the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Dec 2024
Characterisation and modelling of lightning strikes as point events in time and space
Abstract. Lightning is a spatio-temporal phenomenon comprised of individual strikes with specific occurrence times and spatial coordinates. This study models and characterises lightning strikes from single thunderstorms, treating each strike as a point event. Utilising real-world datasets, we characterise and model lightning strikes’ physical properties. Our analysis involves two severe UK thunderstorm systems selected based on published synoptic analyses. These systems enable subdivision of the lightning dataset into subsets, each representing a distinct thunderstorm. Our two major storm systems feature three thunderstorms each: Storm system A with 7955, 11988, and 5655 strikes over the English Midlands on 28 June 2012; Storm system B with 4218, 455, and 1926 strikes characterised over northern England on 1–2 July 2015. These six datasets exemplify individual thunderstorms with three physical attributes: movement speed, lightning inter-event time distribution, and spatial spread about the storm track. Applying least-squares plane and linear fits in the spatio-temporal and lag spaces, we estimate movement speeds of 47–59 km/h and 67–111 km/h for Storm systems A and B, respectively. The inter-event time distribution ranges from 0.01 to 100 seconds, with density peaks around 0.1 seconds and at 1–10 seconds. Autocorrelation analysis in natural time reveals significant autocorrelation in all storms, varying from short-range to long-range. For spatial spread, calculated as the distance from the storm track to the strikes, we employ a linear filter to establish the storm track. This analysis yields typical spatial spreads up to 80 km in either northing or easting dimensions, with an outlier of 226 km in the northing dimension for one storm. The paper concludes with a synthetic lightning strike model. This model allows the selection of each storm’s starting points, directions, and movement speeds, generating point events based on our characterisation findings. This comprehensive study of lightning strikes in time and space accurately reflects severe thunderstorms’ behaviour and informs statistical models for simulating lightning events.
Competing interests: Bruce Malamud is on the editorial board of NHESS. Bruce Malamud has co-authored with one of the suggested reviewers (Mario Gonzalez Pereira) in 2011.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.-
Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-2733', Anonymous Referee #1, 06 Jan 2026
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AC1: 'Reply on RC1', Uldis Zandovskis, 16 Feb 2026
Dear Referees 1 and 2:
We thank the two referees (R1 and R2) for their careful and substantive comments on both the content and presentation of our NHESS discussion paper “Characterisation and modelling of lightning strikes as point events in time and space” (egusphere-2024-2733).
We thank R1 for noting that the “second half of the paper (from section 4 onwards) appears very novel and is what the authors should emphasise in their revised manuscript” and we agree with R1 that the manuscript can be reduced in size to enhance readability and the overall contribution. We also thank R2 for their detailed comments, and have attempted to address these issues in our comments.
As this is a discussion paper, our replies in the supplement set out (i) how we interpret each comment, and (ii) the specific changes we propose to implement in the revised manuscript. We will ensure that all modifications are incorporated consistently across the paper, figures and tables.
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AC1: 'Reply on RC1', Uldis Zandovskis, 16 Feb 2026
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RC2: 'Comment on egusphere-2024-2733', Anonymous Referee #2, 22 Jan 2026
It is unclear what new scientific insight is focussed on in this manuscript. The authors focus exclusively on the statistical description of lightning stroke time and location of six thunderstorms, events of which have already been studied, interpreted and published by other researchers, albeit from a more meteorological perspective. The statistical techniques employed do not appear to be new. The authors do however describe a statistical method of creating synthetic lightning data which may be of use to other researchers in the field, although such value must be considered in the context of readily available real lightning time and location archives from sources such as the one used by this study. The aim of describing different lightning characteristics for different types of thunderstorms, whilst commendable, is not novel and the present discussion is limited to a very small subset which does not include any physical interpretation of the results necessary to usefully apply their empirical statistics to other storms. This raises the question of how much their work furthers natural hazard research or broader statistical modelling within the scope of NHESS, which should be the key focus of any resubmission.
Overall, the authors need to reframe their manuscript to ensure any novelty of their study is more apparent, especially in the context of applying it to improve thunderstorm hazard characterisation beyond what is already established amongst the meteorological research community.
