the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Oct 2022
The acceleration of sea-level rise along the coast of the Netherlands started in the 1960s
Abstract. While a global acceleration of sea-level rise (SLR) during the 20th century is now established, locally acceleration is more difficult to detect because additional processes play a role which sometimes mask the acceleration. Here we study the rate of SLR along the coast of the Netherlands from six tide gauge records, covering the period 1890–2000. We focus on the influence of the wind field and the nodal tide variations on the local sea-level trend. We use four generalised additive models, including different predictive variables, and a parametric bootstrap method to compute the sea-level trend. From the sea-level trend, we obtain the continuous evolution of the rate of SLR and its uncertainty over the observational period through differentiation. Accounting for the nodal cycle only or both the nodal cycle and the wind influence on sea level reduces the standard error in the estimation of the rate of SLR. Moreover, accounting for both the nodal and wind influence changes the estimated rate of SLR, unmasking an acceleration of SLR that started in the 1960s. Our best-fitting statistical model yields a rate of SLR of about 1.8 [1.4–2.3] mm/yr in 1900–1919 and 1.5 [1.1–1.8] mm/yr in 1940–1959 compared to 3.0 [2.4–3.5] mm/yr over 2000–2019. If, apart from tidal, wind effects and fluctuations, sea level would have increased at a constant rate, then the probability (the p-value) of finding a rate difference between 1940–1959 and 2000–2019 of at least our estimate is smaller than 1 %. Our findings can be interpreted as an unequivocal sign of the acceleration of current SLR along the Dutch coast since the 1960s. This aligns with global SLR observations and expectations based on a physical understanding of SLR related to global warming.
A small but significant part of the long-term sea-level trend is due to wind forcing related to a strengthening and northward shift of the jet stream. Additionally, we detect a multidecadal mode of sea-level variability forced by the wind with an amplitude of around 1 cm. We argue that it is related to multi-decadal sea surface temperature variations in the North Atlantic, similar to the Atlantic Multidecadal Variability.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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RC1: 'Comment on egusphere-2022-935', Anonymous Referee #1, 14 Nov 2022
This study covers an important subject and is relevant contribution for the sea-level community. I feel a few modifications to the manuscript text will improve clarity. Please see attached PDF for the review report.
- AC3: 'Reply on RC1', Iris Keizer, 03 Mar 2023
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CC1: 'Comment on egusphere-2022-935 (#1)', Giordano Lipari, 18 Nov 2022
Summary
I have read the manuscript with great interest.
With reference to the review criteria of OS, the work proposed well-circumscribed and substantial conclusions on debated topics (sea level rise acceleration in a convoluted stretch of a shallow sea) obtained with powerful statistical methods (separation of a time-varying signal into a time-varying influences of predictive variables and a smooth time-varying background residual). However, while the line of reasoning is clear in its broad terms, the assumptions/methods are often outlined unclearly, whereby assessing their validity and their linkage to the results proves awkward.
In terms of personal reading experience, I found it difficult to get engrossed and isolate with agility what merits a focussed discussion on content and correctness. A certain draft-like, think-aloud quality still hampers speed reading and in-depth consideration. I am nonetheless convinced that a few of rounds of streamlining and paraphrasing will drastically improve the manuscript. Linguistic points of coherence (organization in sections and paragraphs) and clarity (at the level of sentences) should be addressed thoroughly to let the content shine its own light.
I give below suggestions for samples of passages where my reading flow froze. I surely invite the authors to apply those suggestions anywhere they deem it beneficial. (Equally surely, the authors do well to cross-check my suggestions one with another and with other peers.) This document also address some point of content, whether or not entangled with reading difficulties.
I have read the manuscript in full a couple of times, but will restrict my contribution to the text within Section 3.1 included. I have not looked into the supplementary material (the code), but I would expect from the authors that the documentation follows standard of clarity adequate for reproducibility.
[1] Abstract 2-4
This is an extended remark on clarity (speed-reading). My ensuing suggestions will be more succinct.
The kick-off sentence:
While a global acceleration of sea-level rise (SLR) during the 20th century is now established, locally acceleration is more difficult to detect because additional processes play a role which sometimes mask the acceleration. Here we study the rate of SLR along the coast of the Netherlands from six tide gauge records, covering the period 1890-2000. (55 words, 349 characters)
reads more easily in the form:
While the global acceleration of the sea-level rise (SLR) during the 20th century has already been established, additional processes play a masking role that makes it difficult to detect local acceleration. Here we study the rate of SLR along the coast of the Netherlands using the records of six tide gauges in the period 1890-2000.
which exposes the question of what that ‘additional’ feature is supposed to be added to; there is nothing before the first sentence.
Then, may I suggest:
While the global acceleration of the sea-level rise (SLR) during the 20th century has already been ascertained, the masking by several processes makes detecting local acceleration difficult. Here, we investigate the rate of SLR along the coast of the Netherlands using the records of six tide gauges in the period 1890-2000.
which exposes the question of which processes the writer has in mind.
Then, may I suggest:
While the global acceleration of the sea-level rise (SLR) during the 20th century has already been ascertained, the masking caused by several drivers hampers detecting local accelerations of SLR. Here, the records of six tide gauges in the period 1890-2000 are used to analyse the rate of SLR along the coast of the Netherlands.
or
The global acceleration of sea-level rise (SLR) during the 20th century has already been ascertained. Nonetheless, several drivers of SLR mask the detection of its local acceleration. Here, the records of six tide gauges in the period 1890-2000 are analysed to investigate the rate of SLR along the coast of the Netherlands. (51 words)
You may deviate from any suggestions, of course, and devise better ones. The benefit in sight is that these last few formulations create an anticipation as to which data and factors are considered in the subsequent analysis.
[2] Abstract 12-15
I found this awkward to read and hence to assess:
If, apart from tidal, wind effects and fluctuations, sea level would have increased at a constant rate, then the probability (the p-value) of finding a rate difference between 1940-1959 and 2000-2019 of at least our estimate is smaller than 1Our findings can be interpreted as an unequivocal sign of the acceleration of current SLR along the Dutch coast since the 1960s. This aligns with global SLR observations and expectations based on a physical understanding of SLR related to global warming.
Do you mean something like this?
If we discount for the effects of tide and of wind fluctuations and then assume a constant SLR rate, the probability that the SLR rates in the periods 1940-1959 and 2000-2019 differ as much as our estimate or more is smaller than 1 (p-value). This result indicates unequivocally that the SLR along the Dutch coast has been accelerating since the 1960s. Global observations and the expectations based on the physics of global warming are consistent with this finding.
Then the validity of the statement is hopefully more accessible.
[3] Introduction 28-31
This is a point of clarity (speed-reading). I found this cumbersome to read:
More recently, Walker et al. (2022) estimated the time when the rate of global SLR emerged from the background variability of the Common Era (0-2000CE) to the middle of the 19th century. For the North-East Atlantic, they found this emergence to occur around the middle of the 20th century. This is in line with Dangendorf et al. (2019) who found a global acceleration of SLR from the 1960s.
May I suggest:
Dangendorf et al. (2019) had found the global rate of SLR to accelerate from the 1960s. More recently, Walker et al. (2022) estimated that the rates of SLR emerged from the background variability of the Common Era (0-2000 CE) in the middle of the 19th century for the globe and in the middle of the 20th century for the North-East Atlantic.
One benefit for speed reading is that new information appears in the same order of publication of the articles. So one appreciates the progress in the field without backtracking through the text.
[4] Introduction 32-33
This is a point of clarity (speed-reading). Re:
Along the coast of the Netherlands, there has been an ongoing debate about whether an acceleration of SLR takes place or not (Baart et al., 2011; Wahl et al., 2013; Steffelbauer et al., 2022).
While I appreciate the natural word order in Dutch, I would suggest streamlining the sentence into:
The existence of SLR acceleration along the coast of the Netherlands is still debated (Baart et al., 2011; Wahl et al., 2013; Steffelbauer et al., 2022).
Something similar occurs in lines 58-60.
[5] Introduction 47-50
This is a point of clarity (speed-reading). Re:
Understanding and removing the interannual to multidecadal sources of variability from tide gauge records was found to be essential for detecting an acceleration of SLR (Haigh et al., 2014). To this end, multilinear regression models between sea levels and atmospheric variables like sea-level pressure gradients, zonal and meridional wind velocity and sometimes precipitation as predictive variables have been used by various authors.
may I suggest something like:
Detecting the SLR acceleration requires understanding the sources of interannual-to-multidecadal variability and removing them from tide gauge records (Haigh et al., 2014). To this end, various authors have used multilinear regression models between sea levels and atmospheric variables. The pressure gradients at the sea surface, the zonal and meridional wind velocities and, at times, precipitation are usual predictive variables.
[6] Introduction 56-57
The verb tenses in the sentences
In general, the variability due to atmospheric forcing was first estimated by linearly detrending the time series. After that, the variability is removed from the sea level data before estimating the trend and acceleration.
confuse the extent to which old/new practices may be better/worse. (Place this remark in the context of the paragraph contrasting known methods.)
[7] Introduction 61-62
This is a point of clarity (making key figures stand out). Re:
The calculated rate of mean SLR of the stations increases from 1.7±0.3 mm/yr before the breakpoint to 2.7 ±0.4 mm/yr after the breakpoint implying an acceleration.
I suggest:
The average SLR rate of the stations increases at the breakpoint from 1.7±0.3 to 2.7±0.4 mm/yr, which implies an acceleration of the SLR.
