Lightning Interferometry with the Long Wavelength Array

Round 1

Reviewer 1 Report

Review is attached

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

I have had the pleasure of reviewing your manuscript, and I would like to commend you on your excellent work. The topic is of great relevance and interest, and your approach to it is both innovative and thorough. 

The introduction does a superb job of setting the context and highlighting the importance of the research question. The literature review is comprehensive and up-to-date, providing a solid foundation for your study. 

Your methodology is well explained and appropriately rigorous, and the results are clearly presented and convincingly argued. The discussion is insightful, linking your findings back to the broader literature and highlighting their implications. 

The writing is clear and concise, making the paper a pleasure to read. The figures and tables are well designed and effectively support the text. 

In conclusion, I believe this paper makes a significant contribution to the field and I recommend it for publication. I look forward to seeing this work published and anticipate it will be well received by the community.

Author Response

Thank you very much for your kind comments

Reviewer 3 Report

This is a very interesting paper mainly about the interferometry technique for the LWA. It is well written and well organized. Although there is not much new scientific discovery in this paper, it will provide the theoretical foundation for future researches based on the LWA. I have only a few very minor comments, and I think this paper can be published without further reviews.

1. It seems that the length of each trigger is 250 ms (at least for the example flash). How long is the pre-trigger length?

2. The observation of the positive leader is very interesting, and I agree the LWA was seeing radiation directly from the positive leader tip. The exceptionally fast speed of the positive leader is especially interesting. The authors may point out that positive leader speeds estimated from retrograde negative leaders in previous studies were almost always in the range of 1~3*10^4 m/s. Apart from the citations 35-37, the authors may also cite Wu et al. (2019, doi:10.1029/2019JD030783), Lapierre et al. (2014, doi:10.1002/2014JD022080), Shao and Krehbiel (1996, doi:10.1029/96JD01803). The authors may also provide a bit more discussions on why the positive leader has such high speed.

"was" in L263 -> were

"windown" in L347 -> window

Author Response

1. It seems that the length of each trigger is 250 ms (at least for the example flash). How long is the pre-trigger length?

The data is streamed continuously into a 5-second buffer, which allows us to have arbitrary pre- and post-trigger lengths. The LWA self-triggers, using the signals from a subset of the antennas as the trigger input. The output files do not actually retain information about the pre- and post-trigger lengths used, and so I’m not sure how the system was configured for the flash in this study.  This has been made more clear in the text.  

2. The observation of the positive leader is very interesting, and I agree the LWA was seeing radiation directly from the positive leader tip. The exceptionally fast speed of the positive leader is especially interesting. The authors may point out that positive leader speeds estimated from retrograde negative leaders in previous studies were almost always in the range of 1~3*10^4 m/s. Apart from the citations 35-37, the authors may also cite Wu et al. (2019, doi:10.1029/2019JD030783), Lapierre et al. (2014, doi:10.1002/2014JD022080), Shao and Krehbiel (1996, doi:10.1029/96JD01803). The authors may also provide a bit more discussions on why the positive leader has such high speed.

These citations have been added.

Some additional discussion on the speed of the positive leader has been added, although there is no conclusive answer to why it is propagating so fast.

"was" in L263 -> were

Done

"windown" in L347 -> window

Done

Reviewer 4 Report

The manuscript describes the use of Long Wavelength Array (LWA) interferometer located in La Joya, New Mexico, to image the details of lightning activity. This system is composed of 255 dual horizontally polarized VHF antennas operating in the 3-88Mhz range (with a 39.6Mhz bandwidth) and can store 1584 8-bits complex amplitudes in a 5s triggered buffer after FFT conversion.

 

The introduction provides enough background for the reader to understand the main purpose of the work. The main objective is, by using a high-sensitive LWA, to provide even more details of the lightning physical processes by measuring multiple VHF sources simultaneously. However, the authors did not mention the Lightning Mapping Array (LMA) technology, developed by the Los Alamos National Lab in USA and the Interferometer Lightning Mapping Array (InLMA) technology, developed by the Gifu University in Japan. Both systems can provide spectacular 3D description of the lightning processes in the same way of the LOFAR and LWA interferometers.

 

The methodology description discuss how data is produced by the LWA interferometer, how the projected image is computed, the identification of the VHF sources (deconvolution), and the calibration of the antenna signals to minimize the cable delay effect. 

 

The results show the characteristics, limitations, and thresholds of the multi-source detection data. A case of positive leader tracing was presented as an example of how the high-sensitive system can simultaneously identify multiple VHF sources and provide extra details from propagation of negative and positive leaders within the cloud.

