the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Dec 2023
Linear Variation of M2 Tide in the East and South China Seas
Abstract. Considering the time-varying tidal parameters in offshore China, we proposed a harmonic analysis method combined with an additional time-varying mode. Tidal analysis was performed on nearly 20 years of sea surface altimetry data from the Jason 1-3, Envisat, and ERS-2 satellites, and 13 tide stations located along the coast of the southeast China Sea. The results show that there are several peak regions for the amplitude and phase lag change rate of the M2 tide in the East China Sea and the South China Sea, which are mainly located in the estuary areas of inland river basins, such as the Yangtze Estuary, the Pearl River Estuary, and the Nanliu Estuary, and the variation ranges are roughly 2.0–4.0 mm/yr and 0.8–2.0°/yr. The variations in tidal parameters were attributed to the changes in water depth and coastline in the estuaries.
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RC1: 'Comment on egusphere-2023-2878', Philip Woodworth, 03 Jan 2024
Comments on ‘Linear Variation of M2 Tide in the East and South China Seas’ by Hao Ke et al. (Ocean Science)
This paper investigates long-term variations in the M2 component of the ocean tide in the waters near China using both coastal tide gauge and satellite altimeter data. The aim (although it is not very well expressed) is to see the extent to which the large changes in M2 found at the coast in tide gauge data are also found in the neighbouring waters in altimeter data. The authors claim to have devised a new method of tidal analysis in which a linear trend is combined with the usual harmonic terms.
Although the study is potentially of interest, I found the paper rather unsatisfactory in that the text is incomplete and confusing at times, and the authors do not demonstrate satisfactorily that the new tidal analysis method actually works. In particular, the discussion of the results towards the end of the paper is rather messy. To be fair, the latter is inevitable when the record lengths of the individual tide gauge and altimeter data sets are different. The assumption that any changes in M2 are linear in time is probably incorrect (or at least not demonstrated), given the variability in coastal and ocean processes, and so different record lengths will inevitably lead to different rates. (Showing linear rates of unequal length records is ok for general information purposes, of course.) Therefore, I am not sure what value the results would have, even if the data themselves had been perfect. I give some examples of these problems below.
A first comment is that the references in the introduction to the paper are inadequate. M2 is indeed known to be changing in parts of the world (the authors refer to Woodworth and Muller) but there is also a major recent review paper on that topic by Haigh et al. in 2019 (Prog. In Ocean.) which is not mentioned. And there is quite a quite a large literature on the subject with some papers in the Pacific (see the references in Haigh et al.). Also, they do not explain properly in the introduction how difficult it is to measure M2 accurately near to the coast using altimetry, see for example the review paper by Ray et al. in 2010 (Tide predictions in shelf and coastal waters, chapter 8 in S. Vignudelli et al., Coastal Altimetry, DOI: 10.1007/978-3-642-12796-0_8). So, they should explain that measuring changes in M2 near to the coast will be even more difficult than measuring M2 itself. Now, while a number of authors have tried to measure variations in M2 in the global ocean (Cherniawsky et al, CSR 2010 might be mentioned), I don’t know of anyone who has looked seriously at changes near to the coast. Maybe I am wrong about this, but anyway the present authors don’t properly explain what their aims are and what the status of previous work on this subject is.
In lines 27-31, some numbers are quoted from Peng and Tsimplis and Peng et al. but where a trend value is given it should be clearer which one is referred to. One Peng paper used 17 stations and the other 20 for example.
Line 32 might read better ‘… China, tidal constituents were found to exhibit ….’.
A second general comment is to do with the details of eq. (1) and following:
- I would denote mean sea level by Z instead of S, which can be confused with the sine terms following in eq. (3)
- It is usual to use V to represent the astronomical argument of a harmonic term, to which omega*time is added (omega being the speed). But the authors bundle the two together in their V which is unusual.
- The various parameters are all said to be ‘time-dependent’, but that is misleading as it is surely only the amplitude (H) and phase lag (g) which are being considered as time dependent in the sense of the fitting. Of course, V, f and u are also time dependent but they are not actually time dependent free parameters. The f and u must have been assumed to have their equilibrium time dependence but the authors don’t say. All this could be much clearer.
- I guess using just 13 harmonics is ok for present purposes but I have no idea what GB 12327-2022 is. It is not in the reference list.
- Line 48-49, this is not strictly true, in many parts of the world M2 exhibits a seasonal dependence of about 1% in amplitude – see for example the Pugh and Woodworth (2014) book (Cambridge Univ Press).