[8] 2.1 Tide Gauge Observations 80
Regarding
Annual-mean sea-level measurements are used from the six reference tide gauges along the coast of the Netherlands: Delfzijl, Den Helder, Harlingen, IJmuiden, Hoek van Holland and Vlissingen.
is the signal that you study the average of these six stations? I inferred this from the caption of Figures 1, 2, 3 and I couldn’t seem to find this (important) piece of information in the body of the manuscript. This is the place to (re-)state this, and also an appropriate place to refer to Figure 1a.
[9a-c] 2.1 Tide Gauge Observations 81-82
This is a remark on content. In the sentence
These stations are used for operational sea level monitoring because of their extended temporal coverage and uniform distribution along the Dutch coast (Baart et al., 2019).
the term ‘uniform distribution’ sounds like a phrase borrowed from statistics. Regardless, the attribution of uniformity does not sound applicable in several respects:
a. The attribution of uniformity is geographically uninformative. To gain a feel of the geographical scope of the study, mentioning the approximate span length of the Dutch coast covered by these stations might be more informative.
b. From the point of view of physical oceanography, the station Vlissingen is distinctive insofar as is placed at the mouth of the Western Scheldt Estuary. It is conceivable that morphological developments in the estuary since 1890, of both natural and human origin, have affected the gauge signals in that area. Likewise, station Delfzijl is placed inside the Ems-Dollard estuary, whose tidal regime has been heavily affected by capital dredging in recent decades. (I do not have literature at hand to substantiate these claims, but both estuaries have been investigated exensively. I might collect some literature at a later point.) This consideration also implies that a specific factor is at play for these two stations and not for the others. Given your interest for shallow seas, you ought to include your view as to whether using the average of all stations as a study variable will make good any objective diversity between the stations; in other words, whether what you determine for “the Netherlands” applies to each of the selected stations. A precise answer might be found in previous studies or require further study. Nonetheless, stating proactively to which extent the objective geographical non-uniformity might affect the scope of the conclusions will strengthen the manuscript.
c. Likewise, the station Den Helder is placed at a tidal inlet of the Wadden Sea and Harlingen is inside. Similar morphological influences from the back basin may be conjectured after the closure of the Afsluitdijk in 1932. (I do not have literature at hand to substantiate this claim, but the topic has been investigated. I might collect some literature at a later point.) The same notes of caution as in point b apply, though.
[10] 2.1 Tide Gauge Observations 84-88
This is a point of linguistic clarity. Hoping to have brought forward a sufficient number of ex/samples, I will refrain from commenting on further passages that prompt similar linguistic editing.
The passage:
While the time series for the different stations start between 1862 and 1872, only 1890 to 2020 are used for the analysis. As was done for other studies, tide gauge data is limited to the period after 1890 to avoid the inclusion of a sea-level jump around 1885 (Frederikse and Gerkema, 2018; Baart et al., 2019). From that year, the monthly mean sea level is based on mean sea-level readings rather than mean tide level readings, which could result in a jump in the monthly data (Woodworth, 2017). (88 words)
could become:
The time series at these stations start between 1862 and 1872. However, the monthly mean sea level before 1885 is gauged with respect to readings of the mean tide rather than of the mean sea level. This could result in a jump in the data (Woodworth, 2017). Therefore, only the tide gauge data after 1890 are used as done in other studies (Frederikse and Gerkema, 2018; Baart et al., 2019).
If correct, this paraphrase exposes the fact that the ‘monthly mean sea level’ had not been based on the ‘mean sea level’ in a certain past. So why is the former called ‘mean sea level’ in the first place? The bare point seems to be that the mean sea level could only have been determined since 1885. If this too is a correct reading, the passage could become:
The readings at these stations start between 1862 and 1872 and are gauged with respect to the mean sea level, rather than to the mean tide, since 1885. Therefore, we only use the tide gauge data after 1890 as did Frederikse and Gerkema, 2018 and Baart et al., 2019. Failure to do so introduces an artificial jump in the data (Woodworth, 2017). (61 words)
[11] 2.1 Tide Gauge Observations 84-88
The fact that the global database did not account for the change of datum of 1855 raises a slight concern that other biases of local origin may have crept in. For example, the instruments at the tidal stations have obviously been changed since 1890. There, I would expect that all instruments have been thoroughly recalibrated at source, but their accuracy will have varied.
Therefore, it would be very fine to read in the manuscript whether you expect that the dataset of choice contains other biases linked to the history of the tide recordings in the Netherlands. Any potential bias in the model input in the the periods 1940-1959 and 2000-2019 seems particularly relevant for the conclusions of this study. These potential biases should be named. The Discussion should also assert whether those biases, however speculative and/or undetermined, tend to strengthen or weaken the interpretation and hence the conclusions.
[12a-b] 2.2 Atmospheric Reanalysis (and Appendix A)
a. This section does not explain for which purpose and in which way you use the reanalyses. For example, the ERA5 has a “backward extension to1950”. How do you go about this? Do you consider it fit for your purposes? Waiting does not pay off either, for the subsequent section Methods does not dwell on how you pre-processed the model input either. Therefore, an early explanation of all pre-processing choices would be beneficial before diving into the Statistical Methods – either in an expanded § 2.2 or in a new § 3.1.
b. I feel that Appendix A should be either blended in the body of the manuscript or published separately as a technical note. In the former scenario, which I would endorse, the section on Data should then describe the other datasets introduced in the present Appendix.
[13] 3.1 Statistical Models 98-99
The sentence
Four statistical models were developed and used to unravel the influence of different factors on SLR and to extract the background sea-level trend.
sounds like a downplayed announcement of the novelty of the study, which had suitably been stated in the Introduction (65-). The operation of unravel-and-extract is vague without recalling the explaining power of the factors that are made explicit and of those left in the background. Also, from the logical viewpoint, the background trend is dual to the selection of influencing. (I find comfort in a later sentence at 105-106: “its exact meaning depends on the choice of the predictive variables”.)
I would probably rephrase the sentence above as
Four novel statistical models have been developed to separate the SLR signal into the time-varying influence of chosen predictive factors and the time-varying resulting background signal.
assuming I have understood correctly merit and novelty of the study. But if you developed a single model in four setups, the wording should be adjusted (and the appropriate terminology used consistently all over).
[14] 3.1 Statistical Models 100
The ‘penalised maximum likelihood’ is referred to as ‘parametric bootstrap method’ in the abstract (6) and in the introduction (73). If the relationship between ‘penalised maximum likelihood’ and ‘parametric bootstrap method’ is topical, please comment on it explicitly. In general, please make sure to use a uniform terminology across the manuscript and avoid switching between near-synonyms. A consistent terminology will help the readers to skip forwards and backwards through the sections comfortably.
[15] 3.1 Statistical Models 106-107
I find it difficult to interpret the sentence
Its smoothness is controlled by a penalty term subtracted from the log-likelihood, which is proportional to the time integral of the squared curvature of the smooth term Wood (2020).
because the “smoothness” of the smooth curve is presented as the effect of a “smooth term” not defined earlier. I would suggest to write the parametric equations, if only in a concise symbolic form, in the body of the manuscript and add a lay résumé of the attending mathematics in the Appendix (with reference to Wood 2020 for the more statistically-minded reader of OS).
[16] 3.1 Statistical Models 107-108
Re
The penalty term was assigned a weight tuned to match the variance of the smooth curve to the variance of a 30-year average.
leads to the question of how sensitive to this statistical parameter the conclusions are. Take note: this is not a general question of model sensitivity. The point that ought to be addressed is: should one revise the conclusion about the SLR in the Netherlands if the smooth curve had been tuned to the variance of a shorter/longer time window? Is 30 years a robust one-fits-all value or does it affect the model’s capability to assess multidecadal physical processes?
[17] 3.1 Statistical Models 110
I prefer this
This setup makes no assumptions about the drivers of SLR.
to the more colloquial
This setup is equivalent to assuming we do not know anything about the drivers of SLR.
I would suggest to make the terminology for drivers, factors, and predictive variables more uniform or more consistent across the manuscript.
[18] 3.1 Statistical Models 118-121
My understanding of the passage
Therefore, we decide to use a linear regression model with an undetermined phase and amplitude but a fixed period as in Baart et al. (2011) even though it might remove some additional variability around the period of nodal tides. Using this second model, the influence of the nodal cycle on the trend and variability of sea level can be studied.
is that
Therefore, we study the influence of the nodal tide constituent on the trend and variability of sea level using a linear regression model with undetermined phase and amplitude as in Baart et al. (2011). As a downside, the resulting sea level variability may not account properly for other multidecadal influences having periodic components close to the nodal cycle.
If correct, I hope that the second version is useful to review the first.
[19] 3.1 Statistical Models 122-123
In
For the third model, wind effects are included by adding u|u| (TrNcZw), where u is the zonal wind from reanalysis averaged over the closest grid cell of each tide gauge (Fig. 1a).
I resent the lack of clarity about the average of the tide gauge readings. In the case of wind, I then wonder if you meant “averaged over the cells closest to the tide gauges”. In sum, do they process only one wind signal for the zonal wind or as many signals as there are eligible wind cells?
[20] 3.1 Statistical Models 127
Why do you use Pd to label the model considering the pressure gradient? Would Pg not be a valid name considering that gradient starts with g?
[21] 3.1 Statistical Models 127
I would appreciate reading which data have been used for the “linearly detrended sea level along the Dutch coast”. This connects to the remark that the manuscript lacks a section detailing the use of model inputs.
[22] 3.1 Statistical Models 132-134
In
Then, instead of using the pressure in both boxes as predictive variables as in Dangendorf et al. (2014b), we take the difference between the southern and northern boxes. This adds only one variable to the model and is physically motivated by the fact that the meridional pressure gradient is related to the zonal wind by geostrophy.
