Three-Dimensional Parameters of the Earth-Impacting CMEs Based on the GCS Model

Round 1

Reviewer 1 Report

The overall idea of the project is interesting and can add to the understanding of the properties of Earth directed CMEs. However, there a some major concerns that need to be addressed before a more detailed evaluation of the study can be performed.

Major Comments:

1) A major revision and editing in English language is needed.

2) It is not clear in the manuscript how the GCS reconstruction was performed and how the velocity and acceleration profiles were derived. I suggest to present this more clearly, and possibly add example images.

3) I am missing an analysis of the errors and uncertainties in input data, GCS fitting, CME propagation (height, velocity, acceleration, travel time, ...) and forecast.

Minor comments:

1) The introduction is lacking the results of some more recent papers.  (some papers which might benefit the introduction of your study:  Temmer 2021, Dumbovic et al. 2019,  Heinemann et al. 2019, Hinterreiter et al. 2021, Braga & Vourlidas 2021, Wang et al. 2020, Luhmann et al. 2020, ..)

2) There seem to be quality issues with the  some figures (e.g., overlapping lables) that should be corrected.

3) Did the authors compare their CMEs to other catalogs? e.g. HELCATS catalog?

4) Why did the authors choose the timer period 2008-2012. Would it not be better to increase the time period to e.g., 2014 which would make the statistical sample larger and more relevant.

Author Response

Thanks for your advice. The following red texts are our responses to your comments.

Major Comments:

1) A major revision and editing in English language is needed.

Reply: We have revised and edited our manuscript to improve English language. Hope it is better now.

2) It is not clear in the manuscript how the GCS reconstruction was performed and how the velocity and acceleration profiles were derived. I suggest to present this more clearly, and possibly add example images.

Reply: Thanks for your comment. An example which exhibit the GCS fitting results has been added in Section 2 Figure 2 in our manuscript and an example of how the velocity and acceleration profiles were derived has been added in Section 2 Figure 3.

3) I am missing an analysis of the errors and uncertainties in input data, GCS fitting, CME propagation (height, velocity, acceleration, travel time, ...) and forecast.

Reply: Yes, you are right. The uncertainties of these parameters are important issue in this work. In the revised version, we have added the uncertainties for the parameters we analyzed in Section 3. The deviation of the forecast model was also added after corresponding texts. It is found that the uncertainties of these parameters did not change the main results we obtained in this work.

Minor comments:

1) The introduction is lacking the results of some more recent papers.  (some papers which might benefit the introduction of your study:  Temmer 2021, Dumbovic et al. 2019,  Heinemann et al. 2019, Hinterreiter et al. 2021, Braga & Vourlidas 2021, Wang et al. 2020, Luhmann et al. 2020, ..)

Reply: Thanks for your comments. These papers are important. We have added some citations of the results from these papers in our manuscripts.

2) There seem to be quality issues with the some figures (e.g., overlapping lables) that should be corrected.

Reply: Thanks. We adjusted some of the figures in the manuscript to improve their qualities.

3) Did the authors compare their CMEs to other catalogs? e.g. HELCATS catalog?

Reply: Thanks. We have compared our catalogue with HELCATS WP3 COR2 catalogue (https://www.helcats-fp7.eu/catalogues/wp3_kincat.html). It is found that there are only 19 CME events on our catalogue that are identical to HELCATS catalogue. Our catalogue is established from in situ observation extrapolating back to the Sun, but HELCATS catalogue is established using observation from STEREO-COR2. So, CMEs in our catalogue is Earth-arrived while CMEs in their catalogue may be not always Earth-arrived. Thus, the differences between these two catalogues are obvious. So, we do not show the comparison results in the revised version.

4) Why did the authors choose the timer period 2008-2012. Would it not be better to increase the time period to e.g., 2014 which would make the statistical sample larger and more relevant.

Reply: Thanks for your comments. The period in which STEREO-A, B and SOHO all have data is 2007-2014. However, we believe that STEREO A and B have a better perspective during 2008-2012, which is suitable for three-dimensional reconstruction of CMEs. Therefore, we only chose the period from 2008 to 2012 in this work.

Reviewer 2 Report

SEE IN ATTACH FILE

Comments for author File: Comments.pdf

Author Response

Thanks for your advice. The following texts are our responses to your comments.

Title: Three dimensional parameters of the Earth-arrived CMEs based on….

Reply: Thanks for your comment. In the revised version, we added the sentence of ‘based on GCS model’ in the title.

Abstract
Line 8: of Earth-arrived CMEs mainly locate…. Of the majority Earth-arrived CMEs locate

Reply:  Thanks. We have changed this statement into ‘the majority Earth-arrived CMEs originate from….’.

Line 9: …with small value or CPA… delete

Reply:  Thanks. It has been deleted in the revised version.

Line 13-14: ‘both empirical statistic model and aerodynamic drag model should be taken into account for greater accuracy’…. ‘this empirical statistic model should be combined with the aerodynamic drag model in order to achieve better results’.

Reply:  Thanks. According to your comments in the latter, we have deleted this phrase and replaced it with: ‘we develop an empirical statistical model to forecast the arrival time of the Earth-arrived CME. Also included is a comparison between our model and the aerodynamic drag model’.

1. Introduction
   Line 44: from one every other day…one per day

Reply:  Thanks for your comments. I am sorry to make you misunderstanding. We mean 0.5 per day. In the revised version, it has been changed to ‘one every two days’.

Line 50: position…and position

Reply: Thanks. We have changed this phrase into ‘and propagation’.

Line 51: , speed….as well as the speed…

Reply: Thanks. We have changed this phrase into ‘as well as the initial velocity’.

2. Data and method
   Line 102: Data and Method ….Data collection and Method of analysis

Reply: Thanks for your comments. It has been modified in the revised version.

