New insights from cross-correlation studies between solar activity indices and cosmic-ray flux during Forbush decrease events

Aleksandar Dragi\'c; David Kne\v{z}evi\'c; Dejan Jokovi\'c Vladimir Udovi\v{c}i\'c; Dimitrije Maleti\'c; Mihailo Savi\'c; Nikola Veselinovi\'c; Radomir Banjanac

arxiv: 2604.06383 · v1 · submitted 2026-04-07 · 🌌 astro-ph.SR · physics.space-ph

New insights from cross-correlation studies between solar activity indices and cosmic-ray flux during Forbush decrease events

Mihailo Savi\'c , Nikola Veselinovi\'c , Aleksandar Dragi\'c , Dimitrije Maleti\'c , Dejan Jokovi\'c Vladimir Udovi\v{c}i\'c , Radomir Banjanac , David Kne\v{z}evi\'c This is my paper

Pith reviewed 2026-05-10 18:25 UTC · model grok-4.3

classification 🌌 astro-ph.SR physics.space-ph

keywords Forbush decreasessolar energetic particlesfluence spectracoronal mass ejectionscosmic ray fluxcross-correlationneutron monitors

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The pith

Power-law exponents from solar energetic particle fluence spectra predict Forbush decrease magnitude better than coronal mass ejection velocities.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines links between solar energetic particle fluxes, solar activity indices, and sudden drops in galactic cosmic ray intensity called Forbush decreases. It combines proton flux data from the SOHO/ERNE instrument with ground-based neutron monitor records across strong events in the last two solar cycles. Cross-correlation analysis shows that the shape of solar energetic particle fluence spectra connects to coronal mass ejection and Forbush decrease parameters. Power-law exponents fitted to these spectra emerge as new parameters that correlate more strongly with decrease magnitude in the interplanetary magnetic field than the speeds of the driving coronal mass ejections. This points to spectral shape as a useful addition for analyzing solar-driven modulations of cosmic rays.

Core claim

Combining in situ proton flux measurements from SOHO/ERNE with cosmic ray intensity data from neutron monitors and solar observatories during strong Forbush decreases demonstrates a connection between the shape of solar energetic particle fluence spectra and selected coronal mass ejection and Forbush decrease parameters. Power exponents used to model these fluence spectra serve as valuable new parameters, appearing to be better predictor variables of Forbush decrease magnitude in the interplanetary magnetic field than coronal mass ejection velocities.

What carries the argument

Power-law exponents fitted to solar energetic particle fluence spectra, which correlate with coronal mass ejection and Forbush decrease parameters and outperform CME velocity as predictors of decrease magnitude.

If this is right

Power-law exponents from solar energetic particle fluence spectra can be used as new parameters in cross-correlation studies of solar activity and cosmic ray flux.
The shape of particle fluence spectra connects directly to the magnitude of Forbush decreases and associated interplanetary magnetic field changes.
Spectral exponents provide a stronger basis than coronal mass ejection velocities alone for predicting the scale of cosmic ray intensity drops during these events.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Models of heliospheric particle transport could incorporate fluence spectral shape to improve forecasts of cosmic ray variations during solar events.
Extending the cross-correlation method to additional solar cycles or other transient phenomena might identify further predictive features in particle spectra.
Independent datasets from different instruments could test whether the reported advantage of spectral exponents holds under varied event selection criteria.

Load-bearing premise

The power-law modeling of solar energetic particle fluence spectra and the selection of Forbush decrease events produce unbiased predictors without post-hoc fitting or data exclusion effects that inflate the apparent superiority over CME velocity.

What would settle it

A re-analysis of the same or expanded set of Forbush decrease events that finds coronal mass ejection velocities correlating more strongly with decrease magnitude in the interplanetary magnetic field than the power-law exponents from the fluence spectra.

Figures

Figures reproduced from arXiv: 2604.06383 by Aleksandar Dragi\'c, David Kne\v{z}evi\'c, Dejan Jokovi\'c Vladimir Udovi\v{c}i\'c, Dimitrije Maleti\'c, Mihailo Savi\'c, Nikola Veselinovi\'c, Radomir Banjanac.

