Research on a Method for Simulating Multiview Ocean Wave Synchronization Data by Networked SAR Satellites
Round 1
Reviewer 1 Report
Second review of the manuscript „Research on a method for simulating multiview ocean wave synchronization data by networked SAR satellites”
The authors have greatly improved the manuscript by modifying figures and substantial amount of new texts. The current version is more likely to get published once the authors’ responses the minor revisions.
Minor comments
Equation 1, omega is not defined.
Figure 1, x-axis: please replace w with omega
Author contribution: ….., “Xiaolei Shi analyzed the data and drew the flow charts”, flow charts were removed from the manuscript.
Author Response
Dear Editors and Reviewers,
Thank you and reviewers for giving constructive comments for our manuscript. Our manuscript entitled “Research on a method for simulating multiview ocean wave synchronization data by networked SAR satellites” has been revised in response to the comments. Thank you for the opportunity to submit this revision manuscript for possible publication in the journal.
We have given serious consideration to Editor’s and Reviewer’s comments and suggestions, and have revised the manuscript carefully. In order to make your review easy, we have marked modified sections by using the “Track Changes” function in Microsoft Word. All Page number and line number in “Revision detail” are based on the file “jmse-511369-revised”. Manuscript revisions are addressed in detail below.
Reviewer #1:
Thank you very much for valuable suggestions. We have given serious consideration to reviewer #1 comments and replied to the specific points point-by-point. Please attention, all Page number and line number in “Revision detail” are based on the file “jmse-511369-revised”. The responses are as follows:
1. Equation 1, omega is not defined.
Revision detail:
You are correct that omega is not defined in Equation 1. Omega (ω) is the frequency and we have defined omega which is listed as follow：(Page 4 L124-126)
“where a=0.0081, b = 0.74, g is the acceleration due to gravity, U19.5 represents the wind speed at a height of 19.5 m above the sea surface, ω is the frequency and S(ω) is the value of the PM spectrum.”
2. Figure 1, x-axis: please replace w with omega.
Revision detail:
As you said, we have replaced “w” with “omega”. (Page 6 L220)
3. Author contribution: ….., “Xiaolei Shi analyzed the data and drew the flow charts”, flow charts were removed from the manuscript.
Revision detail:
We admire your carefulness and sorry for our carelessness. You are very correct that flow charts were removed from the manuscript so we have rewritten this sentenc which is listed as follow：(Page 16 L466)
“Xiaolei Shi analyzed the data”
We would like to express special thanks to the editors and reviews for their constructive comments on this manuscript again. Please tell us some shortcoming again about this manuscript when reviewing. We hope this manuscript will be accepted by JMSE.
Thanks again, we look forward to your reply.
Best Regards,
Xiaoyu Zhang.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper is well written. The results are well presented apart from the accuracy assessment part. In particular, in lines 322-324 it is stated that the calculation method of the backscattering coefficients had a high precision. The latter is not clearly demonstrated in the RESULTS AND ANALYSIS section. In addition, in lines 380-381 it is stated that the accuracy of the obtained sea surface SAR images is high without relative documentation. Furthermore, quantification of the level of accuracy is missing.
The section CONCLUSION is mostly a summary of the research carried out in the paper. This section needs improvement.
Author Response
Dear Editors and Reviewers,
Thank you and reviewers for giving constructive comments for our manuscript. Our manuscript entitled “Research on a method for simulating multiview ocean wave synchronization data by networked SAR satellites” has been revised in response to the comments. Thank you for the opportunity to submit this revision manuscript for possible publication in the journal.
We have given serious consideration to Editor’s and Reviewer’s comments and suggestions, and have revised the manuscript carefully. In order to make your review easy, we have marked modified sections by using the “Track Changes” function in Microsoft Word. All Page number and line number in “Revision detail” are based on the file “jmse-511369-revised”. Manuscript revisions are addressed in detail below.
Reviewer #2:
Thank you very much for valuable suggestions. We have given serious consideration to reviewer #2 comments and replied to the specific points point-by-point. Please attention, all Page number and line number in “Revision detail” are based on the file “jmse-511369-revised”. The responses are as follows:
1. English language and style are fine/minor spell check required
Revision detail:
You are very correct that English language and style needs improvements. Our manuscript has been edited throughout the article for proper English language, grammar, punctuation, spelling and scientific writing style by one or more of the highly experienced native English speaking editors according to your comment. Some wrong usage of phrases and combination of sentences have been modified.