It would be very useful for future researchers to have in this publication the full list of ICME-CME including all the useful parameters of these events. I suggest it be added as an Appendix.

Reply: Thanks for your comments. We added the information of the start of ejecta by in situ observation in Table 1.

3. Results
   The use of the model GCS manually for each of the 77 ICME-CME events is commendable. It is very useful the presentation of these results in the Table 1.

Reply: Thanks for your comments.

Line 136: two special event…two special events

Reply: Thanks. It has been modified as recommended.

Line 140: the ‘initial fitting time’ is the corresponding of the CME onset time?

Reply: I am sorry for make you misunderstanding. The ‘initial fitting time’ in our manuscript means the first time we started to do GCS fitting. It is the time that there were observations from both STEREO and SOHO. It is not always the CME onset time.

Line 144-146: Is it possible to give a graph of the related geometry, for better
understanding?

Reply: Thanks for your suggestion. We have added a schematic of the GCS model in Figure 1 in Section 2.

4.1 Location
Line 166-169: …with red diamond symbols. The two horizontal dashed blue lines mark the maximum and minimum values of θ, which are 43.00 deg and -30.18 deg, respectively. The enclosed region between two vertical blue dashed lines stands for front-side solar disk (φ between -90 and 90 degrees).

Reply: Thanks for your comments. This paragraph has been changed into ‘with red diamond symbols. The two horizontal dashed blue lines mark the maximum and minimum values of θ, which are 43.00° and -30.18°, respectively. The enclosed region between two vertical blue dashed lines stands for the front-side solar disk (φ between -90 and 90 degrees)’.

Line 172-175: The information about the sunspots is correct. However, the comparison of sunspot-position and CME-position, for reference in an 11-year cycle, has not been examined in the present work. Simply put, the CMEs, in the ascending phase of the solar cycle (2008-2012), as a whole, are within these limits. The correlation of CME position and Active Regions is another issue.

Reply: You are right. The correlation didn't make much sense. In the revised version, we we deleted it.

Line 185: in solar limb… toward to solar limb

Reply: Thanks. It has been modified as recommended in the revised version. We changed the phrase into ‘toward to the solar limb’.

4.2 Central propagation angle and half-angular width
Lines between 193-194: the CPA is equal to the orientation angle ε (see also in Fig. 2). The latter angle except of orientation angle, also defined as deviation angle (see also in line 209). Much names for the same angle…

Reply: Thanks for your comments. We've unified the name to ‘deviation angle’ in the revised version.

Line 198: …a relative small CPA….An angle of > 30 degrees is not characterized ‘small’.

Reply:  You are right. We have deleted this phrase in the revised version.

Line 204: WEO ….ωEO

Reply:  Thanks. It has been modified.

Line 211-213: if ω>ε, CME arrives at the Earth without deviating. If ω<ε, CME arrives at the Earth with some deviating? [See in lines 217-220]. If ω=ε?

Reply:  Thanks for your comments. We divided these CMEs in to two groups with ω >= ε and ω < ε in the revised version.

Line 220-231: The presence of MC or non-MC is appeared almost equivalently in both groups. It is not clear any differentiation…

Reply:  Thanks for your comments. Our results cannot confirm the conjecture, so we changed the statement into ‘There is no discernible difference between Earth-arrived CMEs with ω>=ε and with ω<ε’.

Line 225 and line 243: a image….an image/ a Earth… an Earth

Reply:  Thanks. It has been modified as recommended in the revised version.

Line 231-238: If the authors accept errors in their calculations, they must state it from the beginning and take it into account in the whole analysis and not only selectively. So they will have to correct a lot of what they write.

Reply:   Thanks for your comments. We added the uncertainties in all the parameters we analyzed in Section 3. And in this paragraph, we also added the uncertainty analysis.

Line 239-241: ω>ε is a significant condition (~70% of the events)…and not basic condition…However there is not necessary condition for a CME in order to reach the Earth. There are ~30% of the events which reach the Earth without this condition. The explanation of this percentage of the events is given ‘ …the parts which hit the Earth are not the main part of the flux rope but often their flank parts.’

Reply:  Thanks. We have changed this paragraph into ‘ω>=ε is a rough but significant condition for a CME to reach the Earth. Therefore, this criterion should be considered as an important part of the space weather forecasting model. On the other hand, there are still some events that do not satisfy our criterion but can be Earth-arrived. It means that this criterion is not a necessary condition. A possible explanation of them is that they had some deflections during propagation, which cannot be verified by this work because we didn't derive any large changes for latitude and longitude during the investigated period. It is a subject worthy of further study.’

Figure 2: c) of The Relationship ….of the relationship

Reply:  Thanks. It has been modified as recommended in the caption of Figure 5.

4.3 Simple Kinematics Analysis
Line 243: a Earth… an Earth…

Reply:  Thanks. It has been modified as recommended.

Line 267: ‘the average solar wind speed…during the investigation period’. A detailed calculation has been made and by whom?

Reply:  Thanks, we added some references about this issue in the revised version.

Line 269-271: There is related bibliography….

Reply:  Thanks. We added some references in the revised version.

Lines between 276-277: the best curve is the hyperbolic and not linear fitting. Thus, the linear correlation coefficient offers nothing. We need the correlation coefficient of the hyperbolic fitting. See also in fig. 4.

Reply:  Thanks. It has been modified as recommended. We changed the linear correlation coefficient into the correlation coefficient of the hyperbolic fitting in these two places.

Line 280-281: sun and earth…Sun and Earth

Reply:  Thanks. It has been modified as recommended.

Line 287: For test the equation 2, is necessary to give the diagram of Dpro =f(Tpro). The test of only one value is not safely.

