Hardware Acceleration of Tsunami Wave Propagation Modeling in the Southern Part of Japan

Round 1

Reviewer 1 Report

• Brief summary

The paper aims to present a new tool for fast assessment of tsunami impact on the coast through real time modeling. It is true that it is important for decision makers to have modeled results of the phenomenon as it is evolving, so fast computations are of great value. The authors suggest the use of a new software/hardware tool, which they claim to be faster than other methods. They also use a previous tsunami event for testing their tool. However, although the proposed tool seems promising, its capabilities are not documented thoroughly and a number of aspects remain without proper explanation.

 

• Broad comments

The manuscript is adequately structured, but the English language in many parts is not appropriate and understandable. This results in lack of understanding of several parts. A few improvements have been suggested in the specific comments part, but the manuscript needs rewriting in most parts, especially “Data and Methods” and “Discussion” chapters.

It is not clear if the proposed methodology refers to specific hardware configuration and/or specific modeling code. There is a reference to the MOST code, but it is also not clear if the example presented is with this code or another. The authors mention about acquiring data from DART buoys or other offshore pressure gauges for inverse modeling, but they don’t explain at all how this is incorporated in their methodology.

The results of their test cases are not presented thoroughly and in detailed, while a direct comparison with other competitive methodologies, both for the results as well as the computational time, would be very useful for justifying the significance of the tool they suggest.

 

• Specific comments

Line 19: “However, extreme tsunami heights at some of such a sites caused by local bathymetry” needs rephrase. Consider “However, extreme tsunami heights at some of those areas can be attributed to local bathymetry”.

Line 19-21: “It is possible to provide local authorities with the PC based software/hardware tool for fast (say, in a few minutes) evaluation of tsunami danger for particular village or industrial unit at the coast.” The statement is too optimistic. Tsunami modeling can only be made by experts; otherwise, it could be led to very dangerous decisions. I suggest omitting such a sentence or write something like “such a tool would be useful for expert decision makers”.

Line 33-34: “to enjoy valuable performance gain exploiting Graphic Processing Units” I think this is what is meant “to employ valuable performance gain by exploiting Graphic Processing Units”

Line 148-151: Description is not clear.

Line 178-181: Reference is needed here. Estimation of rupture geometry is based on previously published empirical equations.

Line 186-193: Meaning is not clear.

Line 218-219: The maximum number in the color scale is 5 m, so why do you that “the largest tsunami wave heights (up to 8 m) are expected at Shikoku Island”? Besides that, the scale of the map as well as the color scale doesn’t allow to be so precise “while the coast of Kii Peninsula is practically safe as the expected tsunami wave heights do not exceed 1 m”. A lot of yellowish cells are visible if you zoom in.

Line 219-220: “(points with horizontal index 1340-2000 in Figure 7)” where is such index in the figure?

Line 228-230: For figure 6 it also applies the same comment for the scales as for figure 7.

At which depth does the calculation stops? When you have a ~250m grid, we cannot discuss about values along the shore.

Line 239-248: This should not be part of the discussion, but of the “Data and Methods”.

Also in the discussion, the part of the know problem of cell size vs model accuracy vs computational resources and time takes more space than the results of the paper.

Figures 6 to 8: close up to areas of interest, as they discussed in the text will give a better idea of the values discussed in the text

Figure 9 is not visible.

Author Response

Thanks to reviewer comments, we introduce new pictures, add some references, rewrite “Discussion” chapter and most of “Data and Methods” one, as well as several other parts of the paper body. We also arrange additional numerical experiment to prove that the observed distribution of the wave heights really depends on the model, but not on the computational grid.

We also improve language and grammar.

We stress in Introduction and Conclusion that a specific hardware configuration and the corresponding modeling code were used.

Detailed comments:

Point 1 “However, extreme tsunami heights at some of such a sites caused by local bathymetry” needs rephrase. Consider “However, extreme tsunami heights at some of those areas can be attributed to local bathymetry”. 

Response 1 Accepted

Point 2 “It is possible to provide local authorities with the PC based software/hardware tool for fast (say, in a few minutes) evaluation of tsunami danger for particular village or industrial unit at the coast.” The statement is too optimistic. Tsunami modeling can only be made by experts; otherwise, it could be led to very dangerous decisions. I suggest omitting such a sentence or write something like “such a tool would be useful for expert decision makers”. 

Response 2 Rewritten

Point 3 “to enjoy valuable performance gain exploiting Graphic Processing Units” I think this is what is meant “to employ valuable performance gain by exploiting Graphic Processing Units” 

Response 3 Rewritten to outline, that performance gain could be achieved by using GPU or FPGA.

Point 4 Line 148-151: Description is not clear. 

Response 4 Explanation provided, now in the paper: “We conducted 12 numerical experiments for model tsunami sources (indicated as Si-j in Figure 3). The sources are of the same shape with elevation and subsidence parts (details are given in the next subsection). The selected shape of the initial sea surface displacement has 4 different positions along the coast (indicated with subscripts i=0,1,2,3) and 3 values of the offshore distance (with the indication j=a,b,c).”

Point 5 Line 178-181: Reference is needed here. Estimation of rupture geometry is based on previously published empirical equations. 

Response 5 Explanation and reference provided, now in the paper: “The model source was built according to the elastic-plastic model proposed in [17]. This model is currently used by the NOAA tsunami warning services to calculate the initial displacement in the tsunami source area on the basis of seismic monitoring data. The input data for calculating the ocean floor displacement field are the basic parameters describing the earthquake seismic mechanism.”

Point 6 Line 186-193: Meaning is not clear.

Response 6 Explained, now in the paper: “The 200 x 100 km tsunami sources presenting sea bed displacement due to an earthquake of magnitude 8.0 were used in our computational experiments. The suggested seismic mechanism is similar to the historical tsunamigenic earthquakes at Nankai-Tokai subduction zone. The initial water surface displacement with a maximum elevation of 400 cm and the lowest subsidence of -200 cm caused by such earthquake is presented in Figure 5.”

Point 7 Line 218-219: The maximum number in the color scale is 5 m, so why do you that “the largest tsunami wave heights (up to 8 m) are expected at Shikoku Island”? Besides that, the scale of the map as well as the color scale doesn’t allow to be so precise “while the coast of Kii Peninsula is practically safe as the expected tsunami wave heights do not exceed 1 m”. A lot of yellowish cells are visible if you zoom in.

Response 7 Explained, now in the paper: “The color scale in Figures 6, 8, 9 shows the height-color relation for wave height values between 0 and 5 m. In case the tsunami height exceeds 5 m at certain grid points, we use for visualization the same color as the points with maximum level elevation of 5 m.”

Comments added, now in the paper: “Figures 6, 8 show that for such location of the initial sea surface displacement (sources S0-c and S1-a) the largest tsunami wave heights (5+ m) are obtained at Shikoku Island, while the coast of Kii Peninsula is practically safe as the expected tsunami wave heights do not exceed 1 m.”

“As follows from numerical results, the given position of initial sea surface displacement results in an almost 8-meter tsunami wave at a certain part of Shikoku Island (Figure 8). At the same time, the height of tsunami wave is less then 1 m at the entire coast line of Kii Peninsula (see also points with horizontal index 1340-200 in Figure 10A).”

We also denote Kii Peninsula and Shikoku Island in Figures 6, 8, 9 (formerly Figures 6-8) 

Point 8 Line 219-220: “(points with horizontal index 1340-2000 in Figure 7)” where is such index in the figure?

