Forbush Decreases: Cosmic Ray Flux Variations

• Forbush decreases are transient, short-term depressions in galactic cosmic ray flux triggered by solar disturbances such as CMEs, shocks, and high-speed streams.
• They exhibit canonical one-step and two-step profiles, where the shock/sheath region and magnetic ejecta distinctly modulate the intensity and recovery phases.
• Observational studies across multiple heliocentric distances reveal energy-dependent recovery times and highlight links between FD morphology, magnetic field compressions, and geomagnetic effects.

Forbush decreases (FDs) are transient, short-term depressions in the galactic cosmic ray (GCR) flux observed by ground-based neutron monitors and muon telescopes, as well as by in situ particle instruments at multiple heliocentric distances. In the literature represented here, they are commonly associated with coronal mass ejections (CMEs), interplanetary coronal mass ejections (ICMEs), related shocks, and also high-speed streams from coronal holes or SIRs/CIRs. Their time profiles, amplitudes, and recovery phases are used both as diagnostics of disturbed interplanetary magnetic structures and as constraints on cosmic-ray transport, because they encode the effects of sheath turbulence, magnetic ejecta, solar-wind advection, geomagnetic shielding, and observer location within the heliosphere (Davies et al., 2022, Alemanno et al., 2021, Guo et al., 2017).

1. Phenomenon and principal drivers

FDs are described as sudden or rapid reductions in GCR intensity followed by a gradual recovery. One abstract characterizes them as depletions in the GCR count rate that last typically for about a week and can be caused by CMEs or CIRs (Kirin et al., 2020). Another defines them as short-term depressions in the GCR flux and one of the common signatures of CMEs in the heliosphere (Dumbovic et al., 2024). At Mars, they are associated with CMEs and/or SIRs/CIRs (Guo et al., 2017). In direct lepton measurements, the FD is described as the rapid decrease of the intensities of charged particles accompanied with CMEs or high-speed streams from coronal holes (Alemanno et al., 2021).

The physical interpretation emphasized across the cited work is that FDs arise when propagating solar-wind disturbances reduce cosmic-ray accessibility. Near Earth, CME-driven shocks and magnetic field compressions are repeatedly identified as central agents (P. et al., 2014, Arunbabu et al., 2015). In ICME studies, the sheath region ahead of the ejecta and the magnetic ejecta itself are treated as distinct substructures with potentially distinct modulation roles (Janvier et al., 2021, Dumbović et al., 2020). This framing is broad enough to include both classic neutron-monitor FDs and species-resolved depressions observed directly in space, including electrons and positrons (Alemanno et al., 2021, Alemanno et al., 21 Feb 2026).

FDs are also used pragmatically as event markers. Earth–Mars comparisons explicitly note that they are often used as a proxy for detecting the arrival of ICMEs or corotating interaction regions, especially when sufficient in situ solar-wind measurements are not available (Forstner et al., 2020). Multi-point event studies further treat FD amplitude and shape as physical profiles of passing ICMEs, rather than merely scalar alerts (Kinoshita et al., 14 Oct 2025).

2. Canonical morphology: one-step, two-step, sheath, and ejecta

A recurrent classification distinguishes one-step and two-step FDs. The “textbook” two-step profile is summarized as a first decrease associated with the shock/sheath region and a second decrease associated with the closed magnetic structure (Dumbović et al., 2020). Statistical superposed epoch analysis at 1 au revisits this picture by separating the roles of the sheath and the magnetic ejecta (ME): the first sharp step is attributed to the sheath, whereas the second step, plateau, or slow recovery is associated with the ME (Janvier et al., 2021).

Mercury observations provide a particularly explicit planetary example. Using MESSENGER measurements during orbital operations, 42 ICMEs with corresponding high-quality GCR data were examined; 79% were associated with an FD, yielding 33 ICME-related FDs, of which 24, or 73%, had a two-step structure (Davies et al., 2022). The average FD profile obtained by superposed epoch analysis at Mercury still showed a two-step structure despite event-to-event variability, and that structure was reported as directly linked with the magnetic boundaries of the ICME (Davies et al., 2022).

The same literature also complicates the usual assumption that a sheath is required for a strong FD. A 17-year ACE-based study reports that for ICMEs without a sheath, a magnetic ejecta alone is able to drive significant FDs of comparable intensities, and that comparison of samples with and without a sheath but with similar speed profiles shows that magnetic field intensity, rather than its fluctuations, is the main driver for the FD (Janvier et al., 2021). In that analysis, events with a sheath tend to show earlier, more asymmetric minima, often near the sheath–ME boundary, whereas events without a sheath show more symmetric profiles with minima near the ME center (Janvier et al., 2021).