2. The results are well presented apart from the accuracy assessment part. In particular, in lines 322-324 it is stated that the calculation method of the backscattering coefficients had a high precision. The latter is not clearly demonstrated in the RESULTS AND ANALYSIS section.
Revision detail:
Thanks very much for the valuable suggestion. According to your comments, in the RESULTS AND ANALYSIS section, we have added a section 3.3, named “Accuracy assessment of the multiview ocean wave SAR synchronization data”, to assess the accuracy of the data. When the incident angle of SAR beam is fixed with the angle of wind direction, the backscatter coefficient increases with the increase of wind speed. The simulated results are in agreement with the theory, so we have obtained the conclusion that the accuracy of the backscattering coefficient is relatively high. (Page 13-14 L320-377)
3. In addition, in lines 380-381 it is stated that the accuracy of the obtained sea surface SAR images is high without relative documentation.
Revision detail:
You are very correct. In order to analyze the accuracy of the simulated ocean wave SAR data, we have used Max-Plank-Institute (MPI) algorithm to invert the wave spectrum of SAR wave data, and the results of MPI inversion showed in section 3.3. We have obtained the conclusion that the direction of wave propagation is consistent with the input parameters and the fit wave spectrum is the same as the first guess wave spectrum. The input parameters and output parameters can be matched, we believe that the accuracy of the simulated ocean wave data is relatively high. (Page 13-14 L320-377)
4. Furthermore, quantification of the level of accuracy is missing.
Revision detail:
You are very correct that quantification of the level of accuracy is missing. We have added levels and every figure has a magnitude on the right side now, except figure 7.
5. The section CONCLUSION is mostly a summary of the research carried out in the paper. This section needs improvement.
Revision detail:
You are very correct that the section conclusion needs improvement. We have rewritten this section to make it clear. (Page 16 L447-470)
We would like to express special thanks to the editors and reviews for their constructive comments on this manuscript again. Please tell us some shortcoming again about this manuscript when reviewing. We hope this manuscript will be accepted by JMSE.
Thanks again, we look forward to your reply.
Best Regards,
Xiaoyu Zhang.
Author Response File: Author Response.pdf
Reviewer 3 Report
the paper is presenting a simulation method to describe the feasibility of synchronised SAR acquisition and their impacts on sea state retrieval. the paper is of interest but is the approach is very standardised one that has been used several times and adds no novelty to the literature. The interesting section is 3.2 however I am a bit puzzled with it as no simulation result is described here despite being mentioned in the Discussion Section. I am afraid at this stage it is not ready for publication and should be returned to the Authors for an extensive review.
Author Response
Dear Editors and Reviewers,
Thank you and reviewers for giving constructive comments for our manuscript. Our manuscript entitled “Research on a method for simulating multiview ocean wave synchronization data by networked SAR satellites” has been revised in response to the comments. Thank you for the opportunity to submit this revision manuscript for possible publication in the journal.
We have given serious consideration to Editor’s and Reviewer’s comments and suggestions, and have revised the manuscript carefully. In order to make your review easy, we have marked modified sections by using the “Track Changes” function in Microsoft Word. All Page number and line number in “Revision detail” are based on the file “jmse-511369-revised”. Manuscript revisions are addressed in detail below.
Reviewer #3:
Thank you very much for valuable suggestions. We have given serious consideration to reviewer #3 comments and replied to the specific points point-by-point. Please attention, all Page number and line number in “Revision detail” are based on the file “jmse-511369-revised”. The responses are as follows:
1. Moderate English changes required.
Revision detail:
You are very correct that English needs moderate improvements. Our manuscript has been edited throughout the article for proper English language, grammar, punctuation, spelling and scientific writing style by one or more of the highly experienced native English speaking editors according to your comment. Some wrong usage of phrases and combination of sentences have been modified.
2. the paper is presenting a simulation method to describe the feasibility of synchronised SAR acquisition and their impacts on sea state retrieval. the paper is of interest but is the approach is very standardised one that has been used several times and adds no novelty to the literature.