Response 8 Corrected

Point 9 Line 228-230: For figure 6 it also applies the same comment for the scales as for figure 7.

Response 9 Corrected

Point 10 At which depth does the calculation stops? When you have a ~250m grid, we cannot discuss about values along the shore.

Response 10 Explained, now in the paper: “In this paper we check the possibility of a very rapid numerical simulation of tsunami wave propagation on modern PC with FPGA based acceleration. So, numerical simulation was performed up to the depth of 10 m. The full reflection boundary conditions were used at this depth. To obtain detailed wave heights maxima along the coast in future we will use nested grid approach with the mesh resolution of several meters at coastal areas.”

Point 11 Line 239-248: This should not be part of the discussion, but of the “Data and Methods”.

Response 11 Discussion is rewritten

Point 12 Figure 9 is not visible.

Response 12 We hope that now the Figure 10 (Figure 9 in the previous version) is visible.

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

General impression about the article “Hardware Acceleration of Tsunami Wave Propagation Modeling at Southern Part of Japan”

This manuscript presents a method to reduce the required computational time for calculating the tsunami propagation on a personal computer. To achieve this objective the researchers implemented an existing numerical method (the Mac-Cormack scheme) on a new type of hardware called a “Calculator”. Given (i) the catastrophic effects of recent tsunamis (e.g. 2004 Indian Ocean and 2011 Great East Japan Earthquake) and (ii) the significant uncertainties in predicting numerically the exact tsunami characteristics on the coast before a tsunami event,  it is critical to be able to predict in real-time (or at least as quickly as possible) the tsunami propagation and inundation of coastal communities. The work presented herein seems to contribute towards the direction of real-time prediction and is consequently worthy of publication. Moreover, the authors use the southern part of Japan as a demonstration case of the capabilities of their new software/hardware method, which adds to the value of the manuscript.

The article is generally technically sound with only a few errors, which are shown below in the comments section. Moreover, the reviewer requests the authors to provide additional information or clarifications in specific locations of the manuscript. Overall, the article left a positive impression to the reviewer, and if the authors provide proper answers to the comments of the reviewer, then the article will be suggested for publication

Major Comments:

1. L169-170: The authors state that “Using the advantages of the proposed Calculator, we “drive” tsunami wave over the water area in Figure 3 for only 25 seconds. Estimated travel time of a real wave is compared to 3200 sec”. What do they mean that they "drive" the tsunami wave over the water area for only 25 seconds? Is this the simulated time? If yes, why did they select this number and did not run the whole 3200 sec? Please clarify.

 

2. General comment: How did the authors correlate the ocean surface displacement with the generated wave at the source location? Which equation did they use? Please provide additional information.

 

3. L186-190: The authors state “Tsunami sources used in our computational experiments, shown in Figure 5, were assembled from 4 the so-called unit sources, each being sea bed displacement due to an earthquake of magnitude 7.5. Such initial ocean bed displacements are used by NOAA tsunami warning service to approximate the real tsunami source. This means that we are modeling the event of class M8.0.” It is not clear how the see displacement of four unit sources for a magnitude 7.5 leads to the modeling of an M8.0 event. Please provide additional explanation/clarification.

 

4. Section “Numerical results”: The results presented by the authors are quite interesting. However, they seem to have used only one grid size. How do they know that they have reached an accurate solution that is grid-size independent? Did they conduct a sensitivity study (e.g. select one of the cases and run it for several different grid sizes)? Given the fact that each analysis takes only a couple of seconds, the reviewer would suggest to the authors to add a section that will focus on the sensitivity of the numerical analyses, in order to make the manuscript technically sound. The authors are requested to present both time-histories of recorded wave heights at certain locations and the distribution of the heights for different grid sizes. (at least for a second grid size)

 

5. Comment for Figures 6, 7, 8: It is interesting that the maximum wave height in each figure (based on the color scale) seems to be 5m for all the tsunami sources simulated in this study. Although this maximum 5m seems to occur at different locations of the coast for each source, it is still interesting and strange that the maximum is always 5m. Do the authors have a physical explanation of this observed result? For example, could that be related to the initial energy of the generated wave (or the energy released during the movement of the ocean surface), which would be similar for all the tsunami sources?

 

6. L219: The authors say that the largest tsunami wave height is up to 8m, however, the maximum value in the color scale of Fig. 5 is 5m. So, what is the reason for the inconsistency between the figure and the text? The same inconsistency occurs between Fig.8 (shows 5m) and line 229 (says 6m).

 

7. Figure 9: Please add legends (and units) to the axes of Fig. 9. Since the information presented in this figure is significant and the blue, red and yellow lines are covering each other at certain locations making it difficult for the reader to understand what is going on, the authors are advised to generate next to the existing graphs, the same graphs but reduce the limits of the x axis in the range of the maximum heights. So instead of having a 4x1 figure they will have a 4x2 figure with the second column showing a zoom-in of the same figures (e.g. for the (A) graph the authors could show a zoom-in between 571 and 761). Alternatively, if a second column does not fit well next to the existing column, the authors could generate a new separate figure and show the zoom-ins.

 

8. Line 285-287: The authors state that “Sharp peaks in distribution of maxima of height of a tsunami are caused, as a rule, by local features of near-coastal topography of a bottom and a configuration of the coastline”. This is correct, however, is there a chance that some of the peaks could be caused by the difference in the grid size before and after a certain location? Sometimes if there is a major/abrupt change in the size of the grid, then that could be a source of numerical noise. However, in this study it looks like the authors kept the grid size relatively constant across the domain, which means that the high frequencies could not be generated by changes in the grid size. Please discuss.

 

9. New figure: To increase the value of the manuscript the authors are advised to present also in a new figure some time-histories of the free-surfaces at some selected locations (e.g. at the locations of the coast where the maximum wave heights occur). Such a graph will give an insight into how much time it takes for the specific wave to arrive at a site/location, and what will be the duration of the inundation, which can be a significant parameter in estimating infrastructure damage.

Minor Comments:

10. Title: The title could be improved. For example, the word “at” could be switched with the word “along” or “in the”.
11. Line 15: Replace “at” with “of the” or “in the”
12. Line 16: Replace “area of 100x200km rectangle” with “a rectangular area of 100x200km”
13. Line 19: Replace “such a sites caused by” with “these sites is caused by the”
14. Line18: Replace “location of tsunami source” with “the location of the tsunami source”
15. Line 21: Replace “for particular village” with “for a particular village”
16. Line 45: Replace “time required for numerical study” with “the time required for the numerical study”
17. Line 59: Replace “consists from” with “consists of”.
18. Line 173: Replace “happens” with “happened”
19. Figure 4: What is the dashed yellow line in Figure 4? The legend shows only a solid yellow line.
20. Figure 9: The “Intermediate” word in the legend is not shown clearly. The letter “I” is missing.

Author Response

Thanks to reviewer comments, we introduce new pictures, add some references, rewrite “Discussion” chapter and most of “Data and Methods” one, as well as several other parts of the paper body. We also arrange additional numerical experiment to prove that the observed distribution of the wave heights really depends on the model, but not on the computational grid.

We also improve language and grammar.

