Pith. sign in

REVIEW 3 major objections 6 minor 37 references

Measurements of Cosmic Proton Flux through Neutron Monitors Using Deep Networks and Imputation Techniques in the AMS-02 Era

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A deep residual CNN trained on 18 imputed neutron monitor stations predicts daily AMS proton flux from 1 to 100 GV with $R^2 = 0.9984$ and extends the record to 2024 with hourly resolution.

desk verdict A useful reconstruction of AMS-02 proton flux from neutron monitors, but the headline R2 and the hourly product both rest on validation gaps that need tightening. read the letter →

arxiv 2412.18872 v3 pith:62LSIJIH submitted 2024-12-25 astro-ph.SR astro-ph.HEastro-ph.IMhep-exphysics.space-ph

Pengwei Zhao , Jianqi Yan , Alex P. Leung , Jie Feng This is my paper · ORCID
classification astro-ph.SRastro-ph.HEastro-ph.IMhep-exphysics.space-ph
keywords cosmicrayprotonfluxneutronmonitorAMS-02deepresidualnetworktimeseriesimputationSAITSsolarmodulationForbushdecrease
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to show that ground-based neutron monitor (NM) count rates carry enough information to reconstruct the rigidity-resolved cosmic-ray proton flux that the Alpha Magnetic Spectrometer (AMS) measures in space. It trains a deep residual convolutional network on 18 pre-processed and imputed NM stations to predict daily AMS proton flux in 30 rigidity bins from 1 to 100 GV, reporting $R^2 = 0.9984$ on a held-out test set. If the claim holds, the result is a continuous daily proton-flux record from 2011 to 2024 that fills AMS operational gaps, plus a first hourly rigidity-resolved proton-flux product for studying short-time solar activity. The argument depends on the NM-to-proton relationship learned from daily 2011-2019 data remaining valid after 2019 and at hourly timescales.

What carries the argument

The load-bearing object is a residual-block convolutional neural network: a fully connected layer maps the 1-by-18 vector of daily NM count rates to 64 features, six residual blocks (each with two fully connected layers, batch normalisation, and Gaussian Error Linear Unit activations) extract the nonlinear NM-to-flux relationship, and a final layer emits a 1-by-30 vector of rigidity-binned proton fluxes. Residual connections are what allow the network to converge stably despite missing AMS labels. The other essential piece is SAITS, a self-attention time-series imputer, which reconstructs missing station values so that the NM input is continuous; for hourly output a Fourier filter first removes the ground-based diurnal cycle that has no counterpart in space.

What would settle it

Compare the model's post-2019 daily predictions with a future AMS daily release, or compare its hourly output with independent sub-daily rigidity-resolved spacecraft measurements during a well-observed Forbush decrease; if the predicted flux drifts systematically over time or the hourly depth and timing of the decrease differ by more than the stated total uncertainty, the generalization claim is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that a residual-block CNN can serve as a surrogate for direct space-based proton measurement: given one day's count rates from 18 neutron monitor stations whose gaps have been filled by a self-attention imputer, it outputs the daily AMS proton flux in 30 rigidity bins spanning 1 to 100 GV. On the held-out daily test set the model reaches $R^2 = 0.9984$. The trained model is then applied to the years after AMS daily data end, validated only against coarser monthly AMS data binned by 27-day solar-rotation intervals, and to hourly NM data after the diurnal cycle is removed with a Fourier filter, producing hourly rigidity-resolved proton fluxes that the paper states cannot currently be verified against any published measurement.

Load-bearing premise

The model is trained only on daily AMS proton flux from 2011 to 2019, and the paper assumes the learned NM-to-proton relationship continues to hold for later years and for hourly timescales, even though no daily or hourly space-based measurements are available to check those periods.