Specific comments
- Need to correctly define the measured physical process under analysis, and not refer to lightning as “strikes”, which is not a well-defined scientific term in this context. ATDnet is a VLF radio receiver network that detects lightning strokes, which are the individual pulses of current occurring during the complete lightning discharge process, known as a flash. Since there are normally several strokes in an individual flash (hence the tendency of lightning to flicker when observed optically), the distinction is therefore important for quantitative interpretation. Consequently, clarity is needed throughout, especially section 4.2 where the inter-stroke period and inter-flash periods are merged into a generalised “inter-event” time period, despite being two very different variables.
- Storm cell tracking algorithms based on lightning location data are not new and are already an evolving but well-established feature in both academic research (including recent NHESS publication) and many commercial real-time lightning location products, although not currently for ATDnet. This is contrary to the authors suggestion of novelty (discussion, line 748-9), so further support will need to be presented to clarify the novelty of their approach.
- Distinction on charts is made over the different statistics for northing and easting spatial characteristics, although given the separation is only due to individual storm propagation direction, it is difficult to see how this distinction can be usefully applied to further understanding of lightning spatial characteristics more generally. Instead, using a coordinate system related to storm propagation direction (which in this case appears approximately linear) may offer more scientific insight in lightning spatial distribution during storm evolution.
- Section 2.1 Line 75. Whilst the authors correctly describe the simplified charge structure of a "typical" thunderstorm, it has been well established in geophysical literature that not all lightning-producing thunderstorms have this basic charge configuration, especially those which produce the severe storms described in this manuscript, which would likely have been at least tripolar.
- Section 5.1 First paragraph is confusing. What is meant by storms being visually different in time? The lack of clarity that the “inter event times” is a convolution of both inter-stroke and inter-flash data means that the removal of “relatively large” or “longer” periods is not well justified in terms of separating physical characteristics. Was the separation therefore made considering changes in flash rate?
- Whilst it is acknowledged that the emphasis of their work is on statistical rather than physics-based modelling, the authors cannot adequately interpret their “inter-event” period statistical distributions without acknowledging that two distinct physical processes are responsible for this distribution. These are inter-stroke (the fundamental output of ATDnet, attributed to current pulses during individual flashes, which will account for the ~0.2s peak) and inter-flash period, which will be the peak around a few seconds duration for these quite active storms, related to the charging processes within the storms. Consequently, figure 13 is largely a function of the storm’s flash rate evolution with time, making the description in terms of inter-event time distribution morphology rather over-complicated for what is a common property used to describe thunderstorm activity. The authors make some association with their inter-event periods and previously published inter-stroke means afterwards in the discussion section (around lines 736-744) suggesting they may be already aware of the underlying physical processes involved, although there is still no explicit link made to their bimodal distribution being a combination of inter-stroke and inter-flash periods. This would also allow exploration of any association between inter-stroke variability and flash rate/storm evolution.
- Storm propagation speed is inferred from the lightning data, including RMSE, but no insight on its likely validity to overall cell motion from independent sources is provided. For instance, was a 111 kph (31m/s) storm propagation speed feasible for the synoptic conditions of the time? Even accepting the study is purely statistical, the lack of a basic meteorological plausibility assessment makes it difficult for the reader to form an opinion on the reliability of this statistical technique for simulating or tracking other thunderstorms. It appears that all inter-event durations were used for speed estimation. Since values shorter than ~0.5s represent inter-stroke periods, they relate to the spatial distribution of individual strokes within a lightning flash and not storm motion. It is not clear whether this “noise” was accounted for in the estimation of storm speed, or how the development, motion and dissipation of multiple lightning cores within a single storm relative to the overall storm propagation could be accounted for, noting the interesting propagation of fine elements representing these cores (e.g. figure F6) were identified by the authors.
- Consider reducing the number of graphs to the ones which really demonstrate your points.
Technical correction
- Movement speeds were stated with the units of km/h, but it would be more consistent with broader scientific literature to use the SI units of m/s.
Citation: https://doi.org/10.5194/egusphere-2024-2733-RC2 -
AC2: 'Reply on RC2', Uldis Zandovskis, 16 Feb 2026
Dear Referees 1 and 2:
We thank the two referees (R1 and R2) for their careful and substantive comments on both the content and presentation of our NHESS discussion paper “Characterisation and modelling of lightning strikes as point events in time and space” (egusphere-2024-2733).
