Ensemble modeling of coronal mass ejection dynamics and forecasts at 1 AU with a semi-analytic flux-rope model

¹ Department of Physics, Section of Astrogeophysics, University of Ioannina, 45110 Ioannina, Greece
² Applied Physics Laboratory, Johns Hopkins University, Laurel, MD 20723, USA

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 5 March 2026
Accepted: 1 April 2026

Abstract

Aims. This study quantifies how uncertainty in physically meaningful coronal mass ejection (CME) and solar-wind inputs propagates into forecast-relevant diagnostics from eruption through heliospheric evolution. Using a semi-analytic erupting flux rope (EFR) model, we evaluate how initial eruption parameters (spatial scales, density structure, and magnetic properties) together with background solar-wind conditions shape the distributions of the arrival time, kinematics, magnetic-field measures, and impact duration at 1 AU.

Methods. We used a semi-analytic flux-rope model to simulate CME initiation and Sun-to-1 AU propagation. The model includes Lorentz, gravitational, and drag forces and is driven by a prescribed, time-dependent poloidal-flux injection. Relative to the original EFR formulation, we incorporated sheath and pile-up effects via an effective (virtual) mass and updated the drag term for the CME–solar-wind coupling. We embedded the model in a Monte Carlo scheme with truncated-normal sampling of key inputs to quantify dispersion in the arrival time, kinematics, internal magnetic field, and impact duration at 1 AU.

Results. Across six CME events, the ensembles show moderate event-dependent dispersion in the 1 AU diagnostics. For the ±20% sampling, all reported spreads correspond to the 1σ standard deviation across the ensemble. The ensemble time-of-arrival (ToA) spread is 2.4–7.7 h across the six events, and it is primarily controlled by the poloidal-flux injection history (injected-flux amplitude as well as rise and plateau timing) together with CME–solar-wind coupling (upstream wind speed and drag coefficient), with the top-ranked contributor shifting between events. The leading-edge speed shows a spread of 28–53 km s⁻¹ and is primarily controlled by background-flow properties, while injection-related terms act as secondary contributors in all cases. The magnetic-field diagnostics demonstrate two behaviors: the sheath field is relatively tightly distributed, with a spread of 1–3.5 nT, and is mainly controlled by upstream solar-wind conditions together with global size and expansion scaling, whereas the internal flux-rope field shows a larger spread of 1–7.6 nT and is primarily governed by eruption-driving and flux-content parameters. The spread in the duration of impact spans 2.4–6.3 h and is mainly controlled by geometric size and expansion scaling, with additional sensitivity to the temporal characteristics of the driving.

Conclusions. Embedding the EFR model in a Monte Carlo framework allows us to quantify how uncertainty in its inputs translates into dispersion in Sun-to-1 AU kinematics and in key 1 AU diagnostics for the events studied here. Within this framework, the feature-ranking analysis identifies which EFR inputs most strongly drive that dispersion, yielding a clear ordering of the most important parameters as event-specific information improves. In operational applications or focused event studies, the same workflow can be rerun with progressively narrower input ranges as additional constraints are obtained, yielding correspondingly tighter and more defensible confidence bounds on 1 AU arrival and impact diagnostics.