A Time Delay Calibration Technique for Improving Broadband Lightning Interferometer Locating

Round 1

Reviewer 1 Report

Review of “A time delay calibration technique for improving broadband lightning interferometer locating” submitted to Remote Sensing by Liu et al.

 This manuscript presents a so-called time delay calibration technique that is specifically designed to process broadband lightning interferometer data. Its primary objective is to address the issue of elevated levels of noise in the location results that arise when the data analysis window is shortened. The paper is suitable for the journal of Remote Sensing since the time delay is an essential process for lightning interferometry. However, I find it is a more technical report than an academic paper. There are some issures that should be addressed before the paper can be accepted for publication.

1.      The technique presented in this manuscript is not entirely new as authors acknowledge in lines 100-102. The authors show that directly narrowing the correlation window can lead to noise due to phase ambiguity, and using a wider window to adjust signals can solve this ambiguity. Such a technique is not calibration since the time delay between different antennas is not an error. Shao et al. (2020) refer to this processing as beam steering interferometry. The authors should re-evaluate their contribution to this technique. Li et al. (2021) discussed lightning  interferometry algorithm  in the same journal of Remote Sensing.

References :

Li, F., Sun, Z., Liu, M., Yuan, S., Wei, L., Sun, C., Lyu, H., Zhu, K., Tang, G. A new hybrid algorithm to image lightning channels combining the time difference of arrival technique and electromagnetic time reversal technique. Remote Sensing. 2021，13，4658.

Shao, X.-M., Ho, C., Bowers, G., Blaine, W., & Dingus, B. (2020). Lightning  interferometry uncertainty, beam steering interferometry, and evidence of  lightning being ignited by a cosmic ray shower. Journal of Geophysical Research: Atmospheres, 125, e2019JD032273. https://doi.org/10.1029/2019JD032273

2. In Figures 4 and 5, the authors compare the effects of using windows of different lengths directly. However, the conclusion is unsurprising since it is widely known that using a smaller window can induce errors because the window length determines the maximum time delay.

3. The authors should provide a quantitative indicator to evaluate the result instead of assuming that more location points are better. Figure 6 shows that using a window of 32 points can lead to noisy location results, and the authors should clarify what standard they used to determine a "better location."

4. The authors should analyze whether using a smaller window produces better location results. After aligning the signal from different antennas, how do the location results compare when using windows of different lengths? This analysis is crucial since it would provide insight into the practical use of the technique presented in this manuscript.

5. In my opinion, the authors should consider shortening the paper and adding new analyses that reflect their contribution to this technique.

6. Based on the content of the paper, I believe that it should be classified as a technical note, not an article.

The English needs to be edited.

Author Response

Thank you for your valuable feedback. We sincerely appreciate your comments and have carefully considered the issues you raised. In our response, we address each of your concerns individually.

This manuscript presents a so-called time delay calibration technique that is specifically designed to process broadband lightning interferometer data. Its primary objective is to address the issue of elevated levels of noise in the location results that arise when the data analysis window is shortened. The paper is suitable for the journal of Remote Sensing since the time delay is an essential process for lightning interferometry. However, I find it is a more technical report than an academic paper. There are some issues that should be addressed before the paper can be accepted for publication.

1. The technique presented in this manuscript is not entirely new as authors acknowledge in lines 100-102. The authors show that directly narrowing the correlation window can lead to noise due to phase ambiguity, and using a wider window to adjust signals can solve this ambiguity. Such a technique is not calibration since the time delay between different antennas is not an error. Shao et al. (2020) refer to this processing as beam steering interferometry. The authors should re-evaluate their contribution to this technique. Li et al. (2021) discussed lightning interferometry algorithm in the same journal of Remote Sensing.

response 1

Indeed, as mentioned in our manuscript, the time delay calibration method employed in our study exhibits similar effects to the approach proposed by Shao et al. (2020). However, there are differences in technical details. The beamforming steering interferometry technique described by Shao et al. (2020) firstly locates the signal in the selected window in two dimensions, then aligns the waveforms according to the time delay relationship determined by the preliminary locating result, and finally locates the signal again by using the same analysis window. In contrast, our method is to estimate the time delay in a longer window, then align the waveforms according to the obtained time delay, and then use a shorter analysis window to locate the data. This processing can be understood as aligning the signals within the longer window using the time delay of the strongest signal, and subsequently segmenting and extracting data using a smaller window for precise time delay estimation. The overall effect is a reduction in the relative time delays of all radiation source signals within the larger window. This approach ensures that signals within the shorter analysis windows tend to originate from the same radiation source and mitigates errors in the cross-correlation calculation process caused by the inconsistent data in the window. This also answers what the reviewer mentioned: "such a technique is not calibration since the time delay between different antennas is not an error", that is, the time delay of the strongest signal in a longer window is not an error, but the alignment operation based on it makes the result of time delay estimation using a shorter window no longer wrong or more accurate, which makes the calculation result calibrated.