Major Comments:

Point 1 L169-170: The authors state that “Using the advantages of the proposed Calculator, we “drive” tsunami wave over the water area in Figure 3 for only 25 seconds. Estimated travel time of a real wave is compared to 3200 sec”. What do they mean that they "drive" the tsunami wave over the water area for only 25 seconds? Is this the simulated time? If yes, why did they select this number and did not run the whole 3200 sec? Please clarify.

Response 1 Explained, now in the paper: “Using the advantages of the proposed Calculator, it takes only 25 seconds to compute the tsunami wave propagation over the water area in Figure 3. In practice, travelling time of a real wave through this water area is compared to 3200 sec.”

Point 2 General comment: How did the authors correlate the ocean surface displacement with the generated wave at the source location? Which equation did they use? Please provide additional information.

Response 2 Explained, now in the paper: “We start our study with the given shape of initial sea surface displacement at tsunami source (see Figure 5). Then the shape of sea surface and components of velocity vector are calculated according to shallow water equations (1) in the entire water area under consideration.”

Point 3 L186-190: The authors state “Tsunami sources used in our computational experiments, shown in Figure 5, were assembled from 4 the so-called unit sources, each being sea bed displacement due to an earthquake of magnitude 7.5. Such initial ocean bed displacements are used by NOAA tsunami warning service to approximate the real tsunami source. This means that we are modeling the event of class M8.0.” It is not clear how the see displacement of four unit sources for a magnitude 7.5 leads to the modeling of an M8.0 event. Please provide additional explanation/clarification.

Response 3 Explained, now in the paper: “The 200 x 100 km tsunami sources presenting sea bed displacement due to an earthquake of magnitude 8.0 were used in our computational experiments. The suggested seismic mechanism is similar to the historical tsunamigenic earthquakes at Nankai-Tokai subduction zone. The initial water surface displacement with a maximum elevation of 400 cm and the lowest subsidence of -200 cm caused by such earthquake is presented in Figure 5. The model source was built according to the elastic-plastic model proposed in [17]. This model is currently used by the NOAA tsunami warning services to calculate the initial displacement in the tsunami source area on the basis of seismic monitoring data. The input data for calculating the ocean floor displacement field are the basic parameters describing the earthquake seismic mechanism.”

Point 4 Section “Numerical results”: The results presented by the authors are quite interesting. However, they seem to have used only one grid size. How do they know that they have reached an accurate solution that is grid-size independent? Did they conduct a sensitivity study (e.g. select one of the cases and run it for several different grid sizes)? Given the fact that each analysis takes only a couple of seconds, the reviewer would suggest to the authors to add a section that will focus on the sensitivity of the numerical analyses, in order to make the manuscript technically sound. The authors are requested to present both time-histories of recorded wave heights at certain locations and the distribution of the heights for different grid sizes.

Response 4 Additional numerical test with alternative computational grid was arranged. Difference in tsunami heights, obtained by using two grids, is given in new Figure 7.

Point 5 Comment for Figures 6, 7, 8: It is interesting that the maximum wave height in each figure (based on the color scale) seems to be 5m for all the tsunami sources simulated in this study. Although this maximum 5m seems to occur at different locations of the coast for each source, it is still interesting and strange that the maximum is always 5m. Do the authors have a physical explanation of this observed result? For example, could that be related to the initial energy of the generated wave (or the energy released during the movement of the ocean surface), which would be similar for all the tsunami sources?

Response 5 Corrected, now in the paper:  “The color scale in Figures 6, 8, 9 shows the height-color relation for wave height values between 0 and 5 m. In case the tsunami height exceeds 5 m at certain grid points, we use for visualization the same color as the points with maximum level elevation of 5 m. “

Point 6 L219: The authors say that the largest tsunami wave height is up to 8m, however, the maximum value in the color scale of Fig. 5 is 5m. So, what is the reason for the inconsistency between the figure and the text? The same inconsistency occurs between Fig.8 (shows 5m) and line 229 (says 6m).

Response 6 See comments to remark 5.

Point 7 Figure 9: Please add legends (and units) to the axes of Fig. 9. Since the information presented in this figure is significant and the blue, red and yellow lines are covering each other at certain locations making it difficult for the reader to understand what is going on, the authors are advised to generate next to the existing graphs, the same graphs but reduce the limits of the x axis in the range of the maximum heights. So instead of having a 4x1 figure they will have a 4x2 figure with the second column showing a zoom-in of the same figures (e.g. for the (A) graph the authors could show a zoom-in between 571 and 761). Alternatively, if a second column does not fit well next to the existing column, the authors could generate a new separate figure and show the zoom-ins.

Response 7 Explanations added, now in the paper: “Pictures A, B, C, and D of Figure 10 present the tsunami height distribution according to the along shore variation of the model source position. The longitude position of the coastal grid-points in these distributions is counted along the horizontal axis from 1 at the left boundary up to 3000 on the right (see scale at the bottom of Figure 3). “

Point 8 Line 285-287: The authors state that “Sharp peaks in distribution of maxima of height of a tsunami are caused, as a rule, by local features of near-coastal topography of a bottom and a configuration of the coastline”. This is correct, however, is there a chance that some of the peaks could be caused by the difference in the grid size before and after a certain location? Sometimes if there is a major/abrupt change in the size of the grid, then that could be a source of numerical noise. However, in this study it looks like the authors kept the grid size relatively constant across the domain, which means that the high frequencies could not be generated by changes in the grid size. Please discuss.

Response 8 Additional numerical test with alternative computational grid was arranged. Difference in tsunami heights, obtained by using two grids, is given in new Figure 7.

Point 9 New figure: To increase the value of the manuscript the authors are advised to present also in a new figure some time-histories of the free-surfaces at some selected locations (e.g. at the locations of the coast where the maximum wave heights occur). Such a graph will give an insight into how much time it takes for the specific wave to arrive at a site/location, and what will be the duration of the inundation, which can be a significant parameter in estimating infrastructure damage.

Response 9 New figure has been added.

Points 10-20 Minor Comments:

1. Title: The title could be improved. For example, the word “at” could be switched with the word “along” or “in the”.
2. Line 15: Replace “at” with “of the” or “in the”
3. Line 16: Replace “area of 100x200km rectangle” with “a rectangular area of 100x200km”
4. Line 19: Replace “such a sites caused by” with “these sites is caused by the”
5. Line18: Replace “location of tsunami source” with “the location of the tsunami source”
6. Line 21: Replace “for particular village” with “for a particular village”
7. Line 45: Replace “time required for numerical study” with “the time required for the numerical study”
8. Line 59: Replace “consists from” with “consists of”.
9. Line 173: Replace “happens” with “happened”
10. Figure 4: What is the dashed yellow line in Figure 4? The legend shows only a solid yellow line.
11. Figure 9: The “Intermediate” word in the legend is not shown clearly. The letter “I” is missing.

