Shock Propagation Model version 2 and its application in predicting the arrivals at Earth of interplanetary shocks during Solar Cycle 23

The Shock Propagation Model (SPM) based on an analytic solution of blast waves has been proposed to predict shock arrival times at Earth. Here to reduce the limitations of the SPM theoretical model in real applications and optimize its input parameters, a new version (called SPM2) is presented in order to enhance prediction performance. First, an empirical relationship is established to adjust the initial shock speed, which, as computed from the Type II burst drift rate, often contains observational uncertainties. Second, an additional acceleration/deceleration relation is added to the model to eliminate inherent prediction bias. Third, the propagation direction is derived in order to mitigate the isotropy limitation of blast wave theory in real predictions. Finally, an equivalent shock strength index at the Earth's location to judge whether or not an interplanetary shock will encounter the Earth is implemented in SPM2. The prediction results of SPM2 for 551 solar disturbance events of Solar Cycle 23 demonstrate that the success rate of SPM2 for both shock (W-shock) and nonshock (W/O-shock) events at Earth is approximate to 60%. The prediction error for the W-shock events is less than 12 h (root-mean-square) and 10 h (mean-absolute). Comparisons between the predicted results of SPM2 and those of Shock Time of Arrival (STOA), Interplanetary Shock Propagation (ISPM), and Hakamada-Akasofu-Fry version 2 (HAFv.2) based on similar data samples reveal that the SPM2 model offers generally equivalent prediction accuracy and reliability compared to the existing Fearless Forecast models (STOA, ISPM, and HAFv.2).