Internal Solitary Wave Activities near the Indonesian Submarine Wreck Site Inferred from Satellite Images

Round 1

Reviewer 1 Report

In this paper, nonlinear internal wave activity in the Bali Sea is quantified based on SAR images. A motivation of the authors is to determine whether such waves can be the cause of the crash of the Indonesian Navy submarine KRI 12 nanggala-402. I think the paper is overall well-written and the conclusions are supported by a valid methodology. As far as I can tell, results brought by the paper that are truly new are as follows:

1. It is very likely that a moderate amplitude (41 m) ISW packet was present in the Northwest region of the basin, at the time and near the location of the submarine wreck. Its plausible amplitude, and vertical structure, was inferred based on linear and nonlinear theory (for the vertical and horizontal structure, resp.)
2. The path of ISWs during this period was mostly northwestward, which is different from previously reported observations showing strong ISW activity in the northeastern part of the basin. While the authors did not attempt to determine and quantify its origin, this shows a clear time variability of the ISW propagation in the Bali Sea.

Provided the novelty and the nature of the results fit the scope of JMSE, which I leave to the Editor's judgment, I think the paper deserves publication. I have a few points which I would like to see addressed in a revised version of the manuscript -- see below. "Major comments" are mandatory, in my opinion.

Major comments

• l. 118: please explain how the wave crests are extracted from the images.
• l. 154: please explain why such linear relationship can be expected, based on theoretical arguments (you give most of the necessary material in the paper, but that comes only later on)
• eqs. 4 to 5: I don't understand here. First, continuity would just be $\partial_xu + \partial_zw = 0$, so there must be an approximation made (or are the velocity components rotated). Then, I don't understand how you obtain eq. 5. Overall, why using the conitnuity equation and not just the relations provided (lathough for a two-layer model) by e.g. Zheng et al (2021) or Osborne & Burch (1980, "Internal Solitons in the Andaman Sea", Science)
• At several locations: l. 164-165, Table 1, subsection 3.4 and l. 268-269: it needs to be clarified what is new and what is a verification of previously reported results. As far as I understand, the source of ISWs at LS was already described by Purwandana et al (2021), who at least evidenced the role of the semidiurnal tide (hence the 12h+20-30 minutes period, which you repeat twice as if it were a new result). You are able to make the link between one ISW packet and the tidal peak in Fig. 6 b, but not for the other wave packets. Hence it is not clear how you connect, in Table 1 and Fig. 6 c, the observed wave packets with the suspected tidal peaks that generated them. Unless you can repeat the procedure used for Fig. 6b to every wave packets (tracing back along a mean trajectory using the wave celerity based on measurements and linear extrapolation), which would be great, I feel there is nothing particularly new here. Nonetheless, confirmation of a recent result is valuable, but should be presented as such explicitly.

Minor comments

• l. 29-31: I think this is too much details. In any case, I would suggest not starting with this sentence, which could be moved further in the text, and would rather start at line 35, which is more about science.
• l.54: "the modulations from adjustment ...": unclear to me, I think this could be rephrased
• l. 85--86: I think "Especially" and "respectively" are not appropriate in this sentence
• l. 94: wrong name for the subsection "subsection"
• l. 114: "a" is underlined
• l.127: that would be great if you could make a link between the mesoscale circulation (e.g. from AVISO/DUACS or reanalysis products) and the main path of ISWs, contrasting between April 2021 and previously reported images.
• l.195: It could be interesting to have estimates of the amplitude of the others ISW packets, to get an estimate of typical amplitudes in the area. Likewise, please provide uncertainties associated with your estimate. 
• l. 196: Pleaser provide all values here (C0, expected C and measured C) to give an idea of how much a nonlinear model gives is more appropriate than a linear one.
• l. 216: "Lasted for nearly 10 minutes": not very clear. It is the time for the wave to pass by a point?
• Fig. 6: labels ("a", "b", "c") are missing. In connection with a previous (major) comment, please explain how are determined the vertical lines on panel c.

Author Response

We would like to thank the reviewer for the time you spent reviewing our manuscript and for the constructive comments that helped us improve the analysis results of our study. The following is our response to the comments.

 

Major comments

Point 1: l. 118: please explain how the wave crests are extracted from the images.

Response 1: Using the image processing function of MATLAB, we converted the pixel position of each satellite image into plane coordinates, and then evenly selected dozens of points on an ISW crest and obtained their positions (click these points with the mouse pointer to obtain). Next, since the latitude and longitude range of each satellite image is known, a linear relationship can be established between the plane coordinates and the geographic coordinates, and the geographic coordinates of the wave crest can be obtained using linear interpolation.