Response 10-20 All corrections have been made

Author Response File: Author Response.pdf

Reviewer 3 Report

This article aims to show and discuss the results and effects of tsunami wave propagation on the south coast of Japan, using a computational structure that solves the equations by a numerical method appropriate to the existing hardware characteristics.
This is an interesting topic. The issues raised are pertinent, but the paper lacks a more useful perspective for readers. Indeed, to be useful for readers, various mathematical and numerical contents need deeper and more comprehensive explanations.
Another less positive aspect is related to the non-originality of most of the content. In fact, the current content is essentially based on works already published by the authors, notably references [10], [11] and [12]. In addition, the paper "Mikhail Lavrentiev, Konstantin Lysakov, Andrey Marchuk, Konstantin Oblaukhov, and Mikhail Shadrin, 2019. Fast Evaluation of Tsunami Waves Heights around Kamchatka and Kuril Islands. Journal of Tsunami Society International, Volume 38, Number 1" is not cited/referenced, and content from this publication is also used.
In short, only the results of an application of the computational structure described in those publications appear to be original. However, in my view, there may be suficiente scientific content for a publication in the Applied Sciences journal, provided that some of the contents covered in a very superficial way in this version of the manuscript are deepened and perhaps improved in a review. Accordingly, the following suggestions are considered relevant:
- The mathematical model (equations system (1)) doesn't take into account the dispersive effects. Aren't these effects important in the propagation of a tsunami? This topic should be addressed.
- A numerical model uses several types of boundary conditions. Therefore, to be useful, the implemented boundary conditions must be provided, namely: mathematical definition of the tsunami source model (tsunami input), free passage of the wave out of the domain, and lateral boundary conditions.
- Usually, the grid is not uniform; it is a function of local depth. Clarify how this numerical model can handle a non-uniform spatial grid.
- Usually, spherical coordinates are used to simulate tsunami propagation over large areas. With the model in place (in x, y coordinates), show how the sphericity effect of the Earth is taken into account.  - Regarding the numerical method, a directional bias of the implemented scheme appears for the Saint-Venant equations. As is reported in Carmo (2017), see the reference below, a symmetric application composed of two Lx and two Ly operators that use an alternating sequence of backward and forward finite difference approximations for spatial derivatives at each time step permits removal of most of the directional bias of this scheme. This topic should be addressed as well.    Some non-original contents (text, especially sections 2 and 3, at least three figures, table 1 and most conclusions) are not properly referenced. In addition, at least one reference to the MacCormack numerical scheme must be included.
Finally, several inappropriate terms and/or less correct constructions are found throughout the text. Therefore, a complete revision of English is highly recommended.   REFERENCE
José Simão Antunes do Carmo, 2017. Natural responses to changes in morphodynamic processes caused by human action in watercourses: A contribution to support management. International Journal of Disaster Risk Reduction 24, 109–118.     

Author Response

Thanks to reviewer comments, we introduce new pictures, add some references, rewrite “Discussion” chapter and most of “Data and Methods” one, as well as several other parts of the paper body. We also arrange additional numerical experiment to prove that the observed distribution of the wave heights really depends on the model, but not on the computational grid.

We also improve language and grammar.

 

Point 1 In addition, the paper "Mikhail Lavrentiev, Konstantin Lysakov, Andrey Marchuk, Konstantin Oblaukhov, and Mikhail Shadrin, 2019. Fast Evaluation of Tsunami Waves Heights around Kamchatka and Kuril Islands. Journal of Tsunami Society International, Volume 38, Number 1" is not cited/referenced, and content from this publication is also used.

 

Response 1 We are sorry for missing, we add the reference

Point 2 - The mathematical model (equations system (1)) doesn't take into account the dispersive effects. Aren't these effects important in the propagation of a tsunami? This topic should be addressed.

 

Response 2 Explanation added, now in the paper: “The shallow water system (1) does not take into account dispersive effects because in case of local propagation of the long enough tsunami waves these effects have no time to change valuably the wave parameters at coast. Use of the shallow water approximation is typical among tsunami researchers.”

 

Point 3 - A numerical model uses several types of boundary conditions. Therefore, to be useful, the implemented boundary conditions must be provided, namely: mathematical definition of the tsunami source model (tsunami input), free passage of the wave out of the domain, and lateral boundary conditions.

 

Response 3 Explanation added, now in the paper: “In this paper we check the possibility of a very rapid numerical simulation of tsunami wave propagation on modern PC with FPGA based acceleration. So, numerical simulation was performed up to the depth of 10 m. The full reflection boundary conditions were used at this depth. To obtain detailed wave heights maxima along the coast in future we will use nested grid approach with the mesh resolution of several meters at coastal areas.”

 

The analysis of boundary conditions realized in Mac-Cormack difference scheme was made in PhD thesis of Eletsky and published in [10] (see Bibliographic reference).

 

Point 4 - Usually, the grid is not uniform; it is a function of local depth. Clarify how this numerical model can handle a non-uniform spatial grid.

- Usually, spherical coordinates are used to simulate tsunami propagation over large areas. With the model in place (in x, y coordinates), show how the sphericity effect of the Earth is taken into account. 

 

Response 4 Explanation added, now in the paper: “Mostly the regular rectangular computational grids are used for tsunami numerical modelling. The grid could be also matched with one of geography projection. We take into consideration spherical shape of the Earth by decreasing the grid step with respect to longitude for larger values of latitude. Matching the grid to geographic coordinates we suppose that the length of one arc degree at λ latitude is equal to the length of one equator arc degree multiplied by cos(λ).”

 

In addition, the Coriolis Force is ignored by the shallow-water model used by authors.  

 

Point 5 - Regarding the numerical method, a directional bias of the implemented scheme appears for the Saint-Venant equations. As is reported in Carmo (2017), see the reference below, a symmetric application composed of two Lx and two Ly operators that use an alternating sequence of backward and forward finite difference approximations for spatial derivatives at each time step permits removal of most of the directional bias of this scheme. This topic should be addressed as well. 

Response 5 As we now briefly discuss after equation (1), the non-dispersive models are working properly for modeling the local tsunami events like regarded in our study.

Point 6 Some non-original contents (text, especially sections 2 and 3, at least three figures, table 1 and most conclusions) are not properly referenced. In addition, at least one reference to the MacCormack numerical scheme must be included.

 

Response 6 Several parts of the paper have been rewritten. Reference to Mac-Cormack scheme is added.

We wish to save figures 1 and 4 even if they have been already published. Figure 1 shows quality of the developed computer code in comparison with exact solution and in comparison with the MOST code – official NOAA tool. Figure 4 provides a ground to our interest to the particular water area.

Table 1 has been reduced to 5 lines giving visible comparison of the performance achieved at several platforms.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The improvements made to the revised manuscript with a revision in specific parts, improved the paper overall, making it appropriate for publication. In general, the authors responded to the comments of the review well.

Only two last comments for consideration before publication:

• There should be at least one map (maybe figure 1) with geographic coordinates for reference.
• Regarding -Response 7 Explained, now in the paper: “The color scale in Figures 6, 8, 9 shows the height-color relation for wave height values between 0 and 5 m. In case the tsunami height exceeds 5 m at certain grid points, we use for visualization the same color as the points with maximum level elevation of 5 m.”- at the color scale legend of the figures, authors could use >5m, instead of 5m. It would make it clearer, without the need of extra explanation.

Author Response

Once again, we are grateful for the Reviewers for their comments and criticism as well as for the time they spent analyzing our paper.

 

Point 1: There should be at least one map (maybe figure 1) with geographic coordinates for reference.

Response 1: We add geographic coordinates to Figure 6.

Point 2: Regarding -Response 7 Explained, now in the paper: “The color scale in Figures 6, 8, 9 shows the height-color relation for wave height values between 0 and 5 m. In case the tsunami height exceeds 5 m at certain grid points, we use for visualization the same color as the points with maximum level elevation of 5 m.”- at the color scale legend of the figures, authors could use >5m, instead of 5m. It would make it clearer, without the need of extra explanation.