 

The manuscript is in good shape generally, however there are some points that requires some clarifications before publishing it. 

 

Lines 87-96 and Lines 424-429 - Why do you need to convert back the frequency domain observations instead of using the direct time domain observations made at 204.8MS/s? It seems that the temporal resolution (~4.88ns) of the time domain observation is far enough since the integration period shall be longer than 25ns. By FFT transforming the initial signal and then converting it back to the time domain, aren't you degrading the quality of your original observation?

 

Figure1b and Lines 438-447 - Since the VHF sources are located over a projected image over the surface (Equation 1 defines the image of a source in a 2D plan), the authors shall explain how elevation is computed from the imaging algorithm.  

 

Lines 224-229 - The corresponding lightning pulses were detected by the ENTLN about 7.6km away from the LWA location. Figure 1a shows the directions of the pulses located by the ground-based network. As far as I understand, the LWA is capable to map the lightning propagation (all thousands of VHF sources) only when the flash is almost over it because the gain is maximum at zenith and minimum at the horizon. Since the pulses occur "out of the LWA FOV" (according to EN), how the LWA was able to map a lightning flash that occur ~7.6km away from it?

 

Equation (7) - If sigma(i) is the delay correction of the ith antenna (the unknown variable of the linear system), what is sigma(j)? Is sigma(j) also part of the linear system to be solved? Please clarify this math.

 

Lines 267-268 – Once again, the authors shall discuss observations done by the LMA systems to assure that your observations really have not been made before.

 

Figure 6 is quite confused. The grey scale refers to the leader propagation 264ms after 00:15:15UT. Then, at 264ms, the leader tip got tracked (color coded points). What is the “solid” gray line that extends over the positive branch? Is that a previous channel? Of course, negative / positive channels are inferred based on previous knowledge of lightning bipolar initiation processes. In the LWA, the visible light of VHF sources is detected, which does not allow to identify the corresponding polarity of the sources. It is also not clear how needles are identified since their power is several times lower than the tips. The authors shall better explain Figure 6 and rewrite its description (Lines 369-405). I suggest changing Figure 6 to include a clear identification of needles and tips. 

Author Response

The introduction provides enough background for the reader to understand the main purpose of the work. The main objective is, by using a high-sensitive LWA, to provide even more details of the lightning physical processes by measuring multiple VHF sources simultaneously. However, the authors did not mention the Lightning Mapping Array (LMA) technology, developed by the Los Alamos National Lab in USA and the Interferometer Lightning Mapping Array (InLMA) technology, developed by the Gifu University in Japan. Both systems can provide spectacular 3D description of the lightning processes in the same way of the LOFAR and LWA interferometers.

Given the scope of this study, we have limited the discussion in the introduction to purely interferometric based systems.  The lightning mapping array (developed at New Mexico Tech and not Los Alamos National Lab) is a purely time-of-arrival based system rather than an interferometer, and so was not discussed. While we don’t discuss the instrument in the introduction, there is some discussion of relevant studies made using it in the discussion.  

The recent inLMA paper has been added to the list of general citations on broadband lightning interferometers.  We also took this opportunity to add a citation to the 1985 Richaed and Auffray study.  The body of literature for broadband digital interferometers is extremely large. We have attempted to include at least one citation from each research group on broadband interferometers, but have almost certainly missed some.

Lines 87-96 and Lines 424-429 - Why do you need to convert back the frequency domain observations instead of using the direct time domain observations made at 204.8MS/s? It seems that the temporal resolution (~4.88ns) of the time domain observation is far enough since the integration period shall be longer than 25ns. By FFT transforming the initial signal and then converting it back to the time domain, aren't you degrading the quality of your original observation?

This conversion to the frequency domain is a current limitation of the system. The conversion is indeed lossy, and results in artifacts which are mentioned in the discussion. Unfortunately, there is no easy fix for this. The data are compressed this way so that there is enough network bandwidth to transfer the data from the FPGA based acquisition board to the 5 second buffer continuously. Streaming the input time series to the buffer would increase the bandwidth by a factor of 4 or more and is not possible without a hardware upgrade. That said, the LWA is looking into possibly adding this support in a scheduled upcoming upgrade to the instrument. 

Figure1b and Lines 438-447 - Since the VHF sources are located over a projected image over the surface (Equation 1 defines the image of a source in a 2D plan), the authors shall explain how elevation is computed from the imaging algorithm.

It seems that some of the labels used in our figures, while technically accurate, are a little confusing. In Figure 1b (and indeed the entire paper) the term “elevation” is reserved for elevation angle, not the height above the ground. This is an unfortunate ambiguity of the English language. We have revised the labels and text to hopefully make this more clear.