We thank R1 for noting that the “second half of the paper (from section 4 onwards) appears very novel and is what the authors should emphasise in their revised manuscript” and we agree with R1 that the manuscript can be reduced in size to enhance readability and the overall contribution. We also thank R2 for their detailed comments, and have attempted to address these issues in our comments.
As this is a discussion paper, our replies in the supplement set out (i) how we interpret each comment, and (ii) the specific changes we propose to implement in the revised manuscript. We will ensure that all modifications are incorporated consistently across the paper, figures and tables.
Peer review completion
Post-review adjustments
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-2733', Anonymous Referee #1, 06 Jan 2026
Review of “Characterisation and modelling of lightning strikes as point events in time and space” by Zandovskis et al.
General comments
I have read through this paper and whilst it has some merits, I believe it needs a thorough re-write to be of a reasonable length and accessible to the reviewers and readers. There is so much content presented here that it is very hard to work out what is appropriate and relevant to the investigation and what is just additional material, which could be removed. I have tried to do my best in the remainder of my review, but I feel like it would be best if the authors revise the size of the manuscript down and then resubmit it so I can look through it again and advise on its merits. The paper can really be thought of as two separate halves. The first half is largely unnecessary in my opinion: it is mostly just plotting and re-plotting the lightning data which has been obtained from the Met Office and to me doesn’t add much value to what has already been documented (e.g. by Clark and Webb, 2013 or by Lewis and Silkstone, 2017). Yes, there is some re-clustering here, but it is largely the same data plotted multiple times. The second half of the paper (from section 4 onwards) appears very novel and is what the authors should emphasise in their revised manuscript (and what the reader would be interested in looking through). I do wish the authors all the best with this manuscript and hope to see a revised version in due course.
Major Comments
- Length of the paper. At 66 pages the manuscript it a bit too long for the reader to follow. I also counted 36 figures (including appendices). I suggest that the authors revise the number of pages and figures/tables downwards as this is a bit too long for a reader to follow and understand.
- The novel part of the paper really starts in the authors’ section 4 onwards. Section 3 (which includes 12 figures and tables) over 15 pages appears to be the same data plotted multiple times and I’m not sure how much the additional plots are adding to the paper. Some specifics are below:
a. The same lightning strikes are plotting in three dimensions (northing, easting, time) in figures 2, 3, 4 and 5. You should consider if all these figures are appropriate and if it would be possible to display the same data on just one or two figures.
b. The data presented in figure 8 is the plotted again in figure B2 with different projections. This suggests that the method used to plot the data isn’t that good. Could you instead use 2D subplots (e.g. northing vs time, easting vs time, northing vs easting) instead of a 3D one? This would make the data clearer to visualise.
c. I’m also not sure what the plots in figures 7 and 10 add to the paper (especially in figure 10 where there’s not much spread in the Easting direction).
d. What additional information does Table 2 provide that can’t already be judged from the lightning maps provided? - Similarly, while section 2 is much shorter than section 3, I think you could shrink the size of this section down and provide a smaller Table A1 (just detailing the reference, the natural hazard and a short summary (1-4 words) of the mathematical model). The reader can then read the papers if they need any further information.
- What is the reader meant to understand after studying figure 11? I understand that you want to remove the inter-event data, but this could be shown on a much smaller sample, without having to provide a noisy figure (which is when followed by similar figures in Fig. D1).
- Are Figures F1-F6 and appendix F necessary given the information is summarised in Table 3?
- Overall, what do you want the reader to understand when they read your paper? Emphasize the novel work you have done and don’t include anything which isn’t appropriate to the paper.
Minor Comments
- Repeated citations: there is no need to constantly repeat citations. For example, I can see that Gaffard et al. (2008) is cited in the captions of Figures 1, 5, 6, 8 and 9. It should be possible to just cite once and then
- I can only see two yellow stars on figures 3 and 4, yet I would expect there to be four (2 x radar stations at 2 x times). This may be a function of the way you are plotting the data.
- The text on figure 15 seems a bit grainy, especially in the legends and axis labels. I’m also not sure what the blue #of events bars actually add to your analysis here.
Citation: https://doi.org/10.5194/egusphere-2024-2733-RC1 -
AC1: 'Reply on RC1', Uldis Zandovskis, 16 Feb 2026
Dear Referees 1 and 2:
We thank the two referees (R1 and R2) for their careful and substantive comments on both the content and presentation of our NHESS discussion paper “Characterisation and modelling of lightning strikes as point events in time and space” (egusphere-2024-2733).