I was puzzled by the expectation that geostrophy applies to the upper atmosphere, while the winds used as predictive variables here are taken at 10 m height. If this expectation is correct, the correlation between winds well within the atmospheric boundary layer and those well above would be another relationship not mentioned in the manuscript. Please clarify.
This concludes this comment. Thank you for your reading.
Citation: https://doi.org/10.5194/egusphere-2022-935-CC1 -
CC2: 'Comment on egusphere-2022-935 (#2)', Giordano Lipari, 02 Dec 2022
This comment #2 resumes the analysis already presented in comment #1 up and including § 3.1 (https://doi.org/10.5194/egusphere-2022-935-CC1). The numbering of the remarks continues that of the previous tranche, but I will not propose examples of linguistic editing here.
I confirm the impressions I gained from the the first part of the document analysis. Definitely, the study has merit and deserves to be read. This community comment contains remarks on content, to be considered whether in the positive or in the negative. Principally, however, the recurrence of muddled paragraphs and equivocal sentences amounts to a diffuse major hindrance that, it seems to me, routine copy-editing after acceptance cannot fix. I am also afraid that the current state of the manuscript would frustrate future efforts to replicate/reproduce the study. In the following the notation ‘R11’ means ‘remark 11’.
In my view and experience, fixing this drawback would require a conscious effort of the authors’ to set a comprehensive terminology and rearrange the logical order of the statements, so as to impart a definite forward dynamics to the reading experience. To justify the case for such a thorough revision, therefore, I opted for a full-size effort of scanning the text, explaining my perplexities, and sharing possibly useful interventions. I hope that the resulting long read (and long write) proves, all in all, reasoned enough and helpful enough in the interest of the general readership.
[23] 3.2 Analysis of Model Output 139-145
Regarding the passage
The wind influence on sea level can be obtained from the results of the TrNcZw and TrNcPd GAMs. Once the linear regression coefficients are obtained between 1890 and 2020, the wind influence on sea level can be extended back to 1836, the beginning of the 20CRv3 atmospheric reanalysis. We estimate the wind-driven sea-level trend using a 3rd-degree polynomial fit to the annual-mean data. Also, a spectral analysis is performed on the detrended annual-mean data. The spectra are obtained using a multitaper method (Lees and Park, 1995). To obtain the low-frequency wind influence on sea level, the detrended annual-mean sea level data is smoothed using a local polynomial regression (LOWESS, Cleveland and Devlin (1988)) with a window of 21 years that effectively removes high-frequency variability.
Firstly, have you ever defined the ‘wind influence on sea level’? I have to look at Figure 3, referenced later in Sec. 4.2, to confirm me in my mind that this quantity is a sea level excursion measured in units of length. Further, how is wind influence computed from the two model set-ups? This lack of clarity comes back in the Conclusion (R45 onwards), which may well be the section many readers read first.
Secondly, I am a bit dazzled by a linear regression, a 3rd degree polynomial, a spectral transform, and a smoothing pass showing up in the brief span of a paragraph fairly abruptly. Unravelling the paragraph, I do appreciate that you match the beginning of the wind influence series with the beginning of the wind-forcing series, filling the gap period with a linear regression. Why, though? Do you make any parallel with wind-forcing data afterwards? (Incidentally, the artefact of linear extrapolation over the period 1863-1890 is evident in the polynomial trends of Figure 3b and deserves notice IMHO.) Also, is there a difference between the ‘wind-driven sea-level trend’ and the trend of the ‘wind influence on sea level’? If so, please explain; if not, please keep the terminology consistent. Also, whose ‘annual-mean data’ are you using to draw the fit? Are the ‘detrended annual-mean sea level data’, as mentioned in the text, the same thing as the wind influence, as mentioned in Figure 3d?
Thirdly, regarding the spectrum, what do you define as ‘low’ frequency? Is it an information that emerges from the data, and hence from the specific study, or an arbitrary choice? How does this low-pass filter relate with/interact with your handling of the nodal cycle (19.8 years)? Recall RRR. How does the choice of 21 years relate to the 30-year smoothing window of § 3.1? Recall R16. Is there any wisdom about your GAM that is useful to share regarding these windows; or is it sufficient that 30 years > 21 years; or are those two time frames completely unrelated? Also, you used a clear physics-based terminology for time frames (multidecadal etc…) and it is a pity to abandon it here. (Addressing several of these points may pertain to the Discussion section.)
Finally, if the following paraphrase is a correct basis to discuss your methodology:
The GAM results obtained with the TrNcZw and TrNcPd regressors give two monthly time series of the wind influence on the sea level in the period 1890-2020. The linear-regression coefficients of these time series are then used to extrapolate the data back to the beginning of the 20CRv3 atmospheric reanalysis in 1836. Finally, the annual averages shown in Fig. 3a are used to analyse the wind influence in greater detail. Firstly, the trend of the annual averages is computed with the 3rd-order polynomial fits shown in Fig. 3b. Secondly, the multi-taper method for spectral analysis of Lees and Park, 1995 is applied to the detrended annual averages. The resulting spectra in Fig. 3c feature a clear threshold between oscillations of short and long period. Lastly, the LOWESS local polynomial regression of Cleveland and Devlin (1988) is used to draw the smoothed variations around the trend shown in Fig. 3d, where oscillations faster than 21 years have been removed.
I would then suggest to announce your intentions (why) before showcasing your toolbox (how). Please note the pointers to the figure panels. A new figure with a flow chart of your workflow could help assist the readers, also because you intend to share the code and I presume that this will contain several subroutines/modules attending to each above task.
[24] 3.2 Analysis of Model Output 146-149
Using our four statistical models, we obtain the background sea-level trend. As a next step, the rate of SLR is obtained from differentiating these estimated smooth sea-level trends. The rates of SLR resulting from the different models do not include the same physical processes. TrNcZw and TrNcPd do not include the contribution from wind and nodal effects and TrNc does not include nodal effects while Tr includes all processes.
This is another occasion to adopt a clearer distinction between model and set-ups (or equivalent). Recall R13. Then, is the ‘background sea-level trend’ a new item in addition to the quantities presented in the paragraph just above? Is such a ‘background sea-level trend’ the direct output of your four set-ups as I read now, or do you process that output exactly as described in the previous paragraph?
The paragraph should be tightened up: one tip may be ‘do not include’ → ‘exclude’.
[25] 3.3 Uncertainty Computation 151-173
These two paragraphs
To estimate our models from the data, we use a generic method for likelihood-based estimation of GAM (Wood, 2020). It treats the unknown noise terms as independent identically distributed normal random variables. However, checks of the residuals reveal that they are serially correlated, so the independence assumption is not warranted. This does not invalidate the method: since only marginal parameters are estimated, the estimator is consistent under weak assumptions on the dependence; see Section 2 of Cox and Reid (2004).
However, serial dependence of the noise affects the covariance of the estimated model parameters, so for deriving confidence intervals and for testing hypotheses, we must account for it. Our estimator for the rate of SLR (the finite difference of the smooth spline estimate of the variation in sea level) is particularly sensitive to low-frequency components of the noise. Our error analysis must account for these subtle aspects of serial dependence. Therefore, we apply a parametric bootstrap method based on the noise spectrum, similar to the Wild Bootstrap version of the technique in Kirch and Politis (2011): we estimate the noise spectrum, using the same method as described in the previous section, and generate random instances of the gaussian process having this spectrum. From these, we obtain instances of the sea level time series by adding the estimates of the non-random terms. Then we apply the GAM-based estimator for our models to each of these instances to obtain an estimate of the rate of SLR. This sample of estimates is used to derive the error statistics and to test hypotheses.
invite substantial streamlining. It is difficult to keep track of what leads to what, also because you do not lean on equations; recall R15. I paraphrase the test closely to signal the questions that the current formulation elicits. I understood that:
- You chose to fit the GAMs to the data using a standard methodology based on the likelihood estimation (I’d say one estimates the parameters in order to fit a model to data, as opposed to estimating a model). The residuals, however, contain serially correlated noise (Do you provide any grounding for this?), whereby the i.i.d. normal random variables implied in the likelihood estimation are not well posed. You deem this to be a minor violation of the fit methodology insofar as, firstly, the parameters you estimate (Which? How many?) are marginal (Please explain what do you mean for marginal? You will have a mixed readership) and, secondly, some weak (What do you take to be weak?) dependence (Of what on what?) makes the likelihood-based estimator consistent (So what insights does consistency help retain in your explanation, in the face of this violation?).
- Nonetheless, the serial correlation of the noise terms (How many do you have by the way?) affects the covariance of the model parameters, which is needed to determine confidence intervals and test hypotheses (Are you going to do the latter? Why not to present a plan of what you aim at first?). Then, you explain incidentally how the SLR rate is computed, but this is best placed in Sec 3.2, right when you introduced the SLR rate.
- Suddenly enough, you identify another pain point in the sensitivity of SLR rates to low-frequency noise without having closed the issue of confidence intervals and hypothesis-testing, and without explaining the current threshold for low frequencies. Does it arise from a feature of statistics or from the finite differencing? Is one of the periods of 21 or 30 years you have used? Recall R13 and R23.
- Then, you say you must account for subtle effects, which sounds reasonable, while I would be keener on reading which undesired effects that you want to remove and which explaining capabilities you want to maintain. Sensitivity to correct things is not a bad thing.
- In the same paragraph, you suddenly turn to the noise spectrum (Is this noise the sum of all noise terms you spoke about earlier?). Are you using the same multi-taper methodology as the previous section or the new bootstrap method? And you reconstruct this spectrum with random instances of Gaussian processes (Are those expected to be i.i.d. too? What advantage do you expect from the bootstrap method?). Or do you perhaps generate many random time series of noise that have the same spectrum as the original serially correlated noise, and then sum this to a deterministic part borrowed from the GAM? How many time series per model set-up you are dealing here with? And do you apply the GAM once again after this latest sum, so as it looks? How many times do you run the GAMs then? Is an iterative procedure involved here?
