Mathematical expressions of the drag-based models for predicting the arrival time of coronal mass ejection and their development and evolutionary processes

As one of the most violent solar activities, coronal mass ejections (CMEs) are eruptions of the large-scale magnetized plasma from the Sun’s upper atmosphere into interplanetary space. The Earth-directed CMEs will cause significant disturbances to the solar-terrestrial environment, which in return threaten the safety of the communication, navigation, and ground technology systems. Therefore, predicting whether and when a CME will reach the Earth is an important ingredient of space weather research and forecasting. One commonly used prediction model for the CME’s propagation and arrival time is the Drag-Based Model (DBM), which considers the drag force acting on interplanetary CMEs (ICMEs) to explain how CMEs move through the solar wind. In this paper, we outline five routes for the development and evolution of the family models of DBM: 1. The DBM <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"> <mml:mrow> <mml:mo>→</mml:mo> </mml:mrow> </mml:math> ELEvoHI (Ellipse Evolution Model Based on HI Observations) series; 2. The DBM <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"> <mml:mrow> <mml:mo>→</mml:mo> </mml:mrow> </mml:math> LSF-DBM (Least-Squares Fitting Drag-Based Model) series; 3. The DBM <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"> <mml:mrow> <mml:mo>→</mml:mo> </mml:mrow> </mml:math> PDBM (Probabilistic Drag-Based Model) series; 4. The DBM <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"> <mml:mrow> <mml:mo>→</mml:mo> </mml:mrow> </mml:math> ExDBM (Extended Drag-Based Model); 5. The DBM <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"> <mml:mrow> <mml:mo>→</mml:mo> </mml:mrow> </mml:math> EnDBM (Enhanced Drag-Based Model) Series. We clarify the development and evolution process of the model’s mathematical expressions along each route as well as their connections. Finally, we provide a summary of the various models, comparing their similarities and differences, as well as their strengths and weaknesses, and suggest potential improvements.