Point 2: l. 154: please explain why such linear relationship can be expected, based on theoretical arguments (you give most of the necessary material in the paper, but that comes only later)

Response 2: According to the two-layer model theory, the linear relationship between the ISW propagation speed and the water depth is not accurate. From temperature and salinity profiles acquired during ship surveys, Jackson (2009, JAOT) proposed a nonlinear relation between the ISW phase speed and the depth of the northern South China Sea. However, only 5 cases of wave speed were accurately obtained from MODIS/VIIRS images with intervals of about 175 minutes in April 2021, and it is difficult for us to fit such a nonlinear relation from the limited cases. Considering that the properties of ISWs around the time of submarine wreck were focused and the limited cases during that period, the statements on the relationship between ISW propagation speeds and the water depths has been deleted from the manuscript.

Point 3: eqs. 4 to 5: I don't understand here. First, continuity would just be $\partial_xu + \partial_zw = 0$, so there must be an approximation made (or are the velocity components rotated). Then, I don't understand how you obtain eq. 5. Overall, why using the continuity equation and not just the relations provided (lathough for a two-layer model) by e.g. Zheng et al (2021) or Osborne & Burch (1980, "Internal Solitons in the Andaman Sea", Science)

Response 3: We used the continuity equation to get ISW current following Sandstrom & Oakey (1994). In the original manuscript, we have rotated the horizontal axis of the coordinates to the ISW propagation direction and u in eq.4 is the local horizontal current along propagation direction, so the continuity equation was converted to a two-dimensional form. Then, eq. 5 can be obtained by substituting  in eq. 4. The relations provided by Osborne & Burch (1980) (Sorry that we don't clear which paper Zheng et al (2021) refers to.) are derived from a simplified two-layer model and we can only get two flow value of the upper and lower layers respectively, while the results calculated from continuity equation are continuous, which is why we used it.

Point 4: At several locations: l. 164-165, Table 1, subsection 3.4 and l. 268-269: it needs to be clarified what is new and what is a verification of previously reported results. As far as I understand, the source of ISWs at LS was already described by Purwandana et al (2021), who at least evidenced the role of the semidiurnal tide (hence the 12h+20-30 minutes period, which you repeat twice as if it were a new result). You are able to make the link between one ISW packet and the tidal peak in Fig. 6 b, but not for the other wave packets. Hence it is not clear how you connect, in Table 1 and Fig. 6 c, the observed wave packets with the suspected tidal peaks that generated them. Unless you can repeat the procedure used for Fig. 6b to every wave packet (tracing back along a mean trajectory using the wave celerity based on measurements and linear extrapolation), which would be great, I feel there is nothing particularly new here. Nonetheless, confirmation of a recent result is valuable, but should be presented as such explicitly.

Response 4: Thank you for pointing this out. To predict the generation time of ISWs around the time of submarine wreck, establishing a relationship between the ISW generation and tides in the LS is key. Considering the possible tidal variability, we assessed and characterized the source tides during a specific period (April 12–21, 2021). Purwandana et al. (2021) has demonstrated that the tidal current in the LS was dominated by semi-diurnal component with a M2 tidal frequency, and ISWs were generated in the internal tidal trough. In the revised manuscript, we have cited Purwandana et al. (2021) in subsection 3.4 and express a confirmation about the tidal characteristics to it. Otherwise, the sentence at l. 164-165 have been removed (as part of the deleted section described in comment 2) and the expression of the conclusion at l. 268-269 has been modified (l. 282-284).

We connect the observed wave packets with the tidal peaks that generated them in Table 1 and Fig. 6 c in the way that you might guess. Firstly, based on the evidence provided by this work, the northward propagating ISWs in the LS were proved to be generated by southward tidal peaks. Secondly, we traced back each ISW along the mean trajectory to obtain its generation time at the source according to the propagation speed obtained from satellite images and the calculated theoretical speed. Finally, comparing this time with the adjacent southward tidal peaks, it is not hard to determine the tidal peak that generated the ISW. In the revised manuscript, we have added a short statement of this (l. 256-258).

Minor comments

Point 1: l. 29-31: I think this is too much details. In any case, I would suggest not starting with this sentence, which could be moved further in the text, and would rather start at line 35, which is more about science.

Response 1: Thanks for the suggestion. We have simplified the sentence (l. 50-52) and moved this paragraph to the present third paragraph in the revised manuscript.