Editorial extensions

If this is right

  • The method fills the AMS data gaps of September-November 2014 and July 2018-October 2019 and extends the daily proton-flux record through August 2024.
  • Wavelet analysis of the reconstructed continuous record across the Solar Cycle 24 polar field reversal reproduces the AMS periodicity pattern: 27-day dominance at low rigidity and 13.5- and 9-day periodicities becoming significant at high rigidity.
  • The hourly product resolves the structure of ICME-driven Forbush decreases, such as the two events on 16 and 17 March 2015, which daily AMS sampling cannot distinguish.
  • Total uncertainties are assigned conservatively as the maximum of the AMS measurement error, the pre-2019 model error, and the post-2019 model error estimated from monthly bins.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An extension the paper leaves implicit: the same pipeline could be applied to AMS helium fluxes or DAMPE electron fluxes to build continuous multi-species rigidity-resolved records over the same solar cycle.
  • A testable implication the authors do not pursue: compare the hourly product with independent sub-daily spacecraft measurements during a well-observed Forbush decrease to check the hourly transfer assumption.
  • A robustness question the paper does not address: how much of the accuracy depends on having all 18 stations, since training on station subsets would separate learned physics from network redundancy.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper presents a deep residual convolutional neural network that maps daily count rates from 18 neutron monitor (NM) stations to AMS-02 daily proton flux in 30 rigidity bins from 1 to 100 GV. The NM data are first cleaned with IQR outlier removal and cross-station event checks, then imputed with a self-attention imputation model (SAITS). The flux model is trained on the 2011-2019 AMS daily dataset and is reported to achieve R2 = 0.9984 on a randomly held-out test set. The paper then uses the model to produce continuous daily flux from 2011 to 2024, validates the post-2019 period against monthly Bartels-rotation AMS data, applies wavelet analysis to the 2014 solar polar-field-reversal period, and introduces hourly proton flux products for Forbush decrease studies.

Significance. If the central claim holds, the method would provide a continuous, rigidity-resolved cosmic-ray proton flux record that bridges AMS data gaps and extends beyond the published daily AMS interval, which is valuable for solar modulation and space-weather studies. The paper makes good use of public NMDB and AMS data, applies careful preprocessing with physical cross-checks for outlier retention, and gives an explicit conservative error-estimation procedure for the monthly validation. The wavelet analysis and Forbush-decrease application indicate potentially useful scientific output. The main contribution is therefore a data-product/method paper whose value depends on the credibility of the generalization claims.

major comments (3)
  1. [II B 2 and III B, Eq. (3)] The single reported value R2 = 0.9984 is not sufficient to support the central accuracy claim. The paper does not state whether this R2 is computed by pooling all 30 rigidity bins and all test days, or per bin. Because the mean proton flux decreases by several orders of magnitude from 1 GV to 100 GV, a model that only reproduces the average rigidity spectrum can achieve a very high pooled R2 while failing to capture day-to-day or bin-to-bin variations. In addition, the random day-level split (80/10/10) interleaves test days with training days; since daily flux is strongly autocorrelated on the solar-cycle timescale, the model can effectively interpolate the smooth trend rather than predict a genuinely unseen period. Please report per-rigidity-bin R2 or relative RMSE, and repeat the evaluation with a chronological or block holdout (for example, train on 2011-2016 and test on 2017-2019) so that the out-of-time generalization is measured directly.
  2. [III C] The post-2019 daily extension is validated only against AMS monthly (Bartels-rotation) data with wider rigidity bins. Aggregating over 27-day intervals can cancel errors that oscillate within a Bartels rotation, and the wider rigidity bins can wash out errors localized in a single daily bin. Therefore, the monthly comparison shown in Figure 7 does not establish that the daily, per-bin flux after 2019 is accurate. Please quantify the aggregation effect by applying the same BR binning and rigidity rebinning to the 2011-2019 period where daily ground truth exists: compare the model's daily per-bin error against its BR-aggregated error. If the aggregation substantially reduces the apparent error, the post-2019 daily record should be described as an unvalidated extrapolation rather than as a measurement.
  3. [III E and Conclusion] The hourly proton flux is advertised in the abstract and conclusion as a first-time product, but the model is trained on daily data and the paper explicitly states that hourly accuracy cannot be verified. Fourier-filtering the diurnal NM cycle changes the input distribution, and there is no evidence that the daily NM-to-flux relationship transfers to sub-daily timescales. Please either provide some external check for a known event (for example, comparison with any available sub-daily space-based data, even if for a different species or rigidity range) or reframe the hourly output as an illustrative, unvalidated demonstration and remove the unqualified 'for the first time' claim from the abstract and conclusion.
minor comments (6)
  1. [Eq. (5)] The definition of the effective relative error epsilon is ambiguous: it is not clear whether the maximum is taken only over time points where |F_pred - F_AMS| exceeds sigma_AMS, or whether negative differences are clipped to zero. Please specify the exact computation and state explicitly that this is a conservative upper bound.
  2. [Figure 3, lower panel] The caption describes the histogram as representing 'AMS time-dependent uncertainties' while the blue dots are individual daily errors; please clarify the units of the x-axis and how the histogram is constructed, since a histogram of uncertainties is unusual and the current description is confusing.
  3. [III C] The sentence describing interpolation of the post-2019 BR-derived errors onto daily rigidity bins does not specify the interpolation method; please state whether the interpolation is linear in rigidity, linear in log rigidity, or another monotonic scheme.
  4. [Figure 5 caption] The caption states that during SEP events the proton flux below 3 GV is excluded to match AMS reporting; please explain how this exclusion is applied consistently in training, testing, and the final 2011-2024 product, since the daily AMS dataset already excludes those measurements and the model is expected to predict all 30 bins.
  5. [References] Reference [21] is the same AMS publication as reference [5] but with additional links; please differentiate the two references, for example by citing the original paper once and, if needed, a separate reference for the extended monthly data table.
  6. [Abstract and Introduction] The abstract uses 'simulate the relationship' while the conclusion uses 'establish a correlation' and later 'accurately captures the relationship'; please use consistent terminology for what is an empirical regression model, not a physical simulation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the supervised regression is validated on held-out AMS test data, and post-2019 extrapolation is checked against independent monthly AMS measurements.