Lines 224-229 - The corresponding lightning pulses were detected by the ENTLN about 7.6km away from the LWA location. Figure 1a shows the directions of the pulses located by the ground-based network. As far as I understand, the LWA is capable to map the lightning propagation (all thousands of VHF sources) only when the flash is almost over it because the gain is maximum at zenith and minimum at the horizon. Since the pulses occur "out of the LWA FOV" (according to EN), how the LWA was able to map a lightning flash that occur ~7.6km away from it?

The LWA is very sensitive, and is capable of detecting distant lightning in the sensitivity minimum of the antennas. However, due to basic geometry, the elevation angles of these distant flashes are always very close to the horizon, removing a lot of the detail from the maps. Generally, the detail of the maps is particularly good if the direction to the sources is above 30 degrees elevation, which is the case for almost all of the example flash (there is one positive channel propagating away from the LWA which goes to lower elevation angles). A source which is 7600 meters away from the LWA at the estimated altitude of 6200 meters above the ground would have an elevation angle of 39 degrees. The positive leader discussed in the paper propagated towards the LWA, and so is at a higher elevation angle.

Note, we do not depict the elevation angles to the ENTLN sources because the altitude information provided for the ENTLN locations is not good enough to do so with any level of accuracy. This is also why we estimated the altitude of the flash from the ENTLN plan locations, rather than their altitudes.

Equation (7) - If sigma(i) is the delay correction of the ith antenna (the unknown variable of the linear system), what is sigma(j)? Is sigma(j) also part of the linear system to be solved? Please clarify this math.

sigma_j is the delay correction for the jth antenna, and is part of the linear system to be solved.  Equations have been updated to address this issue, and ones like it. 

Lines 267-268 – Once again, the authors shall discuss observations done by the LMA systems to assure that your observations really have not been made before.

I believe you mean lines 367-368. Because the LMA is a time-of-arrival system, it requires an identifiable peak to be able to locate emission. This makes it not so good at locating continuously radiating radio sources. In the case of the positive leader tips, their emission is below the galactic background radiation level, and so a single LMA sensor would never have triggered on the tip emission.  We have added a few citations of LMA observations in the positive breakdown regions of flashes to the discussion though.  

Figure 6 is quite confused. The grey scale refers to the leader propagation 264ms after 00:15:15UT. Then, at 264ms, the leader tip got tracked (color coded points). What is the “solid” gray line that extends over the positive branch? Is that a previous channel? Of course, negative / positive channels are inferred based on previous knowledge of lightning bipolar initiation processes. In the LWA, the visible light of VHF sources is detected, which does not allow to identify the corresponding polarity of the sources. It is also not clear how needles are identified since their power is several times lower than the tips. The authors shall better explain Figure 6 and rewrite its description (Lines 369-405). I suggest changing Figure 6 to include a clear identification of needles and tips.

The thin grey line is the path followed by the positive leader, determined by looking at the interferometer map at a later time.  Figure 6 has also been annotated with arrows indicating the positive leader tips, and the needles.  

Emission classification is done entirely by visual inspection. While that may seem imperfect, it has been done this way regularly by many researchers for some time. Negative and positive leaders look quite different from one another both in optical and in VHF, with the negative leaders being larger and fuzzier than their positive counterparts. The visual distinction between the leader polarities has been used for VHF classification for some time now, and is the basis of ‘charge analysis’ done at storm scales with the LMA. More recently, there have been some successful attempts at developing ML algorithms to automate the process.

Needle emission is the flickering emission seen in the VHF that is seen along an extended portion of the positive leader channel. The definition of needles in the literature is a little more vague since there is no minimum or maximum length scale for what might be considered a ‘needle’. Still, similar to the situation with positive and negative channels, with some experience needles are readily identified visually.

Round 2

Reviewer 1 Report

In the second revision of “Lightning Interferometry with the Long Wavelength Array,” Stock et al. have significantly added to the paper by including a simulation of their point-spread function and how two sources could interfere (among other minor changes). I believe this tremendously improves the paper as it gives an initial guess as to the scale and types of artifacts that the processing produces, and I believe significantly helps interpretation of this and future works.

This is the first work in the lightning community to employ deconvolution, and (as far as I am aware) the first to see the tip of an intracloud positive leader. Thus, while I could quibble further about details, I think it is a good work that should be published without further revision. 

 

Reviewer 4 Report

The authors have well addressed my comments and questions. Figures were reviewed and became more clear. On my point of view, the paper is ready for publication.