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Assessment of Dynamic Mode Decomposition (DMD) Model for Ionospheric TEC Map Predictions

Remote Sens. 2023, 15(2), 365; https://doi.org/10.3390/rs15020365

by Vlad Landa¹

and Yuval Reuveni^2,3,4,5,*

Reviewer 1: Anonymous

Reviewer 2: Anonymous

Reviewer 3: Anonymous

Remote Sens. 2023, 15(2), 365; https://doi.org/10.3390/rs15020365

Submission received: 19 November 2022 / Revised: 4 January 2023 / Accepted: 5 January 2023 / Published: 6 January 2023

(This article belongs to the Special Issue Latest Developments and Solutions Integrating GNSS and Remote Sensing)

Round 1

Reviewer 1 Report

This paper describes the Dynamic Mode Decomposition (DMD) model applied with global ionospheric vertical Total Electron Content (vTEC) maps to construct a 24-h global Ionospheric vTEC map. The findings are constructive for the improvement of the vTEC map. There are some corrections that have to be made.

1) The authors are advised to check for the language of the writing. Some mistakes in grammar appear at many places of the paper.

2) The reference in the beginning of a sentence needs the author’s name. E.g.: [18] in line 51, [19] in line 56, [20] in line 60 … I only quote a few examples here. Authors are advised to improve these for the whole manuscript.

3) The unit like (゜) is need in the horizontal and vertical coordinates in Figure 1 and 8. Also, the scales of the color bar in Figure 1 are advised to be identical.

As a whole, I recommend this paper to be published in Remote Sensing after making some revisions.

Author Response

Answer to Reviewer #1

We would like to thank the reviewer for the time and effort which spent reviewing our paper. All comments, suggestions, and questions were carefully considered, and all necessary corrections were made in the revised manuscript.

General comments:

Specific comments:

1) The authors are advised to check for the language of the writing. Some mistakes in grammar appear at many places of the paper.

Necessary change has been made in the revised manuscript.

Necessary change has been made – all citations include Author’s name.

3) The unit like (゜) is need in the horizontal and vertical coordinates in Figure 1 and 8. Also, the scales of the color bar in Figure 1 are advised to be identical.

Both Figures have been modified accordingly to the reviewer suggestions.

As a whole, I recommend this paper to be published in Remote Sensing after making some revisions.

We would like to thank the reviewer for the time and effort which spent reviewing our paper.

Author Response File: Author Response.pdf

Reviewer 2 Report

In this study, authors utilized the DMD model in order to evaluate whether it has the ability to predict vTEC GIM for 24 hours in advance, with 2 hours candidate time step. Authors gave some conclusions.

The topic is certainly interesting and important, but in my opinion some corrections should be made in the text before acceptance.

Line 13: Authors should give a real link to the script files on GitHub (https://github.com/vladlanda/Assessment-of-Dynamic-mode-decomposition-DMD-model-for-Ionospheric-TEC-map-predictions) instead of the one given (at vladlanda .com)

Looking at Table 1, it can be seen that very strong flares of class X (mostly X1) were analyzed. Why flares of medium strength, i.e. of class C and class M, are not analyzed?

The quality of most of the figures should definitely be improved (increase the text on axes and legends of Figs.3-8). Only when I increase everything to 200% I can see everything clearly. Also, the caption of the tables should be above and not below the tables.

I suggest that Section 4. Discussion and Conclusion be divided into Discussion and separately Conclusion. Currently this chapter with three tables is very confusing.

Ref 3 missing page number n/a–n/a =>1-9

Incomplete reference 4. Missing journal, pages, etc … Giannattasio, F. Ionosphere Monitoring with Remote Sensing, 2022=> Giannattasio, Fabio. "Ionosphere Monitoring with Remote Sensing." Remote Sensing 14.21 (2022): 5325.

Ref. 8 is incomplete and the doi number is not correct.

Authors should definitely check all references carefully.