full rationale

The derivation chain is not circular. The model is a supervised regression mapping 18 imputed NM count rates to 30 AMS rigidity bins; the paper evaluates it on a held-out test set (Section II B 2) and reports R2 = 0.9984, which is a standard predictive check rather than a reduction of the prediction to the fitted input. The post-2019 extension is a genuine extrapolation, tested against independent monthly AMS data aggregated over Bartels rotations (Section III C), where the paper explicitly matches rigidity bins and quotes a conservative error estimate. The hourly product is explicitly flagged as unverifiable at hourly resolution (Section III E), which is an honest statement of limited evidence, not a circular construction. No load-bearing argument reduces to a self-citation: the AMS data, NMDB data, wavelet toolkit, and imputation libraries are all external, and the cited AMS periodicity results are used as comparison targets, not as premises that define the model output. The random day-split and monthly-bin aggregation issues are real generalization and statistical-rigor concerns, but they are concerns about how well the fitted model extrapolates, not about the model's output being equivalent to its input by construction. The paper is therefore self-contained against external benchmarks and exhibits no significant circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. The free parameters are model and preprocessing choices rather than physical constants. The main axioms are the faithfulness of AMS data, the sufficiency of NM information for rigidity-resolved flux, and the validity of temporal and temporal-resolution extrapolation.

free parameters (3)
  • IQR outlier threshold multiplier = 3
    Chosen by hand as a 'conservative' threshold to avoid removing real signals; not fitted, but a modeling choice that affects the NM dataset.
  • Model architecture hyperparameters = 64-dim FC, 6 residual blocks, lr=1e-3, batch=128, etc.
    Standard hyperparameters chosen without systematic search; not fitted to data in a Bayesian sense, but they affect the result.
  • Morlet wavelet wavenumber omega_0 = 6
    Standard choice in Torrence and Compo wavelet analysis; not fitted to this data.
assumptions (4)
  • domain assumption AMS daily proton flux data are ground truth for the training labels
    The model is trained to match AMS measurements; any systematic error in AMS data propagates into the model. This is standard but is an assumption about the reference data.
  • domain assumption Neutron monitor count rates after pressure/geomagnetic corrections are sufficient to determine proton flux at all rigidities from 1 to 100 GV
    The paper assumes the 18 NM stations with cutoff rigidities up to 16.8 GV can constrain flux up to 100 GV, where NM sensitivity is very low. This is a strong physical assumption, acknowledged partially by the rigidity-dependent errors, but it underpins the entire mapping.
  • domain assumption The trained model remains valid outside the training period (post-2019) and at hourly resolution
    This is the key extrapolation assumption, tested only against monthly BR-averaged data and not against hourly data. The paper explicitly admits it cannot verify hourly accuracy.
  • domain assumption Imputation with SAITS produces realistic NM data that preserve the physical signals needed for flux prediction
    The paper validates imputation on masked data but does not check whether imputed NM values lead to accurate proton flux predictions specifically; any imputation bias propagates.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Measurements of Cosmic Proton Flux through Neutron Monitors Using Deep Networks and Imputation Techniques in the AMS-02 Era." pith.science (2026). https://pith.science/paper/62LSIJIH

