Analysis of Dangerous Sea States in the Northwestern Mediterranean Area
Round 1
Reviewer 1 Report
Manuscript “Analysis of dangerous sea states in the North-Western Mediterranean area“ by Innocenti et al., Review The authors present a series of numerical experiments aimed at inspecting the probability of gathering high crests during marine storms in the northwestern Mediterranean Sea. The approach stems on spectral wave model results (from WAVWATCH III) and phase-resolving model simulations (from HOS) of characteristics sea states in order to produce 3D elevation fields. Their empirical statistics is compared with theoretical distributions (for nonlinear crest heights) to assess the parameters mostly responsible for the occurrence of high waves. While the numerical approach (spectral modelling + HOS) is quite consolidated in the literature and here used purposely, the results are not as clear as the conclusions insinuate, particularly when it comes to the use of the theoretical probability functions. Other aspects of the paper must be improved to make it more understandable and to push ideas further. I thus recommend that the authors revise the manuscript addressing the general and specific comments outlined below (given for line number). - Line 4. It is not actually exact that forecast and hindcast wave models do not estimate any sort of extreme waves. ECWAM (from ECMWF), WAVEWATCH III, and WAM have implemented outputs that provide indication on the possible statistics of the extreme waves. Please refer to the specific literature (e.g. Benetazzo et al., 2021, Ocean Engineering; Barbariol et al., 2017, Ocean Dynamics; ECWAM documentation). - 9. More correctly, I should say “sea-surface elevation field” - 12. The use here and further in the manuscript (e.g., line 43) of the Rayleigh distribution as the reference may seem misleading since it is known that it can describe accurately the wave statistics only under well-specific conditions. Please justify its use in the paper. - 37. Recent works on the spatio-temporal occurrence of rogue waves provide a quite different perspective on their actual number in realistic stormy seas (see e.g., Benetazzo et al., 2017, Scientific Reports). - 43. Define Hs here or before. - 67. Please include a reference and the meaning of LaMMA (not very common in the oceanographic community). - 72. I suggest using instead “crest height distributions” - HOS method. A discussion about its accuracy would be much appreciated and useful for the interpretation of the results (see e.g. https://uis.brage.unit.no/uis-xmlui/handle/11250/2621104). - Section 2.2. Not all variables are defined. - 131. A figure with the different resolution would be of a great help, to judge in what regions the buoys is located. - The symbol S is used here to indicate the source terms and in Figure 5 with a different meaning. - 143. The ST package ST4 should be calibrated (Ardhuin et al., 2010, JPO), at least for the parameter beta_max. If it was not calibrated, I suggest mentioning the value of the parameters used for the simulations. - Please add references for BOLAM and MOLOCH models. - Figure 1. Please make it clear the position of the buoy and specify it in the caption. - 163. It is difficult to judge the agreement from the time series. You should add a scatter plot and provide the error statistics (for instance by computing bias, rmsd, SI, slope of the best fit line). - 171. I guess authors are here mentioning the directional wave spectrum - Table 1. Please add units and list the variables in the caption. I am also surprised that the peak direction is given up to 0.1° resolution, since the directional spectrum is given at 10° bins. - 195 and 208. The way the wavenumber (directional and omnidirectional) spectrum is obtained should be explained. - Figure 3. Variable E is both the total energy (maybe m0 is better) and the spectrum. I suggest changing symbol. Figure’s legend: 100, 250, 500 should be multiplicated by Tp. - 238. It is difficult to judge what comes first. Kurtosis is just a statistical variable that weights the tail of the pdf. If there are high waves, the kurtosis goes up. Please rephrase. - 241. Please quantify “do not differ too much”. In the studies cited, it seems instead the second-order bound harmonic waves play a significant role in rising the crest heights. - 246. “Survival” is not a usual term in this context - 261. I have not understood the procedure used to extract maxima from HOS. A formula or/and figure would help a lot. If all local maxima are isolated in each HOS field, is it the independence between events assured? I mean, in two consecutive fields, it is highly likely the very same crest is taken twice, therefore an individual crest is considered at least twice in the distribution. Is it so? - On the Tayfun distribution. In the paper different definitions of the steepness have been used. It is not clear the purpose of such a strategy, since Tayfun and Fedele (2009, JFM) provided the way to compute the steepness in order to make the Tayfun model more accurate. Moreover, that solution includes the bandwidth (Longuet-Higgins, 1975), which is not considered in the paper. I suggest revising the plots by including the above-mentioned definition of steepness and the discussion accordingly. - Figure 5. It is quite surprising that the second-order Forristall distribution lies above the third-order Tayfun distribution. - Figure 6 (left panel). The lack of correlation between is not surprising since the distribution functions used here does not account for the directional spreading. I think this is a clear limitation of the temporal statistics which implicitly assumes that waves are long-crested. A comment in this respect would be useful - 339-341. Any possible explanation?