 

Response 2: Now we do use >5m, instead of 5m in Figures 6, 9, and 10.

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear authors,

 

thank you for addressing the comments of the reviewer. The updated version is more clear and technically sound. I only have three comments:

• In response to my initial comment (No9) about "presenting in a new figure some time-histories of the free-surfaces at some selected locations (e.g. at the locations of the coast where the maximum wave heights occur)" the authors said that they have added a new figure. Where is this new figure? 
• The equations in line 100-101 look bad because they are not aligned. Some terms are in one line, while the remaining ones are in the next line. Please correct.
• The top graph in Figure 11 is not aligned with the remaining ones. Please make all graphs to be aligned (under the same column).

Author Response

Once again, we are grateful for the Reviewers for their comments and criticism as well as for the time they spent analyzing our paper.

 

Point 1: In response to my initial comment (No9) about "presenting in a new figure some time-histories of the free-surfaces at some selected locations (e.g. at the locations of the coast where the maximum wave heights occur)" the authors said that they have added a new figure. Where is this new figure?

 

Response 1: We add the Figure 7, presenting the calculated tsunami heights near the South-West of Shikoku Island: 1500 sec (left figure) and 2000 sec (right figure) after start of propagation.

Point 2: The equations in line 100-101 look bad because they are not aligned. Some terms are in one line, while the remaining ones are in the next line. Please correct.

Response 2: Equations are now centered

 

Point 3: The top graph in Figure 11 is not aligned with the remaining ones. Please make all graphs to be aligned (under the same column).

Response 3: The top graph in Figure 11 is now aligned with the other ones.

Author Response File: Author Response.pdf

Reviewer 3 Report

GENERAL COMMENTS
This review covers some of the recommendations previously suggested, but does not clarify or touch on equally relevant aspects; therefore, in my view, this version still needs some additional corrections and clarifications.
Neither the mathematical formulation used (shallow water equations) nor the numerical method implemented allow to evaluate the fine processes that occur in very shallow waters (approach to the coast line, well below 10m), including uncovered (emerged) areas that can be affected by possible flooding.
Both the mathematical model and the numerical method used are suitable for large scales (orders of hundreds of kilometers wide) and deep to intermediate waters (till depths of around 10m).
The non-linear effects are sufficiently well simulated by the system of equations (1), but this is not the case with the breaking wave (also not considered) and the dispersive effects, which are particularly important in very winding coastal areas (with great irregularities) as seems to be the case on the south coast of Japan.
For the simulation of fine processes in very shallow waters, mathematical models of the Boussinesq or Serre (or Green & Naghdi) types with improved dispersive properties are more suitable. Currently, these types of models are used frequently and in areas with several hectares.
In this context, considering an entrance boundary at a depth of 10m, the results of the model (1) may provide inputs for models with improved dispersive characteristics.
For the inundation mapping, the use of a 5-10 meter grid step, as mentioned in the Discussion, is clearly gross for the fine analysis of processes in very shallow waters. Of course, this requires a finer bathymetry (well below 5m) to take in due account the various phenomena characteristic of shallow waters. It is understood that the main focus of this work is not related to the fine analysis of the processes in the vicinity of the coast (depths less than 10m); however, in the Introduction and Discussion, these issues must be addressed, as they are really important for studying possible flooding areas. 
As it is a scientific work, and not just a technical or academic work, the positive/innovative aspects are as relevant as the limitations of the implemented approach, which should also be highlighted. Such limitations can/should be pointed out in the Conclusions as recommendations to be researched and implemented in the future. Therefore, I recommend a possible reformulation followed by resubmission of the manuscript, considering the general observations above and incorporating the following specific remarks.   SPECIFIC REMARKS
- At least, Figures 1 and 5 are not original, as well as Table 1; Figure 3 is also adapted. In all captions of these Figures and the Table, the original sources must be cited.
- On page 3, there is no need to discretize the equations in different lines; rewrite each equation on a single line.
- Using constant spatial steps (Δx and Δy), show clearly (embedded in the numerical formulation) how can the numerical model handle a non-uniform spatial grid?
- Usually, spherical coordinates are used to simulate tsunami propagation over large areas, as is the case. Using coordinates (x, y), show clearly (embedded in the mathematical and numerical formulations) how the sphericity effect of the Earth is taken into account.
- Line 209, "Full reflection boundary conditions were used at 10m depth" (sic), why? Shouldn't this be an open boundary (free passage of the wave out of the domain)?
- Provide the mathematical definition of the tsunami source model (tsunami input condition).
- Lines 219-220: "In Figure 3 the distribution of the wave height maxima from the computed tsunami, generated by the model source S0-c, cf. Figure 3" (sic). Is really Figure 3?
- Lines 244-246: "The color scale in Figures 6, 9, 10 shows the height-color relation for wave height values between 0 and 5 m. In case the tsunami height exceeds m at certain grid points, we use for visualization the same color as the points with maximum level elevation of 5 m" (sic). Why not using color scales until the maximum height found in each Figure?
- In Figure 11, the dimensions and placement of all images must be reviewed.
- In the Discussion, the contents related to Figure 11 (shown in lines 337-346) should be reworked. Figure 11(D) should not be framed before Figures 11(A), 11(B) and 11(C).
- The Conclusions should include recommendations for future research, in addition to "a version of software to apply the hardware code acceleration for the nested grids" (sic, lines 363-364), as stated above.   FINAL COMMENT
All comments and remarks above are intended to contribute to the improvement of the manuscript prior to re-submission. However, they do not exhaust all corrections to be made.   

Author Response

Once again, we are grateful for the Reviewers for their comments and criticism as well as for the time they spent analyzing our paper.

We are sorry if we did not respond to some of suggestions during the first iteration. Hope that now we provide responses really line by line.

Point 1: Neither the mathematical formulation used (shallow water equations) nor the numerical method implemented allow to evaluate the fine processes that occur in very shallow waters (approach to the coast line, well below 10m), including uncovered (emerged) areas that can be affected by possible flooding.

Response 1: The following explanations (to clarify the paper goal and choice of the model) has been included into Introduction:

“The main goal of this paper is to demonstrate the advantages of the new super rapid method for modeling of tsunami wave propagation. We do not wish to obtain the detailed wave height maxima distribution along the specified coast.”

“It is of common knowledge that a tsunami warning system (even if we address only its modelling part) should include three basic stages, namely: generation, wave propagation, and inundation of a dry land. In this paper we consider only the wave propagation part in order to make the computations faster but keeping a sufficient accuracy. So, we suppose that the tsunami wave is due to a certain disturbance of a sea surface. This initial disturbance serves as the initial conditions in the governing evolution type equations. We also do not touch the inundation mapping questions. Therefore, we do not compute a wave at small depths (below 10m) and we suggest reflection type boundary conditions at such depth to estimate the wave height in the near-shore area and to account reflected waves.

According to [10-12], where the numerical dispersive models for long waves have been studied, the influence of dispersion is valuable only in case then the depth is of same order as the wave amplitude. We are not studying short waves where dispersion occurs in many cases. So, neglecting the dispersive effects studying the long wave propagation at large enough depths, we use the shallow water approximation as the governing equation. This is common in tsunami simulation even if more precise models (like Boussinesq system, e.g.) are used in a number of research papers. The inundation mapping (or any other fine analysis of the processes in the vicinity of the coast like the breaking waves or low/high tide effects) is not discussed in the paper, even such matters are very important for studying possible flooding areas.”