This body of work therefore rejects an overly rigid mapping between “FD” and “sheath-only barrier.” A plausible implication is that the observed number of steps depends jointly on the intrinsic ICME substructure, the observer trajectory, and the energy response of the instrument, rather than on a single universal morphology.

3. Transport physics and dynamical interpretation

Several complementary transport pictures appear in the recent literature. One near-Earth analysis using GRAPES-3 muon data at rigidities between 12 and 42 GV reports a startling similarity between FD time profiles and magnetic field compressions in the near-Earth interplanetary medium (P. et al., 2014). Cross-correlation coefficients of approximately $0.8$–$0.85$ were obtained for all viewing directions, with the FD lagging the interplanetary field enhancement by 20–23 hours; that lag was interpreted through a combination of magnetic mirroring and cosmic-ray diffusion into the disturbed structure (P. et al., 2014).

A related GRAPES-3 study focused on cutoff rigidities from 14 to 24 GV concludes that the enhancement of the IMF associated with FDs occurs mainly in the shock-sheath region and that the turbulence level is also enhanced there (Arunbabu et al., 2015). It argues that the observed lag between IMF enhancement and FD is quantitatively consistent with the time taken by high-energy protons to diffuse into the magnetic field enhancement via cross-field diffusion, and it identifies the turbulent sheath region between shock and CME as the primary diffusive barrier for high-rigidity FDs (Arunbabu et al., 2015).

A separate Oulu neutron-monitor study of 50 ICME-associated events frames the problem as the relative contribution of the magnetic field barrier and solar-wind speed. Over the entire FD duration, the FD profile is generally well anticorrelated with both $B$ and $V_{\rm sw}$, but the recovery phase is highly anticorrelated with $V_{\rm sw}$ and not with $B$; the mean cross-correlation coefficients reported are $-0.81$ for FD–$B$ and $-0.86$ for FD–$V_{\rm sw}$ in the main phase, and $0.85$0 and $0.85$1, respectively, in the recovery phase (Bhaskar et al., 2016). The same study reports that FD and $0.85$2 profile durations are nearly identical, with duration correlation coefficient $0.85$3, whereas $0.85$4 profile durations are significantly shorter (Bhaskar et al., 2016). This suggests that diffusion across enhanced fields is central to onset, while convection by sustained solar-wind flow is particularly important during recovery.

Shock-specific modeling isolates yet another mechanism. A dedicated shock-interaction study models the shock as a very thin structure with a linearly varying magnetic field and finds that protons with higher energies are less likely to be reflected, while thicker shocks and stronger fields reflect protons more efficiently (Kirin et al., 2020). In that framework, the shock and sheath need not be treated as a single barrier: the shock contributes direction- and energy-dependent reflection, whereas the thicker sheath supports diffusive suppression (Kirin et al., 2020).

Analytical event models formalize these distinctions. The combined modeling framework summarized in the multi-spacecraft study uses a propagating diffusive barrier description for the sheath and ForbMod for the expanding flux rope, with the FR-related depression represented by

$0.85$5

so that the flux-rope contribution depends explicitly on perpendicular diffusion and expansion (Dumbović et al., 2020). In the measurement paper built around this model, ForbMod is used as an explicit best-fit tool for FR-related FDs (Dumbovic et al., 2024).

4. Observational regimes and measurement practice

FDs are observed across a wide instrumental spectrum. Neutron-monitor networks remain the standard ground-based resource and provide global coverage, but they measure integrated responses of secondaries rather than particle species directly (Alemanno et al., 2021). Muon telescopes such as GRAPES-3 extend the rigidity range upward and offer directional information (P. et al., 2014, Arunbabu et al., 2015). In situ and planetary instruments broaden the accessible parameter space: MESSENGER’s Neutron Spectrometer detects GCR-induced particle fluxes at Mercury (Davies et al., 2022); MSL/RAD measures ground-level particle fluxes and radiation dose rate at the Martian surface, while MAVEN/SEP detects corresponding orbital depressions (Guo et al., 2017); SOHO/EPHIN, LRO/CRaTER, Solar Orbiter/HET, and BepiColombo/SPM have each been used in specific multi-point FD analyses (Dumbovic et al., 2024, Kinoshita et al., 14 Oct 2025).

Direct space-based lepton observations substantially refine the standard neutron-monitor picture. DAMPE measured the September 2017 FD in electrons and positrons from 2 GeV to 20 GeV with a time resolution of 6 hours, and reported that both the amplitude and recovery time of the fluxes show clear energy dependence (Alemanno et al., 2021). The same mission’s later survey of eight events from January 2016 to March 2024 found maximum decrease amplitudes of about $0.85$6–$0.85$7, with amplitudes that reduce with energy, while the recovery time showed diverse behaviors: some events were strongly energy dependent, whereas others had nearly constant recovery time across the energy range (Alemanno et al., 21 Feb 2026). In that work the recovery is parameterized as

$0.85$8

and the diversity of $0.85$9 is related to CME geometry through the combined effect of CME velocity, angular spread, and ejection direction (Alemanno et al., 21 Feb 2026).

