Effects of Geomagnetic Cutoff Rigidity Variations during Forbush Decreases

1. Problem Statement

Context:
Forbush Decreases (FDs) are short-term reductions in galactic cosmic ray (GCR) flux caused by interplanetary disturbances like Coronal Mass Ejections (ICMEs). Understanding the rigidity dependence of these events requires high time-resolution data.

• Ground-based Neutron Monitors (NMs): Provide continuous, high-time-resolution (hourly) data but measure integral count rates above station-dependent geomagnetic cutoff rigidities. They cannot directly provide fluxes in specific rigidity bins without reconstruction models.
• Space-based Instruments (e.g., AMS-02): Measure proton flux directly in rigidity bins but currently only provide daily averaged data.

The Core Issue:
During strong ICME events, geomagnetic storms alter the Earth's magnetic shielding, causing the geomagnetic cutoff rigidity ($R_c$) to vary (either increasing or decreasing).

• Previous studies noted that these variations cause localized anomalies in NM-based reconstructions, particularly near 10 GV.
• However, it was unclear if these effects extended to lower rigidities or how significantly they distorted the inferred spectral shape of FDs.
• If uncorrected, these storm-time cutoff variations bias the understanding of heliospheric modulation, making it difficult to distinguish between true cosmic ray changes and local geomagnetic effects.

2. Methodology

The authors propose a hybrid correction method that leverages the strengths of both ground-based and space-based data.

Data Sources:

• Uncorrected Series: Hourly proton fluxes reconstructed from NM data (May 2011 – October 2019) using a deep learning model trained on AMS data.
• Reference Standard: Daily proton fluxes measured by the Alpha Magnetic Spectrometer (AMS-02) in space (1–100 GV). AMS is unaffected by terrestrial geomagnetic cutoffs.

Correction Strategy:

1. Spectral Parameterization: The daily AMS spectrum is parameterized using a specific functional form (Eq. 1):
   $$\gamma(R) = \gamma_\infty + \frac{A}{R^k}$$
   Where $\gamma_\infty$ is the high-rigidity limit, $A$ sets the low-rigidity deviation, and $k$ controls the rate of change.
2. Anomaly Detection:
   • For each ICME event, daily averages of the NM-based reconstruction are compared against AMS daily fluxes.
   • Rigidities (bins) are flagged if the absolute deviation exceeds the AMS uncertainty at the 3$\sigma$ level.
   • Continuous sequences of flagged days are extended by one day on either side to ensure smooth transitions.
3. Reconstruction & Correction:
   • For flagged bins and time intervals, the hourly flux is reconstructed using the AMS-derived spectral parameters ($\gamma_\infty, A, k$) interpolated to hourly resolution.
   • The normalization coefficient ($C_t$) is derived from the uncorrected NM reconstruction in the non-flagged (stable) rigidity bins at the same hour.
   • Crucial Distinction: The corrected product is not a direct insertion of AMS hourly data (which doesn't exist). Instead, it is an NM-based reconstruction constrained by the stable spectral shape provided by AMS, preserving the hourly evolution of the FD while removing localized geomagnetic distortions.

3. Key Contributions

• Extension of Anomaly Range: The study demonstrates that geomagnetic cutoff-induced spectral distortions are not limited to ~10 GV as previously thought; they extend down to 1 GV in some hourly reconstructions.
• Novel Correction Framework: Introduces a method to correct hourly NM-based reconstructions using AMS daily data as a "spectral anchor." This separates local geomagnetic noise from global heliospheric modulation.
• Validation of Spectral Stability: Through Appendix analysis, the authors show that while FDs reduce total flux, the spectral shape parameters ($\gamma_\infty, A, k$) derived from AMS follow the same trends for quiet days and FD days. This confirms that the spectral shape is stable on daily timescales, validating the use of AMS daily fits to correct hourly NM data.

4. Results

• Case Study (June 25, 2015 ICME):
  • Lower Rigidity ([2.15, 2.4] GV): The original NM reconstruction showed a deficit (flux lower than AMS) during the storm. The correction raised the values toward the AMS level.
  • Higher Rigidity ([9.26, 10.1] GV): The original reconstruction showed an excess (flux higher than AMS). The correction lowered the values toward the AMS level.
  • Dst Correlation: The largest deviations coincided with the most negative Dst index (peak geomagnetic storm), confirming the link to geomagnetic shielding changes.
• Outcome: The correction successfully removes localized anomalies while preserving the broader FD evolution. The corrected daily averages in affected bins align much more closely with the AMS reference (approaching a ratio of unity).
• Scope: The correction is local in both time (only during specific storm phases) and rigidity (only in specific bins), leaving the rest of the hourly dataset unchanged.

5. Significance

• Improved Physics Interpretation: By removing geomagnetic artifacts, researchers can more accurately study the true rigidity dependence of Forbush Decreases and heliospheric modulation mechanisms.
• Data Utility: Provides a more reliable dataset for studying short-timescale cosmic ray variability, which is critical for space weather forecasting and understanding particle acceleration/transport in the heliosphere.
• Methodological Benchmark: Establishes a robust protocol for cross-calibrating ground-based integral detectors with space-based direct measurements, a technique applicable to future multi-messenger and multi-platform solar physics studies.

Conclusion:
The paper concludes that short-timescale cosmic ray variability during FDs reflects a combination of heliospheric modulation and storm-time geomagnetic shielding changes. The proposed correction method effectively isolates the latter, providing a cleaner, physically consistent hourly proton flux dataset for the scientific community.