able to predict the occurrence of such events.
The model presented here was devised by Smart et al (1984) in an attempt to predict the arrival time of a shockwave preceding a geomagnetic storm following the observation of events on the Sun which are usually precursors of geomagnetic storms.
WARNING: We should note that the physics on which this model is based is now no longer accepted. Despite this, however, the model continues to be useful purely as an empirical tool and many times has a prediction accuracy comparable with more realistic models.
Geomagnetic storms have long been divided into two classes: sudden commencement storms and gradual commencement storms. The first and potentially most damaging storms arise when the Earth is hit by a coronal mass ejection or CME, a large plasma cloud ejected from the Sun. Ground based magnetometers show a sudden increase in the Earth's magnetic field when the shockwave preceding the CME hits the Earth's magnetosphere. A gradual commencement storm, on the other hand, results when the Earth intercepts a high speed stream in the solar wind. Such a stream flows from a coronal hole in the Sun where the magnetic field lines are open to the interplanetary medium. These streams rotate with the Sun with a period of about 27 days and enable the prediction of such storms through recurrence, until the coronal hole disappears after a few months.
The model here (STOA) aims to predict the travel time and thus the arrival time of the shockwave that pressages the start of a sudden commencement geomagnetic storm.
The following diagram shows the assumed model situation at the Sun,
Although we may not see the CME and associated shockwave when it occurs at the Sun, it is invariable associated with a flare which is observed in hydrogen-alpha light or in x-rays at a location with coordinates latitude μs and a longitude (from the solar central meridian as seen from Earth) λs. This can be used to compute the great circle distance ω from the centre of the solar disc (again as viewed from Earth) to the flare location.
A few minutes after the flare is observed a radio telescope observes a type II / IV complex of emission which is taken to indicate the presence of a CME and a shockwave whose speed through the solar corona can be measured from the slope of the type II radio burst.
The propagation of the shockwave is illustrated by the model graph below.
It is assumed that the shockwave is driven by the CME from a starting point of 1.5 solar radii at the speed indicated by the type II (vII) for a distance given by this speed times a driver distance td which is determined by the duration of the x-ray flare from start to half-power point past the peak. If an x-ray solar flux profile is not available then a 10 cm radio burst profile can be used instead.
Beyond the driven distance the shock converts into a blast wave, propagating over the existing solar wind (speed vw) and decelerating such that the velocity is a function of the square root of the inverse of the distance it travels. The time of travel is obtained by integrating the projected velocity curve from the Sun to the Earth.
The initial component of the shock speed in the direction of the Earth is given by:
Note: We now know that for the CME to couple into the Earth's magnetic field it is also necessary for the interplanetary magnetic field at the Earth to have a southward component.
A QBASIC code to implement this model is available at STOA.BAS.
INTERPLANETARY SHOCKWAVE PREDICTION PROGRAM ******************************************* SOLAR EVENT X2 ( SIMULATION ) 22 SEP 2021 1410 UT HELIOGRAPHIC 10S 25W DURATION 35 MINS TYPE II SHOCK VELOCITY 1200 KM/S SOLAR WIND SPEED 400 KM/S SHOCK ARRIVAL AT EARTH EXPECTED 24 SEP 2021 20:25 UT TRAVEL TIME 54.3 HRS MACH NUMBER 5.5
DS Smart, MA Shea, M Dryer, A Quintana, LC Gentile & AA Bathurst, "Estimating the Arrival Time of Solar-Flare-Initiated Shocks by considering them to be Blast Waves Riding Over the Solar Wind", Solar-Terrestrial Prediction Workshop Proceedings, pp 471-481 (Meudon, 1984).
Australian Space Academy