Furthermore, this kind of processing method of processing data step by step to obtain more accurate calculation results is indeed a consensus of the majority of researchers when obtaining as accurate calculation results as possible with a small amount of calculation, not only Shao et al. (2020) and Li et al. (2021), but also Fan et al. (2018), Lyu et al. (2014) mentioned in this paper and the supplementary reference Scholten et al. (2021) and so on. All of these works exhibit unique characteristics in terms of their equipment and implementation methods, aiming to maximize the utilization of data and obtain the most precise observational results achievable. As far as this work is concerned, the article not only introduces our technical details but also hopes to share the results and related experiences. Taking the work of Shao et al. (2020) and Li et al. (2021) as an example, if our time delay calibration method is used in the first step of “TDOA” calculation, it may also bring some optimization effects for the subsequent positioning calculation.

As an improvement, we added descriptions: “The combination of time delay estimation direction finding and time-reversal direction finding techniques can alleviate the computational complexity issue that arises when using the time-reversal method alone” and related references in the revised manuscript from line 107 to line 110. In the discussion section of lines 398 to 402, a description: “In this method, the signals within the primary window are aligned first using the time delay relationship of the strongest signal, and then the precise time delay is obtained by using a smaller analysis window. This approach allows better matching of the signals within the shorter analysis window and therefore reduces errors caused by the inconsistent data in the window.” is added.

References:

Fan, X.P.; Zhang, Y.J.; Zheng, D.; Zhang, Y.; Lyu, W.T.; Liu, H.Y.; Xu, L.T. A New Method of Three-Dimensional Location for Low-frequency Electric Field Detection Array. J. Geophys. Res. Atmos. 2018.

Lyu, F.; Cummer, S.A.; Solanki, R.; Weinert, J.; McTague, L.; Katko, A.; Barrett, J.; Zigoneanu, L.; Xie, Y.; Wang, W. A low-frequency near-field interferometric-TOA 3-D Lightning Mapping Array. Geophys. Res. Lett. 2014, 41, 7777-84.

Li, F.; Sun, Z.; Liu, M.; Yuan, S.; Wei, L.; Sun, C.; Lyu, H.; Zhu, K.; Tang, G. A New Hybrid Algorithm to Image Lightning Channels Combining the Time Difference of Arrival Technique and Electromagnetic Time Reversal Technique. Remote Sens. 2021, 13, 4658. 

Shao, X.M.; Ho, C.; Bowers, G.; Blaine, W.; Dingus, B. Lightning Interferometry Uncertainty, Beam Steering Interferome-try, and Evidence of Lightning Being Ignited by a Cosmic Ray Shower. J. Geophys. Res. Atmos. 2020, 125.

Scholten, O.; Hare, B.M.; Dwyer, J.; Sterpka, C.; Kolmašová, I.; Santolík, O.; Lán, R.; Uhlíř, L.; Buitink, S.; Corstanje, A.; et al.. The Initial Stage of Cloud Lightning Imaged in High‐Resolution. JGR Atmospheres. 2021, 126.

2. In Figures 4 and 5, the authors compare the effects of using windows of different lengths directly. However, the conclusion is unsurprising since it is widely known that using a smaller window can induce errors because the window length determines the maximum time delay.

response 2

As mentioned by the reviewer, "It is widely known that using a smaller window can induce errors because the window length determines the maximum time delay." In our study, the observation utilized baseline lengths of approximately 15m, resulting in a maximum time difference of around 70 ns (hypotenuse). This value is smaller than the analysis window lengths used in Figure 4, which were 256 ns and 128 ns. Therefore, it falls within the permissible range for time delay estimation. Initially, we suspected that the noise observed in Figure 4 (a, c) was caused by invalid signals in the data when using such analysis windows. However, during the testing of the time calibration method using our observational data, we found that the majority of the noise was successfully localized after calibration. This outcome holds certain reference significance in our observational practice.