I notice that the Author Contributions, Funding, … template sections are missing.

Author Response

Answer to Reviewer #2

We would like to thank the reviewer for the time and effort spent reviewing our paper. All comments, suggestions, and questions were carefully considered, and all necessary corrections were made in the revised manuscript.

General comments:

The topic is certainly interesting and important, but in my opinion some corrections should be made in the text before acceptance.

Specific comments:

The link has been corrected in the revised manuscript.

Looking at Table 1, it can be seen that very strong flares of class X (mostly X1) were analyzed. Why flares of medium strength, i.e. of class C and class M, are not analyzed?

The “quiet events” column in Table 1, is mostly consisted of low-magnitude class C events. In general, we argue that examining the abilities of DMD model with class X events, is more informative regarding the limitation of a ML model to predict the desired output, as these are the most disturbed types of flares.

In addition, we also included additional DMD results over nine Coronal Mass Ejections (CME) events during the years 2015-2019.

The caption positions are fixed in the revised manuscript, and all figures and plots were modified accordingly to the reviewer suggestions.

I suggest that Section 4. Discussion and Conclusion be divided into Discussion and separately Conclusion. Currently this chapter with three tables is very confusing.

The revised manuscript was reorganized based on the reviewer suggestions and additional explanations were added to each section.

Ref 3 missing page number n/a–n/a =>1-9

The reference was fixed in the revised manuscript: the page section were removed from the citation as they were not published by the journals.

Incomplete reference 4. Missing journal, pages, etc … Giannattasio, F. Ionosphere

Monitoring with Remote Sensing, 2022=> Giannattasio, Fabio. "Ionosphere Monitoring with Remote Sensing." Remote Sensing 14.21 (2022): 5325.

The reference was fixed in the revised manuscript

Ref. 8 is incomplete and the doi number is not correct.

The reference was fixed in the revised manuscript, and the DOI is rechecked.

Authors should definitely check all references carefully.

All references were carefully checked in the revised manuscript.

I notice that the Author Contributions, Funding, … template sections are missing.

Author contributions and Funding sources were added:

Author Contributions: All authors have made significant contributions to the manuscript. V.L. processed the GPS-TEC and EUV data, designed and implemented the DMD algorithm development, wrote the main manuscript, and prepared the figures and tables; Y.R. conceived and designed part of the algorithm, analyzed the data and results, and is the main author who developed and revised the manuscript. All authors have read and agreed to the published version of the manuscript.

Funding: This research was funded in part by Ariel University Data Science and Artificial Intelligence Center, grant number: RA22-235

Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Author Response File: Author Response.pdf

Reviewer 3 Report

I found the article to be very useful. It makes a 24-h forecast for global TEC distribution. There is a comparison with the CODE forecast (C1PG maps). There are different models some of them involve maps only, but some EUV data also. The authors provided all software codes on GitHub so the results can be implemented by the GNSS community. I think that the article is worth publishing in remote sensing, but some issues should be corrected.

1) The main shortcoming of the article is that the authors considered a disturbance the effects of the solar flares, while solar flares' effects are just quite small in time and in vTEC variation [Afraimovich et al., 2002]. Moreover, time-spatial interpolation in GIM reduces short-time effects, so the effect on absolute TEC in GIM is quite low. However, the results in this part are also useful, but their interpretation is wrong. I would say that it is almost quiet conditions. That’s why the results seem to be the same. The most significant TEC disturbance are during magnetic storms. So the authors should consider strong storms. I would suggest at least most powerful in the previous solar cycle: March 17, 2015; June 22-23, 2015; 25-26 August 2018 (CME-storms) and September 2017, 28; September 1, 2019; April 20, 2018 (SSH-storms). That’s will be real storm conditions.

2) Could you indicate computational costs? Is it possible to perform calculations during the whole solar cycle and obtain statistics at the different solar and geomagnetic activities?

3) Nothing is said about the model.

4) Abstract should be more clear.

- What is “2-hours temporal resolution maps” in the end of first sentence?