Reply:  Thanks for your suggestion. It is true that our test is not convincing enough. It is not reasonable to use the initial velocity times the propagation time to calculate the propagation distance. In the revised version, we deleted this paragraph and added the deviation between the calculated results and the actual value in the revised version.

Line 289-290: The 22 events are the same in which ω<ε? (See in lines 220-225).

Reply:  Yes. All of these 22 events satisfy the relation that ω<ε, which made the equation have no real roots.

Line 293: Add the phrase: This relation uses the values of initial velocity (Vcme) and real distance (Drl) computing by the GCS model.

Reply:   Thanks. We added the following phrase in the revised version: ‘The calculation uses the values of initial velocity (VGCS) computing by the GCS model as the initial value of vCME in Equation (4) and actual propagation distance Dact computing by Equation (3) as the final value of r’.

 ‘…propagation time …by numerical calculation… ’ To give more details on how to calculate.

Reply:   Thanks. We added a description in Appendix A.1 of the calculation details.

 ‘actual propagation time….’ Whence take this parameter?

Reply:   Thanks. We used to explain this value in the footnote, now we have moved it to the phrase where we first mentioned this value (two paragraphs above Equation 2).

Add the diagram dV=f(Drl) and Drl =f( Tpro) which results from ADM model.

Reply:   Thanks. We add a figure as Figure 8 to show dV=f(Drl) and Drl =f( Tpro) in the revised version.

Figure 5: change the symbol Tpro for the actual propagation time. It is the same with the symbol of figure 4.

Reply:   Thanks. We changed the symbol Tpro into Tact which means actual propagation time, and we also changed the Drl into Dact.

Lines 311-317: delete these lines. They do not offer a satisfactory explanation.

Reply:   Thanks. It has been modified as recommended.

Line 318-321: delete these lines. This conclusion is not substantiated by the above. As already mentioned, more work is needed on this issue.

Reply:   Thanks. It has been modified as recommended.

5. Conclusion and discussion
   Line 326: change the phrase: ‘… and established a simple propagation model of them’ ‘…and an attempt was made to find a simple propagation model of them’.

Reply:   Thanks. It has been modified as recommended.

Line 336: delete the word ‘small’.

Reply:   Thanks. It has been modified as recommended.

Line 337-340: ‘And if…27’. Delete this phrase.

Reply:   Thanks. Since we have edited in above paragraph in Section 4.2, the paragraph here is still available. We have changed some statements to ` And if taking CMEs' other configurations into account, such as the half-angular width (ω), considering the effect of the errors, most Earth-arrived CMEs (92%) still satisfy ω>=ε, which shows that this criterion should be an important part for Earth-arrived CMEs forecasting’.

Line 334: a empirical….an empirical

Reply:   Thanks. It has been modified as recommended.

Line 345: change the phrase: ‘…can roughly calculate…’ , ‘can give with a good
approximation…’

Reply:   Thanks. It has been modified as recommended.

Line 346-348: To amend the proposal: ‘However, this proposed empirical statistic model….more analysis’. Should be preceded by a reference to the proposed model.

Reply:   Thanks. It has been modified as recommended. We added the equation of this model in this paragraph.

Line 348-352: This conclusion does not follow from the description given in the text.

Reply:  Thanks. You are right. We have deleted some phrases and added the conclusion which could be derived by our analysis: ‘A rough comparison of these two models shows that the deviations between calculated results and actual values of our empirical statistic model are smaller than the aerodynamic drag model and the equation of the latter we used has low performance in low speed events.’

Line 353-356: The text should be changed. There are two separate things: a) the database based on GCS model and b) the preliminary statistical work which led the authors to an empirical model etc…

Reply:   Thanks. It has been modified as recommended.

Line 362-364: ‘…GCS model itself also contribute to errors. Owing the assumption…vice versa.’ What exactly does it mean?

Reply:   Thanks. I am sorry that we make you misunderstanding. We mean that GCS model does contribute to errors which cannot be eliminate by any human adjustment in the process of fitting. Our statements are ambiguous and we have changed the statement of this paragraph.

 

 

Round 2

Reviewer 1 Report

The authors significantly improved the readability and presentation of the paper and adequately addressed my comments. There are still some comments (mainly minor) that should be addressed before publication but it will be a valuable addition to the scientific community.

 

General Comments:

• The authors did not clearly state how remote sensing data and in-situ measurements of CMEs could be uniquely linked. How did the authors find the corresponding CMEs, under what conditions?

 Especially during times of higher solar activity, i.e. multiple CMEs launched during a short time period, it can be hard to associate CMEs from coronagraphs with CMEs measured in-situ using the time only. Did the authors consider to resolve this ambiguity with e.g., j-maps?

• Around Page 10, Line 275: There might be an issue with the determination and/or definition of the acceleration phase in the analysis. The acceleration phase is defined as the phase where the CME is launched/ speeds up. In that sense, the peak acceleration should always be positive. There might be a problem with the fitting/derivative of the height-time profile.

The authors should compare their results with other studies to avoid systematic errors in the analysis. (see e.g. https://ui.adsabs.harvard.edu/abs/2011ApJ...738..191B/abstract )

It might be that your height-time plot starts in a region in which the initial acceleration already ceased. In that case I recommend to either lower the starting height (possibly with EUV data in addition to white light data) or the full removal of the acceleration from the study because in this case it would be more a property of the environment (e.g. drag) than of the CME itself. Also, I could be that its just a problem of the fit or derivation.

As a further comment: Some CMEs start at higher solar height that others, meaning that their acceleration profile is different e.g., their peak acceleration might or might not fall into the chosen height range. To study the propagation speed and the resulting acceleration or deceleration, the peak acceleration as well as the subsequent propagation phase need to be clearly identified.

This is an important issue that needs to be addressed before publication.