Author Response
Response to Referee 1
We thank the Reviewer for his/her interesting and stimulating comments. We have considered all the remarks and added some comments in the manuscript to answer his/her doubts and to x the issues pointed out.
Please and below a point-by-point response. Changes in the manuscript are marked in red.
Line 4. It is not actually exact that forecast and hindcast wave models do
not estimate any sort of extreme waves. ECWAM (from ECMWF), WAVE-WATCH III, and WAM have implemented outputs that provide an indication on the possible statistics of the extreme waves. Please refer to the specific literature (e.g. Benetazzo et al., 2021, Ocean Engineering; Barbariol et al., 2017, Ocean Dynamics; ECWAM documentation). The comment is correct, it is true that talking only of 'indices' might be limiting, although the references suggested by the Reviewer are very recent and a thorough validation and assessment of such methodology for different sea conditions and locations has not been completed yet. The results shown in the references are very promising for a prediction of the probability of extreme events from forecast wave models, and in some sense our work goes in the same direction, yet with a complementary methodology. We have changed the sentence in the abstract and added some comments in the introduction (Lines 78-83), including the references.
9. More correctly, I should say sea-surface elevation field
We have fixed it. Thanks.
12. The use here and further in the manuscript (e.g., line 43) of the Rayleigh distribution as the reference may seem misleading since it is known that it can describe accurately the wave statistics only under well-specific conditions. Please justify its use in the paper.
We agree that the use of the Rayleigh distribution in a nonlinear context might be misleading. However the use of such distribution is intended to have a xed reference, that with the non-dimensional variable c=Hs is constant for all cases. In this way it is possible: (a) to know the probability of extreme events in "absolute" sense when we compare the distributions obtained with the HOS method with it; (b) to have an idea of the degree of non-linearity of each case. Moreover we think that it could result useful for the readers who are not very familiar with nonlinear models. We have added a comment at Lines 297-300. 37. Recent works on the spatio-temporal occurrence of rogue waves provide a quite different perspective on their actual number in realistic stormy seas (see e.g., Benetazzo et al., 2017, Scienti c Reports). We have rephrased the sentence diminishing the emphasis on the rarity of such events.
43. Define Hs here or before.
Fixed, Line 44.
67. Please include a reference and the meaning of LaMMA (not very common in the oceanographic community). We have spelled the LaMMA acronym, and added a reference to the hindcast work also at this point (Line 95).
72. I suggest using instead crest height distributions. We have fixed it (Line 98). HOS method. A discussion about its accuracy would be much appreciated and useful for the interpretation of the results (see e.g. https://uis.brage.unit.no/uis-xmlui/handle/11250/2621104).
We have added several references to the validation and assessment of the HOS method performance at Lines 144-150. Namely we referred to published articles and phd thesis of the developers of the numerical code used in our study, where the method has been validated with regular and irregular waves by comparison with theory and wave tank experiments.
Section 2.2. Not all variables are de ned.
We apologize for this deficiency. We have added all the missing definitions.