-Which GIM were used? IGSG?

- “global Ionospheric”.

- “argue that the commonly adopted vTEC map comparison RMSE metric fails to correctly reflects an informative impact with L1 single frequency” – not sure. It depends on the task.

- What are the input parameters for the model?

- Could you provide any digits for the models? “Both the DMD and DMDc predictions present close RMSE scores compared with the available CODE’S 1-day predicted ionospheric maps, both for quiet and disturbed solar activity.” and “which shows an improvement in the vTEC Root Mean Square Error (RMSE) values compare”.

- I am not sure, that DMDc description is correct enough. Do you create two models: one is 24-hours forecast based on the current map only and the second use also EUV as an input?

-Which EUV do you use? 10-50 nm?

- Keywords are not clear: “DMD”, DMDc”. I do not see in the abstract and in the article “Machine Learning”.

5) I would suggest being more accurate with citations (especially, with self-citations. Please check that all your references really provide the information you cite and they are pioneering papers rather than just re-cite previous publications. For example, 2-3 can not provide some evidence about “The ionization processes in the Ionosphere, Earth’s upper atmosphere layer which ranges between 60km to 1000km, are considered as space weather phenomena, driven by x-ray and Extreme Ultra Violet (EUV) solar irradiance which ionize the air molecules and consequently creating a layer of free electrons”.

6) The technique should be shown more clearly and more structured. Why do you need Machine learning? What are training/validation/test sets? What are input parameters? Moreover split results and techniques.

7) Provide full information on the articles cited. For example Giannattasio, F. Ionosphere Monitoring with Remote Sensing, 2022. What is it? If it is a textbook there should be the place of publication, publisher, and pages.

8) I did not get the logic of the paragraph “Since 1998, the International Global Navigation Satellite Systems (GNSS) Service (IGS) provides Ionosphere vertical TEC maps derived from the dual-frequency GNSS data using more than”. It mixes a lot of different things.

9) It is not clear from the review if you consider Machine learning just neural networks or other ML techniques.

10) Do not use uppercase where it is unnecessary, like “Latitude” etc.

11) I would not recommend embedding links. It would be better to show them as text with a hyperlink.

12) In my view the introduction is hard to read because it is quite long and prevents understanding the main task of the article. I would shift most of the information to the discussion (and some to the method), where I strongly recommend not only citing papers but discussing briefly the differences and if possible accuracy/precision.

13) I do not understand the issue about the data array. Why 13 maps? Do you use 24h from GIM? So you will provide a forecast for 26 hours - at least if you use 0h also. The same is with spatial resolution. Actually, GIM is 71*72 because -180°E and +180°E are the same points.

14) Take attention that TEC values for 24 h from day 1 and 0 h from day 2 can be different while it is the same time moment. How do you work with it? I personally, exclude 24h when analysing GIM data for consistency. You can choose your own way but should understand and indicate arising problems.

15) I understand that some days are absent, but could you indicate which exact days are absent in the data sets?

16) Why do you discuss DMD reprocessing before you explain what is DMD. I can’t get what is DMD data-set matrix reprocessing just from Fig. 3 without explanation.

17) Each paragraph should be a separate idea.

18) Technique should be structured and explained more clearly.

19) There are outliers in EUV data. What do you do with it?

20) Would you show modes in the technique section? Is it possible to show in the technique section how control influences the results?

21) What solution do you use for positioning? Is it a single-frequency iterative non-smoothed solution based on P1 (or C1)? Do you use sp3 or broadcasted coordinates? Split method and results.

22) I do not get about 2h shift and 72h length. Are these different models involving lagged EUV and TEC values?

23) Please, provide error distributions.

24) What is “Local Ionospheric Maps” and why do you need such a term? As I see you just plot part of the map. Usually, the local ionospheric maps term is used when they calculate local TEC distribution (in Australia or in Europe) and use the local functions for TEC expansion. It is unclear if Fig. 2 shows IGSG maps.