3. The authors should provide a quantitative indicator to evaluate the result instead of assuming that more location points are better. Figure 6 shows that using a window of 32 points can lead to noisy location results, and the authors should clarify what standard they used to determine a "better location."

response 3

Indeed, as the reviewer has expressed concerns, a higher number of location results does not necessarily indicate better performance. In our manuscript, we describe the increase in the number of location points after time calibration as a beneficial impact for three reasons.

Firstly, in Figure 4, the increase in the number of location points after applying the time calibration method is a positive outcome because it enables the resolution of previously unsolvable data segments. This demonstrates the beneficial effect of the time calibration method and effectively improves the time resolution of the location results.

Secondly, in Figure 6, even with a 32 ns analysis window, the number of localized results steadily increases and remains concentrated in the area where lightning events occur. This work explores whether the time resolution capability of the location results can be further enhanced under a sampling rate of 1 GS/s, utilizing the aid of time calibration.

Lastly, as observed, after using a 32 ns analysis window, the location results exhibit some noise. Therefore, we further analyze the characteristics of signal intensity and correlation coefficients corresponding to the location results. We explain that the scattered points correspond to data with weaker intensities and smaller correlation coefficients. This finding not only highlights the second beneficial effect brought by time calibration, i.e., the ability to separate weaker radiation sources but also raises the issue of quality control, which the reviewer also inquired about: "What standard they used to determine a 'better location.'"

We believe that the notion of "better" location results largely depends on the purpose of the data usage. Firstly, objectively speaking, more accurate location results are considered better, as mentioned earlier, the time calibration technique improves the accuracy of time estimation, resulting in an increased number of location results, which are regarded as better. However, lightning is a complex phenomenon, and this has always been a challenge faced by lightning detection techniques. Until lightning detection techniques reach perfection, our research on location results still requires subjective judgment based on specific applications.

As illustrated in the example provided in lines 447-453 of our manuscript, "If the main goal is to show a clear discharge path, a relatively high correlation coefficient threshold can be used to eliminate sporadic locating points around the channel so that the distribution path of the locating results can be as clear and concentrated as possible. However, if the analysis of lightning discharge involves the spatial range or discharge details of specific discharge events, the quality control scheme should choose a slightly lower correlation coefficient threshold to retain some discrete locating points around the main path."

In summary, the determination of "better location" depends on the specific purpose of the data analysis, and in our study, we highlight the importance of subjective judgment based on the application requirements and provide guidance on adjusting the correlation coefficient threshold accordingly.

4. The authors should analyze whether using a smaller window produces better location results. After aligning the signal from different antennas, how do the location results compare when using windows of different lengths? This analysis is crucial since it would provide insight into the practical use of the technique presented in this manuscript.

response 4

As mentioned by the reviewer, the choice of analysis window length and its impact on location results is crucial. As illustrated in Figure 8 of our manuscript, the distribution of location results with different correlation coefficients varies across different lightning physical processes when using a 32ns window. In fact, when analyzing specific lightning physical processes, the selection of window length is also an aspect of quality control for locating. As previously mentioned, this may depend on the specific analysis at hand. In future research focusing on specific lightning physical processes, we will further investigate and address this issue.

5. In my opinion, the authors should consider shortening the paper and adding new analyses that reflect their contribution to this technique.

response 5

As mentioned earlier, this paper not only presents the technical details of our time-delay calibration but also demonstrates the improvement achieved by this technique in our observations. The proposed technique itself exhibits certain differences compared to similar works, and the equipment and observational parameters used have their characteristics. Moreover, as mentioned in the response to the first question, this work can be mutually beneficial and informative when compared to similar studies. To further elucidate the improvement brought about by this method, we provide additional explanations in the discussion section at lines 398-402 as mentioned in response 1.

6. Based on the content of the paper, I believe that it should be classified as a technical note, not an article.

response 6

Based on the comprehensive responses to the previous questions, we have made modifications and improvements to the manuscript, and we believe that the current content is in line with the focus of the journal.

Author Response File: Author Response.docx

Reviewer 2 Report

The reviewer feels the difficulty to understand if this article is based on TOA or digital interferometer because the authors do not refer on phase difference of VHF pulses. 

On the other hands because of the calibration of time delay procedure, caliculated results show the clear inprovement. From this aspect the article is worth to be published. the followings are the requirement to be accepted.

1. Clear discussion on ITF

2. If not, change the title of article to be TOA system. 

Author Response

Thank you for your valuable feedback. We sincerely appreciate your comments and have carefully considered the issues you raised. In our response, we address each of your concerns individually.

The reviewer feels the difficulty to understand if this article is based on TOA or digital interferometer because the authors do not refer on phase difference of VHF pulses. 