131. A figure with a different resolution would be of great help, to judge in what regions the buoys is located.
We have added a Figure 1(b) zooming on the area of the accident, showing the positions of the ship and the buoy. We hope the Reviewer will find it clarifying.
The symbol S is used here to indicate the source terms and in Figure 5 with a different meaning. Following the comments of another Reviewer we have decided to omit the presentation of the wave model equations to improve readability and concise-
ness. We have replaced it with a brief textual description of the model and the parametrization used (Lines 157-163). The symbol S is now used only to identify the wave spectrum.
143. The ST package ST4 should be calibrated (Ardhuin et al., 2010, JPO), at least for the parameter beta max. If it was not calibrated, I suggest mentioning the value of the parameters used for the simulations. We have added a comment specifying that we have used the default parameters (including max) (Line 162). We prefer to avoid listing the specific values of the hindcast parameters in such instance, since they are numerous and the hindcast is not the main focus of the manuscript. In any case we have referred to a previous work focused on the validation and calibration of the hindcast where the reader could find all the additional details.
Please add references for BOLAM and MOLOCH models.
Thanks for pointing to these missing references. We have added them (Line 166).
Figure 1. Please make it clear the position of the buoy and specify it in the caption.
See the answer to a previous point.
163. It is difficult to judge the agreement from the time series. You should add a scatter plot and provide the error statistics (for instance by computing bias, rmsd, SI, slope of the best t line).
As discussed in a previous point our focus is not on the validation of the hindcast, however we agree that a more quantitative comparison can help in drawing conclusions on the overall accuracy. We have added an inset to show the time series in the vicinity of the accident time and an additional panel with a scatter plot showing the correlation between observed and model significant wave height. Lines 182-187 in the text point to this new figure.
171. I guess authors are here mentioning the directional wave spectrum
Yes, we apologize for the incorrect mention. We have fixed it at Line 207.
Table 1. Please add units and list the variables in the caption. I am also surprised that the peak direction is given up to 0.1 resolution since the directional spectrum is given at 10 bins.
We have revisited the heading and the caption of the Table listing all variables and adding units for the dimensional ones. Peak directions have been directly taken from WW3 output files. We have now rounded their values to make them more consistent with the directional discretization.
195 and 208. The way the wavenumber (directional and omnidirectional) spectrum is obtained should be explained.
We have added a comment to explain how the spectra are evaluated at Lines 235 and 248.
Figure 3. Variable E is both the total energy (maybe m0 is better) and the spectrum. I suggest changing the symbol.
We made it now consistent throughout the manuscript referring to the spectrum with S.
Figures legend: 100, 250, 500 should be multiplicated by Tp.
We have fixed it. Thanks.
238. It is difficult to judge what comes first. Kurtosis is just a statistical variable that weights the tail of the pdf. If there are high waves, the kurtosis goes up. Please rephrase.
The sentence was misleading and the message not well expressed. We have rephrased it (Lines 279-281).
241. Please quantify do not di er too much. In the studies cited, it seems instead the second-order bound harmonic waves play a significant role in rising the crest heights. In this point we wanted to remark that those studies have found non-Gaussian distributions of wave crests associated to quasi-Gaussian PDFs, in particular concerning the kurtosis, showing that extreme events were related only to second-order bound harmonics, differently from ad-hoc wave tank experiments or long-crested seas numerical simulations where the kurtosis can be strongly non-Gaussian. We have rephrased it to make it clearer (Lines 283-285).
246. Survival is not a usual term in this context
We have changed it with 'exceedance probability'. Line 294.
261. I have not understood the procedure used to extract maxima from HOS. A formula or/and figure would help a lot. If all local maxima are isolated in each HOS eld, is it the independence between events assured? I mean, in two consecutive fields, it is highly likely the very same crest is taken twice, therefore an individual crest is considered at least twice in the distribution. Is it so?