@misc{pith2026241218872,
  author       = {Pith},
  title        = {Pith review of: Measurements of Cosmic Proton Flux through Neutron Monitors Using Deep Networks and Imputation Techniques in the AMS-02 Era},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/62LSIJIH}},
  note         = {Machine review of arXiv:2412.18872}
}
read the original abstract

Accurate measurements of cosmic proton flux are essential for studying the modulation processes of cosmic rays during the solar activity cycle. A proton flux measurement method, based on ground-based neutron monitor (NM) data and deep learning techniques, is presented. After the necessary pre-processing of ground-based NM data using a convolutional neural network (CNN) model, we model the relationship between NM observations and proton flux measured by the Alpha Magnetic Spectrometer (AMS). The daily cosmic proton flux, ranging from 1 GV to 100 GV, is obtained for the period from 2011 to 2024, showing strong agreement with the observed values. In addition, daily proton flux is computed for periods when AMS measurements were unavailable due to operational reasons. For the first time, hourly proton flux as a function of rigidity are calculated for the study of the short-time solar activities.

Figures

Figures reproduced from arXiv: 2412.18872 by the authors.

Figure 1
Figure 1. FIG. 1. The relative variations of the AMS proton flux in three different rigidity ranges compared with those of the rate [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Illustration of the workflow for proton flux calculation and the architecture of the CNN. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (Upper plot) Distribution of (Flux [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Total error estimation for the model. The black [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The left plot shows the daily proton flux for five different rigidities, ranging from low to high, between 1 July 2014 and [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 5
Figure 5. Figure 5: The results of the wavelet analysis are visualized by plotting the time series of proton flux alongside the wavelet power spectrum. For each rigidity bin, we plot the proton flux time series along with the global wavelet power. This approach enables us to visually comp…
Figure 6
Figure 6. Figure 6: FIG. 6. Comparative imputation performance of SAITS and iTransformer models on temporal cosmic ray flux data from the [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Model calculations aggregated at BR resolution compared with AMS proton flux measurements. Three representative [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Comparison of relative proton flux variations during a solar activity between AMS daily measurements (red points) and [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

37 extracted references · 29 canonical work pages

  1. [1]

    nmdb.eu/, which compiles measurements from over 50 stations worldwide, covering a wide range of longitudes and latitudes

    Neutron Monitor Data The NM data used in this study are obtained from the Neutron Monitor Database (NMDB) https://www. nmdb.eu/, which compiles measurements from over 50 stations worldwide, covering a wide range of longitudes and latitudes. NMs measure cosmic ray flux, which varies across stations due to differences in geomagnetic cutoff rigidity. The rig...

    work page 2011

  2. [2]

    Since its installation in May 2011, it has accumu- lated 13 years of cosmic ray data

    Alpha Magnetic Spectrometer Data The Alpha Magnetic Spectrometer (AMS) is a parti- cle detector installed on the International Space Station (ISS). Since its installation in May 2011, it has accumu- lated 13 years of cosmic ray data. The dataset used in this study includes proton flux measurements collected by AMS from May 20, 2011, to October 29, 2019, c...

    work page 2011

  3. [3]

    These partially- observed time series can be a significant barrier to further analysis and modeling

    NM Data Imputation After the pre-processing described in Section II A, the preprocessed NM data still retains some missing val- ues due to the downtime of the NMs. These partially- observed time series can be a significant barrier to further analysis and modeling. To address this issue, we employ four advanced time-series imputation algorithms, SAITS [12]...

    work page

  4. [4]

    Time dependence of the electron and positron components of the cosmic radiation measured by the PAMELA experiment between July 2006 and December 2015

    O. Adriani et al., Time Dependence of the Electron and Positron Components of the Cosmic Radiation Measured by the PAMELA Experiment between July 2006 and December 2015, Phys. Rev. Lett. 116, 241105 (2016), arXiv:1606.08626 [astro-ph.HE]

    work page Pith review arXiv 2016

  5. [5]

    Therefore, we align the imputed NM data with AMS data by date, thereby creating a paired NM-AMS dataset that serves as inputs and outputs for training a calculated model

