The "cause and effect" concept embodied in the classical initial-boundary value problem has been used with some success in the meteorological weather forecasting realm. Now, as researchers-turned-space weather forecasters, it is our turn to use the same concept. That is, given reasonable-known initial solar and interplanetary solar wind and magnetic field conditions, we are challenged to use real-time observations of the Sun to mimic various solar and heliospheric events such as erupting prominences, stream-stream interactions, flares, and destabilized helmet streamers. Simply put, the task is to model ICMEs (interplanetary counterparts of coronal mass ejections and their shock waves) with accuracy sufficient to predict the temporal series at Earth of the solar wind's dynamic pressure (or momentum flux) and the meridian component, Bz, of the interplanetary magnetic field. Following some remarks about the "Solar Flare Myth" and recent developments, this review will start with the August 1972 events (where 1D MHD was used), consider similarity theory briefly, and discuss real-time experience with the "April Fool Epoch" in April 2001. Real-time shock arrival forecasting with the kinematic Hakamada-Akasofu-Fry model, version 2 (HAFv.2) will be discussed in the latter context. Finally, shock arrival statistics (contingency tables and skill scores for this model, plus two other models, will be given for an extended case study (N = 173) from February 1997 to October 2000.
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