On the other hands because of the calibration of time delay procedure, caliculated results show the clear inprovement. From this aspect the article is worth to be published. the followings are the requirement to be accepted.

1. Clear discussion on ITF

response 1

Thank you for the suggestions provided by the reviewer. Indeed, in our understanding, a pure interferometer should first meet the following requirements on the observation equipment: 1) Sufficient distance between the antenna array and the radiation source to satisfy the plane wave incidence assumption, and 2) Strict synchronization of the data acquisition devices to ensure coherence among the signals from different channels. In the locating calculation, the phase difference information between different channels is initially solved in the frequency domain. Subsequently, the direction of arrival is calculated based on the plane wave incidence model.

For broadband interferometers, during the locating calculation, although phase difference from multiple frequencies can be obtained from each analysis window, it is generally assumed that all frequencies originate from the same direction. In this case, the unwrapping calculation can be performed using the slope of the phase difference spectrum or the time delay of the incident signal, and then calculate the incident direction of the radiation source signal through the phase differences. However, as observational research has evolved, some researchers have started using time delay estimation methods directly for the direction of arrival calculation. This kind of calculation method still utilizes the plane wave incidence model and assumes that each analysis window contains only one radiation source. These methods can be considered as a time-domain approach for interferometric direction finding, and are equivalent to those obtained in the frequency domain.

Therefore, the equipment and observation scheme used in our study fully satisfy the requirements of interferometric direction finding, and the calculation method employed is a time-domain solution based on the plane wave model for interferometer direction finding.

As a supplement, we have added the following content in lines 38 to 43: " In TDOA systems, each lightning radiation source is considered as a point in space, emitting electromagnetic waves that propagate through space in the form of spherical waves. Such systems could provide three-dimensional (3D) source location accuracy on the order of tens of meters with a temporal resolution on the order of tens of microseconds. In interferometric systems, the electromagnetic wave from each radiation source is treated as a plane wave arriving at each pair of antennas. ", and in lines 90 to 99: " For broadband interferometers, during the locating computation, although the cross-power spectrum of the data from each analysis window contains phase difference information from multiple frequencies, it is generally assumed that all frequencies originate from the same incident direction. In this case, we can either utilize the slope of the phase difference spectrum, which corresponds to the time delay of the incident signal, to unwrap the phase differences and determine the incident direction based on the phase difference information. Alternatively, we can directly employ the time delay estimation method for incident direction computation. This approach can be considered as a time-domain solution for interferometric direction finding. ".

Citation [27] is a newly added document: " Akita, M.; Stock, M.; Kawasaki, Z.; Krehbiel, P.; Rison, W.; Stanley, M. Data processing procedure using distribution of slopes of phase differences for broadband VHF interferometer. J. Geophys. Res. Atmos. 2014, 119, 6085-104.".

2. If not, change the title of article to be TOA system.

response 2

As mentioned in response 1, we think that the equipment and observation scheme used in our study fully satisfy the requirements of interferometric direction finding, and the calculation method employed is a time-domain solution based on the plane wave model for interferometer direction finding.

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments for author File: Comments.pdf

Author Response

Thank you for your valuable feedback. We sincerely appreciate your comments and have carefully considered the issues you raised. In our response, we address each of your concerns individually.

The paper by Liu et al shows a new technique to significantly reduce the noise sources which are produced when using short analysis windows in a broadband interferometer. The paper is well written and should be published after minor revisions. The authors do a good job with the figures they use to display the results.

My main complaint is that the authors do not explain why their technique works. The only explanation is in Lines 269-272 where the authors state “... time delay calibration roughly aligns the signals within each analysis window, making the signals tend to come from the same radiation source." I do not think that is the reason for dramatically reducing the number of noise sources. When the signals are not shifted a significant amount of the waveform from Channel A is not in the waveform from Channel B and a significant amount of the waveform from Channel B is not in the waveform for Channel A. This will probably lead to an incorrect value of the time delay. With smaller windows the proportion of signals from one antenna not in the other antenna gets larger-with a 128 sample window and a 50 ns delay between antennas almost half of the waveform from one antenna is not in the waveform from the other antenna which will almost certainly result in an incorrect value for Δt_n.

