Using Modified Harmonic Analysis to Estimate the Trend of Sea-Level Rise around Taiwan
Round 1
Reviewer 1 Report
The topic of the article is related to the topic of global climate change, which leads to an increase in temperature, melting of glaciers, and, consequently, a predicted rise in sea level. The structure of the article is unclear, since first the sea level rise is demonstrated at various stations, then there is a discussion of the processing methods used, the results of using various methods are shown, then it is said that for each observation station there is a change in the position of the observation point according to GPS data, then this different change in the level of observation points is taken into account, and ultimately it is said that the sea level change is the same for all observation stations. It is necessary to significantly rebuild the article: 1) provide experimental data on all observation stations, 2) provide GPS data on changes in the level of observation points, 3) subtract GPS readings from the readings of tidal stations, 4) then proceed to processing using various methods, followed by a comparison of the results obtained.
What else is bad. The authors of the article believe that the temperature rise is linear, the sea level rise is linear. But this is not true! And where is the accounting of solar activity? In addition, non-linear greenhouse gas emissions do not lead to a linear increase in temperature and sea level. And what is the relationship of sea level variations with seismic and volcanic activity? It is very difficult to answer these questions. It is necessary to at least evaluate this contribution in this article and show that all these variations do not significantly contribute to the observed sea level rise and, therefore, the authors of the article consider this increase to be linear.
About some methods. It is known that the Hilbert-Huang transformation is not quite good, the series does not converge. Even before applying it in this article, every person involved in processing can say that it will give a bad result. This can be said for other processing methods. They do not need to be compared when processing the readings of tidal stations. The applicability of these methods should be studied on model ranges. And then use the best of them when processing full-scale data. And why didn't the authors consider several more methods, for example, the maximum likelihood method? Its basis is modeling, accounting for harmonic attenuation, nonlinear behavior of harmonics, etc.
I think that the article should be substantially revised taking into account the above comments.
Author Response
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Reviewer 2 Report
In this paper, the rising trend of sea level around Taiwan island is analyzed based on long-term tidal level observation data series using Hilbert-Huang Transform and Modified Harmonic Analysis and other methods. By comparing the two versions of the paper, it is found that the author has made significant improvements to the paper. However, I have two major comments that may be helpful to the paper.
Comment 1. What needs to be clarified in this paper is how to see that MHA is better than the other two methods, especially HHT? The point that “It has the advantage to represent the tidal harmonic motion as well as the long-termed trend of SLR more accurately (in Abstract)” needs more sufficient. Indeed, the advantages of the MHA algorithm are verified and discussed by constructing an example (Eq. 3), but there are some problems in such verification
(1) The tide level given in Eq. 3 fluctuates ten times in 2 seconds, the frequency is even higher than the surface wave. The difference between this period and the tide period is too great, so it is not appropriate to use such an example to verify the advantages or disadvantages of the algorithms.
(2) Figure 3 can be seen to be the most important figure in the whole paper. It shows that the MHA algorithm can better fit the sea surface rising trend given in the example (Eq. 3) compared with HHT and linear fitting. However, in the verification of Fig. 3, the X(t) is given according to Eq. 3, which is a special case of Eq. 2. Note that the MHA method in this paper is calculated according to Eq. 2. In other words, using the method of Eq. 2 to solve the X(t) given by formula 2 is naturally better than using other formulas. Therefore, it is unreasonable to design the verification through such a special case.
(3) Figure 7 and Figure 9 use the real observation data to calculate the sea level change trend by three methods. However, it does not indicate which result is more reasonable. From the 70 years, the overall change trend calculated by the three methods is similar. However, the results given by the HHT method seem more detailed. My opinion is that there is no need to explain whether HHT is better or MHA is better. We might as well give the results of the two methods at the same time. As for which method is better, let the follow-up research judge.
(4) The change of tide level not only has a long-term (about one hundred years) trend but also should have certain interdecadal (about ten years) change characteristics. The complete linear growth is unreasonable. In this way, the result of HHT seems more reasonable. Of course, whether the decadal changes presented by HHT are correct or not still needs further research (perhaps in follow-up research).
(5) "Traditional harmonic analysis methods cannot analyze sea level risk (L200)" is incorrect. Harmonic analysis is used to get the tide information. By deducting the tide information from the water level sequence, we can get the water level change after removing the influence of tide factors. The SLR can be obtained by linear regression of the latter. It can be seen that although harmonic analysis cannot directly obtain SLR, it is easy to obtain SLR after harmonic analysis. The principle of the MHA method in this paper is the same, such as Eq. 2.
