the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 Oct 2025
Threshold Atmospheric Electric Fields for Initiating Relativistic Runaway Electron Avalanches: Theoretical Estimates and CORSIKA Simulations
Abstract. We examine the threshold Atmospheric Electric Field (Eth) needed to initiate a runaway avalanche process in Earth's atmosphere. We compare the traditional, thirty-year-old theoretical threshold value with its recently updated value, along with the threshold derived from CORSIKA-simulated avalanches (Ez). The altitude dependence of these threshold values is analyzed, considering changes in air density and their effects on avalanche development. This study is vital for understanding high-energy atmospheric phenomena in both the lower and upper atmosphere, including thunderstorm ground enhancements (TGEs) and gamma glows, as well as for refining AEF models based on particle flux measurements.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-4153', Anonymous Referee #1, 02 Nov 2025
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CC1: 'Comment on egusphere-2025-4153', Liza Hovhannisyan, 25 Nov 2025
Dear Referee,
Thank you for your review and the helpful comments.
We have revised the manuscript accordingly and addressed all points in the attached documents.Attached:
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Response to Reviewer (point-by-point)
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Revised manuscript with tracked changes
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Clean revised manuscript
We hope the updated version satisfies the requirements.
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CEC1: 'Comment on egusphere-2025-4153 - No compliance with the policy of the journal', Juan Antonio Añel, 05 Dec 2025
Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.htmlFirst, you have not published the code of the CORSIKA model. I am sorry to have to be so outspoken, but this is unacceptable, forbidden by our policy, and your manuscript should have never been accepted for Discussions given such violation. Our policy clearly states that all the code and data necessary to replicate a manuscript must be published openly and freely to anyone before submission.
Also, you have archived your data on a Mendeley and yerphi.am servers. However, neither Mendeley nor yerphi.am servers are suitable repositories for scientific publication.
Therefore, we are granting you a short time to solve this situation. You have to reply to this comment in a prompt manner with the information for the repositories containing the CORSIKA model and the data that you use to produce and necessary to replicate your manuscript. The reply must include the link and permanent identifier (e.g. DOI). Also, any future version of your manuscript must include the modified section with the new information.
Note that if you do not fix these problems as requested, we can not consider your manuscript for publication in our journal.
Juan A. Añel
Geosci. Model Dev. Executive Editor
Citation: https://doi.org/10.5194/egusphere-2025-4153-CEC1 -
AC3: 'Reply on CEC1', Ashot Chilingarian, 12 Dec 2025
We appreciate the editor’s detailed review and the opportunity to clarify our compliance with the GMD Code and Data Policy.
CORSIKA is not authored by us and is not legally redistributable. It is a licensed simulation framework maintained and distributed exclusively by the Karlsruhe Institute of Technology (KIT). As such, third-party publication of the CORSIKA source code is prohibited.
In accordance with GMD policy in such situations, our manuscript already contains the exact CORSIKA version, the complete input cards, and CORSIKA output files.
These components fully enable any researcher with legitimate access to the CORSIKA framework to replicate all simulations.
We also note that CORSIKA is one of the most widely used and internationally recognized Monte-Carlo tools in cosmic-ray physics and high-energy particle physics. Its role as a reference simulation framework for the global CR community is well established. Many major experiments (e.g., KASCADE, Pierre Auger Observatory, LHAASO, TA, IceTop) rely on CORSIKA as their standard comparison and calibration tool. We will add additional references to foundational CORSIKA publications to make this clear in the revised manuscript. All numerical data used in the figures and tables have already been deposited in an openly accessible repository. The manuscript includes the repository link and DOI of TGE events allowing downloading multivariate information on particle fluxes and climate conditions, and the repository contains everything required to reproduce the results.
We will add to MS the following information:
The CORSIKA simulation framework used in this study (version 7.400) is a licensed scientific code developed and maintained at the Karlsruhe Institute of Technology (KIT). According to its license conditions, the CORSIKA source code cannot be redistributed or archived by third parties; therefore, it cannot be deposited in an external public repository. The code is available free of charge for scientific use directly from the official KIT distribution portal (Heck et al., 1998). CORSIKA is one of the most widely used and internationally recognized Monte Carlo models in the cosmic-ray and high-energy particle-physics communities, serving as a reference simulation framework for major experiments such as KASCADE, the Pierre Auger Observatory, the Telescope Array, LHAASO, and IceTop. Its status as a community-standard tool enables consistent comparison of results across different research groups and atmospheric conditions.To ensure reproducibility, all user-provided components required to run the simulations—complete input cards, atmospheric profiles, and the exact electric-field configurations—areavailable to users. The post-processing and analysis procedures applied to the simulation output are documented in the manuscript and therefore do not require separate archival. These materials define the simulation environment sufficiently for any researcher with legal access to CORSIKA to reproduce the results presented in this study.