Quantification of FD depth and rate is also formalized. In Earth–Mars comparisons, the FD magnitude and main-phase steepness are written as

$B$0

and

$B$1

evaluated over 1-hour intervals during the decrease phase (Forstner et al., 2020). At Mars, the event-size distribution is reported to follow a power law,

$B$2

for both surface and orbital measurements (Guo et al., 2017).

Measurement methodology has also become more model-aware. A best-fit ForbMod procedure evaluates all possible curves constrained within flux-rope borders and minimizes the mean square error,

$B$3

to estimate the FR-related FD amplitude (Dumbovic et al., 2024). On synthetic tests and on 30 SOHO/EPHIN events, it performs similarly to the traditional minimum-based approach but typically returns slightly smaller amplitudes because it accounts for noise, and it retains a clear advantage when the FD onset contains a data gap (Dumbovic et al., 2024).

5. Heliocentric and planetary variation

The literature here consistently treats FD properties as functions of heliocentric distance and local environment, though not in a purely radial sense. Mercury provides the innermost well-sampled case in this set of studies. The MESSENGER analysis reports that the percentage decrease in GCR flux is greater at Mercury on average than at Earth and Mars, decreasing with increasing heliocentric distance (Davies et al., 2022). The same paper asks whether two-step FDs are more commonly observed closer to the Sun and concludes that this is likely, but not conclusive when compared with the wide range of results from Earth-based studies (Davies et al., 2022).

Earth–Mars comparison isolates one specific radial signature: the relation between total FD amplitude and maximum hourly decrease differs systematically between the two planets. For the same set of ICME-induced events, the reported proportionality factor is $B$4 hr at Earth and $B$5 hr at Mars, with a Mars/Earth ratio of approximately $B$6 (Forstner et al., 2020). The analysis explains this through sheath broadening as ICMEs propagate outward, deriving a sheath broadening factor between about $B$7 and $B$8, consistent with theoretical considerations and previous measurements closer to the Sun (Forstner et al., 2020).

Mars observations add an atmospheric dimension to this radial picture. Over two Earth years, 121 FDs were identified at the Martian surface with MSL/RAD and 77 of these were also detected in orbit by MAVEN/SEP (Guo et al., 2017). For the coincident sample, the mean FD magnitude was $B$9 at MAVEN and $V_{\rm sw}$0 at MSL, and the average ratio of MAVEN to MSL FD magnitude was $V_{\rm sw}$1 (Guo et al., 2017). The systematic reduction at the surface is attributed mainly to energy-dependent modulation by both the interplanetary disturbance and the Martian atmosphere, which filters out lower-energy GCRs more strongly than higher-energy particles (Guo et al., 2017).

Multi-point observations show that radial evolution alone is not sufficient. In the March 2022 ICME study, Solar Orbiter at 0.44 AU recorded an FD of $V_{\rm sw}$2, while LRO/CRaTER near Earth recorded $V_{\rm sw}$3; at a similar radial distance to Solar Orbiter but $V_{\rm sw}$4 away in longitude, BepiColombo measured $V_{\rm sw}$5 (Kinoshita et al., 14 Oct 2025). The study interprets the radial decrease as a consequence of ICME expansion and weakening, but the longitudinal disparity as evidence that shielding effectiveness depends strongly on the observer’s path through the ICME, including core versus flank traversal (Kinoshita et al., 14 Oct 2025). This suggests that statistical FD comparisons require explicit identification of the relationship between observer position and ICME internal structure.

6. Geomagnetic effects, anisotropy, and simultaneity

At Earth, the observed FD profile can be modified by geomagnetic shielding changes as well as by heliospheric modulation. A recent AMS-constrained neutron-monitor analysis shows that storm-time changes in geomagnetic cutoff rigidity can extend to 1 GV in some events, not merely to the neighborhood of 10 GV emphasized in earlier work (Zhao et al., 8 Apr 2026). In that study, bins and days where the daily NM–AMS discrepancy exceeds the AMS statistical uncertainty by more than $V_{\rm sw}$6 are flagged and corrected, removing localized anomalies while preserving the broader FD evolution (Zhao et al., 8 Apr 2026). The key point is that short-timescale cosmic-ray variability during FDs reflects both heliospheric modulation and storm-time changes in geomagnetic shielding (Zhao et al., 8 Apr 2026).