Minor Comments:

• Replace Earth-arrived with Earth-directed throughout the manuscript. If the authors want to differentiate between CMEs that are Earth-directed from a remote sensing perspective and CMEs that are measured at Earth I suggest a different wording. Earth-arrived does not sound correct.
• Page 1, Line 1: the CME > a CME
• Page 1, Line 1-2: CMEs may cause hazardous space weather events, they don’t necessarily always do.
• Page 1, Line 2: of the Earth-arrived CMEs > of Earth-directed CMEs
• Page 1, Line 5: the Earth > Earth
• Page 1, Line 5: the observations > observations
• Page 1, Line 8: in the solar disk > on the solar disk
• Page 1, Line 12-13: is it the aerodynamic drag model or the drag-based model (DBM)?
• Page 1, Line 17: A Coronal Mass Ejection (CME) is a powerful solar …
• Page 1, Line 21: could be > can be
• Page 1, Line 27: remove the “and so on” and move the “and” to the sentence before.
• Page 1, Line 35: the properties at L1 are usually measured in-situ, thus the forecasting time is roughly one hour, for remote sensing observations (imaging) the forecasting time is higher. I suggest to add in-situ such that the sentence becomes:   “… mainly obtained from in-situ observations ….”
• Page 2, Line 46: at the vicinity of the Earth > in the vicinity of Earth
• Page 2, Line 52: the Earth > Earth
• Page 2, Line 63: Multiple points observation> Multi-spacecraft observations
• Page 2, Line 63: of the Solar TE…
• Page 2, Line 68: I do not think it is possible to completely eliminate the projection effect but significantly reduce it.
• Page 2, Line 83: are the authors sure that its an aerodynamic model not drag based model? https://ui.adsabs.harvard.edu/abs/2013SoPh..285..295V/abstract
• Page 2, Line 88-90: rephrase or remove this sentence: Halo CMEs are not necessarily Earth-directed, firstly it depends on the observing spacecraft, and secondly on the propagation direction and width (as you mention throughout). I suggest not to oversimplify. I agree that halo-CMEs commonly arrive at Earth, however I have not heard of non-Earth directed CMEs arriving at Earth (within observational uncertainties of course). I think the authors should state their definitions more clearly.
• Page 3, Line 99: is organized as follows:
• Page 3, Line 102: make > give
• Page 4, Line 127: and further: try to avoid backets in brackets i.e. (Figure (a,b)) > (Figure a,b)
• Page 4, Figure 2: The CME is not well visible in the coronagraph images, the authors should think about adjusting this or presenting a more clear example.
• Page 5, Figure 3: I suggest to increase the resolution of the image: e.g., use the plot function instead of the routine in IDL. Also show the acceleration profile. For the values I suggest to use: 584 ± 27 km s^{-1   ­} instead of 583.89(27.06) (km*s^-1 ) 
• Page 5, Line 151: ..CMEs that could be used for the analysis.
• Page 5, Line 153: … among the 77 events are not suitable to be modeled by the GCS model and should be excluded.
• Page 5, Line 163: deflection by what?
• Page 8, Line 210: radial direction?
• Page 8, Line 213: the Earth > Earth
• Page 9, Line 222: maybe add something like: “as expected” .  As the shown behavior is what one would expect of CMEs that arrive at Earth.
• Page 9, Line 223: the other configurations > the other geometrical parameters of GCS CMEs also …
• Page 9, Line 224: configurations > parameters
• Page 9, Line 235: dashed line
• Page 9, Line 239: Where should a CME be deflected in interplanetary space. If you make such a claim, you should back it using references.

e.g., https://ui.adsabs.harvard.edu/abs/2020SoPh..295...61L/abstract

https://ui.adsabs.harvard.edu/abs/2017SoPh..292...64L/abstract

• Page 9, Line 239:

Although they could also reach the vicinity of the Earth in the end, the parts which hit

the Earth are not the main part of the flux rope but often their flank parts.

->> Rephrase this sentence to make it clearer.

• Page 9, Line 243:  which ICMEs are not MCs? State clearer what is your hypothesis and what is the subsequent analysis you are performing.
• Page 9, Line 257: is a good result.
• Page 10, Line 263: Do the authors think that a large scale deflection is possible in interplanetary space (beyond the GCS/coronagraph FOV)? Are there other possibilities that these CMEs reach Earth?
• Page 12, Line 320: computing > computed
• Page 12, Line 321-322: computing by > computed using
• Page 13, Line 339: move > remove  

Does this result suggest that the ADM is much more affected by outliers or that in both cases the statistical sample is to small? You should elaborate on this.

• Page 14, Line 366: Rephrase first sentence especially this part: .. which gets a lot of common features about ….      Its not clear to me what you are referring to.
• Page 14, Line 370: We conclude the following:
• Page 15, Line 377: Assuming a radial ….
• Page 15, 3. : see general comments, and additionally I suggest the main reason for the anti-correlation to be the drag (of which of course the background solar wind is a major part).
• Page 15,16, Line 425-437: Shorten or remove those paragraphs. They are too long and not really thematically relevant

 

 

 

 

 

 

 

 

Author Response

General Comments:

• The authors did not clearly state how remote sensing data and in-situ measurements of CMEs could be uniquely linked. How did the authors find the corresponding CMEs, under what conditions?

 Especially during times of higher solar activity, i.e. multiple CMEs launched during a short time period, it can be hard to associate CMEs from coronagraphs with CMEs measured in-situ using the time only. Did the authors consider to resolve this ambiguity with e.g., j-maps?

Reply: Thanks. I am sorry that we didn’t state clearly how we deduced the progenitor solar CMEs from in-situ measurements. In the revised version, we add more description of our methods, which is similar to method illustrated in Chi et al. (2018). And, the j-maps had been used in the process of our deduction.