- One complication mentioned in Feng et al. concerns the fact that N2 will not be determined well with eq.1 because of its degree-3 component. That will have little effect on M2 but it could be mentioned for completeness.
- Line 56 - where
- Line 60 - the use of a notation of a dot over HC is confusing, I thought at first it referred just to H. I would put HC in brackets and make it clear that the dot refers to the whole bracket.
- In the matrix of eq.4 I would put the superscripts as subscripts as they could be confused with squared etc. Similarly in eq. 7, this reads to me as HC multiplied by delta-t, rather than being a function of delta-t, with the delta-t then squared. I know what the authors are doing here but it is not the best way of writing the algebra.
- m is the number of hourly values? (not mentioned). Also what is P in eq. 5?
Section 3 – why don’t the authors use T/P data from 1992 which would provide a much longer record?
Line 87 – exactly 35 days – the ‘exactly’ is important as the Envisat orbit is sun-synchronous
Table 1 – there is no point giving the start/stop in seconds for this general information purpose, could not the format used in Table 2 be used here?
Line 95 – give references or web sites for UHSLC and the Hydrology Bureau. Also mention these data sources in the Acknowledgements.
Line 99 – ‘can meet .. analysis’. This is obvious, you can do a tidal analysis on, say, a fortnight of data if necessary.
Figure 1 – please add Longitude (deg E) and Latitude (deg N) to the x-y annotation, add East and South China Seas to the map
Table 2 – deg E and deg N
Section 3 has altimeter data mentioned before tide gauges, but the reverse in Section 4. Reverse the order in section 3.
Section 4 – the authors do not use the new fitting method here, but compute trends in M2 from those obtained from individual annual sets of data. Do the two methods give the same results? They don’t say. That would then inspire confidence in its use with the altimeter data.
Have subsection headings in section 4 as in section 3.
Para at line 310 – more words of comparison to the results of Feng and Tsimplis and Feng et al. would be useful. If they differ, why so? Line 309 reword ‘… River, is the second longest, with an amplitude …’
Line 112 – basically ==> of the order of
Line 113 – ditto
Line 114 – this is a rather obvious statement. Say something like ‘… calculated at each point along-track’ saying what the separation between points is.
Line 115 – call it ‘time varying term’. It doesn’t seem to me there is a ‘mode’ here, just an extra linear term.
How does the fitting method handle gaps in the records? Presumably for the annual tide gauge analyses, years of data were used only if they were, say, at least 80% complete.
Figures 2-4 have a really poor colour scale with too much blue. Could not they be white at zero with pale to strong blue for negative values, and pale to strong red for positive ones (for example).
Fig 2 caption lines 1 and 2 – M2 amplitude and phase lag
Fig 3 caption – ditto
Line 124 – drop ‘The following’.
Line 131 – ‘inconsistent values’ is a strange expression. Say explicitly what is meant e.g. mean or absolute difference or root-mean-difference of M2 values at cross-over points of the ground tracks.
Table 4 – what is CR of M2? Does this mean rate of change of M2? Phase should be phase lag. ‘Discrepancy Mean’ should be ‘Mean Difference’?
I think lines 135-170 need to be rewritten, perhaps with subheadings, to make it clearer what is being compared with what. There are 2 sorts of altimetry being compared with each other, and then altimetry with tide gauges, but the text is jumbled.
Line 139 – derived from ERS2/Envisat is much poorer.
Drop ‘The specific ..’
Line 145 – I can’t see any dots in Fig 4 but I can in Figs 2 and 3. Those dots are not mentioned in the text.
‘Beyond the research scope’? What does that mean? Outside the gridded area?
‘Belongs to extrapolation’ ==> ‘has been obtained by extrapolation’
Line 152 – I think should read ‘Comparing the rates of change of M2 obtained at the tide gauges and altimetry at tide gauge locations …’
What are the standard deviations’? You mean the root mean squares?
Line 154 – ‘crossing points in general’
Is Table 5 using just Jason data or the combined altimetry mapping? Actually I thought these values were quite interesting – what is the correlation between the sets of trend-differences?
Line 159 – ‘According to ..’. But MS4 is not actually listed in Table 2. I agree MS4 could be a complication in the case of Envisat.
Line 161 – ‘to be poorer’
Line 164 – by mainland do you mean the Chinese mainland and not Taiwan or do you mean the coast in general? Reword.
As mentioned, I thought Table 5 interesting but does this use just Jason altimetry or combined? Also what are the modes? – you mean just the gridded altimetry data sets. Why is the mean of the absolute difference used here whereas mean difference is used in Table 4?