Crests are identified as local space maxima at a given time instant and we have considered snapshots every peak period Tp. This should guarantee a suffcient lag to avoid considering identical fields multiple times. Similar time spacing between the analyzed fields have been used in analogous works with the HOS method (Bonnefoy et al. 2010, To oli et al. 2010, Trulsen et al. 2015), as already pointed out in the former version of the manuscript at Line 229. In any case we do not consider the absolute number of extreme waves, but their probability, normalizing with the total number of crests considered. Thus, in case, all crests are considered multiple times, which does not affect the distribution.
We have added a comment at Lines 290-292.
On the Tayfun distribution. In the paper different definitions of the steepness have been used. It is not clear the purpose of such a strategy, since Tayfun and Fedele (2009, JFM) provided the way to compute the steepness in order to make the Tayfun model more accurate. Moreover, that solution includes the bandwidth (Longuet-Higgins, 1975), which is not considered in the paper. I sug-
gest revising the plots by including the above-mentioned definition of steepness and the discussion accordingly.
We thank the Reviewer for this interesting remark. Tayfun & Fedele 2009 distribution has been shown to significantly improve the accuracy with respect to the standard Tayfun distribution, but has not been tested extensively, and therefore cannot be considered as definitive. Our purpose is indeed to help finding an optimal strategy in the prior calculation of the distributions, relying on the HOS method, which can make possible the analysis of many different sea conditions without changing other external factors that may affect
the computations. We think therefore that a complete comparisons with di erent methodologies can be helpful. Moreover, in a more recent work (Fedele et al. 2016 Scienti c Reports) they have sticked to the classical Tayfun de notion finding still accurate results. We guess that in that case, where a nite depth was considered, the dispersion relation helped in lowering the mean steepness
used in the Tayfun distribution. This is just an example to point out how the choice of this definition can be sensitive. We have added the Tayfun & Fedele 2009 distribution in Figure 8(a) to have a more complete comparisons between the different distributions, and we have added it in the discussion.
Figure 5. It is quite surprising that the second-order Forristall distribution lies above the third-order Tayfun distribution.
We thank the Reviewer for pointing this issue. The Forristall distribution was incorrect, we have fixed it. It follows now approximately the second order Tayfun.
Figure 6 (left panel). The lack of correlation between is not surprising since the distribution functions used here does not account for the directional spreading. I think this is a clear limitation of the temporal statistics which implicitly assumes that waves are long-crested. A comment in this respect would be useful
We thank the Referee for the comment. We have removed the word "correlation" in the text which is misleading. In Fig 6 (a) we are discussing how the probability of finding a large crets depends on the angular spreading of the spectrum. The data do not show any signifficant trend because, even though one may expect that long crested waves may undergo to some instability process,
the steepness could be small so that the instability is not triggered. We mention that our data are well described by the Tayfun distribution which is derived in case of long crested waves. Such distribution represents an upperbound for the tail; therefore, the reason why it works in our fully 3D simulation is not obvious at all.
339-341. Any possible explanation?
The idea of Figure 10 was to investigate if some characteristics circulation conditions could be associated with 'more dangerous situations', and is somehow exploratory. The relation between waves direction and extreme events probabilities is a preliminary analysis that has been done in this work in a future optics of generating risk maps associating enhanced probabilities with precise conditions. A complete study of this type would require the analysis of different locations in association with a large scale analysis of the atmospheric and sea conditions. Of course this was not possible in a single study and will be investigated in future works. We have added a comment in the manuscript considering a possible association between crossing seas conditions and some characteristic conditions associated with easterly coming waves, since there is an evidence that those cases with higher probabilities correspond mainly to crossing seas.
We believe that the quality of the manuscript has been improved thanks to the review process.
Reviewer 2 Report
The study provides an interesting analysis of cases with severe sea states in the north-western Mediterranean Sea in comparison to the situation of a documented ship accident. The study uses input from a spectral wave hindcast to perform and analyze phase resolving simulations of these cases and to link spectral quantities to results from the phase resolving simulations. The methods and analyzes are clear, straightforward, and to my knowledge new. They are perfectly suited for this Journal and worth publication. Apart from this, I have a couple of mostly minor comments.