• Around Page 10, Line 275: There might be an issue with the determination and/or definition of the acceleration phase in the analysis. The acceleration phase is defined as the phase where the CME is launched/ speeds up. In that sense, the peak acceleration should always be positive. There might be a problem with the fitting/derivative of the height-time profile.

The authors should compare their results with other studies to avoid systematic errors in the analysis. (see e.g. https://ui.adsabs.harvard.edu/abs/2011ApJ...738..191B/abstract )

It might be that your height-time plot starts in a region in which the initial acceleration already ceased. In that case I recommend to either lower the starting height (possibly with EUV data in addition to white light data) or the full removal of the acceleration from the study because in this case it would be more a property of the environment (e.g. drag) than of the CME itself. Also, I could be that its just a problem of the fit or derivation.

As a further comment: Some CMEs start at higher solar height that others, meaning that their acceleration profile is different e.g., their peak acceleration might or might not fall into the chosen height range. To study the propagation speed and the resulting acceleration or deceleration, the peak acceleration as well as the subsequent propagation phase need to be clearly identified.

This is an important issue that needs to be addressed before publication.

Reply: Thanks. I am sorry that we make you misunderstanding. The process we focus on is from >3 solar radii to about 20 solar radii, but most of CMEs reach their peak acceleration at <0.5 solar radii (Bein et al. 2011), so the acceleration is more likely an effect from the environment as your comments have suggested. In our study, we don’t want to study the acceleration phase of a CME during its propagation or the acceleration of CME itself, the acceleration that we obtain from quadratic polynomial fitting is the kinematic characteristics rather than dynamic characteristics of a CME. We analyze this parameter in this work to study the velocity changes and the effect of the drag. The statements “within 20 solar radii” in the paper is incorrect, we have changed it into “from 3 solar radii to about 20 solar radii”.

Minor Comments:

• Replace Earth-arrived with Earth-directed throughout the manuscript. If the authors want to differentiate between CMEs that are Earth-directed from a remote sensing perspective and CMEs that are measured at Earth I suggest a different wording. Earth-arrived does not sound correct.

Reply: You are right, ‘Earth-arrived’ sounds incorrect. we have change it to ‘Earth-impacting’ in the revised version rather than ‘Earth-directed’ because we focus on CMEs which arrived at Earth rather than CMEs with Earth-directed. The ‘Earth-impacting’ has been used in Davis et al. 2009 (https://doi.org/10.1029/2009GL038021).

• Page 1, Line 1: the CME > a CME

Reply: Thanks. It has been changed in the revised version.

• Page 1, Line 1-2: CMEs may cause hazardous space weather events, they don’t necessarily always do.

Reply: You are right. We changed the statement into ‘When a CME arrives at the Earth, it will interact with the magnetosphere, sometimes causing hazardous space weather events.’

• Page 1, Line 2: of the Earth-arrived CMEs > of Earth-directed CMEs

Reply: Thanks. We have changed it into ‘of CMEs which arrived at Earth (hereinafter, Earth-impacting CMEs)’.

• Page 1, Line 5: the Earth > Earth

Reply: Thanks. We delete ‘the’ in the revised version.

• Page 1, Line 5: the observations > observations

Reply: Thanks. We delete ‘the’ in the revised version.

• Page 1, Line 8: in the solar disk > on the solar disk

Reply: Thanks. It has been modified as recommended.

• Page 1, Line 12-13: is it the aerodynamic drag model or the drag-based model (DBM)?

Reply: Thanks for your comments. We believe that the aerodynamic drag model is also a kind of DBM, but in our study, we use a quadratic dependence in Equation (4), so we prefer call it aerodynamic drag model (Maloney et al. 2010, Byrne et al. 2010, Vrsnak et a. 2013).

• Page 1, Line 17: A Coronal Mass Ejection (CME) is a powerful solar …

Reply: Thanks. It has been modified as recommended.

• Page 1, Line 21: could be > can be

Reply: Thanks. It has been modified as recommended.

• Page 1, Line 27: remove the “and so on” and move the “and” to the sentence before.

Reply: Thank you for comments. It has been modified as recommended

• Page 1, Line 35: the properties at L1 are usually measured in-situ, thus the forecasting time is roughly one hour, for remote sensing observations (imaging) the forecasting time is higher. I suggest to add in-situ such that the sentence becomes:   “… mainly obtained from in-situ observations ….”

Reply: You are right. We have changed the statement into ‘these ICMEs' properties are mainly obtained from in-situ observations close to the Earth’.

• Page 2, Line 46: at the vicinity of the Earth > in the vicinity of Earth

Reply: Thanks. It has been modified as recommended.

• Page 2, Line 52: the Earth > Earth

Reply: Thanks. We delete ‘the’ in the revised version.

• Page 2, Line 63: Multiple points observation> Multi-spacecraft observations

Reply: Thanks. It has been modified as suggested.

• Page 2, Line 63: of the Solar TE…

Reply: Thanks. We have added ‘the’ in the revised version.

• Page 2, Line 68: I do not think it is possible to completely eliminate the projection effect but significantly reduce it.

Reply: Yes, you are right. We have changed the statement into ‘The possible projection effect from single perspective observation can be significantly reduced’.

• Page 2, Line 83: are the authors sure that its an aerodynamic model not drag based model? https://ui.adsabs.harvard.edu/abs/2013SoPh..285..295V/abstract

Reply: Thanks for your comments. In this phrase, we just use the original statement from Shen et al. (2014). After comparison between this model and previous studies like Maloney et al. 2010, Vrsnak et a. 2013, and Dumbovic et al. 2021, we believe that the model could be called aerodynamic model which is also a kind of drag based model.