Comment 2. It is necessary to add a section in the discussion part to specifically discuss the following two aspects.
(1) Discuss the rationality of the method, that is, the difference between MHA and HHT shown by the results, which may be more reasonable? Also to my first opinion.
(2) Discuss the reasons for the differences in the results of different stations. For example, in Figure 11, Mailiao, Wengang, Dongshi, and Jiangjun are not far away. Why is there such a big difference in the sea level rising trend? Appropriate explanations should be supplied.
Other minor aspects:
(1) The caption of Figure 1 should indicate that the X(t) is given by Eq. 3.
(2) Section 2 only introduces the method, not the source of tide level data.
(3) The last paragraph of the Introduction mentions five methods to make the reader think you have compared them. Only three of them are compared, and only three are mentioned in the Abstract.
(4) The “in” of the title should be “around”.
(5) L94: EMD appears for the first time, but it is not defined.
(6) L112-114: Wordy, can be deleted.
(7) In Figure 2, IMF and EMD appear in the figure for the first time, but they are not defined.
(8) If I understand correctly, the EMD in Figure 3 is the trend in Figure 5, that is, the HHT in Figure 7. Their descriptions should be unified.
(9) It should be noted in Figure 3 that "1 + 2T" is a comparison result, which is the input setting condition, which is equivalent to a "real value". The calculation result should be closed to it.
(10) What do the numbers beside the stations in Figure 4 mean?
(11) The missing data in figures 5 and 6 should not be connected with a straight line and should be left blank.
(12) What is the relationship between trend and signal, IMF1, IMF2 ... in Figure 5? Eqs. 1, 2, and 3 cannot reflect this relationship, and the formula description should be supplemented.
(13) IMF and HHT in Figure 5 are not defined.
(14) Is the “signal” in Figure 5 the “tide level” of the title? The expressions should be consistent.
(15) The middle part of Figure 11 is repeated with Figure 4.
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
A lot has changed for the better in the article. It can be published.
Author Response
thank you
Reviewer 2 Report
The author has carried out a lot of supplementary work and made in-depth revisions. However, there are still some problems in expressions, and also major deficiencies in the comparison between their results and previous literature. The author has given me detailed explanations for the comments. It is difficult to find where are the modifications relative to the authors’ responses. I think a lot of the responses to the comments can be incorporated into the main text. The author should show the supplementary results well.
The biggest problem existing in this paper is that there is still much room for improvement in the integration level of the results with existing literature. For example, Sections 3.1 and 3.2 have no reference and Section 3.3 has only one reference. In addition, the references cited in the Introduction have not appeared in the following text. This shows that the results of this paper are lacking in comparison with previous studies in terms of compatibility and differentiation.
The references cited in this paper are relatively old, only one reference was published in recent 10 years.
The Abstract gives the comparison results of different methods for calculating the trend of sea-level rise. However, it should also describe the results of the trend of sea-level rise around Taiwan, because it is the topic (the title).
In Figures 1, 2, and 3, the units of parameters are required for all axes.
The author has written response regarding what the numbers beside the stations mean in Figure 4. This should also be noted in the caption in Figure 4. In addition, the title of the figure and the figure should be typeset on the same page.
Figure 5: Note what the three red, blue, and green lines mean respectively.
Figure 10 can be combined with Figure 9. Even if not, Figure 10 should indicate that they are the results for the Hsinchu station.
Author Response
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Round 3
Reviewer 2 Report
I counted that there were only two references (Huang et al., 2004 and Ching et al., 2011) in the Results and Discussion section. Neither of them appears in the Introduction section. No references cited in the Introduction section are mentioned in the following text. This weakness has been raised in the last review. However, the authors have solved other relatively simple problems but did not respond to this most important issue.
Why do the authors not compare and merge their results with the others’ studies? I suggest that the editor give the authors enough time (at least two weeks) to solve this issue.
Author Response
Dear Associate Editor:
Enclosed please find the 3rd revised version of the resubmitted manuscript entitled” Using modified harmonic analysis to estimate the trend of sea level rising around Taiwan”, by Prof. Chih-Min Hsieh, Prof. Dean Chou and I. The paper number is 169448.
We make our effort to revise the manuscript on the basis of reviewer’s comments. Hopefully the paper can be published in the Sustainability Journal. Thank you so much for your kind consideration and help.
The best wishes
Tai-Wen Hsu
President and Chair Professor
Center of Excellence for Ocean Engineering,
Department of Harbor and River Engineering,
National Taiwan Ocean University, Keelung 202301, Taiwan
Author Response File: Author Response.pdf