We thank R1 for noting that the “second half of the paper (from section 4 onwards) appears very novel and is what the authors should emphasise in their revised manuscript” and we agree with R1 that the manuscript can be reduced in size to enhance readability and the overall contribution. We also thank R2 for their detailed comments, and have attempted to address these issues in our comments.
As this is a discussion paper, our replies in the supplement set out (i) how we interpret each comment, and (ii) the specific changes we propose to implement in the revised manuscript. We will ensure that all modifications are incorporated consistently across the paper, figures and tables.
-
RC2: 'Comment on egusphere-2024-2733', Anonymous Referee #2, 22 Jan 2026
It is unclear what new scientific insight is focussed on in this manuscript. The authors focus exclusively on the statistical description of lightning stroke time and location of six thunderstorms, events of which have already been studied, interpreted and published by other researchers, albeit from a more meteorological perspective. The statistical techniques employed do not appear to be new. The authors do however describe a statistical method of creating synthetic lightning data which may be of use to other researchers in the field, although such value must be considered in the context of readily available real lightning time and location archives from sources such as the one used by this study. The aim of describing different lightning characteristics for different types of thunderstorms, whilst commendable, is not novel and the present discussion is limited to a very small subset which does not include any physical interpretation of the results necessary to usefully apply their empirical statistics to other storms. This raises the question of how much their work furthers natural hazard research or broader statistical modelling within the scope of NHESS, which should be the key focus of any resubmission.
Overall, the authors need to reframe their manuscript to ensure any novelty of their study is more apparent, especially in the context of applying it to improve thunderstorm hazard characterisation beyond what is already established amongst the meteorological research community.
Specific comments
- Need to correctly define the measured physical process under analysis, and not refer to lightning as “strikes”, which is not a well-defined scientific term in this context. ATDnet is a VLF radio receiver network that detects lightning strokes, which are the individual pulses of current occurring during the complete lightning discharge process, known as a flash. Since there are normally several strokes in an individual flash (hence the tendency of lightning to flicker when observed optically), the distinction is therefore important for quantitative interpretation. Consequently, clarity is needed throughout, especially section 4.2 where the inter-stroke period and inter-flash periods are merged into a generalised “inter-event” time period, despite being two very different variables.
- Storm cell tracking algorithms based on lightning location data are not new and are already an evolving but well-established feature in both academic research (including recent NHESS publication) and many commercial real-time lightning location products, although not currently for ATDnet. This is contrary to the authors suggestion of novelty (discussion, line 748-9), so further support will need to be presented to clarify the novelty of their approach.
- Distinction on charts is made over the different statistics for northing and easting spatial characteristics, although given the separation is only due to individual storm propagation direction, it is difficult to see how this distinction can be usefully applied to further understanding of lightning spatial characteristics more generally. Instead, using a coordinate system related to storm propagation direction (which in this case appears approximately linear) may offer more scientific insight in lightning spatial distribution during storm evolution.
- Section 2.1 Line 75. Whilst the authors correctly describe the simplified charge structure of a "typical" thunderstorm, it has been well established in geophysical literature that not all lightning-producing thunderstorms have this basic charge configuration, especially those which produce the severe storms described in this manuscript, which would likely have been at least tripolar.
- Section 5.1 First paragraph is confusing. What is meant by storms being visually different in time? The lack of clarity that the “inter event times” is a convolution of both inter-stroke and inter-flash data means that the removal of “relatively large” or “longer” periods is not well justified in terms of separating physical characteristics. Was the separation therefore made considering changes in flash rate?
- Whilst it is acknowledged that the emphasis of their work is on statistical rather than physics-based modelling, the authors cannot adequately interpret their “inter-event” period statistical distributions without acknowledging that two distinct physical processes are responsible for this distribution. These are inter-stroke (the fundamental output of ATDnet, attributed to current pulses during individual flashes, which will account for the ~0.2s peak) and inter-flash period, which will be the peak around a few seconds duration for these quite active storms, related to the charging processes within the storms. Consequently, figure 13 is largely a function of the storm’s flash rate evolution with time, making the description in terms of inter-event time distribution morphology rather over-complicated for what is a common property used to describe thunderstorm activity. The authors make some association with their inter-event periods and previously published inter-stroke means afterwards in the discussion section (around lines 736-744) suggesting they may be already aware of the underlying physical processes involved, although there is still no explicit link made to their bimodal distribution being a combination of inter-stroke and inter-flash periods. This would also allow exploration of any association between inter-stroke variability and flash rate/storm evolution.