• Page 2, Line 88-90: rephrase or remove this sentence: Halo CMEs are not necessarily Earth-directed, firstly it depends on the observing spacecraft, and secondly on the propagation direction and width (as you mention throughout). I suggest not to oversimplify. I agree that halo-CMEs commonly arrive at Earth, however I have not heard of non-Earth directed CMEs arriving at Earth (within observational uncertainties of course). I think the authors should state their definitions more clearly.

Reply: You are right. Halo CMEs are not necessarily Earth-directed, an “Earth-directed CMEs” is CME which could be found the associated frontside solar event (Wang et al. 2002), so a non-Earth-directed CME is hard to believe that they could arrive at Earth.

We changed the statements of this paragraph into “A CME which could be found the associated frontside solar event is considered to be frontside or Earth-directed, while a halo CME is thought to have an apparent size greater than 130° (Wang et al. 2002). Hence, to study what kind of CMEs are Earth-impacting, Earth-directed or frontside halo CMEs are obviously of first interest. Many studies on Earth-impacting CMEs or geoeffective CMEs have focused on such CMEs (Wang et al. 2002, Shen et al. 2014, Ameri et al. 2017, Bhardwaj et al. 2018, Goswami et al. 2019, Soni et al. 2020), however, sometimes an Earth-impacting CME is not necessarily to be halo……”.

• Page 3, Line 99: is organized as follows:

Reply: Thanks. It has been modified as suggested.

• Page 3, Line 102: make > give

Reply: Thanks. It has been modified as suggested.

• Page 4, Line 127: and further: try to avoid backets in brackets i.e. (Figure (a,b)) > (Figure a,b)

Reply: Thanks. They have been modified as suggested.

• Page 4, Figure 2: The CME is not well visible in the coronagraph images, the authors should think about adjusting this or presenting a more clear example.

Reply: Thanks. We have changed the example using the event on 14 June 2012, and we also adjusted the image to make it clearer.

• Page 5, Figure 3: I suggest to increase the resolution of the image: e.g., use the plot function instead of the routine in IDL. Also show the acceleration profile. For the values I suggest to use: 584 ± 27 km s^{-1   ­}instead of 583.89(27.06) (km*s^-1 ) 

Reply: Thanks for your comments. We have used the plot function in IDL to plot this figure and adjusted the format of the texts as your suggestions. As for the acceleration profile, I am sorry that the acceleration is a constant for one CME in our study, so we don’t have this kind of figure.

• Page 5, Line 151: ..CMEs that could be used for the analysis.

Reply: Thanks. It has been modified as suggested.

• Page 5, Line 153: … among the 77 events are not suitable to be modeled by the GCS model and should be excluded.

Reply: Thanks. It has been modified as suggested.

• Page 5, Line 163: deflection by what?

Reply: Thanks. We believe that it is possible that CMEs are deflected by Parker spiral magnetic field (Wang et al. 2004) even within the field of view of STREREO-COR2, so we just use the initial value of some parameters. Here, we add ‘by Parker spiral magnetic field’ in the revised version.

• Page 8, Line 210: radial direction?

Reply: You are right. We have changed the statement into ‘move outward almost in radial direction’.

• Page 8, Line 213: the Earth > Earth

Reply: Thanks. We delete ‘the’ in the revised version.

• Page 9, Line 222: maybe add something like: “as expected” .  As the shown behavior is what one would expect of CMEs that arrive at Earth.

Reply: You are right. We added the ‘as expected’, so this phrase becomes ‘As expected, the result also suggests……’.

• Page 9, Line 223: the other configurations > the other geometrical parameters of GCS CMEs also …

Reply: Thanks. We changed it into “the other geometrical parameters of CMEs from GCS” in the revised version.

• Page 9, Line 224: configurations > parameters

Reply: Thanks. It has been modified as suggested.

• Page 9, Line 235: dashed line

Reply: Thanks. It has been modified as suggested.

• Page 9, Line 239: Where should a CME be deflected in interplanetary space. If you make such a claim, you should back it using references.

e.g., https://ui.adsabs.harvard.edu/abs/2020SoPh..295...61L/abstract

https://ui.adsabs.harvard.edu/abs/2017SoPh..292...64L/abstract

Reply: You are right, these references are necessary. We have added in the revised version.

• Page 9, Line 239:

Although they could also reach the vicinity of the Earth in the end, the parts which hit

the Earth are not the main part of the flux rope but often their flank parts.

->> Rephrase this sentence to make it clearer.

Reply: Thanks. I am sorry for unclear statements. In revised version, we change this paragraph into “When a CME or flux rope structure that doesn't satisfy ω>=ε arrives at Earth after deflection, the parts through which the spacecraft pass is their flanks but not the central flux rope structures. So, the in-situ observation may present a non-MC appearance (Luhmann et al. 2020). On the contrary, if a CME arrives at the Earth without deflection (ω>=ε), the in-situ observation will present an MC structure”.

• Page 9, Line 243:  which ICMEs are not MCs? State clearer what is your hypothesis and what is the subsequent analysis you are performing.

Reply: Thanks. I am sorry for unclear statements. Statements about MCs or non-MCs have present in previous reply. And, we changed the phrase about analysis into “To test this idea, we divided the events into two groups. One with red diamond symbols represent the CME with MCs observed in-situ, the other with blue diamond symbols represent those with Non-MCs observed in-situ”.

• Page 9, Line 257: is a good result.

Reply: Thank you.

• Page 10, Line 263: Do the authors think that a large scale deflection is possible in interplanetary space (beyond the GCS/coronagraph FOV)? Are there other possibilities that these CMEs reach Earth?

Reply: Thanks for your question. We believe CME may be deflection in interplanetary space, and there are some studies which focus on or introduce the deflection like Wang et al.2004. Gopalswamy 2006, Jian et al. 2011, Luhmann et al. 2020, Temmer 2021, and so on.