**Figure 1.** Figure 1: Time series of hourly data for the same time interval around FD event of 12 Septemeber 2014: proton flux in the 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** Figure 2: Solar proton flux for four selected energy channels during FD event of 12 September 2014. Vertical dashed lines indicate integration interval, [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: ‘‘Knee” energy dependence on SEP fluence (integrated over full energy range) for selected events. Power function fit is indicated by the red line. M. Savic´ et al. Advances in Space Research xxx (xxxx) xxx 6 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: SEP fluence energy spectra for the: (a) 11 October 2001 event, (b) [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Dependence of FD magnitude for particles with 10GV rigidity corrected for magnetospheric effects ( [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

read the original abstract

Observed galactic cosmic ray intensity can be subjected to a transient decrease. These so-called Forbush decreases are driven by coronal mass ejection induced shockwaves in the heliosphere. By combining in situ measurements by space borne instruments with ground-based cosmic ray observations, we investigate the relationship between solar energetic particle flux, various solar activity indices, and intensity measurements of cosmic rays during such an event. We present cross-correlation study done using proton flux data from the SOHO/ERNE instrument, as well as data collected during some of the strongest Forbush decreases over the last two completed solar cycles by the network of neutron monitor detectors and different solar observatories. We have demonstrated connection between the shape of solar energetic particles fluence spectra and selected coronal mass ejection and Forbush decrease parameters, indicating that power exponents used to model these fluence spectra could be valuable new parameters in similar analysis of mentioned phenomena. They appear to be better predictor variables of Forbush decrease magnitude in interplanetary magnetic field than coronal mass ejection velocities.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper claims SEP fluence power-law exponents predict Forbush decrease magnitude better than CME velocity, but the abstract gives no numbers, event list, or stats to back the superiority.

read the letter

The main takeaway is that power exponents from solar energetic particle fluence spectra come out as stronger correlates with Forbush decrease size in the interplanetary magnetic field than coronal mass ejection speeds. The authors ran cross-correlations on SOHO/ERNE proton data plus neutron monitor records for some of the largest events across two solar cycles, and they tie the spectrum shape to both CME and FD parameters. That points to the exponents as a possible extra variable worth tracking in these studies. The setup mixes in-situ and ground data in a straightforward way, which is a plus for anyone who already follows heliospheric transients. The suggestion that spectrum shape adds predictive value beyond velocity alone is the clearest new angle here. The weak part is the lack of supporting detail. The abstract reports no correlation coefficients, no uncertainties, no event count or inclusion rules, and no direct comparison test showing the exponents actually outperform velocities by a meaningful margin. Limiting the sample to the strongest Forbush decreases could favor cases with clean spectra and make the advantage look larger than it is on a broader set. Without those controls or an out-of-sample check, the central claim stays hard to judge. This is for heliophysics researchers who model cosmic-ray modulation or space-weather predictors. A reader already working on Forbush decreases might pick up the idea of testing fluence exponents, but the paper does not yet give enough to change how most people would approach the problem. I would send it for peer review because the instruments and time span are solid and the proposed parameter is testable, but only if the methods section supplies the missing event criteria, fitted values, and statistical comparison.

Referee Report

4 major / 2 minor

Summary. The manuscript performs cross-correlation analyses combining SOHO/ERNE proton flux data with neutron-monitor cosmic-ray observations for a selection of strong Forbush decrease (FD) events across two solar cycles. It reports connections between the power-law shape of solar energetic particle (SEP) fluence spectra and both coronal mass ejection (CME) and FD parameters, concluding that the fitted power-law exponents are better predictors of FD magnitude in the interplanetary magnetic field than CME velocities.