25) Is average deviation to be the mean average error? Or does it is mean absolute error?

26) Take care of small numbers and remember, that GIM errors are several TECU (see RMS at the end of IONEX file). So 0.008 seems to be a zero. Actually, GIM does not provide digits less than 0.1, so I would suggest rounding mentioned digits to the same level.

27) What is “48h shift 8” and similar? Actually, I would see the distribution for errors at different values over appropriate statistics.

28) Check the digits in Table 3.

29) I do not get why the “commonly adopted vTEC map comparison RMSE metric fails to reflect the impact with L1 single frequency positioning solutions using Ionospheric corrections”. I do not see enough research for a such strong conclusion.

30) Figures.

- The axis captions and marks are too small.

- Exclude unclear captions from figures like “iir_1216_1nm”.

- Exclude unnecessary grey backgrounds from figures.

- Make lines thicker.

- Do not use the title of the figures as a caption. For exampleб in Fig. 2 you can shift information about cadence to the caption. And you can omit the title at all.

- Do not discuss results in captions!

31) References.

- For radio wave propagation I would suggest [Davies, 1969].

- For space weather influence on GNSS – [Demyanov and Yasyukevich, 2021]: the ionosphere could deteriorate all modes of GNSS positioning.

- For IGSG I would suggest [Hernández-Pajares et al., 2009] – please read carefully. There is no still IGSG in [13], they consider the geneal activity of different partners of IGS.

- For EOF + machine learning long-term forecast see [Zhukov et al., 2021]

- I would note the paper on () machine learning short-term perdition of TEC maps

- Provide a reference for IONEX – [Schaer et al., 1998].

- Provide a reference for C1PG.

32) Small remarks

- “between year 2013 and year 2014” -> ‘during 2013-2014”

- indicate EUV range.

- “32.77899” – last 3 digits seem to be uninformative and can be partly due to the processing technique (the precision is ~1 m).

- “X2” -> “X2.0”

- “with RINEX file”. files?

- Follow to MDPI template. The table title should be above the table, not below.

- "to correctly reflects " -> "to correctly reflect "

References:

Afraimovich EL, Altynsev AT, Grechnev VV, Leonovich LA. The response of the ionosphere to faint and bright solar flares as deduced from global GPS network data. Ann. Geophys. [Internet]. 2002Dec.25 [cited 2022Dec.1];45(1). DOI: https://doi.org/10.4401/ag-3480.

K. Davies. Ionospheric radio wave propagation. Blaisdell Publishing Company, 1969 - 460 p.

Demyanov V. V., Yasyukevich Y. V. Space weather: risk factors for Global Navigation Satellite Systems // Solar-Terrestrial Physics. 2021. no. 2. pp. 28-47. DOI: https://doi.org/10.12737/stp-72202104

Hernández-Pajares, M., Juan, J.M., Sanz, J. et al. The IGS VTEC maps: a reliable source of ionospheric information since 1998. J Geod 83, 263–275 (2009). https://doi.org/10.1007/s00190-008-0266-1

Liu, L., Morton, Y. J., & Liu, Y. (2022). ML prediction of global ionospheric TEC maps. Space Weather, 20, e2022SW003135. https://doi.org/10.1029/2022SW003135

Schaer, S., Gurtner, W., Feltens, J. (1998): IONEX: The ionosphere map exchange formatversion 1. Proceedings of the IGS AC workshop, Darmstadt, Germany.

Zhukov, A.V., Yasyukevich, Y.V. & Bykov, A.E. GIMLi: Global Ionospheric total electron content model based on machine learning. GPS Solut 25, 19 (2021). https://doi.org/10.1007/s10291-020-01055-1

Author Response

Answer to Reviewer #3

General comments:

Specific comments:

We followed your suggestion and evaluated the DMD model’s predictions over nine additional dates, which featured CME storms. Table 1 was expanded to include those new CME events and Figure 6 shows the RMSE vTEC results.