When using a data window of 2,002 data points almost all the waveforms from the two antennas match and almost all the waveforms are from approximately the same region of the lightning flash so there are very few time delays with large errors- this is why there are very few noise sources in Figure 2 using 1024 point windows, and presumably there would be even fewer noise sources in the authors showed a plot using 2002 point windows. Once the waveforms are shifted by τ₀. the two waveforms now align well. Using smaller windows now means that there is very little mismatch between the two windows. The value of τ_n in each secondary window is presumable much smaller the τ₀. For example, if τ₀ is 50 ns and τ_n is 5 ns, then even with a 32 point window almost all the waveform in the window from antenna A is in the waveform from antenna B.

A possible way to improve the method would be to find τ₀ using 2002 point windows. Shift the waveforms using this value. Then use 1024 point windows to find a τ₁. Shift the waveforms by this amount (τ₀ +τ₁.). Then go to 512 point windows to find τ₂. Keep shifting the waveforms as the windows get progressively smaller and smaller. The only issue I had with reading the paper is that in Figure 5 the authors use “N" and “O" without explaining what those are. One can figure it out by reading the text, but the authors should but an explanation in the figure caption, something like “Results of the original method (“O") are shown in white, and results from the new method using time delay calibration “N" are shown in blue". In summary I recommend publishing the paper after an explanation of why the technique works is added.

Response

Thank you very much for the valuable evaluation and suggestions. Indeed, as you mentioned, this method improves the matching degree of signals from different channels within the analysis window through time delay calibration. We fully agree with your suggestion that using progressively smaller windows for finer-level time delay calibration may lead to better time delay estimation results. As a supplement, we have added the following content in the discussion section, lines 398 to 402: " In this method, the signals within the primary window are aligned first using the time delay relationship of the strongest signal, and then the precise time delay is obtained by using a smaller analysis window. This approach allows better matching of the signals within the shorter analysis window and therefore reduces errors caused by the inconsistent data in the window. " providing further explanation on the reasons behind the effectiveness of the time delay calibration method.

The issue you pointed out in Figure 5 is indeed our oversight, and we have made the necessary correction to the figure caption in the revised manuscript: " The white color represents the results obtained by the original calculation method(Marked as “O” in the legend), and the blue color represents the results obtained after time delay calibration(Marked as “N” in the legend) ". 

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Author Response File: Author Response.docx

Reviewer 4 Report

In their introduction the authors appear unfamiliar with the recent developments in the field of VHF imaging. In particular they should refer to https://doi.org/10.1038/s41586-019-1086-6 where it is shown for the first time that even meter scale accuracy can be reached with a 3D interferometer using LOFAR VHF-broadband antennas. In a paper https://doi.org/10.1103/PhysRevD.105.062007 it is shown from simulations that the resolution is in fact much better and can be argued to be of the order of cm for 3dimensional imaging. Essential is indeed the time calibrations of the antennas, where a procedure to achieve this is discussed in https://doi.org/10.1029/2020JD033126. All three papers are most relevant for the present work and these need to be worked into a thoroughly rewritten introduction.

In the article a considerable improvement of the image quality is reported due to the time-calibration procedure, which is a significant result. From the article it was not clear what kind of timing accuracy is achieved and how this compares with the results of the LOFAR calibration.

In relation to the remarks on lines 410-412, the authors should be aware that in one of the two imaging methods used in LOFAR (the Impulsive imager, see https://doi.org/10.1029/2020JD033126 ) also a chi^2 fitting procedure is applied.

Author Response

Thank you for your valuable feedback. We sincerely appreciate your comments and have carefully considered the issues you raised. In our response, we address each of your concerns individually.

1 In their introduction the authors appear unfamiliar with the recent developments in the field of VHF imaging. In particular they should refer to https://doi.org/10.1038/s41586-019-1086-6 where it is shown for the first time that even meter scale accuracy can be reached with a 3D interferometer using LOFAR VHF-broadband antennas. In a paper https://doi.org/10.1103/PhysRevD.105.062007 it is shown from simulations that the resolution is in fact much better and can be argued to be of the order of cm for 3dimensional imaging. Essential is indeed the time calibrations of the antennas, where a procedure to achieve this is discussed in https://doi.org/10.1029/2020JD033126. All three papers are most relevant for the present work and these need to be worked into a thoroughly rewritten introduction.