Point 2: l.54: "the modulations from adjustment ...": unclear to me, I think this could be rephrased

Response 2: Thank you for pointing this out. The sentence has been rephrased. “Numerical simulation results also showed that the occurrences of ISWs in the LS area varied significantly over monthly and interannual timescales under the modulation of thermocline structure adjustment, monsoon and the Indonesian Throughflow.” (l. 46-49)

Point 3: l. 85--86: I think "Especially" and "respectively" are not appropriate in this sentence

Response 3: Thank you for pointing this out. The two words have been removed.

Point 4: l. 94: wrong name for the subsection "subsection"

Response 4: We apologize for the negligence and it has been modified. The subsection name is Spatial distribution of ISWs.

Point 5: l. 114: "a" is underlined

Response 5: Thank you for pointing this out. The underline has been removed.

Point 6: l.127: that would be great if you could make a link between the mesoscale circulation (e.g. from AVISO/DUACS or reanalysis products) and the main path of ISWs, contrasting between April 2021 and previously reported images.

Response 6: Thanks for the suggestion. We have checked for mesoscale activities in April 2021 using AVISO data and HYCOM products, but there is no direct evidence of this link. The low accuracy of these two data sets for the simulation of small marginal sea may be an important reason. The relationship between the mesoscale circulation and the main path of ISWs needs further in-depth and detailed study.

Point 7: l.195: It could be interesting to have estimates of the amplitude of the others ISW packets, to get an estimate of typical amplitudes in the area. Likewise, please provide uncertainties associated with your estimate. 

Response 7: We agree with the reviewer's suggestion and we have tried to estimate the amplitude of the others ISW. However, we found that although all ISW crests were distinguishable from MODIS images, it is difficult to obtain most of the ISW half-wavelength through image gray level change along the ISW propagation direction (Fig. 4b) due to the limitation of satellite image resolution and other interference factors in the images, so amplitude of many ISWs was not obtained. Fortunately, the ISW selected for amplitude inversion in our study was not only close to the submarine crash site, but also had a relatively clear crest in the satellite image. Nevertheless, we use the result of averaging five sections to reduce error, as shown in Figs. 4a and 4b.

Point 8: l. 196: Pleaser provide all values here (C0, expected C and measured C) to give an idea of how much a nonlinear model gives is more appropriate than a linear one.

Response 8: The values have been provided in the revised manuscript. In that case, and  are 2.51 m/s and -0.0166, respectively, and  is 2.73 m/s calculated by  (l. 212-213). The linear component accounts for 92% of the phase speed.

Point 9: l. 216: "Lasted for nearly 10 minutes": not very clear. It is the time for the wave to pass by a point?

Response 9: Yes, we have revised the expression of the sentence to “spent nearly 10 minutes passing by the site where the ISW crest located”. (l. 221-222)

Point 10: Fig. 6: labels ("a", "b", "c") are missing. In connection with a previous (major) comment, please explain how are determined the vertical lines on panel c.

Response 10: The labels have been added in the lower right corner of each figure. The latter has been explained in the previous major comment 4.

 

 

References

Jackson, C. R. (2009). An empirical model for estimating the geographic location of nonlinear internal solitary waves. Journal of Atmospheric and Oceanic Technology, 26(10), 2243-2255.

Sandstrom, H., & Oakey, N. S. (1995). Dissipation in internal tides and solitary waves. Journal of Physical Oceanography, 25(4), 604-614.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

I think this is a good paper, and have no suggestions, other than changing the name of subsection 3.1. You'll see why.

Author Response

Thank you for your evaluation of our manuscript. We apologize for the wrong name of the subsection 3.1. The subsection name is Spatial distribution of ISWs and the correction has been made in the revised manuscript (l. 123).

Reviewer 3 Report

Review of the manuscript “Internal solitary wave activities near the Indonesian submarine wreck site inferred from satellite images”

 

In this study, authors collected the optical remote sensing images covering Bali Sea (BS) from 12 to 21 April 2021, and investigated the distribution, propagation and underwater structure of ISWs around the time (early morning of 21 April 2021) of the KRI Nanggala-402 wreck. They quantified the characteristics of BS ISWs with crest lengths (~200 km), propagation speed (2.69 m/s in the deep basin to 0.71 m/s in the shallow water), amplitude (inversed to be 41 m), and vertical velocity (10 cm/s). As previously known, the ISWs propagate northwestward across the BS deep basin originating from the Lombok Strait, and shoaled onto the shelf west of Kangean Islands. They demonstrated the near-source evidence of ISWs near the Nusa Penida sill of the LS and possible generation mechanism related to the southward tidal current. This paper presents novel results about the characteristics of BS ISWs around the time of the KRI Nanggala-402 wreck and their possible generation. Thus, I think it is important that this paper can be ultimately published after some revision, and recommend publication with straightforward revision considering the suggestions/comments below.