- Storm propagation speed is inferred from the lightning data, including RMSE, but no insight on its likely validity to overall cell motion from independent sources is provided. For instance, was a 111 kph (31m/s) storm propagation speed feasible for the synoptic conditions of the time? Even accepting the study is purely statistical, the lack of a basic meteorological plausibility assessment makes it difficult for the reader to form an opinion on the reliability of this statistical technique for simulating or tracking other thunderstorms. It appears that all inter-event durations were used for speed estimation. Since values shorter than ~0.5s represent inter-stroke periods, they relate to the spatial distribution of individual strokes within a lightning flash and not storm motion. It is not clear whether this “noise” was accounted for in the estimation of storm speed, or how the development, motion and dissipation of multiple lightning cores within a single storm relative to the overall storm propagation could be accounted for, noting the interesting propagation of fine elements representing these cores (e.g. figure F6) were identified by the authors.
- Consider reducing the number of graphs to the ones which really demonstrate your points.
Technical correction
- Movement speeds were stated with the units of km/h, but it would be more consistent with broader scientific literature to use the SI units of m/s.
Citation: https://doi.org/10.5194/egusphere-2024-2733-RC2 -
AC2: 'Reply on RC2', Uldis Zandovskis, 16 Feb 2026
Dear Referees 1 and 2:
We thank the two referees (R1 and R2) for their careful and substantive comments on both the content and presentation of our NHESS discussion paper “Characterisation and modelling of lightning strikes as point events in time and space” (egusphere-2024-2733).
We thank R1 for noting that the “second half of the paper (from section 4 onwards) appears very novel and is what the authors should emphasise in their revised manuscript” and we agree with R1 that the manuscript can be reduced in size to enhance readability and the overall contribution. We also thank R2 for their detailed comments, and have attempted to address these issues in our comments.
As this is a discussion paper, our replies in the supplement set out (i) how we interpret each comment, and (ii) the specific changes we propose to implement in the revised manuscript. We will ensure that all modifications are incorporated consistently across the paper, figures and tables.
Peer review completion
Post-review adjustments
Journal article(s) based on this preprint
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Uldis Zandovskis
Davide Pigoli
Bruce D. Malamud
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(6542 KB) - Metadata XML
Review of “Characterisation and modelling of lightning strikes as point events in time and space” by Zandovskis et al.
General comments
I have read through this paper and whilst it has some merits, I believe it needs a thorough re-write to be of a reasonable length and accessible to the reviewers and readers. There is so much content presented here that it is very hard to work out what is appropriate and relevant to the investigation and what is just additional material, which could be removed. I have tried to do my best in the remainder of my review, but I feel like it would be best if the authors revise the size of the manuscript down and then resubmit it so I can look through it again and advise on its merits. The paper can really be thought of as two separate halves. The first half is largely unnecessary in my opinion: it is mostly just plotting and re-plotting the lightning data which has been obtained from the Met Office and to me doesn’t add much value to what has already been documented (e.g. by Clark and Webb, 2013 or by Lewis and Silkstone, 2017). Yes, there is some re-clustering here, but it is largely the same data plotted multiple times. The second half of the paper (from section 4 onwards) appears very novel and is what the authors should emphasise in their revised manuscript (and what the reader would be interested in looking through). I do wish the authors all the best with this manuscript and hope to see a revised version in due course.
Major Comments
a. The same lightning strikes are plotting in three dimensions (northing, easting, time) in figures 2, 3, 4 and 5. You should consider if all these figures are appropriate and if it would be possible to display the same data on just one or two figures.
b. The data presented in figure 8 is the plotted again in figure B2 with different projections. This suggests that the method used to plot the data isn’t that good. Could you instead use 2D subplots (e.g. northing vs time, easting vs time, northing vs easting) instead of a 3D one? This would make the data clearer to visualise.
c. I’m also not sure what the plots in figures 7 and 10 add to the paper (especially in figure 10 where there’s not much spread in the Easting direction).
d. What additional information does Table 2 provide that can’t already be judged from the lightning maps provided?
Minor Comments