Citation: https://doi.org/10.5194/egusphere-2025-4153-AC3 -
CEC2: 'Reply on AC3', Juan Antonio Añel, 12 Dec 2025
Dear authors,
Many thanks for your reply. We fully understand the situation regarding the CORSIKA model. In this case, please, contact the CORSIKA developers, and ask them to store the code in one of the suitable repositories according to our policy. It could be a private Zenodo repository if they need to keep under control the distribution of the code.
I must not that you have not addressed the issues related to storing your assets in Mendeley and yerphi.am servers, which I insist, GMD does not accept.
In the meantime, until this lack of compliance is solved, the situation regarding the stall of the peer-review process for your manuscript should continue.
Juan A. Añel
Geosci. Model Dev. Executive Editor
Citation: https://doi.org/10.5194/egusphere-2025-4153-CEC2 -
AC4: 'Reply on CEC2', Ashot Chilingarian, 13 Dec 2025
Dear Prof. Añel,
Thank you for your clarification and for acknowledging the licensing constraints associated with the CORSIKA model.
Regarding your suggestion to contact the CORSIKA developers: while we fully understand the motivation behind this request, we must respectfully note that redistribution or re-archiving of the CORSIKA source code is entirely outside the authors’ authority. CORSIKA is maintained and distributed by KIT under a long-standing licensing scheme, and any change in its distribution policy (including storage in Zenodo, public or private) would require an institutional decision by KIT. Such a process cannot be initiated, negotiated, or completed by individual users within the timeframe of a manuscript review.
We would like to emphasize that this situation is not specific to our work; CORSIKA has been used for decades as a reference Monte-Carlo framework in the cosmic-ray and high-energy physics communities under exactly these conditions, including in numerous peer-reviewed publications where reproducibility is achieved via version control, detailed configuration files, and open access to all user-supplied inputs.
Concerning the data repositories, we acknowledge your point and agree that this issue must be resolved. We therefore commit to the following immediate actions:
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All simulation input files, atmospheric profiles, electric-field configurations, and numerical output data required to reproduce the results will be moved from Mendeley and the yerphi.am server to Zenodo, a repository fully compliant with GMD policy.
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A new Zenodo DOI will be generated and included in the revised manuscript.
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The Code and Data Availability section will be updated accordingly, removing references to Mendeley and yerphi.am.
With these changes, all assets under the authors’ control will fully comply with GMD policy. Reproducibility will be ensured by:
– the public Zenodo archive (data + inputs + configurations),
– the explicit CORSIKA version and references,
– and the detailed methodological description provided in the manuscript.We kindly ask the editor to consider that requiring authors to alter the distribution model of a third-party licensed community code is beyond reasonable compliance expectations and outside our legal and institutional control.
We remain fully committed to resolving all issues that are within our responsibility and appreciate your guidance in bringing the manuscript into full policy compliance.
Sincerely,
Ashot Chilingarian
(on behalf of the authors)Citation: https://doi.org/10.5194/egusphere-2025-4153-AC4 -
CEC3: 'Reply on AC4', Juan Antonio Añel, 13 Dec 2025
Dear authors,
Regarding the CORSIKA model, I do not agree that an institutional decision by KIT is necessary to publish it in a private Zenodo repository. KIT is not the owner of such code, but simply the institution where the developers of the model work. We deal in GMD with similar issues very often, and I am quite sure that in this case the developers can store the code in Zenodo. Therefore, again, I kindly ask you to contact the authors of CORSIKA, make them aware of the our request, and explore the possibility to host the code in a private repository, to better comply with the replicability of your work, which moreover will be beneficial for them, improving the scientific soundness of all the works performed with such model.
In addition, I think it is necessary to make you aware of what seems to be a wrong interpretation of our policy by your part. First, it is not that it is not possible solve the issues related to sharing code and data in the timeframe of a review process as you say. First, a review process for your manuscript should never happen in GMD, as it does not comply with the Code and Data policy of the journal. Therefore, the timeframe for the review of your manuscript must include the compliance with the policy of the journal on the very first, and only when the compliance is solved we can begin to consider the remainder parts of the evaluation of your work, that is, other comments from reviewers and additional scientific issues with it. Compliance with our code and data policy it is not something extra, something on the side, but a fundamental part of the philosophy of GMD.