Point 2:  The non-linear effects are sufficiently well simulated by the system of equations (1), but this is not the case with the breaking wave (also not considered) and the dispersive effects, which are particularly important in very winding coastal areas (with great irregularities) as seems to be the case on the south coast of Japan.

Response 2: The following part is now in Introduction:

“The inundation mapping (or any other fine analysis of the processes in the vicinity of the coast like the breaking waves) is not discussed in the paper, even such matters are very important for studying possible flooding areas.”

Point 3: For the simulation of fine processes in very shallow waters, mathematical models of the Boussinesq or Serre (or Green & Naghdi) types with improved dispersive properties are more suitable. Currently, these types of models are used frequently and in areas with several hectares.
In this context, considering an entrance boundary at a depth of 10m, the results of the model (1) may provide inputs for models with improved dispersive characteristics.

Response 3: We add some references and explanations to justify the possibility to neglect dispersive effects in our study:

“According to [10-12], where the numerical dispersive models for long waves have been studied, the influence of dispersion is valuable only in case then the depth is of same order as the wave amplitude. So, neglecting the dispersive effects studying the long wave propagation at large enough depths, we use the shallow water approximation as the governing equation. This is common in tsunami simulation even if more precise models (like Boussinesq system, e.g.) are used in a number of research papers.”

10. Fedotova, Z.; Khakimzyanov, G. Characteristics of finite difference methods for dispersive shallow water equations. Russian Journal of Numerical Analysis and Mathematical Modelling, 2016, 31(3), 149-158.
11. Khakimzyanov, G.; Dutykh, D.; Fedotova, Z.I.; Mitsotakis, D. Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space. Communications in Computational Physics. 2018, 23(1), 1-29.
12. Khakimzyanov, G.; Fedotova, Z.; Gusev, O.; Shokina, N. Finite difference methods for 2D shallow water equations with dispersion. Russian Journal of Numerical Analysis and Mathematical Modelling. 2019, 34(2), 105-117.

Point 4: For the inundation mapping, the use of a 5-10 meter grid step, as mentioned in the Discussion, is clearly gross for the fine analysis of processes in very shallow waters. Of course, this requires a finer bathymetry (well below 5m) to take in due account the various phenomena characteristic of shallow waters. It is understood that the main focus of this work is not related to the fine analysis of the processes in the vicinity of the coast (depths less than 10m); however, in the Introduction and Discussion, these issues must be addressed, as they are really important for studying possible flooding areas. 

Response 4: The corresponding details are now in the:

Introduction - “We also do not touch the inundation mapping questions. Therefore, we do not compute a wave at small depths (below 10m) and we suggest reflection type boundary conditions at such depth to account reflected waves.”

Discussion - “The main goal of our study is to provide fast and accurate evaluation of tsunami wave maximal heights along the coastline. We are neglecting the fine analysis of the processes at the depths less than 10m, even if such analysis is really important for mapping possible flooding areas. To our understanding, the computed distribution of the wave heights provides the basis for such researches, and we are going to arrange the corresponding studies in the future. Note also, that, according to [23,24], it is possible to use formulae for recalculating the obtained tsunami wave height at the vertical wall at a depth of 10-20 m for the rough determination of the long wave run-up height. Such a coefficient is pre-determined for each coast point and is obtained by tsunami numerical modeling using more accurate (in some cases three-dimensional) hydrodynamic models.”

23. Choi, B.; Kaistrenko, V.; Kim, K.; Min, B.; Pelinovsky, E. Rapid forecasting of tsunami runup heights from 2-D numerical simulations. Hazards Earth Syst. Sci., 2011, 11, 707-714.
24. Choi, B.; Kim, K.; Yuk, JH.; Kaistrenko, V.; Pelinovsky, E. Analytical Rapid Prediction of Tsunami Run-up Heights: Application to 2010 Chilean Tsunami. Ocean and Polar Research, 2015, 37(1), 1-9.

Point 5: As it is a scientific work, and not just a technical or academic work, the positive/innovative aspects are as relevant as the limitations of the implemented approach, which should also be highlighted. Such limitations can/should be pointed out in the Conclusions as recommendations to be researched and implemented in the future. Therefore, I recommend a possible reformulation followed by resubmission of the manuscript, considering the general observations above and incorporating the following specific remarks.  

Response 5: The following lines are now in the Conclusion:

“The proposed software tools and hardware code acceleration devices should be used together with the wave generation models and special approaches for the inundation mappings. In the forthcoming studies, the authors will present an approach to determine the initial sea surface disturbance at tsunami source and an implementation of the code acceleration at the nested grids. These two steps will contribute to let loose the aforementioned limitations of our approach. However, even now the proposed tool can be used as the input data generator for more precise inundation modeling.”

SPECIFIC REMARKS
Point 6: - At least, Figures 1 and 5 are not original, as well as Table 1; Figure 3 is also adapted. In all captions of these Figures and the Table, the original sources must be cited.

Response 6:  All the references have been included.

Point 7: - On page 3, there is no need to discretize the equations in different lines; rewrite each equation on a single line.

Response 7: This has been done

Point 8: - Using constant spatial steps (Δx and Δy), show clearly (embedded in the numerical formulation) how can the numerical model handle a non-uniform spatial grid?

Response 8: To stress the point, we add the following:

“In order to account spherical shape of the Earth we use a decreasing grid step with respect to longitude for larger values of latitude.” (Lines 126-127)

“We take into consideration spherical shape of the Earth by decreasing the grid step with respect to longitude for larger values of latitude. Matching the grid to geographic coordinates we suppose that the length of one arc degree at λ latitude is equal to the length of one equator arc degree multiplied by cos(λ).” (Lines 201-204)

Point 9: - Usually, spherical coordinates are used to simulate tsunami propagation over large areas, as is the case. Using coordinates (x, y), show clearly (embedded in the mathematical and numerical formulations) how the sphericity effect of the Earth is taken into account.

Response 9: We wish to use the suggested implementation of numerical computation to study tsunami at the regional scale, for the computation areas within a few geographical degrees. For these situations sphericity of the Earth is not able to have valuable impact on the tsunami wave parameters. 

This is now mentioned in the Conclusion.

Point 10: - Line 209, "Full reflection boundary conditions were used at 10m depth" (sic), why? Shouldn't this be an open boundary (free passage of the wave out of the domain)?

Response 10: As is well known, the coast line reflects tsunami wave very well. So, it is natural to apply perfect reflection boundary condition at the corresponding nodes. Depth of approximately 10m is minimal, where the shallow water model describes the long wave behavior well enough. At the parts of the boundary, which separate our computational domain from the ocean, we use free passage of the wave out of the domain. 

Now we note this fact in the paper.

 

Point 11: - Provide the mathematical definition of the tsunami source model (tsunami input condition).

Response 11: Now we add the following:

“So, we suppose that the tsunami wave is due to a certain disturbance of a sea surface. This initial disturbance serves as the initial conditions in the governing evolution type equations.”

“The model source was built according to the elastic-plastic model proposed in [21]. This model is currently used by the NOAA tsunami warning services to calculate the initial displacement in the tsunami source area on the basis of seismic monitoring data. The input data for calculating the ocean floor displacement field are the basic parameters describing the earthquake seismic mechanism. In this paper we use such displacement as the sea surface disturbance at the initial time moment.”