Lines 173-on and Figure 4 – I thought Figure 4 was potentially quite interesting, with large changes off-shore, although I suspect some of that is due to noise in the altimetry mapping. It seems to me that, if the paper had been written first as a mapping exercise for M2 trend from altimetry, then it would have read much better. As it stands there is a mixture being discussed in the paper of that mapping using data from different missions, and also consideration of what is happening at the coast at the tide gauges compared to the altimetry. And, as I mentioned above, the different spans of data do not make for an easy discussion. The speculation that any tidal changes are due to water depths and coastline changes is probably correct, but speculation it remains, there is no research on that presented here. Maybe if the text of the paper was revised then some of these objections could be removed.
Citation: https://doi.org/10.5194/egusphere-2023-2878-RC1 -
AC1: 'Reply on RC1', Hao Ke, 01 Feb 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-2878/egusphere-2023-2878-AC1-supplement.pdf
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RC2: 'Comment on egusphere-2023-2878', Anonymous Referee #2, 05 Jan 2024
The paper examines tide gauge data and satellite altimeter data in the East and China Seas in an attempt to determine possible linear trends for the M2 ocean tide. That topic is timely, but unfortunately I do not find the quality of this work high enough to meet the standards of Ocean Science. The analysis is pedestrian (at best), the English rather poor, and the discussion superficial. Below I briefly mention major shortcomings; I do not bother tabulating minor problems. My overall recommendation is that OS rejects the paper.
1. I had hope that a discussion of tide-gauge trends around China might bring forth new data. Alas, the authors use the standard set of old data archived at the University of Hawaii which has not been updated since 1997. (The exceptions are two gauges from Taiwan, which are recent, and Hong Kong and one other site, mentioned below.) Evidently the government of China continues to withhold tide gauge data from scientific study. For this reason, there is nothing new in the tide gauge analysis that was not already published by Feng, Tsimplis, and Woodworth (2015). Moreover, the analysis and results of Feng were superior and more complete than the work reported here.
On this same point of missing modern data: The authors emphasize the large amount of coastal changes now ongoing along the Chinese coast. And yet they use tide-gauge time series that stop 25 years ago. It seems more modern data, and not just from Taiwan, are required to examine properly this problem.
2. There is not a single error bar in the entire paper. There is no way to know if any of the computed trends are significant or not. Error analysis (confidence intervals) are critical to this kind of work. Moreover, a proper error analysis is not trivial -- i.e., one cannot just use uncertainties given by some regression package that assumes white noise. Thus, this critical part of the work is missing.
3. There is no appreciation for the fact that 18.6-year nodal modulations of tides can potentially impact estimation of tidal trends, if the modulations are non-equilibrium. In fact, an important result from Feng et al. (2015) is that, indeed, the nodal modulations at many of these stations are non-equilibrium. The authors should have considered this point, since it was stressed by Feng et al.
4. There is no reference to the work by Bij de Vaate et al. (doi: 10.1029/2022JC018845 ), who made a much more thorough study of possible tidal trends from satellite altimetry. They reported trends (with uncertainty analysis) in the East China Sea, which should have been compared here. They also found that trends in the South China Sea were not significant, at least at satellite cross-over locations.
5. There is no appreciation for the possible existence of systematic errors in satellite altimetry which could impact trend estimation. Nor is there discussion of the apparently large errors in M2 (not M2 trends) seen at Jason cross-overs -- 12.8 cm, according to Table 4. It is difficult to see how mm/year trends in M2 could be determined in the presence of such large noise in the mean M2.
6. Much of the mathematics laid out, especially the large matrix in Eq (4), is not needed. Everybody already knows how to set up a least-squares problem.
7. In both the Abstract and the Conclusions, it is stated that the detected tidal trends in M2 are caused by changes in water depth and coastlines of estuaries. There is no evidence presented that backs up these statements. They are merely assertions.
8. As far as I can tell, there is one tide gauge used here that is not from the UHSLC: the gauge at Lianxinggang. In the "Data Availability" statement, the authors give a web site for these data, but the link did not work for me.
9. I had difficulty with the color scale used in Figures 3 and 4. It is not easy to distinguish positive trends from negative trends, let alone decipher the magnitudes.
Citation: https://doi.org/10.5194/egusphere-2023-2878-RC2 -
AC2: 'Reply on RC2', Hao Ke, 13 Mar 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-2878/egusphere-2023-2878-AC2-supplement.pdf
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AC2: 'Reply on RC2', Hao Ke, 13 Mar 2024
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