Revision detail:
We have to admit that the simulation approach is very standardised and adds no novelty to the literature. Sorry that we did not innovate in the process of SAR observation of ocean waves, and the purpose of simulating multiview SAR wave synchronization data is mainly for future research work, which is the wavelength cutoff compensation mentioned in the paper. And the innovation of this paper is based on the simulation method to simulate the virtual networked SAR satellites and generate the multiview wave synchronization data. By using this data, what we want to achieve is to use the simulated multiview SAR wave synchronization data for data fusion, and analyze the fused data to compensate for the azimuth cutoff wavelength. In order to prove the feasibility of the simulation method and ocean wave data, we have added a section 3.3, named “Accuracy assessment of the multiview ocean wave SAR synchronization data”, to assess the accuracy of the data. Through the verification of MPI algorithm, the accuracy of simulated wave data is acceptable, which can also prove that the simulation method adopted is feasible, although the method is not innovative.
3. The interesting section is 3.2 however I am a bit puzzled with it as no simulation result is described here despite being mentioned in the Discussion Section.
Revision detail:
Thank you for your valuable suggestions. You are very correct that no simulation result is described in section 3.2 and it will make the structure of the paper inconsistent. We have readjusted the chapter structure that the simulation results are put into section 3.2 and the analysis of results part remains in the Discussion Section. (Page 11-12 L310-318)
We would like to express special thanks to the editors and reviews for their constructive comments on this manuscript again. Please tell us some shortcoming again about this manuscript when reviewing. We hope this manuscript will be accepted by JMSE.
Thanks again, we look forward to your reply.
Best Regards,
Xiaoyu Zhang.
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
I am happy with the modifications and the changes to the manuscript. I think it states clearly now what the objectives are and -in spite of some limitations outlined in the previous review and acknowledged properly - the manuscript still has value for publication. I would like to have the quality of the figure improved (as well as the figure captions), as some have legends or axes that are difficult to read, but I leave the Editor that decision. Section 3.2 that was missing in the previous version is now included.
I would suggest a check of the reference formatting so to adhere to the Journal standards, but overall I think this should not stop the paper from the publication
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
Reviewer:
Thank you very much for valuable suggestions. We have given serious consideration to reviewer comments and replied to the specific points point-by-point. Please attention, all Page number and line number in “Revision detail” are based on the file“jmse-482893-revised”. The responses are as follows:
1. It is too long; there are many obvious facts and lots of typos.
The quality of the text should be substantively improved before it became acceptable for publication.
Important; for me the first problem of the manuscript is the quality of the text (crucial: construction of sentences, English style, minor: missing of spaces and references).
Revision detail:
You are very correct that English needs significant improvements.Our manuscript has been edited throughout the article for proper English language, grammar, punctuation, spelling and scientific writing style by one or more of the highly experienced native English speaking editors according to your comment. Some wrong usage of phrases and combination of sentences have been modified.We have rewritten the introduction section and references from recent years are cited.
2. Important; the discussion section must be improve, expand on your discussion and add conclusionsto make it abundantly clear what NEW findings your study reached.
Discussion section is too short, irrelevant and out of focus.
Revision detail:
You are very correct that the discussion section must be improve and expand. We have rewritten discussion section and added conclusion section to make it abundantly clear what new findings our study reached.In discussion section, firstly, we analyzed in detail the results of each step of the imaging simulation based on section 3.1. Secondly, we analyzed in detail the simulation of networked satellites based on section 3.2. Especially important, the multi-view SAR wave synchronization data are generated, which is the most innovative part of this paper, and we make it abundantly clear in conclusion section.
3. The text is difficult for reading, with lots of trivial information, so I suggest rewriting the sections 2 and 3 to make them shorter and more condense.
Revision detail:
You are very correct that the text is difficult for reading, we have rewritten section 2 and 3 to make them shorter and more condense. We have removed some trivial information such as formulas, figures and diagrams.(Page 3-11 L117-310)
4. The figures 4-8 are black-white and are not very important, I suggest making them more condense, and in color.
Revision detail:
You are very correct, we have removed figure 7-8 and the remaining figures are colored.(Figure 4: Page 9 L266-269;Figure 5: Page 9 L275-278; Figure 6: Page 10 L293-296)
5. Please explain why the “future works” are important for readers of your manuscript. I suggest removing it.
For me, the future research work is not so important. For sure it is not important to take half of conclusion section. I suggest removing it completely or making it significantly shorter.