As for other possibilities that these CMEs reach Earth, we believe that the interaction of CME-CME (Dumbovic et al. 2019) or CME and other structures like HSS (Heinemann et al. 2019) can make CME be deflected and change the possibility of it to reach Earth.

• Page 12, Line 320: computing > computed

Reply: Thanks. It has been modified as suggested

• Page 12, Line 321-322: computing by > computed using

Reply: Thanks. It has been modified as suggested

• Page 13, Line 339: move > remove  

Reply: Thanks. It has been modified as suggested

Does this result suggest that the ADM is much more affected by outliers or that in both cases the statistical sample is to small? You should elaborate on this.

Reply: Thanks for comments. The outliers are the results of ADM, they make the value of Δ much larger, so it is the value of Δ which is much more affected by outliers rather than ADM itself. We assume that the reason for outliers is that the coefficients are influenced by velocities (Dumbovic et al. 2021). And, the effect of small sample size on our results is not obvious, but it's also a possibility, and we'll try to study the effect in following work.

• Page 14, Line 366: Rephrase first sentence especially this part: .. which gets a lot of common features about ….      Its not clear to me what you are referring to.

Reply: Thanks. In revised version, we changed it into “This work is a systematic research and analysis of 71 Earth-impacting CMEs from 21 July 2008 to 11 December 2012. The three-dimensional parameters of these CMEs are obtained using the GCS model, and they have been used to analyze their geometric and kinematics characteristics, and an attempt has been made to find a simple propagation model of them.”.

• Page 14, Line 370: We conclude the following:

Reply: Thanks. It has been modified as suggested.

• Page 15, Line 377: Assuming a radial ….

Reply: Thanks. It has been modified as suggested.

• Page 15, 3. : see general comments, and additionally I suggest the main reason for the anti-correlation to be the drag (of which of course the background solar wind is a major part).

Reply: Thanks. You are right, the main reason for the negative correlation is the drag. We have changed the statement into “……follow each other with a negative correlation owing to the drag from the environment of which the background solar wind is a major part, so we use the v-axis intercept 341 km. s^-1 as the average solar wind……”.

• Page 15,16, Line 425-437: Shorten or remove those paragraphs. They are too long and not really thematically relevant

Reply: Thanks. We have shortened this paragraph. Now it becomes “Recently, some new solar probe spacecraft have been launched (e.g., Parker Solar Probe and Solar Orbiter), and other concepts to monitor the Sun and inner heliosphere are proposed by Wang et al. (Solar Ring mission). With the help of the observation of PSP, Solar Orbiter, and possible Solar Ring, we can observe the generation, propagation and interaction of CMEs from more perspectives (e.g., Braga and Vourlidas 2021), and some more accurate forecast models of Earth-impacting CMEs can be established”.

Author Response File: Author Response.docx

Reviewer 2 Report

REW 2

LINE 95: …all Earth-arrived CMEs recorded by STEREO (2008-2012)…

LINE 109: we investigate whether ICMEs…corresponding CMEs. Based on which criterion?

LINE 108: from STEREO…ADD THE RELATED SITE…

LINE 113: …an ICME-CME list…This list should be given to one Appendix. A Table with 9 Columns: Number of event, CME’s onset time, initial time (recorded by LASCO COR), Position Angle, Width, Linear Speed, Acceleration, (all of them as recorded in NASA catalog), ICME’s start ejecta and Velosity of the ejecta (from WIND catalog).

LINE 144: Fgiure…Figure

Figure 3: …’we did the linear fitting for the time series of h_front to get the average initial velocity….initial acceleration…’. How to select points from the time series and how many points? In this figure, there are 8 points.

The method of calculating the velocity and acceleration is analogous to the method used in the list of SOHO/LASCO.  However, the results differ (e.g. for the event of 6 June 2012, the value of initial velocity is 494 km/sec, from SOHO/LASCO and 584 km/sec, from model calculations, in Table 1). There should be some comment on this difference and on the difference that exists in the data of the two calculations.

Table 1: Time fit for the event 6 June 2012 is 20:39 UT. However, in fig. 2, the panels of fitting correspond to 21:24:…Is there any explanation for this time difference?

LINE 248-249: ‘There is no…. ω<ε’.  DELETE THIS PHRASE.

LINE 249-256: The error of θ, φ and ε or CPA (3.3 deg) is negligible. The error of ω (half angular width) is between +13.1 deg and -7.1 deg. This means that, e.g. if ω is equal to 50 deg. The width of CME is 100 deg. According to the values of error, the width of this CME is between 93 and 113 deg and approximately, the width 93-113 deg is the same with the width of 100 deg. Consequently, the errors are not so important in order to change dramatically the conclusion ω=ε.

It is not clear to me, how the reasoning of the equation ω +13.1= ε – 3.3 arises and how it enters the graph.

LINE 377-383: The first part is resulted from the lines 219-222, in which presented a clustering of the points of histogram (fig. 5b). The histogram of ε (CPA) covers the values 0-70 deg. The second part is based on lines 231-239, ‘…the CME can arrive at the Earth without deviating when its half angular width in not less than the deviation angle i.e. ω > ε or ω=ε.’ According to fig.5c, 69% of the events fulfill this condition.  It seems that the results of fig. 5b and fig. 5c are in accordance. The remaining events do not meet this requirement ‘without deviating’.

The phrase ‘…considering the effect of the errors, most Earth-arrived CMEs (92%) still satisfy (ω > ε or ω=ε)…’, it is not formulated correctly. This percentage is 69%. The ‘effect of the errors’ is not so important as to dramatically affect this result (see above LINE 249-256).

LINE 395-396: ‘And the equation of the latter we used seems to have low performance in low speed events. The matter needs further investigation.’