- The authors several times mention that they have selected their cases “among the most energetic ones” but remain unspecific. I would appreciate it if the authors could be more specific and precise. If the main objective is the comparison with the situation during the Louis Majesty accident, what exactly were their criteria?
- In the conclusions, the objectives are clearly stated (lines 358-362). They occur less clear and less specific in the introduction. I would encourage the authors to re-write the introduction taking up the more specific version from the conclusions.
- Related to comment #1: The statement “… with the final aim of gathering useful information for the improvement of the safety of navigation” (lines 74-75) is rather unspecific and not explicitly addressed in the study. I suggest removing this phrase.
- Similarly, lines 88-89 “to establish if that day the wave field was particularly dangerous for the navigation” was not addressed. While conclusions can be drawn on how usual or unusual the conditions have been, no immediate assessment for navigation can be made.
- Lines 79-80: If the objective was “to verify the probability that the Louis Majesty had to encounter extreme conditions” (lines 358-362), this is not a decision but mandatory.
- The study notes several underlying assumptions. It would be helpful if the authors would take up these points, for example, in the discussion to address whether or not, or to what extent these assumptions may have an impact on their results or conclusions; that is, how valid/plausible they are for the given area, the selected cases, etc. Examples are in lines 68-69, 113-114, or 121-122.
- Line 81 (significant wave height of 4m): This is probably an underestimation. The accident happened between 14-15 UTC when the buoy measured 5 m. The accident occurred eastward of the buoy where wave heights can be expected to be even higher. Please revise.
- Figure 1: An additional time series (zoom-in) for the time of the accident would be helpful. The numbers from the hindcast used here are somewhat smaller than those from that used in Cavaleri et al. (2012), right? While I would not say one is better than the other at least this reflects uncertainty. Can you mention this briefly and shortly discuss whether or not you expect this to have an impact on the conclusions?
- Line 163 “very good overall agreement” is rather unspecific. Please provide some measures. Also, how was the agreement for the Luis Majesty accident?
- Lines 171 ff. Maybe I missed the point, but how was the phase initialized? Wouldn't Monte Carlo simulations be needed to fully assess the developments in the HOS domain (such as done for the Louis Majesty case)? Maybe addressing this point here could foster readability.
- A few thoughts on Table 1: The gray bar needs to be explained in the caption. Please also mention that directions are “coming-from”. Regarding the cases with crossing sea states: How useful are peak direction and period?
- Figure 5: The vertical dashed line needs to be mentioned in the caption.
- Figures 6, 7, 8, 9: Please explain the error bar in the caption.
- Figure 7 is hard to read. There are two different y-axes on the left panel not clearly explained. Further, strictly the caption mostly explains the left but not the right panel. One could have an idea what e.g. the blue squares mean on the right, but a clear caption would help substantially.
- Line 334: Figure 6 shows probabilities relative to the Rayleigh distribution, not absolute values.
- Figure 8 has different symbols for the Louis Majesty accident case in the plots and the caption.
- Figure 9: Please mention that direction is “coming from”. How representative is the direction for the cases with crossing sea states?
- Lines 370-371 state that skewness oscillates around a stationary value. This is not consistent with Figure 4 and the discussion in the text.
Author Response
We thank the Reviewer for his/her comments on the manuscript. We have
considered the remarks and added some comments in the manuscript.
Please nd below a point-by-point response to the Reviewer's comments.
Changes in the manuscript are marked in red.
The authors several times mention that they have selected their cases among
the most energetic ones but remain unspeci c. I would appreciate it if the au-
thors could be more speci c and precise. If the main objective is the comparison
with the situation during the Louis Majesty accident, what exactly were their
criteria?
We have selected the cases on the basis of the signi cant wave height, se-
lecting those cases approximately above 2m at their peak. When more peaks
were present in a short time window we have considered all of them only if they
showed signi cantly di erent sea conditions. We have added a sentence to point
this out (Lines 197-199).