17/03/2015 – 8-

22/06/2015 – 8+

23/06/2015 – 8-

08/09/2017-28/09/2017 (8+/7-)

25/08/2018 – 4+

26/08/2018 – 7+

20/04/2018 - 6

01/09/2019 – 5+

2) Could you indicate computational costs? Is it possible to perform calculations during the whole solar cycle and obtain statistics at the different solar and geomagnetic activities?

The computational cost depends on the size of matrix X (where X is described in section 2.2) and on the chosen algorithms for calculating SVD and matrix multiplication. We utilize the “linalg” package from python Numpy library. In general, generating ten days of global TEC maps from X matrix which contain 120 days of TEC maps history, takes around 8 minutes of runtime (based on Intel i9-9900K and 32.0 GB of ram).

3) Nothing is said about the model.

The Methodology section was reorganized and clarified in the revised manuscript.

4) Abstract should be more clear.

- What is “2-hours temporal resolution maps” in the end of first sentence? We have modified it to - available 2-hours cadence vTEC maps.

-Which GIM were used? IGSG? GIM refers to Global Ionospheric Map - we use Global Ionospheric Maps provided by IGS final solutions.

- “global Ionospheric”.

- “argue that the commonly adopted vTEC map comparison RMSE metric fails to correctly reflects an informative impact with L1 single frequency” – not sure. It depends on the task. Explanation and terminology were added in the revised conclusion section. The sentence was changed to: “Based on these results, we argue that the commonly adopted vTEC map comparison RMSE metric does not entirely reflect the impact with L1 single frequency positioning solutions using Ionospheric corrections, thus requires a further investigation”.

- What are the input parameters for the model? Both, the DMD and DMDc are applied with a data set matrix of snapshots, where one can select the number of snapshots [columns] in the data set - this choice will influence the number of modes extracted and thus the overall runtime. In turn, one can chose truncation parameter for SVD - as described in Eq 6.

We expressed the improvement in percentage, describing how much RMSE vTEC area the DMDc [i.e., the area between DMDc and C1P] has improved compared to the area of the DMD [i.e., the area between DMD and C1P].

- I am not sure, that DMDc description is correct enough. Do you create two models: one is 24-hours forecast based on the current map only and the second use also EUV as an input? The DMDc is an expansion of the DMD, as it is designed for system which are influenced by external forces. Basically, we identify new set of modes for every 24 hour target of GIMs.

-Which EUV do you use? 10-50 nm? We used 1 minute average Lyman-alpha 121.6 nm data.

- Keywords are not clear: “DMD”, DMDc”. I do not see in the abstract and in the article “Machine Learning”. The DMD and DMDc are a data driven methods for extracting dynamic mode from a set of system states [snapshots]. These modes can be used either for system analysis or future state predictions. Intuitively, system modes can be considered as analogy to the component of Fourier/Taylor series.

DMD, DMDc and Machine learning acronyms were added in the revised manuscript

This is a basic informative statement which describes the ionosphere and the different sources of ionization within: “Solar radiation plays a crucial role in forming the different layers of the ionosphere. Different wavelengths of solar radiation (from ultraviolet to X-rays) are the source of free electrons at different heights during daytime. Non-solar ionizing sources, such as precipitating energetic electrons, meteoric ionization, and cosmic rays, maintain the smaller free electron concentration at night. Low-level Lyman a radiation from the exosphere, also called ‘‘nightglow’’, dominates over the galactic cosmic radiation as a source of ionization at the lower part of the ionosphere at night. We have also added additional pioneering paper citations in the revised manuscript.

The manuscript was reorganized, and additional explanations were added to each section in the revised manuscript based on your comments.

Full information on the articles cited were add in the revised manuscript.

The paragraph was rephrased in the revised manuscript: “Since 1998, the International GNSS Service (IGS) provides global Ionosphere vTEC maps derived from the dual-frequency GNSS data, using more than 380 IGS stations with approximately 11 days latency for the final vTEC maps solution”.