• Alexeev, A.; Gusyakov, V. Numerical simulation of tsunami generation and propagation in the ocean with a real bathymetry. In Provis D.G., Radok R. (eds) Waves on Water of Variable Depth. Lecture Notes in Physics, 1977, 64. Springer, Berlin, Heidelberg, 63-71.

 

Point 12: - Lines 219-220: "In Figure 3 the distribution of the wave height maxima from the computed tsunami, generated by the model source S0-c, cf. Figure 3" (sic). Is really Figure 3?

Response 12: This misprint is now corrected, thanks to the Reviewer.

Point 13: - Lines 244-246: "The color scale in Figures 6, 9, 10 shows the height-color relation for wave height values between 0 and 5 m. In case the tsunami height exceeds m at certain grid points, we use for visualization the same color as the points with maximum level elevation of 5 m" (sic). Why not using color scales until the maximum height found in each Figure?

Response 13: Height-color legends have been corrected according to suggestion of Reviewer 1 by using >5m, instead of 5m in Figures 6, 9, and 10.

Point 14: - In Figure 11, the dimensions and placement of all images must be reviewed.

Response 14: Placement was corrected.

Point 15: - In the Discussion, the contents related to Figure 11 (shown in lines 337-346) should be reworked. Figure 11(D) should not be framed before Figures 11(A), 11(B) and 11(C).

Response 15: All the Figures 11 (A-D) are first quoted in line 355, then in line 363. So, we believe acceptable to discuss in some details Figure 11 (D) (line 373) and then Figures 11 (A,B) in lines 377-380.

 

Point 16: - The Conclusions should include recommendations for future research, in addition to "a version of software to apply the hardware code acceleration for the nested grids" (sic, lines 363-364), as stated above.  

Response 16: The following part has been added to the Conclusion:

“The proposed software tools and hardware code acceleration devices should be used together with the wave generation models and special approaches for the inundation mappings. In the forthcoming studies, the authors will present an approach to determine the initial sea surface disturbance at tsunami source and an implementation of the code acceleration at the nested grids. These two steps will contribute to let loose the aforementioned limitations of our approach. However, even now the proposed tool can be used as the input data generator for more precise inundation modeling.”

Author Response File: Author Response.pdf

Round 3

Reviewer 3 Report

This new version of the manuscript improves some aspects and also clarifies some contents. However, in essence, it maintains the same weaknesses and limitations as the previous version. My biggest concerns are related to the lack of originality and the high number of self-citations in relation to the number of references.   The text reads: "It is of common knowledge that a tsunami warning system (even if we address only its modelling part) should include three basic stages, namely: generation, wave propagation, and inundation of a dry land" (sic) (lines 66-68).
Yes, certainly, but given that a tsunami propagates always in shallow water conditions, from generation to the final stage of coastal flooding, any of the stages can be simulated in a single model that solves fully non-linear and dispersive (or, at least, weakly dispersive) shallow water equations of the Boussinesq or Serre-Green-Naghdi types with improved dispersive characteristics. These issues should be addressed in the Introduction, requiring, of course, a deeper bibliographic analysis.   The text also reads: "In this paper we consider only the wave propagation part...." (line 68) and also "Only the wave propagation over sufficiently large depth (10m and more) is considered." (lines 390-391). It is precisely these limitations that, in essence, little distinguish this manuscript from other publications by the same authors, notably [14], [15], [16], [17], and to which can be added [20], although not so focused. Therefore, this is yet another publication without sufficient originality to justify a scientific article.   Apart from some original figures, the main focus and most of the contents are basically far-fetched among the texts of other authors' publications on the same topic. However, it must be recognized that three of these publications come from proceedings and that the remaining two are publications of journals with little relevance; one of them still doesn't seem to have an impact factor and the other has a very low impact factor (and Q4 Scimago).   An insufficiently addressed issue concerns the need to justify the proposed code, comparing it with results and running times of other current models, particularly the MOST propagation code, which uses nonlinear shallow water equations written in spherical coordinates. I understand that these equations written in spherical coordinates, including additional equally important terms, are not  appropriate for numerically solved using the MacCormack method. The basic methodologies of both models and the running times should be addressed, also to justify the differences in results, which are not necessarily worse (Figure 1).   Nor is the "full reflection boundary conditions used at 10 m depth" are also not clear or even justified. A partial reflection boundary condition can be justified, depending on the topography slope, but it will certainly be far from being a vertical non-rough wall to justify the full reflection boundary condition.   In addition, although the number of self-citations in the first version has improved (9/16, 56%), the current ratio of self-citations (co-authors of this manuscript)/references is 11/25 (44%), which remains unacceptable.   Finally, English syntax is not always fluent; a careful review of the entire document is recommended, including some grammatical constructions, style and syntax.   In short, this manuscript does not meet the key requirements for possible publication in the Journal of Applied Sciences as an "original article". However, after the authors address the aspects identified above and update the references, especially with regard to the different approaches of wave propagation models and, possibly, with fewer citations, this manuscript can be accepted as a "Review Article".  

Author Response

We are grateful for the 3^rd review of our manuscript. However, to our opinion we have already answer to almost all the points of the 3^rd review in our response to the 2^nd review.

 

Point 1: The text reads: "It is of common knowledge that a tsunami warning system (even if we address only its modelling part) should include three basic stages, namely: generation, wave propagation, and inundation of a dry land" (sic) (lines 66-68).
Yes, certainly, but given that a tsunami propagates always in shallow water conditions, from generation to the final stage of coastal flooding, any of the stages can be simulated in a single model that solves fully non-linear and dispersive (or, at least, weakly dispersive) shallow water equations of the Boussinesq or Serre-Green-Naghdi types with improved dispersive characteristics. These issues should be addressed in the Introduction, requiring, of course, a deeper bibliographic analysis.  

 

Response 1: We use the shallow water model equations with the full reflection boundary conditions as the MOST software package is based exactly on this model. Method Of Splitting Tsunami (MOST) is, perhaps, the number 1 reference code for tsunami modeling worldwide. This is the official instrument of the USA Tsunami Warning Centers. Moreover, according to the references [8-10] in our paper, dispersion has a weak influence the amplitude of a long wave at deep water area. This point is shared by all the participants of the last International Tsunami Symposiums. This is clearly stated in our manuscript.

 

After the 2^nd review we add several paragraphs to the manuscript, where we stress on the paper goals – calculation of tsunami wave heights along the coast. We absolutely agree that for the short waves it is necessary to account for dispersion. We would like to note that the initial parameters of tsunami wave at source are determined only approximately. So, it is reasonable to neglect phenomena, which gave rather small impact on tsunami wave height.

 

Here below is our previous response:

2nd Review Point 1: Neither the mathematical formulation used (shallow water equations) nor the numerical method implemented allow to evaluate the fine processes that occur in very shallow waters (approach to the coast line, well below 10m), including uncovered (emerged) areas that can be affected by possible flooding.

 

2nd Review Response 1: The following explanations (to clarify the paper goal and choice of the model) has been included into Introduction:

“The main goal of this paper is to demonstrate the advantages of the new super rapid method for modeling of tsunami wave propagation. We do not wish to obtain the detailed wave height maxima distribution along the specified coast.”