Response 1

Thank you for the valuable suggestions. In fact, we have been following the research progress related to LOFAR since the appearance of some relavent reports and presentation slides on the internet. The fine 3D lightning locating effect provided by LOFAR system are really great. It was indeed an oversight on our part to forget mentioning LOFAR in the introduction of the manuscript, as we focused on the typical lightning locating system such as lightning interferometer and LMA, and failed to think of LOFAR, an observation system with "interdisciplinary" significance. We have now included relevant information and references regarding LOFAR in lines 48 to 53 of the manuscript: " In recent years, the radio astronomy telescope LOFAR (LOw Frequency ARray) has achieved highly precise 3D lightning location results with a high temporal-spatial accuracy, utilizing its wide-ranging and high-density VHF signal receiving array. It can be considered as an advanced TDOA lightning localization system, incorporating certain technical features of existing broadband lightning interferometers.".

2 In the article a considerable improvement of the image quality is reported due to the time-calibration procedure, which is a significant result. From the article it was not clear what kind of timing accuracy is achieved and how this compares with the results of the LOFAR calibration.

Response 2

The system we used employed 4 synchronized data acquisition channels from oscilloscopes with a sampling rate of 1 GS/s and a vertical resolution of 8 bits. To improve the stability of the sampling clock, the oscilloscopes utilized a 10 MHz signal from a GPS device's OCXO temperature-compensated crystal oscillator. In comparison, the system in the paper utilized an antenna array much smaller in scale than that of LOFAR, an OCXO with lower clock stability than LOFAR's atomic clock, lower vertical resolution in data acquisition, but a significantly higher sampling rate than LOFAR. From a location technology perspective, these are indeed two different systems. In terms of three-dimensional location accuracy, as previously reported in our work, the achieved accuracy is on the order of hundreds of meters[1], far inferior to LOFAR. However, in terms of the two-dimensional resolution capability for single-site direction finding, this system possesses the ability to resolve small-scale discharge processes with fine resolution too[2]. Recent observational study of similar systems have also demonstrated that interferometer systems possess resolution capabilities for small-scale discharge events comparable to LOFAR[3]. LOFAR is large in scale, technologically advanced, and works in three-dimensional locating. Conversely, traditional lightning interferometer systems are smaller in scale, convenient for observation, and, when properly configured, can achieve higher time resolution and two-dimensional spatial resolution.

To highlight the differences between the lightning location systems, we have supplemented and adjusted the explanations in lines 38 to 46 of the paper as follows: " In TDOA systems, each lightning radiation source is considered as a point in space, emitting electromagnetic waves that propagate through space in the form of spherical waves. Such systems could provide three-dimensional (3D) source location accuracy on the order of tens of meters with a temporal resolution on the order of tens of microseconds. In interferometric systems, the electromagnetic wave from each radiation source is treated as a plane wave arriving at each pair of antennas. Despite having a smaller physical footprint, interferometric systems can provide high-precision two-dimensional (2D) locations with temporal resolutions on the order of microseconds, but slightly less accurate 3D locations so far compared to TDOA location systems.".

3 In relation to the remarks on lines 410-412, the authors should be aware that in one of the two imaging methods used in LOFAR (the Impulsive imager, see https://doi.org/10.1029/2020JD033126 ) also a chi^2 fitting procedure is applied.

Response 3

As mentioned by the reviewer, the time delay calibration method and even part of the process of locating calculation provided in this paper are similar to the process of time calibration and radiation source calculation of LOFAR system from the view of realization effect. However, there are differences:

1. complexity of observation equipment use by the two systems and the form of data are different, so the technical details of specific implementation are correspondingly different;
2. In terms of localization methods, our system performs direction finding calculations based on the plane wave incidence model, while LOFAR utilizes the time-of-arrival information obtained from a large number of antennas for three-dimensional location of radiation sources.

As an improvement, we have added the following description in lines 398 to 402 of the revised manuscript: " In this method, the signals within the primary window are aligned first using the time delay relationship of the strongest signal, and then the precise time delay is obtained by using a smaller analysis window. This approach allows better matching of the signals within the shorter analysis window and therefore reduces errors caused by the inconsistent data in the window. ".

References:

1. Liu, H.; Qiu, S.; Dong, W. The Three-Dimensional Locating of VHF Broadband Lightning Interferometers. Atmosphere. 2018, 9, 317.
2. Liu, H.; Dong, W.; Wu, T.; Zheng, D.; Zhang, Y. Observation of compact intracloud discharges using VHF broadband interferometers. Journal of Geophysical Research: Atmospheres. 2012, 117, D1203.
3. Pu, Y.; Cummer, S.A. Needles and Lightning Leader Dynamics Imaged with 100–200 MHz Broadband VHF Interferometry. Geophys. Res. Lett.2019, 46, 13556-63.

Author Response File: Author Response.docx

Round 2

Reviewer 4 Report

none