In the conclusions, the objectives are clearly stated (lines 358-362). They
occur less clear and less speci c in the introduction. I would encourage the au-
thors to re-write the introduction taking up the more speci c version from the
conclusions.
We have revisited some parts of the introduction, explaining more clearly
our objectives. We think it is now more clear and readable.
Related to comment 1: The statement with the nal aim of gathering use-
ful information for the improvement of the safety of navigation (lines 74-75) is
rather unspeci c and not explicitly addressed in the study. I suggest removing
this phrase.
The Reviewer is right, we have removed this sentence that was too vague.
Similarly, lines 88-89 to establish if that day the wave eld was particularly
dangerous for the navigation was not addressed. While conclusions can be drawn
on how usual or unusual the conditions have been, no immediate assessment for
navigation can be made.
This sentence is no longer present due to the thorough revision of the intro-
duction.
Lines 79-80: If the objective was to verify the probability that the Louis
Majesty had to encounter extreme conditions (lines 358-362), this is not a de-
cision but mandatory.
We have highlighted this point in the revised version of the introduction.
We start now remarking our interest on the accident enlarging the analysis to
other cases in a second moment.
The study notes several underlying assumptions. It would be helpful if the
authors would take up these points, for example, in the discussion to address
whether or not, or to what extent these assumptions may have an impact on
their results or conclusions; that is, how valid/plausible they are for the given
area, the selected cases, etc. Examples are in lines 68-69, 113-114, or 121-122.
This is an interesting point. Of course we have made several assumptions
which could a ect our results quantitatively. Starting from the hindcast, we
have used only a wave model (WW3) with a given set of parameters which,
nevertheless, has been extensively validated and calibrated. However very re-
cent studies (Kokina & Dias 2020, JMSE) have shown how di erent choices on
the wave spectral model could a ect statistical properties. On the other side the
assumptions made on the HOS model regarding the sea depth and other kind
of interactions do not rely necessarily on physical basis and should be veri ed.
However they are quite intrinsic with this methodology, which is conceived to
solve the free nonlinear evolution of waves without external constraints, even if
in some cases other authors have tried to model them and include their e ect
in the HOS method, but they are still premature. Addressing all these uncer-
tainties is not possible in a single study, bearing in mind also that this coupled
methodology is recent and that an optimal con guration has not been devised
yet. However we think that for the scope of our work it is not crucial, since
we base our analysis on an inter-comparison of di erent cases with xed model
conditions. Moreover having chose to analyze a xed location reduce the uncer-
tainties related to hindcast resolution, and partially wave-current interactions.
The assumption on in nite depth should be negligible since the sea depth at the
analyzed location is around 1200m.
We have pointed this out at Lines 128-129 and in the conclusions (Lines
458-465).
Line 81 (signi cant wave height of 4m): This is probably an underestima-
tion. The accident happened between 14-15 UTC when the buoy measured 5 m.
The accident occurred eastward of the buoy where wave heights can be expected
to be even higher. Please revise.
We have changed it adding the reference and the estimated values of Hs of
two di erent works. We have reported also the height registered by the Begur
buoy (Lines 58-59).
Figure 1: An additional time series (zoom-in) for the time of the accident
would be helpful. The numbers from the hindcast used here are somewhat smaller
than those from that used in Cavaleri et al. (2012), right? While I would not
say one is better than the other at least this re ects uncertainty. Can you mention this brie y and shortly discuss whether or not you expect this to have an
impact on the conclusions?
The Reviewer has appropriately pointed out a certain degree of uncertainty
in the hindcast results, compared to previous analysis. To clarify this point we
have added an inset on Figure 2 which show an underestimation of Hs with
respect to the buoy observation (and also to Cavaleri et al. 2012). For the
same motivations reported in a previous comment we think that this should not
have an important impact for this type of analysis. We have added a few lines
(189-193) to remark this point.
Line 163 very good overall agreement is rather unspeci c. Please provide
some measures. Also, how was the agreement for the Luis Majesty accident?