Author Response

LINE 95: …all Earth-arrived CMEs recorded by STEREO (2008-2012)…

Reply: Thanks. We added “all Earth-impacting CMEs recorded by STEREO and SOHO (2008-2012)” in the revised version.

LINE 109: we investigate whether ICMEs…corresponding CMEs. Based on which criterion?

Reply: Thanks. I am sorry for unclear statements of our method. In revised version, we have added more details of our method.

LINE 108: from STEREO…ADD THE RELATED SITE…

Reply: Thanks. It is important to give the site, we have added it in the revised version.

LINE 113: …an ICME-CME list…This list should be given to one Appendix. A Table with 9 Columns: Number of event, CME’s onset time, initial time (recorded by LASCO COR), Position Angle, Width, Linear Speed, Acceleration, (all of them as recorded in NASA catalog), ICME’s start ejecta and Velosity of the ejecta (from WIND catalog).

Reply: Thanks for suggestion. We have added an ICME-CME in Appendix A.1.

LINE 144: Fgiure…Figure

Reply: Thanks. It has been modified as suggested.

Figure 3: …’we did the linear fitting for the time series of h_front to get the average initial velocity….initial acceleration…’. How to select points from the time series and how many points? In this figure, there are 8 points.

Reply: Thanks. I am sorry that we make you misunderstanding. We didn’t select the points from the time series and there are 10 points in this figure. The reason why the points is small is that we start our fitting only when all three spacecraft have clear observations of CME, and we finish our fitting when CME have move beyond the field of view of more than one spacecraft. So, if CME is fast, the data points we can get are little. This can also be seen in Discussion, we mention that we need more observations by more instruments like STEREO-HI 1,2.

The method of calculating the velocity and acceleration is analogous to the method used in the list of SOHO/LASCO.  However, the results differ (e.g. for the event of 6 June 2012, the value of initial velocity is 494 km/sec, from SOHO/LASCO and 584 km/sec, from model calculations, in Table 1). There should be some comment on this difference and on the difference that exists in the data of the two calculations.

Reply: Thanks for your comments. The velocity in SOHO/LASCO CME catalog is the projected velocity, while the velocity we get is three-dimensional, so one could expect that the three-dimensional velocity should be no smaller than projected velocity. However, there are some events which have a projected velocity larger than three-dimensional velocity. There are some studies having analyzed this phenomenon like Shen et al. 2012 (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2013JA018872).

Table 1: Time fit for the event 6 June 2012 is 20:39 UT. However, in fig. 2, the panels of fitting correspond to 21:24:…Is there any explanation for this time difference?

Reply: Thanks. I am sorry that we make you misunderstanding. The figure of GCS fitting (Figure 2) is an example of the fitting result of GCS model we selected for presentation. We did GCS fitting for every moment during CME’s propagation within field of view of three spacecraft.

LINE 248-249: ‘There is no…. ω<ε’.  DELETE THIS PHRASE.

Reply: Thanks for your comments. It has been deleted in revised version.

LINE 249-256: The error of θ, φ and ε or CPA (3.3 deg) is negligible. The error of ω (half angular width) is between +13.1 deg and -7.1 deg. This means that, e.g. if ω is equal to 50 deg. The width of CME is 100 deg. According to the values of error, the width of this CME is between 93 and 113 deg and approximately, the width 93-113 deg is the same with the width of 100 deg. Consequently, the errors are not so important in order to change dramatically the conclusion ω=ε.

It is not clear to me, how the reasoning of the equation ω +13.1= ε – 3.3 arises and how it enters the graph.

Reply: Yes, you are right. The errors are not so significant, and it’s inappropriate that we use the equation ω +13.1= ε – 3.3 as a new boundary. We have removed the line “ω +13.1= ε – 3.3” in Figure 5c in revised version. However, since the uncertainties differ from one another, we believe that the proportion of CMEs which satisfy ω>=ε is larger than 69% as shown in the figure.

LINE 377-383: The first part is resulted from the lines 219-222, in which presented a clustering of the points of histogram (fig. 5b). The histogram of ε (CPA) covers the values 0-70 deg. The second part is based on lines 231-239, ‘…the CME can arrive at the Earth without deviating when its half angular width in not less than the deviation angle i.e. ω > ε or ω=ε.’ According to fig.5c, 69% of the events fulfill this condition.  It seems that the results of fig. 5b and fig. 5c are in accordance. The remaining events do not meet this requirement ‘without deviating’.

Reply: Thanks for your comments. In Figure 5b, we focus on a clustering of the CPA, but in Figure 5c, we talk about the influence of other geometric parameters on whether a CME is Earth-impacting. For the latter, it suggests that when a CME satisfy ω>=ε, even its CPA is larger e.g. >50°, it still has the possibility to arrive at Earth as long as its size is large enough. So, the discussion of Figure 5c is an extension of Figure 5b.

The phrase ‘…considering the effect of the errors, most Earth-arrived CMEs (92%) still satisfy (ω > ε or ω=ε)…’, it is not formulated correctly. This percentage is 69%. The ‘effect of the errors’ is not so important as to dramatically affect this result (see above LINE 249-256).

Reply: Yes, you are right. As the mentioned above, we also changed the statements in this paragraph. In revised version, it becomes “And if taking CMEs' other geometric parameters into account, such as the half-angular width (ω), considering the effect of the errors, the proportion of Earth-impacting CMEs which satisfy ω>=ε is no less than 69%, it suggests that this inequality should be an important part for Earth-impacting CMEs forecasting”.

LINE 395-396: ‘And the equation of the latter we used seems to have low performance in low speed events. The matter needs further investigation.’

Reply: Thanks. We added “The matter needs further investigation” in the revised version

Author Response File: Author Response.docx