 

1. Organization of the manuscript: the title of Section 2 had better be changed to “Data and methods” and descriptions on the methods applied in this study may be moved into the Section 2 instead of Section 3. For example, Section 3.3 currently contains methods, results, and discussions. Descriptions on methods of estimating the amplitude, propagation speed, and vertical/horizontal currents (Lines 178-192 and 203-213) should be moved to Section 2.
2. Methods: the waveshape to estimate the vertical/horizontal currents was based on the ordinary KdV equation, e.g., equation (3), yet the combined KdV theory usually better explains the observed ISWs in many regions. My suggestion is to estimate the waveshape and vertical/horizontal currents using the combined KdV equation, and to compare the results, also citing the previously published literatures on ISWs in other regions (particularly providing information on the two theories against the in-situ or remote sensing observations in other seas).
3. Methods (presentation): the amplitude was estimated from the distance between the center of light and that of dark stripes (or the half wavelength, not clearly described) using the equation (1). The equation needs to be changed into the explicit form, e.g., the amplitude equals ~, not the distance equals to ~.
4. Discussion: the results presented in this paper were not discussed sufficiently in comparison to previous works on ISWs in this and other regions. Although the study focuses on the BS ISWs on specific period (April 12–21, 2021), the results should be compared to what has been investigated previously. For example, the propagation speeds of northward propagating ISWs estimated from different satellite images in different period of time are often not consistent with what is presented in this study (Figs. 3c and 3d). What are the uncertainty range of the propagation speed, e.g., horizontal (not only vertical) bars need to be added in Fig. 3c and vertical bars need to be added in Fig. 3d, considering the previously reported speeds at different location/depth? Those propagation speeds are available from Susanto et al. (2005), Matthews et al. (2011), Lindsey et al. (2018; Remote Sensing of Environment) as well as Karang et al. (2019). Not all the previous works were included in this paper. My suggestion is to include all the previously reported speeds in Figs. 3c and 3d and to provide better discussions on the propagation speed.
5. Discussion: the relationship between barotropic tides at source and ISWs had better be better discussed to include more analysis such as Froude number. The Lee-wave generation mechanism can be easily diagnosed with the Froude number estimation, e.g., equations (1) and (2) of Nam et al. (2018; Scientific Reports).

 

Author Response

We would like to thank the reviewer for the time you spent reviewing our manuscript and for the constructive comments that helped us improve the analysis results of our study. The following is our response to the comments.

 

Note: The original comments of the and Reviewers are in black, and our responses are in red.

 

Point 1: Organization of the manuscript: the title of Section 2 had better be changed to “Data and methods” and descriptions on the methods applied in this study may be moved into the Section 2 instead of Section 3. For example, Section 3.3 currently contains methods, results, and discussions. Descriptions on methods of estimating the amplitude, propagation speed, and vertical/horizontal currents (Lines 178-192 and 203-213) should be moved to Section 2.

Response 1: Thank you for the suggestion. We have adjusted the organization of the manuscript according to the advice. The title of section 2 has been changed to “Data and methods”, and we have moved the equations in Section 3.3 to Section 2.

Point 2: Methods: the waveshape to estimate the vertical/horizontal currents was based on the ordinary KdV equation, e.g., equation (3), yet the combined KdV theory usually better explains the observed ISWs in many regions. My suggestion is to estimate the waveshape and vertical/horizontal currents using the combined KdV equation, and to compare the results, also citing the previously published literatures on ISWs in other regions (particularly providing information on the two theories against the in-situ or remote sensing observations in other seas).

Response 2: Thank you for the suggestion. However, when constructing the ISW underwater structure, we first estimate the amplitude of the ISW using Eq. 1, which is derived from the ordinary KdV equation (Zheng et al. 2001). To keep the results consistent, we used the ordinary KdV equation to get ISW waveshape. Here we give the structure of the ISW derived from the extended KdV (eKdV) equation. The waveshape and vertical/horizontal currents pattern obtained by the eKdV equation are almost the same as that obtained by the KdV equation, except that the current peak values (63 cm/s of horizontal current and 8.3 cm/s of vertical current) are slightly smaller, because the theoretical ISW speed calculated by the eKdV equation is 2.51 m/s, smaller than the results obtained by the observation and the ordinary KdV equation.