Revision detail:
You are very correct that the future work is not important, so we removed it completely. Only at the end of discussion section, we mentioned the future research work to illustrate the importance and significance of multi-view ocean wave synchronization data.(Page 13 L373-377)
“In future research, wave spectrum inversion can be realized based on simulated SAR data and compared with the buoy omnidirectional spectrum or wave spectrum data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) to study the energy loss under different degrees of azimuth cutoff.The compensation of the azimuth cutoff wavelength can be realized based on multiview SAR sea wave synchronization data.”
6. The abbreviations (like RD, CS, PM, VV…) are not defined.
L40. “SAR” is not “defined”.
Revision detail:
Abbreviations and acronyms are typically defined the first time the term is used within the main text and then used throughout the remainder of the manuscript. We have defined the abbreviations(RD, PM ,SAR, 2-D) in Abstract. SAR stands for Synthetic Aperture Radar, PM means Pierson Moskowitz (wave spectrum), RD represents Range Doppler (imaging algorithm), and 2-D is an abbreviation for two-dimensional. (Page1L11-21)
SWH is an abbreviation for significant wave height. (Page 2 L49)
VV stands for vertical polarization. (Page 5 L169)
7. L139-140, 154, 156……..: Please remove the dimensions “(m/s2) and (m/s) and (rad)” it is trivial information.
Revision detail:
You are correct that the dimensions “(m/s2) and (m/s) and (rad)” are trivial information, so we have removed the dimensions completely. (Page 4 L125-126, 137-139)
8. Please add the space between the numbers and units (L283, 284, 324, 325,…..)
In the section lots of “spaces” are missing (like “simulation[13].In”).
Revision detail:
Sorry for our imprecision. We have added the spaces between the number and units.
9. Please connect (cite) the equations from section 2 with the text and figures in the section 3, otherwise you can remove some the equations.
Revision detail:
We have rewritten section 2 and section 3 to make them more condensed. Some redundant information are removed and equations from section 2 are cited with the text and figures in the section 3. The changes are as follows:
(1) “Wind speeds of 10 m/s, 13 m/s, and 15 m/s were assigned equation (1), and the 1-D PM spectrum was simulated, as shown in Figure 1.” (Page 6 L216-217)
(2) “A wind direction angle of 45° and wind speeds of 10 m/s and 15 m/s at a height of 10 m were assigned to equation (4), and the 2-D PM wave spectra were simulated.” (Page 7 L224-225)
(3) “The 2-D sea surface was simulated by using the 2-D PM wave spectrum as the spectral model, as shown in Figure 3(a) and (b). These results are based on equations (5) and (6).” (Page 8 L245-247)
(4) “The ocean surface backscattering coefficient of wind speeds of 10 m/s and 15 m/s could be obtained by equations (7) – (9), as shown in Figure 4.” (Page 8 L261-262)
(5) “After calculating the backscattering coefficient, the ocean surface echo signals were calculated based on equations (10) and (11), as shown below.” (Page 9 L271-272)
10. The introduction section is very difficult to read. The section is out of focus. There are few references and they are too old. I am not the native English speaker, but I suggest improving the (English) style of the text and rewriting the introduction section.
Revision detail:
Thanks for your valuable suggestions. We have to admit that the introduction section is badly written. According to your comment, we have rewritten the introduction section and the changes are as follows: (Page 1-3 L31-116)
(1) We have rewritten the first paragraph to explain the significance of ocean wave detection.
(2) In the second paragraph, the length of numerical model and field observations has been shortened, and the advantages of SAR have been highlighted. References from recent years are cited in this paragraph.
(3) In the third paragraph, we briefly introduce the causes of the azimuth cutoff wavelength and its impact on SAR images.
(4) In the next two paragraphs, we introduce the research status of azimuth cutoff wavelength and SAR imaging simulation. References from recent years are cited in the paragraphs.
11. In the section 2, diagram between lines 122-125 (263-264) appear as “Deus ex machina”, please add the sentences describing the diagram, numerate it, make the caption or remove it. Add the references.
L263-264 please corrected as suggested in board comments.