9) It is not clear from the review if you consider Machine learning just neural networks or other ML techniques.

We reviewed the most recent works in order to emphasize that nowadays the methodology leans toward AI and data driven approaches in general.

10) Do not use uppercase where it is unnecessary, like “Latitude” etc.

Necessary modifications were applied in the revised manuscript.

11) I would not recommend embedding links. It would be better to show them as text with a hyperlink.

According to your suggestion, hyperlink to the source code has been modified in the revised manuscript.

The introduction was revised. The last paragraph in the introduction section is focused specifically on the proposed study and main task. The discussion and conclusion parts were modified accordingly.

Every IGS IONEX file contain 13 GIMs with two hours cadence. The first GIM corresponds to EPOCH 00:00 the second GIM corresponds to EPOCH 02:00 and so on. The thirteenth GIM corresponds to EPOCH 00:00 of the next IONEX file, therefore we exclude it from the data set in order to avoid duplicate and unnecessary data repetition. Indeed, the GIM is 71*72, but it doesn’t affect the system dynamics.

Therefore, we utilized only twelve GIMs available in every IGS IONEX file. The first GIM corresponds to EPOCH 00:00 and the twelve GIM corresponds to EPOCH 22:00. The following GIMs are taken from the following IGS IONEX day file.

15) I understand that some days are absent, but could you indicate which exact days are absent in the data sets?

After rechecking, it seems that all the IGS IONEX files are present on the source server.

We reevaluated our results with those files and delete this section from the revised manuscript.

16) Why do you discuss DMD reprocessing before you explain what is DMD. I can’t get what is DMD data-set matrix reprocessing just from Fig. 3 without explanation.

The manuscript sections were reorganized such that the DMD is presented in the methodology part, which is before the data and forecast section.

17) Each paragraph should be a separate idea.

The manuscript sections were reorganized, and additional explanations were added to each section.

18) Technique should be structured and explained more clearly.

Necessary changes were made in the revised methodology section.

19) There are outliers in EUV data. What do you do with it?

We are not sure what do you mean by the term “outliers”, as outliers refers to data points in a data set which might bias the model training (it can be arguable what is considered as an outlier). But if you are refering to the four indicator flags (good_quality(0), eclipse(1), lunar_transit(2), bad_or_no_data(4)) included in the GOES-15 and GOES-16 EUV netcdf4 file, then, every point in the time series of 121.6 nm that corresponds to any flag that is greater than 0 is interpolated using nearest neighbor interpolation.

20) Would you show modes in the technique section? Is it possible to show in the technique section how control influences the results?

We can show the modes for a particular case study, but this is out of the scope of this study and won’t contribute to the conclusions.

The impact of EUV time series as a control input source is projected via vTEC RMSE improvement over the DMD

21) What solution do you use for positioning? Is it a single-frequency iterative non-smoothed solution based on P1 (or C1)? Do you use sp3 or broadcasted coordinates? Split method and results.

We used the following parameters for gLab:

"-pre:smooth":"100",

"-pre:smoothMeas":"1 L1P",

"-model:trop:nominal":"UNB3",

"-model:trop:mapping":"Simple",

"-filter:nav":"kinematic",

"-filter:select":"2 C1C L1P",

The config json file is present in the source code.

It is also noted in the abstract that we use Single Point Positioning (SPP) solutions. We also use the sp3 files as an input.

22) I do not get about 2h shift and 72h length. Are these different models involving lagged EUV and TEC values?

In order to investigate what can be considered as the optimal/best EUV input control, we evaluated the DMDc with EUV as control inputs with variable control signal lengths (24h,48h and 72h) and in addition we examine “how far” (how many hours before the first daily GIM prediction) this control signal should be taken (2h,4h,6h,8h,10h,12h).

23) Please, provide error distributions.

We generated new figures for ENU and added error distributions in the revised manuscript, in addition the RMSE distributions are shown as the semi-transparent band around the RMSE average line.