 

Point 3: Methods (presentation): the amplitude was estimated from the distance between the center of light and that of dark stripes (or the half wavelength, not clearly described) using the equation (1). The equation needs to be changed into the explicit form, e.g., the amplitude equals ~, not the distance equals to ~.

Response 3: Thank you for pointing this out. The form of the equation has been changed to the following form. (l. 89)

Point 4: Discussion: the results presented in this paper were not discussed sufficiently in comparison to previous works on ISWs in this and other regions. Although the study focuses on the BS ISWs on specific period (April 12–21, 2021), the results should be compared to what has been investigated previously. For example, the propagation speeds of northward propagating ISWs estimated from different satellite images in different period of time are often not consistent with what is presented in this study (Figs. 3c and 3d). What are the uncertainty range of the propagation speed, e.g., horizontal (not only vertical) bars need to be added in Fig. 3c and vertical bars need to be added in Fig. 3d, considering the previously reported speeds at different location/depth? Those propagation speeds are available from Susanto et al. (2005), Matthews et al. (2011), Lindsey et al. (2018; Remote Sensing of Environment) as well as Karang et al. (2019). Not all the previous works were included in this paper. My suggestion is to include all the previously reported speeds in Figs. 3c and 3d and to provide better discussions on the propagation speed.

Response 4: Thank you for the suggestion. In Section 3.2, we have added and discussed the results of previous work. With respect to the ISW phase speed in the LS, Lindsey et al. (2018) obtained a value of 2.5 m/s with a shorter 10-min time steps, which is very close to our result. Based on the assumption that the time interval of ISW generation in the LS is consistent with the tidal cycle, Susanto et al. (2005) estimated the speeds of northward propagating ISWs from the Lombok Strait as 1.97 and 1.96 m/s using ERS-1/2 SAR images of 23 and 24 April 1996, and Karang et al. (2019) obtained a speed of 2.05 m/s using Landsat 8 image of 17 May 2015 (l. 174-180). The above results have also been added to Fig. 3c (Fig.3d has been removed from the revised manuscript). It can be seen that the speed of ISW in the LS is not the same at different periods, and we show a variation range of about 0.5m/s. Moreover, Matthews et al. (2021) defined the ISW mean speeds between two wave packets about 1.6 to 2.3 m/s in the BS by measuring the distances between the leading signals in adjacent wave packets generated 12.4 h apart (l. 193-195). However, considering that those ISWs propagated in a north-easterly direction in the BS, which is different from the path defined in our work, the result was not added to Fig.3c.

Point 5: Discussion: the relationship between barotropic tides at source and ISWs had better be better discussed to include more analysis such as Froude number. The Lee-wave generation mechanism can be easily diagnosed with the Froude number estimation, e.g., equations (1) and (2) of Nam et al. (2018; Scientific Reports).

Response 5: Thank you for this suggestion. We have calculated the Froude number over the Nusa Penida sill at the time of the labeled tidal trough in Fig. 6b. The calculated Froude number of 1.25 is greater than 1, which provided evidence that the ISWs in the LS are generated through the lee wave mechanism. In the revised manuscript, we have added the content of Froude number in Section 3.4 (l. 236-240).

 

References

Zheng, Q. N.; Yuan, Y. L.; Klemas, V.; Yan, X. H. Theoretical expression for an ocean internal soliton synthetic aperture radar image and determination of the soliton characteristic half width. Journal of Geophysical Research-Oceans 2001, 106, 31415-31423.

Susanto, R. D.; Mitnik, L.; Zheng, Q. Ocean Internal Waves Observed in the Lombok Strait. Oceanography 2005, 18, 80-87.

Karang, I. W. G. A.; Chonnaniyah, C.; Osawa, T. Landsat 8 Observation of the Internal Solitary Waves in the Lombok Strait. Indonesian Journal of Geography 2019, 51.

Lindsey, D. T.; Nam, S.; Miller, S. D. Tracking oceanic nonlinear internal waves in the Indonesian seas from geostationary orbit. Remote Sensing of Environment 2018, 208, 202-209.

Matthews, J. P.; Aiki, H.; Masuda, S.; Awaji, T.; Ishikawa, Y. Monsoon regulation of Lombok Strait internal waves. Journal of Geophysical Research 2011, 116.

 

Author Response File: Author Response.pdf