“It is of common knowledge that a tsunami warning system (even if we address only its modelling part) should include three basic stages, namely: generation, wave propagation, and inundation of a dry land. In this paper we consider only the wave propagation part in order to make the computations faster but keeping a sufficient accuracy. So, we suppose that the tsunami wave is due to a certain disturbance of a sea surface. This initial disturbance serves as the initial conditions in the governing evolution type equations. We also do not touch the inundation mapping questions. Therefore, we do not compute a wave at small depths (below 10m) and we suggest reflection type boundary conditions at such depth to estimate the wave height in the near-shore area and to account reflected waves.

According to [10-12], where the numerical dispersive models for long waves have been studied, the influence of dispersion is valuable only in case then the depth is of same order as the wave amplitude. We are not studying short waves where dispersion occurs in many cases. So, neglecting the dispersive effects studying the long wave propagation at large enough depths, we use the shallow water approximation as the governing equation. This is common in tsunami simulation even if more precise models (like Boussinesq system, e.g.) are used in a number of research papers. The inundation mapping (or any other fine analysis of the processes in the vicinity of the coast like the breaking waves or low/high tide effects) is not discussed in the paper, even such matters are very important for studying possible flooding areas.”

2nd Review Point 2:  The non-linear effects are sufficiently well simulated by the system of equations (1), but this is not the case with the breaking wave (also not considered) and the dispersive effects, which are particularly important in very winding coastal areas (with great irregularities) as seems to be the case on the south coast of Japan.

 

2nd Review Response 2: The following part is now in Introduction:

“The inundation mapping (or any other fine analysis of the processes in the vicinity of the coast like the breaking waves) is not discussed in the paper, even such matters are very important for studying possible flooding areas.”

 

2nd Review Point 3: For the simulation of fine processes in very shallow waters, mathematical models of the Boussinesq or Serre (or Green & Naghdi) types with improved dispersive properties are more suitable. Currently, these types of models are used frequently and in areas with several hectares.
In this context, considering an entrance boundary at a depth of 10m, the results of the model (1) may provide inputs for models with improved dispersive characteristics.

 

2nd Review Response 3: We add some references and explanations to justify the possibility to neglect dispersive effects in our study:

“According to [10-12], where the numerical dispersive models for long waves have been studied, the influence of dispersion is valuable only in case then the depth is of same order as the wave amplitude. So, neglecting the dispersive effects studying the long wave propagation at large enough depths, we use the shallow water approximation as the governing equation. This is common in tsunami simulation even if more precise models (like Boussinesq system, e.g.) are used in a number of research papers.”

8. Fedotova, Z.; Khakimzyanov, G. Characteristics of finite difference methods for dispersive shallow water equations. Russian Journal of Numerical Analysis and Mathematical Modelling, 2016, 31(3), 149-158.
9. Khakimzyanov, G.; Dutykh, D.; Fedotova, Z.I.; Mitsotakis, D. Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space. Communications in Computational Physics. 2018, 23(1), 1-29.
10. Khakimzyanov, G.; Fedotova, Z.; Gusev, O.; Shokina, N. Finite difference methods for 2D shallow water equations with dispersion. Russian Journal of Numerical Analysis and Mathematical Modelling. 2019, 34(2), 105-117.

 

 

Point 2:  The text also reads: "In this paper we consider only the wave propagation part...." (line 68) and also "Only the wave propagation over sufficiently large depth (10m and more) is considered." (lines 390-391). It is precisely these limitations that, in essence, little distinguish this manuscript from other publications by the same authors, notably [14], [15], [16], [17], and to which can be added [20], although not so focused. Therefore, this is yet another publication without sufficient originality to justify a scientific article.   Apart from some original figures, the main focus and most of the contents are basically far-fetched among the texts of other authors' publications on the same topic. However, it must be recognized that three of these publications come from proceedings and that the remaining two are publications of journals with little relevance; one of them still doesn't seem to have an impact factor and the other has a very low impact factor (and Q4 Scimago).   An insufficiently addressed issue concerns the need to justify the proposed code, comparing it with results and running times of other current models, particularly the MOST propagation code, which uses nonlinear shallow water equations written in spherical coordinates.

 

Response 2: We would like to stress that all the numerical tests are original and never have been conducted before. So, we do not understand why our present paper is qualified as “little distinguish”. Only 3 figures/pictures from 11 (15 different pictures) are not original and we refer to the corresponding sources thanks to Reviewer. Figure 1 is necessary to compare our results with the MOST reference code, and Figure 4 to justifies our interest to the region under consideration. Figure 5, presenting the presenting the initial sea surface displacement, can not be avoid, too.

 

We agree with the Reviewer that it is reasonable to remind some of the previous results as they have been published in conference proceedings and in journals of little relevance. To our understanding this is just justification of the number of self references. In the first review Reviewer suggests us to include the reference to one more our paper, namely: Mikhail Lavrentiev, Konstantin Lysakov, Andrey Marchuk, Konstantin Oblaukhov, and Mikhail Shadrin, 2019. Fast Evaluation of Tsunami Waves Heights around Kamchatka and Kuril Islands. Journal of Tsunami Society International, Volume 38, Number 1.

We did that.

Now, according to the new opinion, we cut 5 our self-references.

 

Figure 1 and Table 1 provide the comparison of our code with the MOST code, official tool of the NOAA (USA) tsunami warning centers.

 

Point 3:  I understand that these equations written in spherical coordinates, including additional equally important terms, are not  appropriate for numerically solved using the MacCormack method. The basic methodologies of both models and the running times should be addressed, also to justify the differences in results, which are not necessarily worse (Figure 1).  

 

Response 3: We agree that if the model was different an alternative approach (and another numerical scheme) would be used. However, a change in the model would be solving a different scientific objective. It is unclear how the reviewer’s comment is relevant to the objective of the current study.

 

Also, we did address the running time in the Table 1 (reduced version of our previous studies). To justify the results we have carried out numerical experiments on 2 different model bottom topographies for testing our method.

 

Point 4:  Nor is the "full reflection boundary conditions used at 10 m depth" are also not clear or even justified. A partial reflection boundary condition can be justified, depending on the topography slope, but it will certainly be far from being a vertical non-rough wall to justify the full reflection boundary condition.  

 

Response 4: Once again, we consider the model and boundary conditions, standard in tsunami simulation. The same are used in the aforementioned MOST code. We agree that for fine studying fine phenomena in the coastal zone and inundation mapping the model should be another. However, it is out of the purposes of our paper and it is stated several times in the Introduction and in the Discussion.

 

Point 5: In addition, although the number of self-citations in the first version has improved (9/16, 56%), the current ratio of self-citations (co-authors of this manuscript)/references is 11/25 (44%), which remains unacceptable.   Finally, English syntax is not always fluent; a careful review of the entire document is recommended, including some grammatical constructions, style and syntax.  

 

Response 5: In the first review round, Reviewer 3 suggested that we include a reference to one more of our papers, namely: M. Lavrentiev, K.Lysakov, An.Marchuk, K.Oblaukhov, and M.Shadrin, 2019. Fast Evaluation of Tsunami Waves Heights around Kamchatka and Kuril Islands. Journal of Tsunami Society International, Volume 38, Number 1. After we did as suggested, in the subsequent round of comments, Reviewer 3 noted that we were making too many citations to our previous results.

So, in the presented version we reduce the rate of self-citation to 6/20 (30%).

 

 

Author Response File: Author Response.pdf