Extreme geomagnetic storms can produce even more explicit departures from the canonical FD profile. An analysis of five ICME-induced extreme storms finds that sudden storm commencement coincides with FD onset, but also that a gradual increase in neutron counts occurs during the main and recovery phases of the geomagnetic storm (Raghav et al., 2021). The maximum neutron-count enhancement coincides with the minimum Sym-H index and is most pronounced in monitors sensitive to higher-energy neutrons; for 20 November 2003, when Sym-H was approximately $V_{\rm sw}$7 nT, an increase of about $V_{\rm sw}$8 was reported after the initial FD onset (Raghav et al., 2021). The interpretation is that weakening of Earth’s magnetic shield allows more cosmic rays to reach the ground, so FD models for extreme events need to include time-varying geomagnetic shielding explicitly (Raghav et al., 2021).

These terrestrial complications also affect event cataloging and simultaneity studies. An automated R-based detection framework identified 229 daily FDs at Magadan, 230 at Oulu, and 224 at Inuvik, as well as 4032, 4144, and 4055 hourly events, respectively; only 99 daily and 261 hourly events were simultaneous at all three stations (Alhassan et al., 2021). A broader five-station study covering 1998–2006 identified 80 days with the most simultaneous events and concluded that solar-cycle oscillation significantly impacts FD amplitude and timing, so its influence should be removed before event selection (Eya et al., 2024). Complementary statistical work on hourly data argues that enhanced cosmic-ray diurnal anisotropy can obscure smaller FDs or shift their apparent timing and that FFT-based correction is necessary for meaningful simultaneity tests (Okike et al., 2024). Together, these results caution against treating all neutron-monitor depressions as globally equivalent manifestations of a single heliospheric structure.

7. Quantitative inference, classification, and forecast relevance

Recent work increasingly treats FDs as structured, high-dimensional events rather than isolated minima. A graph-based framework represents each neutron-monitor FD as an event network constructed from pairwise dissimilarities between station time series and then sparsifies the complete graph to its minimum spanning tree (Perez-Navarro et al., 18 Feb 2026). From this tree, compact geometric and topological fingerprints are extracted, including global efficiency, Estrada index, modularity, assortativity, average Katz centrality, average betweenness, entropy, fractal dimension, and Hurst exponent (Perez-Navarro et al., 18 Feb 2026). With strict leave-one-event-out validation, the best multi-class classification of geomagnetic storm intensity $V_{\rm sw}$9 achieved accuracy $V_{\rm sw}$0 and macro-F1 $V_{\rm sw}$1 for $V_{\rm sw}$2, the best binary severity screening achieved accuracy $V_{\rm sw}$3 and macro-F1 $V_{\rm sw}$4, and partial least squares drop regression yielded $V_{\rm sw}$5 with $V_{\rm sw}$6 (Perez-Navarro et al., 18 Feb 2026). This suggests that FD morphology contains measurable information about storm severity even after network heterogeneity is reduced to a controlled backbone.

Forecast-oriented event analysis has also advanced. In minute-resolution studies of strong geomagnetic storms, FDs are classified as one-step, two-step, three-step, complex, or CIR-driven, and superposed epoch analysis is used to compare their interplanetary drivers (Ahmed et al., 13 Aug 2025). For 57 events, the majority, 63%, showed the FD leading the geomagnetic storm by 1.5 to 4.0 hours, with the remainder showing small lags under 1.5 hours (Ahmed et al., 13 Aug 2025). The same study reports that FD amplitude correlates more strongly with moderate and strong CME-driven storms than with extreme storms, and that events with fast shocks and sheath regions show stronger correlations than those without shocks (Ahmed et al., 13 Aug 2025). Using twelve neutron-monitor stations, it further derives a two-step linear rigidity spectrum in which FD amplitude decreases sharply at low rigidity and more gradually at higher rigidity (Ahmed et al., 13 Aug 2025).

Species-resolved electron measurements extend this quantitative program beyond the neutron-monitor domain. DAMPE’s eight-event survey from 2016–2024 reports that the recovery-time power-law index $V_{\rm sw}$7 in $V_{\rm sw}$8 ranges from approximately $V_{\rm sw}$9 to about $B$0, and that stronger, broader, more centrally directed CMEs are associated with more negative $B$1, hence stronger energy dependence in recovery (Alemanno et al., 21 Feb 2026). This does not reduce FDs to a single amplitude metric; rather, it frames them as transport responses to the three-dimensional geometry and dynamics of CME disturbances.

Taken together, these developments depict FDs as multi-regime observables. They are simultaneously signatures of heliospheric compression and shielding, probes of diffusion and convection, indicators of planetary atmospheric and geomagnetic filtering, and increasingly, inputs to event classification and short-lead-time space-weather assessment.