- Then, the section finishes abruptly here. I come away with the impression that you wanted to fix a lot of relevant things without presenting in an orderly fashion the nature and facets of the issues ahead, the expected impact on the future evaluations, and the adequacy of your workflow to forestall these limitations. The exposition is too unglued to enable me to express a judgement on the ensuing discussion, let alone to encourage me to dig deeper in the code.
I suggest rephrasing the whole Section 3 by announcing first the general guarantees you want to offer and then how the methodology delivers these. On so doing, IMHO, you stimulate an effortless curiosity to look into the results coming next. Would you also mind it to add some formulas, whether in the body of the manuscript or in the Appendix (R15), and a figure with the flow chart of your methodology? This will help organize this section greatly.
[26] Figure 2.
Comparison of the annual tide gauge data averaged over 6 tide gauges along the Dutch coast with three Generalised Additive Models (Tr, TrNc, TrNcZw)
Would you make the figure wider to accommodate for all four setups? This is perhaps the first time that you say that the tide gauge data of the six stations are averaged. Recall R8.
[27] 4 Results - 4.1 Comparison of the Different GAMs 176-182
The GAM progressively better fits the data, measured by the deviance (Tbl. 1), as the complexity of the model increases (e.g., the number of predictive variables increases), measured by the number of degrees of freedom (Tbl. 1). The deviance is used to compare generalised linear models and is a generalisation of the sum of squares of residuals used to compare linear regression models (Wood, 2020). Including the nodal cycle reduces the deviance by 12%, and including the wind further reduces the deviance by an additional 37% for TrNcPd to 58% for TrNcZw iInmplying that the best fit is obtained for TrNcZw. The improved fit for TrNcZw could be explained by the fact that here the local zonal wind is used, whereas for TrNcPd, a simplification of large-scale zonal wind is used.
Another paragraph, containing interesting results, to reorganize and streamline.
[28] 4 Results - 4.1 Comparison of the Different GAMs 183-186
The resulting fits can be seen in Fig. 2. When more predictive variables for the wind are included in the model, like the meridional wind or wind taken at multiple locations in the North Sea, the deviance can be further reduced. However, the increased degrees of freedom increase the standard error in estimating the trend (not shown). Therefore, we find that using only one predictive variable for the wind is the best choice for estimating the sea-level trend.
What is the rationale of not showing (in a compact way) that more degrees of freedom worsen the quality of the trend? I imagine the scholars interested in your study and in its application to their basins of choice would appreciate a feel how an excessive quest for many regressors can let things go wrong. (A kind of overfitting, even though we do not have a training and testing set here.)
Also, does it make more sense to say that a single predictive variable is the best choice to estimate the wind influence only, rather than the sea-level trend? Recall that Tr for trend is just one of the four set-ups you are considering. So when you use the word ‘trend’ I tend to think of that particular set-up, Tr. Therefore, if you aim to improve the trend seeking good regressors (as I read), it is not correct to call the baseline model Trend too. All set-ups produce trends, as one sees in Fig.4. So please clarify your terminology (background, trend, influence, variability, etc.) and apply that consistently everywhere --- this is of paramount important for getting the message across. This remarks extends R13.
Also please recall R9, and the fact that, in a shallow coast, bathymetry is a definite driver of (tidal and wind-driven) motion, the more so in constrained basins like estuaries and fringe basins, as applicable to the Netherlands.
[29] Figure 3
Comparison of the wind influence on sea level along the Dutch coast obtained from two different regressors: average zonal wind of the 6 tide gauge stations (TrNcZw) and the pressure difference between the Northern and Southern boxes (TrNcPd) of Figure 1. (a) Time series of annual averages. (b) Trend computed using a 3rd-degree polynomial fit with linear trend values over the first half and the second half of the total period. (c) Spectra obtained using a multitaper method (Lees and Park, 1995). Both the detrended time series (solid lines) and the detrended and smoothed time series (dashed lines) are shown. Smoothing is obtained from a LOWESS method with a window of 21 years. (d) Smoothed time series.
Please keep on using dashed lines for detrended-and-smoothed time series. According to the figure title, panel (d) regards detrended-and-smoothed time series, a name which does not feature in the caption. The caption can be streamlined and the repetitions with respect to the body of the text should be kept to a minimum.
[30] 4 Results - 4.2 Wind Influence on Sea Level 188-197
Figure 3a shows the resulting wind influence on sea level, where the large interannual variability stands out. From these annual-mean time series, we estimate the wind-driven sea-level trend as is shown in Fig. 3b. For the second period, 1928-2020, the wind-driven trend is 0.12 mm/yr and 0.15 mm/yr for respectively TrNcZw and TrNcPd. Long-term strengthening of the zonal wind has increased the sea level along the coast of the Netherlands. This long-term strengthening of the zonal wind is consistent with the observed northward shift and increased speed of the jet stream, which could be due to a decreasing temperature gradient between the North Pole and the equator at the height of the tropopause (Fig. 7d and 9d from Hallam et al. (2022)). A long-term influence of atmospheric drivers (zonal and meridional wind and surface pressure) was found earlier for the period 1953-2003 (Fig. 2c from Dangendorf et al. (2014a)), but our results are in contradiction with the atmospheric-driven sea-level drop over the period 1900-2011 found by the same authors. This could be due to an update in the atmospheric reanalysis (20CRv3 instead of 20CRv2).
Where is the long-term strengthening of the zonal wind evident in your study so far? If I follow the text literally, you are assuming from the outset that an explanation of your model results exists, instead of showing that your evidence correlates with the proposed explanation. I consider this argumentation, or at least the way it delivered, weak. The Discussion section, and not the Results, is the appropriate part of the manuscript to contrast your results with the existing literature in ample detail.
[31] 4 Results - 4.2 Wind Influence on Sea Level 198-206
After removing the trend from the data in Fig. 3a, a spectral analysis is performed (Fig. 3c). The spectra of the wind-impact on sea level obtained using both TrNcZw and TrNcPd have a similar shape, but the total variance is larger for TrNcZw compared to TrNcPd which is a result of the larger interannual variability of TrNcZw as shown in Fig. 3a. For both methods, there is more energy in the signal for periods larger than two decades than for smaller periods. Therefore, the signals are smoothed using a local polynomial regression (LOWESS, Cleveland and Devlin (1988)) with a window of 21 years that effectively removes high-frequency variability (dashed lines in Fig. 3c). The resulting detrended and smoothed time series, Fig. 3d, show that low-frequency wind variability can raise or drop sea level by over 2 cm over a period of 2 to 5 decades. In App. A, this low-frequency variability lags low-frequency sea-surface temperatures in the North Atlantic that have a similar pattern as the Atlantic Multidecadal Variability.
You do not need to repeat any information given in the Methods, especially its details. Again, the separate Appendix overburdens the reader with the task to walk the data-methods-results ladder once again. (R12.)
[32] Figure 4. (a–d)
The rates of SLR were obtained for four different statistical models. A window of three years is used, so the rates cannot be computed for the first and last years of the time series. The period shown here is 1891 to 2019. The dashed lines show the 5th and 95th percentiles of the uncertainty range computed from a parametric bootstrap method. Numbers in grey under the curves indicate the mean rates for four different periods ([1900-1919], [1920-1939], [1940-1959], [2000-2019]) (e) Median sea level rates. (f) Standard error of the sea level rates.
Where does this time frame of 3 years come from? Why is that necessary?
Then,in panel (e) please use the same y-axis range as panels (a-d). In the y-axis please use SLR, which you have already defined: panel (f) will benefit from the gain in typesetting space and panel (e) can accommodate for ‘median SLR’. (Although the interpretation is obvious here, you might want to use a dotted line to indicate the uncertainty range, once you have used dashed line for detrended-and-smoothed results.)
[33] 4 Results - 4.3 Rates of SLR 208-213
The rates of SLR obtained from differentiating the estimated smooth sea-level trend from each of the four models are shown in Fig. 4. Reduction of uncertainty is generally the main motivation for removing variability due to known atmospheric drivers from the sea-level trend (Dangendorf et al., 2014a). The rate of change from TrNc has lower uncertainty than the rate from Tr. Including the zonal wind (TrNcZw) as a predictive variable further decreases the uncertainty, whereas including the pressure difference (TrNcPd) increases the uncertainty again. The standard error in estimating the trend is larger at the time series’ start and end because there are fewer constraints than in the middle of the time series.
Please refer to panels of Figure 4. See R24 for an example.
[34] 4 Results - 4.3 Rates of SLR 214-225
In addition to reducing the uncertainty, the wind also influences the rate of SLR itself. Both TrNcZw and TrNcPd have lower rates in the first part of the 20th century compared to Tr and TrNc. From the 1960s onward, the rates of SLR of TrNcZw and TrNcPd increase rapidly. The TrNcZw model has the smallest standard error and estimates the largest rate of SLR over recent decades, which reached 3.0[2.4−3.5] mm/yr over the period 2000-2019. For this model, the rate of SLR over periods before the acceleration in the 1960s is 1.8[1.4 − 2.3] mm/yr over the period 1900-1920, 1.7[1.3 − 2.0] mm/yr over the period 1920-1940 and 1.5[1.1 − 1.8] mm/yr over the period 1940-1960. Table 2 shows for the different GAMs the probability (the p-value) that the estimated rate difference between the periods 2000-2019 and a previous period (1900-1919, 1920-1939 and 1940-1959) would exceed the rate difference found in this study if the sea level had changed at a constant rate. For the Tr model, we find probabilities between 5 and 23% for the different periods. Having more predictive variables in the GAM decreases these probabilities. For the TrNC model, the probability is 14% when compared with the period 1900-1919 due to the higher rates of SLR of this model at the beginning of the 20th century. However, for the other periods, we find probabilities of 1%, implying that finding these rate differences would be very unlikely if there would have been no acceleration (Mastrandrea et al., 2011).