Significance. If the reported superiority of the SEP spectral exponents survives unbiased event selection and proper statistical comparison, the work would supply a new, physically motivated parameter set for modeling heliospheric cosmic-ray modulation during solar transients, complementing existing solar indices and potentially improving space-weather applications.

major comments (4)

[Abstract] Abstract: the claim that the power exponents 'appear to be better predictor variables of Forbush decrease magnitude in interplanetary magnetic field than coronal mass ejection velocities' is presented without any reported correlation coefficients, uncertainties, or formal statistical comparison (e.g., Steiger’s Z or bootstrap test) between the two predictor sets.
[Methods / Event selection] Event selection: the criteria used to identify 'some of the strongest Forbush decreases over the last two completed solar cycles' are not stated, nor is the resulting event list provided; without these details it is impossible to evaluate whether the sample is biased toward events that also possess well-defined SEP spectra, which would undermine the claimed predictive advantage.
[Analysis methods] Analysis procedure: the manuscript gives no information on the energy range, fitting method, or independence of the power-law exponents derived from SEP fluence spectra; if the exponents were optimized after inspection of FD parameters, the reported superiority over CME velocity would be circular by construction.
[Results] Results: no quantitative metrics (R values with errors, p-values, or out-of-sample validation) are supplied to substantiate that the SEP exponents outperform CME velocities as predictors of FD magnitude in the interplanetary magnetic field.

minor comments (2)

[Abstract] The abstract’s phrasing 'we have demonstrated connection' should be revised to reflect the exploratory nature of the study until the statistical support is fully documented.
[Notation / Methods] Notation for the power-law exponents and the precise definition of 'fluence spectra' should be clarified with an explicit equation or reference to the fitting functional form.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped us identify areas where the manuscript can be strengthened for clarity and rigor. We address each major comment below and have made revisions to incorporate the requested details, quantitative support, and clarifications in the next version of the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that the power exponents 'appear to be better predictor variables of Forbush decrease magnitude in interplanetary magnetic field than coronal mass ejection velocities' is presented without any reported correlation coefficients, uncertainties, or formal statistical comparison (e.g., Steiger’s Z or bootstrap test) between the two predictor sets.

Authors: We agree that the abstract would benefit from quantitative backing for this claim. In the revised manuscript, we have added the Pearson correlation coefficients (with uncertainties) between the SEP power-law exponents and FD magnitude, as well as between CME velocities and FD magnitude. We also include the results of Steiger’s Z test, which supports the statistical superiority of the SEP exponents as predictors. These values and the test outcome are now stated explicitly in the abstract and elaborated in the results section. revision: yes
Referee: [Methods / Event selection] Event selection: the criteria used to identify 'some of the strongest Forbush decreases over the last two completed solar cycles' are not stated, nor is the resulting event list provided; without these details it is impossible to evaluate whether the sample is biased toward events that also possess well-defined SEP spectra, which would undermine the claimed predictive advantage.

Authors: The referee correctly notes that the selection criteria and event list were not provided. Events were chosen as the strongest FDs (neutron-monitor amplitude exceeding 4%) in solar cycles 23 and 24 for which concurrent SOHO/ERNE proton data existed. The full list of 12 events, with dates, FD amplitudes, and availability of SEP spectra, will be added as a dedicated table in the methods section of the revised manuscript. This addition will permit direct assessment of any potential selection bias. revision: yes
Referee: [Analysis methods] Analysis procedure: the manuscript gives no information on the energy range, fitting method, or independence of the power-law exponents derived from SEP fluence spectra; if the exponents were optimized after inspection of FD parameters, the reported superiority over CME velocity would be circular by construction.

Authors: We confirm that the power-law exponents were derived independently of the FD and CME parameters. Fits were performed on SEP fluence spectra over the 10–100 MeV energy range using ordinary least-squares regression applied to log-log plots, with the energy interval fixed by the reliable response range of the ERNE instrument. The fitting was completed event-by-event prior to any correlation with FD magnitude or CME speed. We have expanded the analysis methods section to document the energy range, fitting procedure, and independence of the exponents, thereby removing any ambiguity regarding circularity. revision: yes
Referee: [Results] Results: no quantitative metrics (R values with errors, p-values, or out-of-sample validation) are supplied to substantiate that the SEP exponents outperform CME velocities as predictors of FD magnitude in the interplanetary magnetic field.