    Proton Flux calculation In this study, we aim to establish the relationship be- tween NM data and proton flux on AMS. Therefore, we align the imputed NM data with AMS data by date, thereby creating a paired NM-AMS dataset that serves as inputs and outputs for training a calculated model. Specifically, the input data encompasses complete NM 6 data from May...

    work page 2011

  6. [6]

    DAMPE Collaboration, Observations of Forbush De- creases of Cosmic-Ray Electrons and Positrons with the Dark Matter Particle Explorer, The Astrophysical Jour- nal Letters 920, L43 (2021), arXiv:2110.00123 [astro- ph.HE]

    arXiv 2021

  7. [7]

    A. T. Monk and A. H. Compton, Recurrence phenomena in cosmic-ray intensity, Reviews of Modern Physics 11, 173 (1939)

    work page 1939

  8. [8]

    J. A. Lockwood, Forbush Decreases in the Cosmic Radi- ation, Space Science Reviews 12, 658 (1971)

    work page 1971

Show all 37 references
  1. [9]

    Moraal and P

    H. Moraal and P. H. Stoker, Long-term neutron monitor observations and the 2009 cosmic ray maximum, Journal of Geophysical Research (Space Physics) 115, A12109 (2010)

    2010

  2. [10]

    Aguilar et al

    M. Aguilar et al. (AMS), Properties of Daily Helium Fluxes, Phys. Rev. Lett. 128, 231102 (2022). 15

    2022

  3. [11]

    AMS Collaboration, Periodicities in the Daily Proton Fluxes from 2011 to 2019 Measured by the Alpha Mag- netic Spectrometer on the International Space Station from 1 to 100 GV, Physical review letters 127, 271102 (2021)

    2021

  4. [12]

    W. Du, D. Cˆ ot´ e, and Y. Liu, Saits: Self-attention-based imputation for time series, Expert Systems with Appli- cations 219, 119619 (2023)

    2023

  5. [13]

    V¨ ais¨ anen, I

    P. V¨ ais¨ anen, I. Usoskin, and K. Mursula, Seven Decades of Neutron Monitors (1951-2019): Overview and Evalu- ation of Data Sources, Journal of Geophysical Research (Space Physics) 126, e28941 (2021)

    2021

  6. [14]

    Moraal, A

    H. Moraal, A. Belov, and J. M. Clem, Design and co- Ordination of Multi-Station International Neutron Mon- itor Networks, Space Science Reviews 93, 285 (2000)

    2000

  7. [15]

    However, iTransformer initially lacked the capability to directly handle partially-observed time series

    architecture, aims to enhance feature extraction ca- pabilities by learning dependencies among sequences. However, iTransformer initially lacked the capability to directly handle partially-observed time series. To over- come this limitation, the PyPOTS toolbox applies to iTran...

  8. [16]

    Mavromichalaki, A

    H. Mavromichalaki, A. Papaioannou, C. Plainaki, et al., Applications and usage of the real-time neutron monitor database, Advances in Space Research 47, 2210 (2011)

    2011

  9. [17]

    Du, PyPOTS: a Python toolbox for data min- ing on Partially-Observed Time Series, arXiv preprint arXiv:2305.18811 (2023)

    W. Du, PyPOTS: a Python toolbox for data min- ing on Partially-Observed Time Series, arXiv preprint arXiv:2305.18811 (2023)

    2023 arXiv

  10. [18]

    K. He, X. Zhang, S. Ren, and J. Sun, Deep residual learn- ing for image recognition, inProceedings of the IEEE con- ference on computer vision and pattern recognition(2016) pp. 770–778

    2016

  11. [19]

    H. Wu, T. Hu, Y. Liu, H. Zhou, J. Wang, and M. Long, Timesnet: Temporal 2d-variation modeling for general time series analysis, arXiv preprint arXiv:2210.02186 (2022)

    2022 arXiv

  12. [20]

    Y. Liu, T. Hu, H. Zhang, H. Wu, S. Wang, L. Ma, and M. Long, itransformer: Inverted transformers are effective for time series forecasting, arXiv preprint arXiv:2310.06625 (2023)

    2023 arXiv

  13. [21]

    Vaswani, Attention is all you need, Advances in Neural Information Processing Systems (2017)