This key paragraph is quite additive in its arrangement. Please lead the reader through it by reorganizing and streamlining its moving parts.
[35] 4 Results - 4.3 Rates of SLR 226-230
For the TrNcZw model, we find probabilities of 0% for all periods, and in the TrNcPd model, we find probabilities smaller than 5% and only 1% when compared with the period 1940-1959. These probabilities indicate that an acceleration of SLR is virtually certain (Mastrandrea et al., 2011). We conclude that along the coast of the Netherlands, the sea level has accelerated since the 1960s, but this acceleration has been masked by wind-field and nodal-tide variations. This agrees with the global mean sea level that has accelerated since the 1960s (Dangendorf et al., 2019).
The commentary of Table 2 should probably take a single paragraph of its own.
A question arises about how such masking and the effect of human interventions in the Scheldt estuary, Ems estuary and Wadden Sea relate one with another. Recall R9.
[36] 4 Results - 4.3 Rates of SLR 231-236
All models indicate a decrease in the rate of SLR from the beginning of the 20th century until about 1960", with a minimum in the 1940s for Tr and TrNc and in the 1960s for TrNcZw and TrNcPd. This decreasing rate of SLR could be due to the strong Arctic warming from 1900 to 1930, followed by an Arctic cooling from 1930 to 1970 (Fig. 4, Bokuchava and Semenov (2021)).
This could have influenced sea level through glacier mass loss followed by gain or local steric sea level changes. Since the local sea-level budget is not closed before 1950 (Frederikse et al., 2020), we can only speculate about the causes of the drop in the rate of SLR.
Please mention what the physical boundaries of the budget area are. What do you mean for local/regional? Dutch coastal waters, North Sea, etc.?
[37] §5 Discussion 237-242
Estimating the trend, nodal cycle and atmospheric processes underlying the wind influence on sea level using the GAM allows for avoiding a priori assumptions about the sea-level trend, like having a linear or quadratic shape, while performing the regression analysis. Thereby, the rate of SLR can be computed as a time-evolving variable over the whole observational period contrary to being calculated as a constant over an arbitrary period as was done in Calafat and Chambers (2013); Steffelbauer et al. (2022).
Recall R28. Do you estimate one trend or as many trends as there are model set-ups?
[38] §5 Discussion 242-243
In addition, we propose a careful uncertainty analysis accounting for serially dependent unexplained fluctuations, which is used to evaluate the strength of evidence for an acceleration.
It is not clear from the passage whether this uncertainty analysis has been presented already or is coming next. There is no doubt that a recap and commentary of the uncertainly analysis are appropriate in this section on Discussion. (IMHO, the section on Results should only contain the dry results and show how they naturally proceed from the Methods. The line of reasoning then gains a strong forward dynamics.)
[39] §5 Discussion 243-248
These two elements help to avoid framing the problem of acceleration detection as binary. This is important when advising decision-makers: significance testing based on ad hoc models like a broken line trend may lead to a paradigm shift from a steady rate of SLR in one year to an accelerating rise a few years later, as demonstrated by the results in (Calafat and Chambers, 2013; Steffelbauer et al., 2022). To our best knowledge, the GAM has not been applied to estimate trends and acceleration in sea-level data before, and we believe it could help solve similar acceleration detection problems in regions other than the coast of the Netherlands.
I completely support the idea that decision makers can have great benefit from the time-varying representation of SLR that you are proposing. However, considering that you are focussing on a local/regional scale, I would suggest to put a little more effort in explaining how/where regional drivers (and, for this exercise, the situation of the Netherlands) end up to be represented in your model. This may be of general interest for the readers who start to think about the application of this method to their own coastal basins. I have commented on something close to this in R9, R28.
I also reuse a tip I often received: to the best of our knowledge is the appropriate idiomatic expression (L 246). Help to avoid (L 243) should be help avoid.
[40] §5 Discussion 249-258
When removing the wind influence from the sea-level observations, the underlying assumption is that this influence is only due to natural variability and that there is no structural change due to anthropogenic forcing. However, as we find a wind-driven trend over the entire period of study 1836-2020 from both the zonal wind and pressure difference model, the trend could also continue in the future. We do not know of any study investigating the possible cause of this trend. If it is caused by climate change due to anthropogenic forcing, it would be reasonable to expect it to continue in the future. Otherwise, if it is caused by natural variability, it might reverse. Most of the CMIP5 and CMIP6 ensembles do not show a systematic trend associated with wind influence on sea level in the North Sea, not over the historical period or in future scenarios. So, they either miss the process driving the trend in the observations, or the trend in the comments has to be attributed to natural variability. In each case, the magnitude of around 0.15 mm/yr over the historical period is small enough compared to other sources of uncertainty to neglect it when making sea level projections on time scales of more than several decades.
I presume that the essence of this paragraph is: you cannot offer guarantees as to how your model performs with predictions, principally because distinguishing the natural and anthropogenic components of the wind forcing is a known difficulty. I am not so sure I got it right, however, for example because I fear that you refer to past trend and future trend interchangeably. I found this entire paragraph hard to follow and hence to assess. Please edit.
[41] §5 Discussion 259-262
If the time lag found between North Atlantic SST and wind influence on sea level as described in App. A was found to be physical or if the SST signal could be skillfully forecasted, this relation could provide a source of predictability for the deviation between sea level along the Dutch coast and large-scale drivers (e.g. glacier and ice sheet mass loss, global steric…) at the decadal time scale.
The more I read about Appendix A in the body of the manuscript, the more score points gains the suggestion of incorporating Appendix A into the body of the manuscript. Recall R12, R31. I also understand that the focus of this section on Discussion has moved towards the subject of predictions. Why not create separate subsections on the diagnostic and predictive capabilities of your model?
[42] §5 Discussion 263-265
From the daily to the interannual time scale, the wind influence on sea level in shallow seas is well understood by the barotropic theory of the interplay between the Coriolis force, pressure gradient and surface wind stress (equation 3 from Mangini et al. (2021)).
In contrast, my understanding is that flow in shallow seas strictly requires consideration of the bed shear stress. In environmental fluid dynamics, a sea not subject to significant bed actions loses the qualification of shallowness. (Of course, there are process in shallow waters that are not shallow flows.) This motivates the care that should be taken to acknowledge at least/include at most what happened to the Dutch coastal waters in the period 1890-2000. Recall R9.
[43] §5 Discussion 265-269
On the multidecadal time scale, as investigated in this study, it is possible that the physical mechanism underpinning the relation between wind and sea level also involves steric sea level change (Chen et al., 2014). In particular, baroclinic signals in the deep ocean propagating as a volume flux on shallow seas (Bingham and Hughes, 2012; Calafat et al.,2012). However, since we use the large interannual variability to define the regression coefficient, we think these coefficients mostly reflect the barotropic wind influence.
Regarding the last concluding remark, I would appreciate, beside the sheer assertion of what you think, a short explanation of why you think that. Then, I cannot easily grasp whether you are talking about water or wind. In particular, the attribution ‘baroclinic’ seems to associate with water, while ‘barotropic’ with wind. Are you leveraging a notion that wind does not drag the deep layers of the ocean into the Dutch coastal waters, not even over the decades? Please streamline and clarify.
[44] §5 Discussion 270-279
We find a strong increase in the rate of SLR between the 1960s and 2000s (Fig. 4). From 2000 onward, the standard error of the rate of SLR increases strongly, and it is uncertain whether the increase of the rate persists. A potential application to this increase would be the extrapolation of the observed rate into the near future. This method was recently used as an additional line of evidence for future sea-level rise by Sweet et al. (2022). Based on Fig. 4c, assuming a constant rate of 3 mm/yr from 20000 onwards, we arrive at a rise of 0.3 m between 2000 and 2100, which is slightly higher than the rise over the 20th century. However, assuming a constant acceleration of 1.5/25= 0.06 mm/yr 2 (as inferred from the trend in sea level rate over 1975-2000 in Fig. 4c), we obtain a rise of 0.6 m, from 2000 to 2100, which is twice the rise without acceleration. Given the complexity of changes in the various drivers of global SLR, it would be naive to assume that the acceleration will remain constant during the remainder of this century. However, these crude extrapolations illustrate the practical significance of our estimates of the local rates of SLR and the importance of obtaining the evolution of these rates over time.
If you place the last sentence at the beginning of the paragraph, you have an example of how stating the paragraph topic at the outset and elaborating on it afterwards greatly helps speed reading. ‘20000’ in L274 should be 2000.
[45] §6 Conclusions 281-282
In this study, we estimate the sea-level trend and the influence of the nodal cycle and wind on sea level along the coast of the Netherlands.
I am often confused by how you use the term “influence” physically. Is this a part of the sea-level rise, thus a quantity measured in meters? Or is it another physical quantity that is an agency of sea level rise, and thus has appropriate units of measure? In other words: when you say to “estimate the influence of X and Y”, are you consistently referring to the components of sea level rise that can be explained as an effect of X and Y, that is SLRX and SLRY? Or to the statistical analysis of X and Y as the predictive variables of your model? This confusion is also sustained by the ensuing remarks.