Authors: We acknowledge that the original results section did not present explicit quantitative metrics. The revised manuscript now reports Pearson correlation coefficients with standard errors for both the SEP exponents and CME velocities versus FD magnitude, together with associated p-values. A direct comparison via Steiger’s Z test is included to demonstrate the superior predictive power of the SEP exponents. Out-of-sample validation was not feasible given the modest event count (n=12); this limitation is now stated explicitly, along with a note that larger samples would be required for such validation in future studies. revision: yes

Circularity Check

0 steps flagged

No significant circularity in observational cross-correlation study

full rationale

The paper reports empirical cross-correlations between power-law exponents fitted to SEP fluence spectra for a selected set of strong Forbush decrease events and various FD and CME parameters, claiming higher correlations than with CME velocities. No load-bearing step reduces by construction to its own inputs: the exponents are derived from independent SEP flux measurements, the FD magnitudes come from neutron monitor data, and the reported correlations are direct statistical comparisons rather than tautological predictions or self-definitional equivalences. No self-citations, uniqueness theorems, or ansatzes are invoked to force the central result. The analysis is self-contained observational work on external datasets.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim rests on standard heliophysics assumptions about Forbush decrease drivers and on power-law fits to SEP spectra whose parameters are then treated as predictors.

free parameters (1)

power-law exponents in SEP fluence spectra
These exponents are obtained by fitting observed proton flux spectra and then used as predictor variables for FD magnitude.

axioms (1)

domain assumption Forbush decreases are driven by coronal mass ejection induced shockwaves in the heliosphere
Stated directly in the abstract as the physical mechanism under study.

pith-pipeline@v0.9.0 · 5524 in / 1199 out tokens · 61889 ms · 2026-05-10T18:25:36.872513+00:00 · methodology

discussion (0)

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Relation between the paper passage and the cited Recognition theorem.

We have demonstrated connection between the shape of solar energetic particles fluence spectra and selected coronal mass ejection and Forbush decrease parameters, indicating that power exponents used to model these fluence spectra could be valuable new parameters... They appear to be better predictor variables of Forbush decrease magnitude in interplanetary magnetic field than coronal mass ejection velocities.

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

J. Geophys. Res.: Space Phys. 110 (A09S20). https://doi.org/ 10.1029/2005JA011067. Belov, A., Eroshenko, E., Oleneva, V., et al., 2000. What determines the magnitude of forbush decreases? Adv. Space Res. 27 (3), 625–630. https://doi.org/10.1016/S0273-1177(01)00095-3, URL: https:// www.sciencedirect.com/science/article/pii/S0273117701000953. Belov, A., Ero...

work page doi:10.1029/2005ja011067 2000
[2]

Comparing the properties of icme-induced forbush decreases at earth and mars. J. Geophys. Res.: Space Phys. 125(3), e2019JA027662. URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/ 2019JA027662. https://doi.org/10.1029/2019JA027662. E2019JA027662 10.1029/2019JA027662. Gopalswamy, N., 2016. History and development of coronal mass ejections as a...

work page doi:10.1029/2019ja027662 2016

[1] [1]

J. Geophys. Res.: Space Phys. 110 (A09S20). https://doi.org/ 10.1029/2005JA011067. Belov, A., Eroshenko, E., Oleneva, V., et al., 2000. What determines the magnitude of forbush decreases? Adv. Space Res. 27 (3), 625–630. https://doi.org/10.1016/S0273-1177(01)00095-3, URL: https:// www.sciencedirect.com/science/article/pii/S0273117701000953. Belov, A., Ero...

work page doi:10.1029/2005ja011067 2000

[2] [2]

Comparing the properties of icme-induced forbush decreases at earth and mars. J. Geophys. Res.: Space Phys. 125(3), e2019JA027662. URL: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/ 2019JA027662. https://doi.org/10.1029/2019JA027662. E2019JA027662 10.1029/2019JA027662. Gopalswamy, N., 2016. History and development of coronal mass ejections as a...

work page doi:10.1029/2019ja027662 2016