    A. Vaswani, Attention is all you need, Advances in Neural Information Processing Systems (2017)

    2017

  14. [22]

    Ioffe, Batch normalization: Accelerating deep net- work training by reducing internal covariate shift, arXiv preprint arXiv:1502.03167 (2015)

    S. Ioffe, Batch normalization: Accelerating deep net- work training by reducing internal covariate shift, arXiv preprint arXiv:1502.03167 (2015)

    2015 arXiv

  15. [23]

    Hendrycks and K

    D. Hendrycks and K. Gimpel, Gaussian error linear units (gelus), arXiv preprint arXiv:1606.08415 (2016)

    2016 arXiv

  16. [24]

    At lower rigidity levels, the proton flux predominantly ex- hibits a dominant 27-day periodicity, which corresponds to solar rotation

    and its potential impact on cosmic ray variations. At lower rigidity levels, the proton flux predominantly ex- hibits a dominant 27-day periodicity, which corresponds to solar rotation. In higher rigidity ranges (e.g., 16.6–22.8 GV), we observe additional shorter periodicities...

    1998

  17. [25]

    Y. Yao, L. Rosasco, and A. Caponnetto, On early stop- ping in gradient descent learning, Constructive Approxi- mation 26, 289 (2007)

    2007

  18. [26]

    Tsichla, M

    M. Tsichla, M. Gerontidou, and H. Mavromichalaki, Spectral Analysis of Solar and Geomagnetic Parameters in Relation to Cosmic-ray Intensity for the Time Period 1965 - 2018, Solar Physics 294, 15 (2019)

    2019

  19. [27]

    Aguilar and et al., Periodicities in the daily proton fluxes from 2011 to 2019 measured by the alpha magnetic spectrometer on the international space station from 1 to 100 gv, Phys

    M. Aguilar and et al., Periodicities in the daily proton fluxes from 2011 to 2019 measured by the alpha magnetic spectrometer on the international space station from 1 to 100 gv, Phys. Rev. Lett. 127, 271102 (2021), the Φ p data up to June 2022 including the 11-year average fl...

    2021

  20. [28]

    AMS Collaboration (AMS Collaboration), Antiprotons and elementary particles over a solar cycle: Results from the alpha magnetic spectrometer, Phys. Rev. Lett. 134, 051002 (2025)

    2025

  21. [29]

    Torrence and G

    C. Torrence and G. P. Compo, A Practical Guide to Wavelet Analysis., Bulletin of the American Meteorolog- ical Society 79, 61 (1998)

    1998

  22. [30]

    A. K. Tiwari, A. Singh, and S. Agrawal, Study of the diurnal variation of cosmic rays during different phases of solar activity, Solar Physics 279, 253 (2012)

    2012

  23. [31]

    B. T. Kress, M. K. Hudson, R. S. Selesnick, C. J. Mertens, and M. Engel, Modeling geomagnetic cutoffs for space weather applications, Journal of Geophysical Research (Space Physics) 120, 5694 (2015)

    2015

  24. [32]

    D. F. Smart and M. A. Shea, The space-developed dy- namic vertical cutoff rigidity model and its applicability to aircraft radiation dose, Advances in Space Research 32, 103 (2003)

    2003

  25. [33]

    Manchester, E

    W. Manchester, E. K. J. Kilpua, Y. D. Liu, N. Lugaz, P. Riley, T. T¨ or¨ ok, and B. Vrˇ snak, The Physical Pro- cesses of CME/ICME Evolution, Space Science Reviews 212, 1159 (2017)

    2017

  26. [34]

    H. V. Cane, Coronal Mass Ejections and Forbush De- creases, Space Science Reviews 93, 55 (2000)

    2000

  27. [35]

    I. G. Richardson, Solar wind stream interaction regions throughout the heliosphere, Living Reviews in Solar Physics 15, 1 (2018)

    2018

  28. [36]

    Wawrzynczak and M

    A. Wawrzynczak and M. V. Alania, Modeling and data analysis of a forbush decrease, Advances in Space Re- search 45, 622 (2010)

    2010

  29. [37]

    S. Wang, V. Bindi, C. Consolandi, C. Corti, C. Light, N. Nikonov, and A. Kuhlman, Properties of Forbush De- creases with AMS-02 Daily Proton Flux Data, The As- trophysical Journal 950, 23 (2023)

    2023

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.