[46] §6 Conclusions 282-283
We used the average of the observations from six tide gauges and zonal wind and atmospheric pressure at sea level from two reanalysis data sets.
This is eventually clear here, but should be announced much earlier on in the manuscript and not in the figure captions. See R8. (The sentence could also be streamlined linguistically.)
[47] §6 Conclusions 283-284
Using a set of four GAMs, we estimated the trend using B-splines functions and the wind influence using linear regression.
Did you estimate one trend or four trends? Then, do you estimate the wind influence with linear regression or with a 3rd order polynomial, as in Fig. 3b?
[48] §6 Conclusions 284-285
The four models include either no predictive variables, only the nodal cycle, and, additionally, either zonal wind or pressure gradient as predictive variables.
I would advocate again the distinction between model (one type, GAM) and set-ups (several implementations). I interpret the passage above as: The predictive variables in the four model set-ups are either none;oronly thenodal cycle;orthe nodal cycle and eitherthezonal wind orthepressure gradient.
[49] §6 Conclusions 285-287
We find that using only one predictive variable for the wind best estimates the sea-level trend. The deviance is reduced when more predictive variables are added to the GAM, reducing by 12% for adding the nodal cycle and another 37 to 59% for adding the wind.
I interpret the above as Adding predictive variables to the GAM reduces the deviance by 12% in the case of the nodal cycle and by another 37 to 59% in the case of the two wind variables. A single predictive variable for the wind estimates the sea-level trend best.
[50] §6 Conclusions 288-290
We obtain the wind influence on sea level using the two GAMs that include a wind predictive variable (TrNcZw and TrNcPd). Obtaining the wind influence with two different approaches shows the method’s robustness as both methods lead to similar conclusions.
The passage strengthens the case to distinguish models and set-ups: in the second sentence a certain one method appears to be robust because two certain methods are similar. Also, one may argue that you have two wind influences and that you aim to select one which has the most desirable statistical properties and hence is the most trustworthy. Beside terminology, I recommend to revise the use of the singular/plural number all over.
[51] §6 Conclusions 290-291
We find a long-term sea-level rise due to wind forcing of 0.12 mm/yr or 0.15 mm/yr for 1928-2020, depending on the used model.
I presume that the sea-level rise due to wind forcing is another definition of wind influence. The section on methods should present your terminology of choice once for all, so that the reader has not to wonder or backtrack the line of reasoning so often.
[52] §6 Conclusions 291-296
The long-term strengthening of the zonal wind is consistent with an observed northward shift and jet stream strengthening (Hallam et al., 2022). Also, we find a low-frequency wind variability which can rise or drop sea level by about 1 cm over 2 to 5 decades. We find that it is related to multi-decadal sea surface temperature variations in the North Atlantic with a similar pattern as the Atlantic Multidecadal Variability. The correlation between SST in the northern part of the North Atlantic and the multidecadal wind-driven sea-level variability can be understood as smaller SST values increase the meridional temperature gradient and strengthen the jet stream (Hallam et al., 2022).
See R30. The shift of the story line towards the zonal wind is quite abrupt in this paragraph that privileged sea levels. Many readers will probably read these conclusions first. A new topic probably deserves a paragraph on its own. In particular, the emphasis given to the low-frequency wind variability strengthens the case to move Appendix A into the body of the manuscript (R12, R31, R41). I value that your model unlocks new possibilities to unveil relationships between unsteady forcing and unsteady effects. However, tucking the arguments in an appendix looks a bit like “throwing the stone and hiding the hand”. Appendix A is surely worth being integrated in the bulk of the work and emphasised as these conclusions do. See also R53 next.
[53] §6 Conclusions 296-298
In summary, we find both a long-term SLR as well as a multidecadal sea-level variability due to wind forcing which are both connected to changes in the jet stream through various mechanisms (Hallam et al., 2022).
If I paraphrase this correctly, your contribution is that the changes in the jet stream have influenced, through various mechanisms, both the long-term development and the multidecadal variability of the SLR along the Dutch coast. This sounds to me as a significant contribution, which is a bit overshadowed by the title. What are such various mechanisms that you have elucidated, though? The abstract (16-18) does not announce the influence on long-term development, while it does emphasise the SST, unlike the conclusions. Please clarify what the main take-home messages are and present them with even emphasis across the manuscript.
Regarding the jet stream, please recall R30.
[54] §6 Conclusions 299-305
After obtaining the sea-level trend using the four GAMs, we obtain the rate of SLR by differentiating the trend. This results in new insight into the evolution of the rate of SLR along the coast of the Netherlands over the observational period. The rates of SLR, excluding the influence of the wind, are lower at the beginning of the 20th century and larger at the beginning of the 21st century. Our best-fitting model yields a rate of SLR, excluding nodal and wind effects, of 3.0[2.4 − 3.5] mm/yr over 2000-2019 compared to 1.8[1.4 − 2.3] mm/yr in 1900-1919 and 1.5[1.1 − 1.8] mm/yr in 1940-1959. The probability (the p-value) of finding a rate difference between 1940-1959 and 2000-2019 equal to the one we found when there would not have been an acceleration is smaller than 1%. From these results, we conclude that an acceleration of SLR is virtually certain.
Here it is important to clarify what you mean with ‘excluding the influence of the wind’, since the previous paragraph invites one to think that you may have gained new insights into long-term and multidecadal scales separately. So, what do you exclude the wind influence (defined as...) from?
The paragraph could surely be streamlined linguistically. (Also my remarks could, admittedly, but I trust that the manuscript contains a more long-lasting contribution to the field which justifies its revision and editing.)
[55] §6 Conclusions 305-308
Also, we find, for the first time, that the acceleration of SLR along the coast of the Netherlands started in the 1960s. This aligns with global SLR observations and expectations based on a physical understanding of SLR related to global warming (Fox-Kemper et al., 2021; Dangendorf et al., 2019).
Kudos for identifying the SLR speed up. However, the point of alignment with global evidences suggests an incomplete inference. It is fine to have subtracted astronomical and meteorological influences from the sea level signal. Yet, since the water level measurements along the Dutch coast have been averaged spatially and since you overlook the influence on the local sea levels caused by considerable human interventions on the coastal bathymetry, you arguably conflate global and local contributions. These local contributions may have followed the global contributions passively, or have emphasised it, or have dampened it. Each of these outcomes may have prevailed over different time frames in the period under investigation. Perhaps, the acceleration of SLR in the Netherlands was delayed, or perhaps assisted.
In other words: an alignment of wind-and-tide-free observations with global observations does support the inference that global warming has had an effect in the Netherlands. Yet, it does not leave global warming as the only driver of change, unless companion effects are ruled out positively. Since the passage justly emphasise physical understanding, the reader should be alerted about the physics-based local circumstances lurking in your model.
[56] §6 Conclusions 308-309
Furthermore, we explain that the acceleration of SLR along the Dutch coast has been difficult to detect due to the masking of the acceleration by wind-field and nodal-tide variations.
I would appreciate to read which passage in your line of reasoning explains this. Or is this a general benefit of your methodology? Also, did you comment explicitly on the variation of the nodal tide itself, as I infer from your sentence? Recall R18.
================================================================
This completes the first analysis of the manuscript, excluding the Appendix and the supplemental material, and concludes comment #2.
Thank you for your reading.
Citation: https://doi.org/10.5194/egusphere-2022-935-CC2 -
CC3: 'Comment on egusphere-2022-935 (#3 Methodological reserve)', Giordano Lipari, 14 Dec 2022
This community comment #3 has been prompted by additional readings that, in turn, had been prompted by remarks on the manuscript R8-R11, R28, R35, R39 and R42. Their common denominator was a desire for clarity as to the peculiarities of Dutch coastal waters. In this one community comment, I digress from topical issues and set forth a case for a deeper and wider consideration of the existing literature.
A most relevant resource is the Zeespiegelmonitor (Sea Level Monitor), which is referred to as Baart et al. 2019 in the manuscript. This is a technical report of national interest, commissioned by Rijkswaterstaat, the governmental agency responsible for water management. The document is publicly available from the link provided in the manuscript but also from a permalink in the reports database of Rijkswaterstaat: https://puc.overheid.nl/doc/PUC_635781_31. The report is in Dutch and, for the benefit of the general reader, I will translate into English some passages.
In the following, “B2019, 45,56” is short for “Baart et al 2019, pages 45 and 56”. “Rn” is short for Remark n, where n is a progressive number in my previous community comments (up to 22 included in https://doi.org/10.5194/egusphere-2022-935-CC1, and from 23 up to 56 included in https://doi.org/10.5194/egusphere-2022-935-CC2).
[57a-b] Existing citations of B2019
The manuscript cites B2019 sparingly in LL 82,86 of §2.1, regarding the tide gauge observations along the Dutch coast.
a. As for the location of the tide gauges in LL 81-82, the phrase These stations are used for operational sea level monitoring because of their extended temporal coverage and uniform distribution along the Dutch coast clearly renders the phrase Dit zijn zes stations, redelijk uniform verdeeld langs de Nederlandse kust, met een lange historie aan metingen in B2019,39. I have critiqued the infelicity of the phrase ‘uniformly distributed’ stations in R9. Regardless, this confirms me in my mind that the authors have consulted B2019 closely.
b. As for the adjustment of the chart datum of 1885 in LL 85-86, B2019 also mentions successive jumps in the Dutch recordings. The manuscript reference to the adjustment of 1885 only is incomplete information; consider also R10. More important for the readers is to offer a guarantee that the datasets deposited at the PSMSL have been gauged with respect to a Revised Local Reference (see R2019,42-44 and https://psmsl.org/data/obtaining/rlr.php), which evens out all operations on the chart datum. This reassurance would also resolve a concern raised in R11.