- The Local Ionospheric Maps (LIM) definition is necessary to examine the RMSE between vTEC map counting only for the difference grid cells that corresponds to IPPs. In such way investigating areas of vTEC that influence the Ionospheric correction used by position estimation algorithms.

Figure 2 was modified in the revised manuscript.

25) Is average deviation to be the mean average error? Or does it is mean absolute error?

Figures that shows RMSE - projects two metrics : RMSE - average over the candidate case studies and RMSE standard deviation as the semi-transparent bands.

Indeed, IGS IONEX files include RMSs, but CODE and other rapid solutions do not have RMS, therefore we present the difference as they are.

27) What is “48h shift 8” and similar? Actually, I would see the distribution for errors at different values over appropriate statistics.

Explanation added to all Tables in the revised manuscript.

28) Check the digits in Table 3.

Table 3 digits corresponds to statistics shown in Figures 7 and 8 (newly generated).

Clarifications were added to the revised discussion section.

30) Figures.

- The axis captions and marks are too small.

- Exclude unclear captions from figures like “iir_1216_1nm”.

- Exclude unnecessary grey backgrounds from figures.

- Make lines thicker.

- Do not use the title of the figures as a caption. For exampleб in Fig. 2 you can shift information about cadence to the caption. And you can omit the title at all.

- Do not discuss results in captions!

Necessary changes were made to the relevant Figures, while some Figures were regenerated.

31) References.

- For radio wave propagation I would suggest [Davies, 1969]. (Added)

- For space weather influence on GNSS – [Demyanov and Yasyukevich, 2021]: the ionosphere could deteriorate all modes of GNSS positioning. (Added)

- For IGSG I would suggest [Hernández-Pajares et al., 2009] – please read carefully. There is no still IGSG in [13], they consider the geneal activity of different partners of IGS. (Added)

- For EOF + machine learning long-term forecast see [Zhukov et al., 2021]. (Added).

- I would note the paper on () machine learning short-term perdition of TEC maps.

- Provide a reference for IONEX – [Schaer et al., 1998]. (Exists on reference no. 42)

- Provide a reference for C1PG. we are providing a data source link reference in the paper: “IGS and CODE data are available at CDDIS FTP server, as a daily IONEX file which consists of 13 GIMs at 2 hours resolution time span (note, that the last (thirteen) GIM of each day is overlapping with the first GIM of the following day).”

Corrections were made in the revised manuscript.

32) Small remarks

- “between year 2013 and year 2014” -> ‘during 2013-2014” (modified)

- indicate EUV range.

- “32.77899” – last 3 digits seem to be uninformative and can be partly due to the processing technique (the precision is ~1 m). (Lat,Long degree accuracy of 5 decimal points is equal to 1.11m)

- “X2” -> “X2.0” (modified)

- “with RINEX file”. files?

- Follow to MDPI template. The table title should be above the table, not below. (modified)

- "to correctly reflects " -> "to correctly reflect " (modified)

Corrections were made in the revised manuscript.

References:

Davies. Ionospheric radio wave propagation. Blaisdell Publishing Company, 1969 - 460 p.

Demyanov V. V., Yasyukevich Y. V. Space weather: risk factors for Global Navigation Satellite Systems // Solar-Terrestrial Physics. 2021. no. 2. pp. 28-47. DOI: https://doi.org/10.12737/stp-72202104

Hernández-Pajares, M., Juan, J.M., Sanz, J. et al. The IGS VTEC maps: a reliable source of ionospheric information since 1998. J Geod 83, 263–275 (2009). https://doi.org/10.1007/s00190-008-0266-1

Schaer, S., Gurtner, W., Feltens, J. (1998): IONEX: The ionosphere map exchange formatversion 1. Proceedings of the IGS AC workshop, Darmstadt, Germany.