We have added a new gure 2(b) to show the correlation between the ob-
served and the model signi cant wave height, reporting also the error estimates
(Lines 185-188).
Lines 171 . Maybe I missed the point, but how was the phase initialized?
Wouldn't Monte Carlo simulations be needed to fully assess the developments in
the HOS domain (such as done for the Louis Majesty case)? Maybe addressing
this point here could foster readability.
While the amplitudes are initialized from the wavenumber spectrum, the
phases are initialized randomly. One simulation corresponds therefore to a sin-
gle realization and for this reason we have performed multiple realizations at
least for the Louis Majesty case, to have an idea of the statistical error. Such
strategy would have been impractical for all the cases that have been analyzed,
implying a very large number of simulations, keeping in mind that this method-
ology is computationally demanding. In any case we have done time averaging
to reduce statistical error. We have added some comments at Lines 209-212.
A few thoughts on Table 1: The gray bar needs to be explained in the caption.
Please also mention that directions are coming-from. Regarding the cases with
crossing sea states: How useful are peak direction and period?
The gray bar is now explained, and we have mentioned that directions are
"coming-from". Regarding the peak direction in the crossing sea states, of
course this parameter can give only a qualitative measure. However as we have
pointed out in the text, most of the crossing seas cases have a clear dominant
peak that contains the greater amount of energy, thus the peak direction re-
mains relevant. We have added some comments at Lines 204-206.
Figure 5: The vertical dashed line needs to be mentioned in the caption.
It refers to the threshold used to identify extreme events. We have xed it.
Figures 6, 7, 8, 9: Please explain the error bar in the caption.
A brief explanation of error bars have been added in all captions.
Figure 7 is hard to read. There are two di erent y-axes on the left panel not
clearly explained. Further, strictly the caption mostly explains the left but not
the right panel. One could have an idea what e.g. the blue squares mean on the
right, but a clear caption would help substantially.
We have slightly changed this Figure following the comments also of another
reviewer. We have replaced the Forristall distribution with another parametriza-
tion of the Tayfun one. Now on the left panel we show 4 di erent normalizations,
all with second-order Tayfun distribution with di erent steepness parameters.
We have better explained in the caption all the symbols for both panels.
Line 334: Figure 6 shows probabilities relative to the Rayleigh distribution,
not absolute values.
The Reviewer is right, nonetheless since the Rayleigh distribution is the same
for all cases with the normalized variable (only function of c=Hs), it can be
considered as a constant reference and therefore Figure 6 can give an idea of
the absolute probability. We have rephrased this sentence (Lines 394-398).
Figure 8 has di erent symbols for the Louis Majesty accident case in the
plots and the caption.
We have xed it. Thanks.
Figure 9: Please mention that direction is coming from. How representative
is the direction for the cases with crossing sea states?
We have added the mention "coming from". For the crossing sea states we
remand the Reviewer to the previous comment.
Lines 370-371 state that skewness oscillates around a stationary value. This
is not consistent with Figure 4 and the discussion in the text.
We have xed this sentence to make the conclusions consistent with the text.
We believe that the overall quality of the manuscript has been signi cantly
improved thanks to the review process, notably with additional precise com-
ments answering the points raised by the Reviewer.
Reviewer 3 Report
Great work! Suggested a minor revision. Best of luck with your future research
Recommendation - the paper can be published after a minor revision.
The paper presents a comprehensive physical and statistical analysis of extreme wave generation and development under different sea state conditions with an emphasis on the reported ship accident. The findings are substantiated and look promising for future practical applications. The logical order of the paper is consistent. However, some issues need to be addressed before the paper can be recommended for publication. Above all, thorough copy-editing is recommended, with a focus on sentence length and paragraph structure, text flow, missing articles and prepositions, repetition, and concision. Careful proofreading of the Conclusions section will also help make the summary more compelling.