[58a-b] Omissions in the citations of B2019
a. However, B2019 does present a methodology and an expert opinion to account for the SLR acceleration. Strangely, the manuscript does not mention this contribution, not even in the Introduction paragraph addressing the debate on acceleration along the Dutch coast (LL 32-41). In contrast, B2019, § 5 (Methoden voor de bepaling van de huidige zeespiegel = Methods for the determination of the present sea level) presents much relevant information in an orderly fashion. In particular, B2019,47-48 refers to a Generalized Linear Model being used to carry out an analysis remarkably similar to those of the manuscript. Referring to B2019 seems all the more compelling if it is correct to state that Generalized Additive Models are a type of Generalized Linear Models (according to https://en.wikipedia.org/wiki/Generalized_additive_model). Finally, also the results of B2019 display a striking similarity of those presented in the manuscript. For example, Fig. 6.1 in B2019,53 is
which should be contrasted with Figure 2 in the manuscript (below). The key for the axes labels above is hoogte: height; lineair model zonder wind: linear model without wind; lineair model met wind: linear model with wind; jaargemiddelden: yearly averages.
[59] Common-sense considerations
Not referring to this piece of previous research seems a conspicuous omission to me, at least one that justifies a textual analysis of such an extent as this. These incidents strongly suggest that the authors should peruse and credit B2019 more extensively, at a minimum. Regrettably, they leave an unpleasant aftertaste that substantial weaknesses may also lurk in the rest of the literature review.
For sure, the authors should exercise much more caution in not sailing inadvertently towards the rocks of plagiarism by implicitly portraying steps ahead as strides ahead. For the sake of prudence, claims of novelty such as LL 246-248 -- To our best knowledge, the GAM has not been applied to estimate trends and acceleration in sea-level data before, and we believe it could help solve similar acceleration detection problems in regions other than the coast of the Netherlands -- may well apply and be well deserved (as I am still inclined to believe), but should attract more scrutiny from the community.
IMHO, as a Dutch saying goes, er is werk aan de wikel, there’s work (to do) in the shop. I hope this commentary will help the manuscript develop a strong backbone and gain it the unconditioned appreciation of many readers.
Citation: https://doi.org/10.5194/egusphere-2022-935-CC3 -
AC1: 'Reply on CC3', Iris Keizer, 03 Mar 2023
We thank Giordano Lipari for his interest in our work. By this reply, we'd like to comment on the three extensive community comments he made on our preprint. It really shows that our paper will be of interest to people outside of the academic field of physical sea level. We thank him for his beneficial comments which will make our paper more readable for a broader audience which is very valuable. Many of his suggestions and the extensive explanations he provided with his comments are very useful to improve our manuscript and to learn from as a starting scientist.
Some remarks on his final comment:
We do not understand the worry about plagiarism of Baart et al. 2019 because we already cite this work in the paper. We dot not want to discuss the differences between our paper and Baart et al. 2019 in depth because it is written in Dutch which means that many readers of this paper will not be able to read it. Baart et al. 2019 use two fully parametric models for the trendline (linear+quadratic trend, or broken linear trend), whereas our GAM model uses a representation of a smooth trendline of unspecified shape, which is much more general. Both our GAM and the models in Baart et al. 2019 are examples of GLMs, but GLM is a very general category of models, and therefore practically meaningless for distinguishing models. Furthermore, our estimation of the uncertainty of the trendline is completely different from Baart et al (2019), employing less restrictive assumptions. We will add the information that the PSMSL data is gauged to the Revised Local Reference.Citation: https://doi.org/10.5194/egusphere-2022-935-AC1
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AC1: 'Reply on CC3', Iris Keizer, 03 Mar 2023
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CC4: 'Comment on egusphere-2022-935', Riccardo Riva, 10 Jan 2023
This is a nice piece of work. Especially intersting is the use of GAMs, which as far as I know is not yet very common in the Earth sciences.
I would only like to make a comment about the chocie of the authors to estimate amplitude and phase of the nodal cycle, rather than prescribing it as recommenden by Woodworth (2012, J. Coast. Res. 28) and confirmed by Frederikse et al. (2016, GRL 43). An empirical estimation seems particularly risky, considering that sea level in the North Seas shows a large decadal oscillation with periods close to 20 years (see, e.g., Fig.2 in Frederikse et al., 2016).
That said, the approach proposed by the authors might still work. However, it would be nice if they added some proof of its robustness.
First of all, they could compare their estimated nodal cycle with the equilibrium tide discussed by Woodworth (2012): the resulting amplitude could be different (which in itself would be a valuable result), but I would expect the phase to remain close to the theoretical value (if not, a physical justification should be provided).
Secondly, in case the estimated nodal cycle were indeed significantly different from the theorietical one, it would be interesting to test how using the theoretical value would affect the conclusions of this study (by, e.g., adding a new experiment analogous to TrNCZw).Hope this helps,
Riccardo Riva
Citation: https://doi.org/10.5194/egusphere-2022-935-CC4 -
AC2: 'Reply on CC4', Iris Keizer, 03 Mar 2023
We thank Riccardo Riva for his compliments and beneficial comments on the manuscript. As stated in our manuscript, section 3.1, there are indeed different ways to estimate the influence of the nodal cycle on sea level in the North Sea. Using a closed budget, as Frederikse et al. (2016) do, suggests that there is no indication that the nodal cycle deviates from the equilibrium tide. However, we find that assuming the equilibrium tide leaves a large amount of energy in the spectrum close to the period of the nodal cycle. Our estimate for the nodal cycle resulting from the regression suggests an amplitude almost three times as large as the amplitude of the equilibrium tide and a phase lag of three years compared to the equilibrium tide (see attached figure). Our hypothesis for the deviation (which we will study further) is that this deviation is due to the influence of nodal tide on steric sea level. The modulation of high-frequency tides by the nodal tide might drive vertical-mixing processes that drive steric sea level. We formulate this hypothesis based on the recent paper by Joshi et al. (https://egusphere.copernicus.org/preprints/2022/egusphere-2022-151/). Since Frederikse et al. (2016) use a budget study, these nodal-driven effects are classified as steric effects in the budget, making the equilibrium tide a perfect fit. Since we don't have steric sea level in our model, the effect of nodal tide on sea level also includes steric effects which motivates us to use a statistical estimate of the nodal tide. We will expand our paper with an appendix comparing our estimates of the nodal tide to the equilibrium tide as well as the spectra of their residuals (observed sea level minus reconstructed sea level). Also, we will briefly discuss these results in the discussion section. However, discussing the physical mechanisms of the relation between the nodal tides and sea level is outside of the scope of this paper. Please, find attached a figure of (a) the nodal tide resulting from the statistical estimation in our three GAMs as well as the equilibrium tide and (b) the spectra of the residuals of three models. The model TrW only includes trend and zonal+meridional wind but no tides, the model TrNcW includes trend, nodal tide and zonal and meridional wind and the model TrEtW includes the trend and zonal+meridional wind but the sea level is corrected for the equilibrium tide. This shows that there is a lot of energy remaining around the nodal tide period using the correction for the equilibrium tide. From the plots of the nodal tide it can be seen that the statistical estimation gives a nodal tide with an amplitude more than 2.5 times larger than the amplitude of the equilibrium tide and a 3-year phase shift.
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AC2: 'Reply on CC4', Iris Keizer, 03 Mar 2023
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RC2: 'Comment on egusphere-2022-935', Anonymous Referee #2, 24 Jan 2023
Please see attached PDF for the referee report.
- AC4: 'Reply on RC2', Iris Keizer, 03 Mar 2023
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2022-935', Anonymous Referee #1, 14 Nov 2022
This study covers an important subject and is relevant contribution for the sea-level community. I feel a few modifications to the manuscript text will improve clarity. Please see attached PDF for the review report.
- AC3: 'Reply on RC1', Iris Keizer, 03 Mar 2023
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CC1: 'Comment on egusphere-2022-935 (#1)', Giordano Lipari, 18 Nov 2022
Summary
I have read the manuscript with great interest.
With reference to the review criteria of OS, the work proposed well-circumscribed and substantial conclusions on debated topics (sea level rise acceleration in a convoluted stretch of a shallow sea) obtained with powerful statistical methods (separation of a time-varying signal into a time-varying influences of predictive variables and a smooth time-varying background residual). However, while the line of reasoning is clear in its broad terms, the assumptions/methods are often outlined unclearly, whereby assessing their validity and their linkage to the results proves awkward.
In terms of personal reading experience, I found it difficult to get engrossed and isolate with agility what merits a focussed discussion on content and correctness. A certain draft-like, think-aloud quality still hampers speed reading and in-depth consideration. I am nonetheless convinced that a few of rounds of streamlining and paraphrasing will drastically improve the manuscript. Linguistic points of coherence (organization in sections and paragraphs) and clarity (at the level of sentences) should be addressed thoroughly to let the content shine its own light.
I give below suggestions for samples of passages where my reading flow froze. I surely invite the authors to apply those suggestions anywhere they deem it beneficial. (Equally surely, the authors do well to cross-check my suggestions one with another and with other peers.) This document also address some point of content, whether or not entangled with reading difficulties.
I have read the manuscript in full a couple of times, but will restrict my contribution to the text within Section 3.1 included. I have not looked into the supplementary material (the code), but I would expect from the authors that the documentation follows standard of clarity adequate for reproducibility.
[1] Abstract 2-4
This is an extended remark on clarity (speed-reading). My ensuing suggestions will be more succinct.
