A new method of measuring Forbush decreases

¹ University of Zagreb, Faculty of Geodesy, Hvar Observatory, Zagreb, Croatia
e-mail: mdumbovic@geof.hr
² University of Zagreb, Faculty of Transport and Traffic Sciences, Zagreb, Croatia
³ Swedish Institute of Space Physics, Uppsala, Sweden
⁴ Christian-Albrechts University in Kiel, Department of Extraterrestrial Physics, Kiel, Germany

Received: 23 May 2023
Accepted: 14 December 2023

Abstract

Context. Forbush decreases (FDs) are short-term depressions in the galactic cosmic ray (GCR) flux and one of the common signatures of coronal mass ejections (CMEs) in the heliosphere. They often show a two-step profile, the second one associated with the CME’s magnetic structure. This second step can be described by the recently developed analytical FD model for flux ropes (FRs) – ForbMod.

Aims. The aim of this study is to utilise ForbMod to develop a best-fit procedure to be applied on FR-related FDs as a convenient measurement tool. Our motivation is to develop a best-fit procedure that can be applied to a data series from an arbitrary detector. Thus, the basic procedure would facilitate measurement estimation of the magnitude of the FR-related FD, with the possibility of being adapted for the energy response of a specific detector for a more advanced analysis.

Methods. The non-linear fitting was performed by calculating all possible ForbMod curves constrained within the FR borders to the designated dataset and minimising the mean square error (MSE). In order to evaluate the performance of the ForbMod best-fit procedure, we used synthetic measurements produced by calculating the theoretical ForbMod curve for a specific example CME and then applying various effects to the data to mimic the imperfection of the real measurements. We also tested the ForbMod best-fit function on the real data, measured by detector F of the SOHO/EPHIN instrument on a sample containing 30 events, all of which have a distinct FD corresponding to the magnetic obstacle. The extraction of FD profiles (from the onset to the end) was performed manually by an observer, whereby we applied two different versions of border selection and assigned a quality index to each event.

Results. We do not find notable differences between events marked by a different quality index. For events with a selection of two different borders, we find that the best fit applied on extended interplanetary coronal mass ejection (ICME) structure borders results in a slightly larger MSE and differences compared to the traditional method due to a larger scatter of the data points. We find that the best-fit results can visually be categorised into six different FD profile types. Although some profiles do not show a visually pleasing FD, the ForbMod best-fit function still manages to find a solution with a relatively small MSE.

Conclusions. Overall, we find that the ForbMod best-fit procedure performs similar to the traditional algorithm-based observational method, but with slightly smaller values for the FD amplitude, as it’s taking into account the noise in the data. Furthermore, we find that the best-fit procedure has an advantage compared to the traditional method as it can estimate the FD amplitude even when there is a data gap at the onset of the FD.