Revision detail:
You are correct that section 2 with lots of trivial information. We removed thediagramsin order to make section 2 more condense.
12. Section 2.1 Please, for easier reading, explain what the starting and target variables are.
Revision detail:
You are correct that section 2.1 is difficult for reading and we have explained the starting and target variables.The explanations are as follows:
(1) “where h is the sea surface height and?? represents the wind speed at different sea surface heights, except 10 m.”(Page 4 L131-132)
(2) “In the equation, the values of a, b, and g are the same as those in equation (1), K denotes the wavenumber, and ???(?,?) represents the wavenumber direction spectrum.”(Page 4 L144-145)
Specific comments
13. L33. The sentence is difficult to read, please make the sentence more readily.
Revision detail:
The sentence is to illustrate the significance of wave detection, and we have rewritten this sentence which is listed as follow: (Page 1L33-36)
“For many situations, itis necessary to understand their internal structures, such as marine transportation, offshore platforms, changes, and ocean wave parameters at specific locations for ports and ocean engineering”
14. L40-41. Please correct the sentence. L41-42. Please correct the sentence.
Revision detail:
We have rewritten the sentence which is listed as follow: (Page 2 L38-42)
“A numerical model uses mainly mathematical operations to calculate and predict the sea state. Although the model can obtain the results of ocean wave parameters of long-term sequences, it is affected by multiple conditions, such as initial condition settings, observation data assimilation and water depth.”
15. L42-46. The sentence is extremely difficult to read, please make the sentence more readily.
Revision detail:
You are correct that L42-46 is difficult to read and we have rewritten the sentence which is listed as follow: (Page 2 L42-45)
“Field observations mainly consist of sea state measurements from buoys. Buoys are recognized as more accurate means in the field observation of ocean waves; however, buoy locations are sparse, and the data records at each position may be discontinuous.”
16. L49. Please explain “scope of observation is limited”.
Revision detail:
We wanted to illustrate by “scope of observation is limited” that the coverage of buoys is not large, and we have rewritten the sentence which is listed as follow: (Page 2 L44-45)
“buoy locations are sparse and the data records at each position may be discontinuous”
17. L49-50. “It is generally only used to verify the parameters of ocean waves obtained by other methods.” Are you sure?! The reference is necessary.
Revision detail:
Sorry that we did not make it clear and we have rewritten the sentence and added the reference which is listed as follow: (Page 2 L45-46)
“Buoys can verify the ocean wave parameters obtained by numerical models and remote sensing.”
18. L51-53. The sentence is difficult to read, please make the sentence more readily.
Revision detail:
The sentence is to illustratealtimeters and scatterometers are not suitable for observing the ocean waves, and we have rewritten the sentence which is listed as follow: (Page 2 L48-52)
“Although altimeters provide uniform, repetitive measurements of the significant wave height (SWH), other wave parameters, such as the mean wave period, cannot be observed by altimeters. Scatterometers are most prominent for the observation of surface winds over global oceans instead of ocean waves.”
19. L54. “Compared with other methods”, what methods?
Revision detail:
Sorry that we did not make it clear and we have replaced “Compared with other methods” by “Compared with numerical models and in situ buoy measurements at a single location, SARs are effective and of great interest because of the high spatial resolution and the almost instantaneous observation potential of large ocean areas.”. (Page 2 L52-55)
20. L55-56. Please correct the sentence.
Revision detail:
We have rewritten the sentence which is listed as follow: (Page 2 L55-58)
“As a powerful instrument to measure ocean waves, a SAR can work all day under almost any weather condition. A SAR has multiband and multipolarization characteristics, which allow the estimation of the spatial distributions of the investigated characteristics.”
21. L54-63 please add the references and expand the paragraph.
Revision detail:
According to your comment, we have rewritten L54-63 and cited references from recent years. Now L54-63 has been divided into two paragraphs. At the end of second paragraphof the introduction, we have highlighted the advantages of SAR.At the third paragraph of the introduction, we briefly introduce the causes of the azimuth cutoff wavelength and itsimpact on SAR images.(Page 2 L52-71)
22. L64-79 is difficult to read, please rewrite it and correct the typos.
Revision detail:
You are very correct that L64-79 is difficult to read, so we have rewritten it and corrected the typos.