In this regards, you mention in your last reply that you will publish the data in a repository we can accept. This is not enough. Again, the code and data policy is the first thing you must fulfill. We can not accept expressions of future compliance. In this regard, you have to reply here in Discussions to this comment with a new text for the "Code and Data Availability" section of your manuscript, that complies with the policy of the journal.
I insist, that until this is solved, we can not consider your manuscript for additional review or future publishing in our journal.
Juan A. Añel
Geosci. Model Dev. Executive Editor
Citation: https://doi.org/10.5194/egusphere-2025-4153-CEC3
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AC4: 'Reply on CEC2', Ashot Chilingarian, 13 Dec 2025
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CEC2: 'Reply on AC3', Juan Antonio Añel, 12 Dec 2025
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AC3: 'Reply on CEC1', Ashot Chilingarian, 12 Dec 2025
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CC2: 'Comment on egusphere-2025-4153', Ekaterina Svechnikova, 05 Dec 2025
The manuscript caught my attention because it tackles a very practical question: what electric field is actually required to trigger and sustain RREAs in realistic conditions at high-mountain stations. Using CORSIKA simulations, it offers a clear comparison between the classical and “updated” theoretical thresholds Eth and the simulation-based value Ez across several altitudes and sites. The important, non-trivial outcome is that realistic avalanche development needs fields systematically stronger than both common theoretical estimates, which is directly relevant for interpreting TGEs, gamma glows, and lightning initiation.
The simulation setup looks physically well motivated: the choice of seed spectrum, realistic cloud–detector distances, and limitation to observationally justified field strengths make the results directly applicable to mountain-station measurements. The provided scaling of the results with altitude is also useful for applying the conclusions to different sites. Overall, the paper is concise, well illustrated, and addresses a central question in interpreting high-energy atmospheric phenomena.
A few points, however, could be improved:
- Units and consistency. The text alternates between kV/m and kV/cm; using a single system throughout would avoid confusion.
- Simulation setup and uncertainties. It would help to briefly specify the length and vertical extent of the uniform field region for each site (and any assumptions about lateral extent), to indicate statistical uncertainties (e.g. in Fig. 6 or in the text), and to add a short comment on sensitivity to the assumed seed spectrum.
- Link to observations. Since the motivation is to describe and analyze TGEs and gamma glows at specific stations, it would be very helpful to include at least a qualitative comparison of inferred AEFs from observations with the simulated thresholds.
- Several minor typographical issues (“Mendelay” vs “Mendeley”, duplicated DOI:10.17632/8gtdbch59z) should be corrected.
In my view, the work is timely, methodologically sound, and provides a useful quantitative refinement of RREA threshold fields with direct relevance to atmospheric electricity studies. After addressing the clarifications and minor additions above, the manuscript will be a solid contribution.
Citation: https://doi.org/10.5194/egusphere-2025-4153-CC2 -
AC1: 'Reply on CC2', Ashot Chilingarian, 12 Dec 2025
Thanks for the comments and corrections. All details mentioned: relation to measurements, elongation of electric fields on different sites, etc., will be included in the final version of the MS.
Citation: https://doi.org/10.5194/egusphere-2025-4153-AC1
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CC3: 'Comment on egusphere-2025-4153', Ivan Shulzhenko, 09 Dec 2025
The article addresses an important issue related to atmospheric electric fields and certainly worth full publication. However, one remark should be done.
The article notes the influence of air density on the threshold values of the atmospheric electric field required for triggering relativistic runaway electron avalanches. In the theoretical calculations, an exponential density model is used: the relative density n is calculated as the ratio of density at a given altitude to the sea-level density according to the standard atmospheric (exponential) model. However, the impact of the atmospheric temperature profile on the density at different altitude levels is not considered, even though the variation of temperature with altitude (the temperature gradient) can modify the density profile, especially under non-standard atmospheric conditions. For more accurate modeling for the specific atmospheric conditions (for example, inside thunderclouds), the results could be refined by taking into account the temperature profile.Citation: https://doi.org/10.5194/egusphere-2025-4153-CC3 -
AC2: 'Reply on CC3', Ashot Chilingarian, 12 Dec 2025
We thank the reviewer for raising this point. In our study, the relative air density n(h) was derived using the standard exponential atmosphere, which is widely employed in RREA modeling and in most previous theoretical works. This approach provides a consistent way to compare threshold fields across altitudes and allows direct comparison with published parametrizations of the RREA e-folding length.
We agree that temperature variations, especially inside real thunderclouds, can modify the density profile and therefore slightly shift the effective threshold field. However, the magnitude and sign of these temperature deviations are highly case-dependent and generally not available with the vertical resolution required for event-by-event modeling. Because our goal here is to present baseline threshold estimates for comparison with CORSIKA simulations at fixed altitudes, the standard atmosphere provides a stable and reproducible reference.
