Constraints to the drag-based reverse modeling

¹ Hvar Observatory, Faculty of Geodesy, University of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia
² Institute of Physics, University of Graz, Universitätsplatz 5, 8010 Graz, Austria

^⋆ Corresponding author; jcalogovic@geof.hr

Received: 11 May 2023
Accepted: 15 December 2024

Abstract

Context. One of the most widely used space weather forecast models to simulate the propagation of coronal mass ejections (CMEs) is the analytical drag-based model (DBM). It predicts the CME arrival time and speed at Earth or at a specific target (planets, spacecraft) in the Solar System. The corresponding drag-based ensemble model (DBEM) additionally takes into account the uncertainty of the input parameters by making n ensembles and provides the most probable arrival time and speed as well as their uncertainty intervals. An important input parameter for DBM and DBEM is the drag parameter γ, which depends on the CME cross-section and mass, as well as the solar-wind density.

Aims. The reverse-modeling technique applied to the DBM allows us to derive γ values that minimize transit time (TT) and arrival-speed (v_tar) errors. The present study highlights the limitations and constraints of such a procedure.

Methods. We searched for optimal γ values that would yield the perfect TT within one hour of the actual observed CME transit time as well as perfect v_tar within ±75 km s⁻¹. This optimal window for v_tar was found by increasing v_tar from ±10 to ±100 km s⁻¹, where the ±75 km s⁻¹ window gave the perfect TT and v_tar in the case of 87% of CMEs compared to the ±10 km s⁻¹ window, which was used in some previous reverse-modeling studies and gave optimal results for only 45% of the events from our CME list. For our analysis, a 31 CME-ICME pair sample is used from the period spanning 1997–2018. The reverse-modeling method is applied using the DBEMv3 tool for different γ ranges from 0.01 to 10 × 10⁻⁷ km⁻¹. We tested whether and how the obtained optimal γ depends on the chosen γ range.

Results. By increasing the γ range, we find that the optimal γ converges to a certain value for two thirds of the analyzed events. The highly constrained γ ranges resulted in shifted and skewed γ distributions. By using the largest γ range (0.01–10 × 10⁻⁷ km⁻¹), the medians of the optimal γ distributions are obtained for two thirds of the events in the common operational DBEMv3 range of 0.01–0.5 × 10⁻⁷ km⁻¹. We also found that the important quantity in determining the range of γ distribution and ability to find an optimal γ is the difference between the CME launch speed and the solar-wind speed (v₀ − w), which together with γ define the drag acceleration in the DBM. For small v₀ − w differences (e.g., < 200 km s⁻¹), the reverse modeling may not be the appropriate method to find the optimal γ due to large divergence of γ values found, which may additionally be caused by larger input uncertainties and physical model limitations in turn leading to inappropriate γ values.