Azimuth cutoff wavenumber is not the focus of this paper, so we have removed part of the research status and rewritten it which is listed as follow: (Page 2 L72-77)
“The azimuth cutoff wavelength is an inherent drawback of SAR and has not received much attention as a helpful sea state parameter. In 1996, Kerbaol V et al. proposed evidence of the azimuth cutoff dependency on the wind speed and SWH. In 2014, Ren et al. proposed two models to directly retrieve the SWH using the azimuth cutoff. In 2015, Justin E. Stopa et al. estimated the wave orbital velocity from the azimuth cutoff wavelength using Envisat advanced synthetic aperture radar (ASAR) measurements.”
23. L64: Please explain “Few scholars at home and abroad”.
Revision detail:
What we want to say in this sentence is that there is little research on the azimuth cutoff wavelength. And we have rewritten the sentence which is listed as follow: (Page 2 L72-73)
“ The azimuth cutoff wavelength is an inherent drawback of SAR and has not received much attention as a helpful sea state parameter.”
24. L81. “The azimuth cutoff wavelength compensation is the future research work of this paper.” Please correct the sentence.
Revision detail:
We have rewritten this sentence which is listed as follow: (Page 2 L79-80)
“Currently, there is no research on compensating the azimuth cutoff wavelength, which is the subject of this paper.”
25. L96-98. “Using simulation methods”. What methods? Please improve (rephrase) the sentences.
Revision detail:
We have rewritten this sentence which is listed as follow: (Page 3 L91-94)
“In general, ocean SAR imaging simulations can be separated into two methods. For the first method, ocean SAR data are simulated at the image level: by using certain equations, SAR imagery is numerically computed.”
26. equation 2: what is “lg”? Maybe log or ln?.
Revision detail:
Sorry that we did not make it clear and we have replaced the “lg(ℎ10)” by “log100.1∗h”. (Page 4 L129 equation (2))
27. L150 reference needed.
Revision detail:
You are correct that “The International Ship Structure Association (ISSC) recommends the following two values” needs reference. But we have rewritten section 2 so that this sentence and corresponding formula were removed.
28. L166 Please remove “also known as linear filtering method”.
Revision detail:
As you said, we have removed “also known as linear filtering method”.(Page 4 L148-149)
29. L173 the are some unknown symbols.
Revision detail:
You are correct that there are some unknown symbolsand we have explained them which is listed as follow: (Page 4L152-155)
“where ??,?? respectively represent the length of 2-D ocean surface in range direction and azimuth direction; M, N represent the sampling points of the ocean surface in range and azimuth directions, respectively, so ??,?? respectively represent the range of sampling points.”
30. L204 “Debye formula” please add the references.
Revision detail:
You are correct that “Debye formula” needs to add the references. And we have added a paper as a reference in Page line and in reference list. (Page 5 L178-179)
31. equation 12. Please explain “rect” and “PRT”.
Revision detail:
We have explained “rect” and “PRF”. Rect is an abbreviation for rectangular function, and PRF is the pulse repetition time.(Page 6L199)
32. Figure 1: caption: please remove “This is”. Y-axis please add amplitude units.
Revision detail:
You are very correct, “This is the spectrum of a one-dimensional PM spectrum at different wind speeds” does not match the naming rules of figures. We have removed “This is” and added amplitude units (m^2/Hz) in Figure 1.(Page7 L222-223)
33. L309, 311 Figure 3? Also, both figure 3 are BW but in figure caption is “The colored bars”.
Revision detail:
Sorry for ourimprecision. Figure 3.(a)(b)(c)(d) are in color now.(Page8 L254-260)
34. L395 Please explain how the Monte Carlo was used.
Revision detail:
In our manuscript, Monte Carlo is a method of simulating two-dimensional ocean surface. We have explained how the Monte Carlo was used which is listed as follow: (Page 11-12 L340-345)
“According to section 2.2, we can summarize the specific steps of the Monte Carlo method. First, 2-D Gaussian white noise is simulated, and then the noise is linearly filtered by the 2-D wave spectrum to obtain the FFT of the ocean surface height fluctuation function, and the ocean surface height fluctuation function can be obtained by IFFT. No time factor was added during the ocean simulation, so the Monte Carlo method is used to simulate the freezing ocean surface.”