At the same time, we acknowledge the reviewer’s suggestion. We have added a short remark in the manuscript noting that, for detailed modeling under specific thunderstorm conditions, particular TGE events, the threshold field could be further refined by incorporating measured or modeled temperature profiles when available. This refinement is outside the scope of the present work but can be implemented in future event-specific simulations.
Citation: https://doi.org/10.5194/egusphere-2025-4153-AC2
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AC2: 'Reply on CC3', Ashot Chilingarian, 12 Dec 2025
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RC2: 'Comment on egusphere-2025-4153', Anonymous Referee #2, 13 Dec 2025
The manuscript presents an interesting and valuable study on threshold atmospheric electric fields required for initiating relativistic runaway electron avalanches. The topic is highly relevant for the community of High-energy atmospheric physics, and the simulations across multiple altitudes provide useful insights. The paper is generally well structured and clearly written.
Minor comments:
1. Line 42: The reference to Fig. 4 in Ambrozova et al. (2023) seems incorrect; the relevant information is in Fig. 3.2. Line 82: EXPACS is not a web calculator but an Excel-based program. The citation is also incorrect. According to the rules for publishing results obtained using EXPACS, the following two papers should be cited: Sato (2015, PLOS ONE 10(12): e0144679) and Sato (2016, PLOS ONE 11(8): e0160390). One of them is listed in the references but is wrongly cited as (Sato, 2018) in line 82; the other should be added.
3. Please use the abbreviation RREA consistently throughout the manuscript. The term “RRE avalanche” (used e.g. at figures 1-4) is not defined in the text and may confuse readers. Consider replacing all occurrences with the standard term “RREA”.
4. The manuscript uses both kV/m and kV/cm when describing atmospheric electric field strengths. This is inconsistent and may confuse readers. Please explain or use only one of them.
5. Figures 1–4 are of the same type and illustrate the same quantity (RREA development) under different conditions. Their captions are nearly identical as well. I strongly suggest combining them into a single multi-panel figure (e.g., Fig. 1a–d). This would make the presentation more compact, improve readability, and save space without loss of clarity.
6. Subscripts should be consistently formatted in the notation Rc, Eth, Ez, ... Please correct throughout the manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-4153-RC2 -
AC5: 'Reply on RC2', Ashot Chilingarian, 13 Dec 2025
We thank the reviewer for the positive assessment of the manuscript and for the helpful and constructive comments.
- The reference to Fig. 4 in Ambrožová et al. (2023) is indeed incorrect. The correct reference is Fig. 3. This will be corrected in the revised manuscript.
- Line 82 – EXPACS description and citation
We agree with the reviewer. EXPACS is an Excel-based program rather than a web calculator, and the citation in line 82 is incorrect. The reference will be corrected accordingly. In addition, we will update the citations to comply with the EXPACS publication rules by citing both:- Sato (2015), PLOS ONE, 10(12): e0144679
- Sato (2016), PLOS ONE, 11(8): e0160390
The incorrect citation “(Sato, 2018)” will be removed.
- Use of RREA vs “RRE avalanche”
We agree that the terminology should be consistent. The abbreviation RREA is defined in the text and is the standard term in the literature. All occurrences of “RRE avalanche” (including in figure captions) will be replaced with “RREA” throughout the manuscript. - Units of atmospheric electric field (kV/m vs kV/cm)
We agree that the mixed use of units is confusing. In the revised manuscript, we will adopt a single unit consistently for atmospheric electric field strength. - Figures 1–4: suggestion to combine into a multi-panel figure
We appreciate this suggestion and agree that it improves clarity and compactness. In the revised version, Figures 1–4 will be combined into a single multi-panel figure (Fig. 1a–d), with a unified caption describing the common quantity (RREA development) and panel-specific conditions indicated clearly. - Formatting of subscripts (Rc, Eth, Ez, etc.)
We agree and thank the reviewer for pointing this out. Subscripts will be consistently formatted throughout the manuscript for all relevant quantities (Rc, Eth, Ez, etc.), including in the main text, equations, figure labels, and captions.
Citation: https://doi.org/10.5194/egusphere-2025-4153-AC5
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AC5: 'Reply on RC2', Ashot Chilingarian, 13 Dec 2025
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I find the study useful in that knowledge of the ambient electric field is crucial to understanding the initiation of a lightning flash discharge. This should help the modeling community in finding decent constraints for future simulations of lightning discharges given a particular altitude. I am enclosing a PDF of my edits/comments.