Zhukov, A.V., Yasyukevich, Y.V. & Bykov, A.E. GIMLi: Global Ionospheric total electron content model based on machine learning. GPS Solut 25, 19 (2021). https://doi.org/10.1007/s10291-020-01055-1

Corrections were made in the revised manuscript.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Now the results seem much more reliable.

1) Check Figure 2 - there are outliers in EUV data (see my comment at previous round).

2) gLab is quite comprehensive tool. Indicate clear type of coordinate treatment.

3) It is quite disappointing when in the rebuttal letter the authors say about corrections, but do not introduce them in the text. For example "CDDIS FTP" hyperlink is still embedded in the text rather than shown next to. Moreover the hyperlink is not aviliable (as I know CDDIS stop using ftp and use https now).

4) Does Table 1 show as a "CME date" the "magnetic storm date"? The delay between CME and corresponding storm can be up to 3 days.

Author Response

Answer to Reviewer #3

General comments:

Now the results seem much more reliable.

Specific comments:

1) Check Figure 2 - there are outliers in EUV data (see my comment at previous round).

Figure 2 presents the time series as we use it. The time series in Figure 1 is after linear interpolation of GOES 15/16 netcdf4 flags preprocessing.

2) gLab is quite comprehensive tool. Indicate clear type of coordinate treatment.

We are specifying in the revised manuscript that the the config gLab file is present in the source code. Furthermore, as mentioned in our first rebuttal letter, we use Single Point Positioning (SPP) solutions, with RINEX observation files, for orbit and clock products we use SP3 and CLK files, for ionospheric source we use IONEX files (either IGS, Klobuchar, c1p or DMD models).

Station data – data decimation 300 sec, and we check for jumps in the code measurements.

Cycle-slip detection - data gaps 40 sec, LLI, N Consecutive Sample 3 samples, L1-C1 difference.

Satellite Options – Elevation Mask 5 degrees, and we Align carrier phase measurements with code.

GNSS Satellite Selection – GPS.

Modelling Options – satellite clock offset correction, check broadcast transmission time, consider satellite movement during signal flight time, consider earth rotation during flight time, receiver antenna reference point correction, relativistic clock corrections (orbit eccentricity), tropospheric corrections – UNB-3 Nominal, Niell mapping function, P1-C1 corrections, wind up corrections, solid tides corrections, relativistic path range correction.

Precise products data interpolation – interpolation degree: orbit – 10, clocks – 0

Max consecutive gaps between samples: orbit – 8, clocks – 2

Total gaps allowed: orbit – 16, clocks – 4

Receiver Antenna reference point correction: Read from RINEX.

Measurements: pseudorange + carrier phase.

Measurements configuration and noise: C1C Fixed StdDev 1 m

L1P Fixed StdDev 0.01 m

Parameters: coordinates – Phi: 0; Q:1e8 m²; Po 1e8 m²;

Receiver clock - Phi: 0; Q:9e10 m²; Po 9e10 m²;

Troposphere - Phi: 1; Q:1e-4 m²/h; Po 0.25 m²;

Phase ambiguities: Phi: 1; Q:0 m²; Po 400 m²;

Available frequencies: single-frequency.

Troposphere: estimate wet troposphere residual

Receiver kinematics: Kinematics.

Thank you for pointing this out. We did our best to answer all your questions and constructive comments in our first rebuttal letter. We initially misunderstood this comment. We modified all hyperlinks to include full URL description.

4) Does Table 1 show as a "CME date" the "magnetic storm date"? The delay between CME and corresponding storm can be up to 3 days.

Table 1, expansion is based on your suggestion to include several CME dates. We expanded Table 1 to contain eight CME dates from your previous comment and one additional with Kp max of 8+.

“I would suggest at least most powerful in the previous solar cycle: March 17, 2015; June 22-23, 2015; 25-26 August 2018 (CME-storms) and September 2017, 28; September 1, 2019; April 20, 2018 (SSH-storms). That’s will be real storm conditions.”

Author Response File: Author Response.pdf

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