Empirical Models — Lindsay et al (1999) and Gopalswamy et al (2001) have developed simple shock time of arrival models based on observed data, inferred from coronograph images.  These models use the initial CME speed and ambient solar wind speed to predict the acceleration or deceleration of the CME in interplanetary space.  The Gopalswamy et al (2001) model assumes that the CME speed will match the solar wind speed at approximately .75 AU, while the Lindsay et al (1999) model does not terminate the acceleration or deceleration of the CME.  Both models are in good agreement with observations, but the Gopalswamy model uses a broader sample of observed events in deriving their results.

Gopalswamy N., A. Lara, S. Yashiro, M. L. Kaiser, and R. A. Howard, Predicting the 1-AU Arrival Times of Coronal Mass Ejections. J. Geophys. Res., 107, 2002.

Lindsay G.M., J.G. Luhmann, C.T. Russel, and J.T. Gosling, Relationship between Coronal Mass Ejection Speeds from Coronograph Images and Interplanetary Characteristics of  Associated Coronal Mass Ejections. J. Geophys. Res., 104, 12, 515, 1999.

Interplanetary Shock Propagation Model (ISPM) — Using flare position and integrated intensity, ISPM estimates the shock time of arrival at 1 AU and the geo-effectiveness of the CME.  ISPM is a 2.5-D magnetohydrodynamic model that uses x-ray flare and Type II radio burst data to estimate the speed, energy, and angular extent of a shock moving outward from the corona.  This model is part of the suite of tools available in the Air Force GEOSpace package.

Smith Z. K., M. Dryer, The Interplanetary Shock Propagation Model: A Model for Predicting Solar-Flare-Caused Geomagnetic Storms, Based on the 2 1/2 D, MHD Numerical Simulation Results from the Interplanetary-Global Model (2D IGM).  NOAA Tech. Mem. ERL SEL-89, 1995.

Shock Time Of Arrival (STOA) — STOA is very similar to ISPM, particularly in regard to its inputs.  The primary difference is the model of shock propagation.  This model uses simple blast wave equations to simulate the propagation of the shock through interplanetary space.  This model is also part of the suite of tools available in the Air Force GEOSpace package.

Smart D.F., M.A. Shea. A Simplified Model for Timing the Arrival of Solar Flare-Initiated Shocks.  J. Geophys. Res., 90, 183-190, 1985.

For more information on ISPM and STOA, click here.

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