Comments
WaveWatch III hindcast - the WW3 hindcast has not been performed for this particular case study. Eq. (4)-(7) can be omitted as unnecessary, as the given description of model setup and boundary conditions is enough for the purposes of the paper.
All used variables (e.g., the peak wave number kp, peak wave period Tp and wavelength, BFI) should be introduced when used for the first time (Lines 168, 175, 179, Table 1). Currently, they are only presented in the Appendix, which can be an inconvenience for the reader.
Lines 130-131 – “The wave data were extracted by the Consorzio LaMMA wave hindcast, covering the period 1990-2018 [30,31]. This wave hindcast was produced in the Mediterranean Sea at high-resolution…” – please stick to the acknowledged prepositions here for consistency. Extracted by should be extracted from, and hindcast was produced in the Mediterranean Sea should read for the Mediterranean Sea.
Figures.
Fig. 4 – Crosses overload the curve and blur the evolution patterns of skewness and kurtosis. Perhaps using small dots (or no symbols at all) would help with figure readability.
Fig. 8 – there are no red diamonds on the plot (b), and there are no error bars on the plot (a). Everything that is stated in the figure legend should be reflected on the plots
Figures 6-9 – Even though the description of the error bars portrayed on the plots is given in the text, it would be best to state it once again in the captions for clarity.
Author Response
We have considered the remarks made by the Reviewer and added some com-
ments in the manuscript.
Please nd below a point-by-point response to the Reviewer's comments.
Changes in the manuscript are marked in red.
Above all, thorough copy-editing is recommended, with a focus on sentence
length and paragraph structure, text ow, missing articles and prepositions, rep-
etition, and concision. Careful proofreading of the Conclusions section will also
help make the summary more compelling.
We have thoroughly revised the English and the text ow of the manuscript.
We think the readability is globally improved.
WaveWatch III hindcast - the WW3 hindcast has not been performed for this
particular case study. Eq. (4)-(7) can be omitted as unnecessary, as the given
description of model setup and boundary conditions is enough for the purposes
of the paper.
We agree with the Reviewer, we have signi cantly reduced the detailed de-
scription of the WW3 model omitting the model equations and rephrasing in a
few lines the model structure and the parametrizations that have been used in
the hindcast (Lines 157-163).
All used variables (e.g., the peak wave number kp, peak wave period Tp and
wavelength, BFI) should be introduced when used for the rst time (Lines 168,
175, 179, Table 1). Currently, they are only presented in the Appendix, which
can be an inconvenience for the reader.
All the variables are now introduced in the main text, at least with a textual
description. In the caption of Table 1 we have listed the variables appearing in
each column. We have left in the appendix the de nitions of integral spectral
quantities.
Lines 130-131 The wave data were extracted by the Consorzio LaMMA
wave hindcast, covering the period 1990-2018 [30,31]. This wave hindcast was
produced in the Mediterranean Sea at high-resolution please stick to the ac-
knowledged prepositions here for consistency. Extracted by should be extracted
from, and hindcast was produced in the Mediterranean Sea should read for the
Mediterranean Sea.
We have xed it (Lines 152-153). Thanks.
Fig. 4 Crosses overload the curve and blur the evolution patterns of skew-
ness and kurtosis. Perhaps using small dots (or no symbols at all) would help with gure readability.
Fig.5 have been replaced, removing the crosses and leaving only lines for a
better readability.
Fig. 8 there are no red diamonds on the plot (b), and there are no error bars
on the plot (a). Everything that is stated in the gure legend should be re ected
on the plots
We apologize for the imprecision. We have changed the symbol from circle
to diamond in panel (b). Error bars in panel (a) are barely visible but present.
Figures 6-9 Even though the description of the error bars portrayed on the
plots is given in the text, it would be best to state it once again in the captions
for clarity.
We have added a brief description of the error bars meaning in Figures 7-10.
We thank the Reviewer for pointing to the above issues, we believe that the
quality of the manuscript has been improved thanks to the review process.
Round 2
Reviewer 1 Report
The authors addressed all my concerns