The kick-off sentence:
While a global acceleration of sea-level rise (SLR) during the 20th century is now established, locally acceleration is more difficult to detect because additional processes play a role which sometimes mask the acceleration. Here we study the rate of SLR along the coast of the Netherlands from six tide gauge records, covering the period 1890-2000. (55 words, 349 characters)
reads more easily in the form:
While the global acceleration of the sea-level rise (SLR) during the 20th century has already been established, additional processes play a masking role that makes it difficult to detect local acceleration. Here we study the rate of SLR along the coast of the Netherlands using the records of six tide gauges in the period 1890-2000.
which exposes the question of what that ‘additional’ feature is supposed to be added to; there is nothing before the first sentence.
Then, may I suggest:
While the global acceleration of the sea-level rise (SLR) during the 20th century has already been ascertained, the masking by several processes makes detecting local acceleration difficult. Here, we investigate the rate of SLR along the coast of the Netherlands using the records of six tide gauges in the period 1890-2000.
which exposes the question of which processes the writer has in mind.
Then, may I suggest:
While the global acceleration of the sea-level rise (SLR) during the 20th century has already been ascertained, the masking caused by several drivers hampers detecting local accelerations of SLR. Here, the records of six tide gauges in the period 1890-2000 are used to analyse the rate of SLR along the coast of the Netherlands.
or
The global acceleration of sea-level rise (SLR) during the 20th century has already been ascertained. Nonetheless, several drivers of SLR mask the detection of its local acceleration. Here, the records of six tide gauges in the period 1890-2000 are analysed to investigate the rate of SLR along the coast of the Netherlands. (51 words)
You may deviate from any suggestions, of course, and devise better ones. The benefit in sight is that these last few formulations create an anticipation as to which data and factors are considered in the subsequent analysis.
[2] Abstract 12-15
I found this awkward to read and hence to assess:
If, apart from tidal, wind effects and fluctuations, sea level would have increased at a constant rate, then the probability (the p-value) of finding a rate difference between 1940-1959 and 2000-2019 of at least our estimate is smaller than 1Our findings can be interpreted as an unequivocal sign of the acceleration of current SLR along the Dutch coast since the 1960s. This aligns with global SLR observations and expectations based on a physical understanding of SLR related to global warming.
Do you mean something like this?
If we discount for the effects of tide and of wind fluctuations and then assume a constant SLR rate, the probability that the SLR rates in the periods 1940-1959 and 2000-2019 differ as much as our estimate or more is smaller than 1 (p-value). This result indicates unequivocally that the SLR along the Dutch coast has been accelerating since the 1960s. Global observations and the expectations based on the physics of global warming are consistent with this finding.
Then the validity of the statement is hopefully more accessible.
[3] Introduction 28-31
This is a point of clarity (speed-reading). I found this cumbersome to read:
More recently, Walker et al. (2022) estimated the time when the rate of global SLR emerged from the background variability of the Common Era (0-2000CE) to the middle of the 19th century. For the North-East Atlantic, they found this emergence to occur around the middle of the 20th century. This is in line with Dangendorf et al. (2019) who found a global acceleration of SLR from the 1960s.
May I suggest:
Dangendorf et al. (2019) had found the global rate of SLR to accelerate from the 1960s. More recently, Walker et al. (2022) estimated that the rates of SLR emerged from the background variability of the Common Era (0-2000 CE) in the middle of the 19th century for the globe and in the middle of the 20th century for the North-East Atlantic.
One benefit for speed reading is that new information appears in the same order of publication of the articles. So one appreciates the progress in the field without backtracking through the text.
[4] Introduction 32-33
This is a point of clarity (speed-reading). Re:
Along the coast of the Netherlands, there has been an ongoing debate about whether an acceleration of SLR takes place or not (Baart et al., 2011; Wahl et al., 2013; Steffelbauer et al., 2022).
While I appreciate the natural word order in Dutch, I would suggest streamlining the sentence into:
The existence of SLR acceleration along the coast of the Netherlands is still debated (Baart et al., 2011; Wahl et al., 2013; Steffelbauer et al., 2022).
Something similar occurs in lines 58-60.
[5] Introduction 47-50
This is a point of clarity (speed-reading). Re:
Understanding and removing the interannual to multidecadal sources of variability from tide gauge records was found to be essential for detecting an acceleration of SLR (Haigh et al., 2014). To this end, multilinear regression models between sea levels and atmospheric variables like sea-level pressure gradients, zonal and meridional wind velocity and sometimes precipitation as predictive variables have been used by various authors.
may I suggest something like:
Detecting the SLR acceleration requires understanding the sources of interannual-to-multidecadal variability and removing them from tide gauge records (Haigh et al., 2014). To this end, various authors have used multilinear regression models between sea levels and atmospheric variables. The pressure gradients at the sea surface, the zonal and meridional wind velocities and, at times, precipitation are usual predictive variables.
[6] Introduction 56-57
The verb tenses in the sentences
In general, the variability due to atmospheric forcing was first estimated by linearly detrending the time series. After that, the variability is removed from the sea level data before estimating the trend and acceleration.
confuse the extent to which old/new practices may be better/worse. (Place this remark in the context of the paragraph contrasting known methods.)
[7] Introduction 61-62
This is a point of clarity (making key figures stand out). Re:
The calculated rate of mean SLR of the stations increases from 1.7±0.3 mm/yr before the breakpoint to 2.7 ±0.4 mm/yr after the breakpoint implying an acceleration.
I suggest:
The average SLR rate of the stations increases at the breakpoint from 1.7±0.3 to 2.7±0.4 mm/yr, which implies an acceleration of the SLR.
[8] 2.1 Tide Gauge Observations 80
Regarding
Annual-mean sea-level measurements are used from the six reference tide gauges along the coast of the Netherlands: Delfzijl, Den Helder, Harlingen, IJmuiden, Hoek van Holland and Vlissingen.
is the signal that you study the average of these six stations? I inferred this from the caption of Figures 1, 2, 3 and I couldn’t seem to find this (important) piece of information in the body of the manuscript. This is the place to (re-)state this, and also an appropriate place to refer to Figure 1a.
[9a-c] 2.1 Tide Gauge Observations 81-82
This is a remark on content. In the sentence
These stations are used for operational sea level monitoring because of their extended temporal coverage and uniform distribution along the Dutch coast (Baart et al., 2019).
the term ‘uniform distribution’ sounds like a phrase borrowed from statistics. Regardless, the attribution of uniformity does not sound applicable in several respects:
a. The attribution of uniformity is geographically uninformative. To gain a feel of the geographical scope of the study, mentioning the approximate span length of the Dutch coast covered by these stations might be more informative.
b. From the point of view of physical oceanography, the station Vlissingen is distinctive insofar as is placed at the mouth of the Western Scheldt Estuary. It is conceivable that morphological developments in the estuary since 1890, of both natural and human origin, have affected the gauge signals in that area. Likewise, station Delfzijl is placed inside the Ems-Dollard estuary, whose tidal regime has been heavily affected by capital dredging in recent decades. (I do not have literature at hand to substantiate these claims, but both estuaries have been investigated exensively. I might collect some literature at a later point.) This consideration also implies that a specific factor is at play for these two stations and not for the others. Given your interest for shallow seas, you ought to include your view as to whether using the average of all stations as a study variable will make good any objective diversity between the stations; in other words, whether what you determine for “the Netherlands” applies to each of the selected stations. A precise answer might be found in previous studies or require further study. Nonetheless, stating proactively to which extent the objective geographical non-uniformity might affect the scope of the conclusions will strengthen the manuscript.
c. Likewise, the station Den Helder is placed at a tidal inlet of the Wadden Sea and Harlingen is inside. Similar morphological influences from the back basin may be conjectured after the closure of the Afsluitdijk in 1932. (I do not have literature at hand to substantiate this claim, but the topic has been investigated. I might collect some literature at a later point.) The same notes of caution as in point b apply, though.
[10] 2.1 Tide Gauge Observations 84-88
This is a point of linguistic clarity. Hoping to have brought forward a sufficient number of ex/samples, I will refrain from commenting on further passages that prompt similar linguistic editing.
The passage:
While the time series for the different stations start between 1862 and 1872, only 1890 to 2020 are used for the analysis. As was done for other studies, tide gauge data is limited to the period after 1890 to avoid the inclusion of a sea-level jump around 1885 (Frederikse and Gerkema, 2018; Baart et al., 2019). From that year, the monthly mean sea level is based on mean sea-level readings rather than mean tide level readings, which could result in a jump in the monthly data (Woodworth, 2017). (88 words)
could become:
The time series at these stations start between 1862 and 1872. However, the monthly mean sea level before 1885 is gauged with respect to readings of the mean tide rather than of the mean sea level. This could result in a jump in the data (Woodworth, 2017). Therefore, only the tide gauge data after 1890 are used as done in other studies (Frederikse and Gerkema, 2018; Baart et al., 2019).
If correct, this paraphrase exposes the fact that the ‘monthly mean sea level’ had not been based on the ‘mean sea level’ in a certain past. So why is the former called ‘mean sea level’ in the first place? The bare point seems to be that the mean sea level could only have been determined since 1885. If this too is a correct reading, the passage could become:
The readings at these stations start between 1862 and 1872 and are gauged with respect to the mean sea level, rather than to the mean tide, since 1885. Therefore, we only use the tide gauge data after 1890 as did Frederikse and Gerkema, 2018 and Baart et al., 2019. Failure to do so introduces an artificial jump in the data (Woodworth, 2017). (61 words)
[11] 2.1 Tide Gauge Observations 84-88
The fact that the global database did not account for the change of datum of 1855 raises a slight concern that other biases of local origin may have crept in. For example, the instruments at the tidal stations have obviously been changed since 1890. There, I would expect that all instruments have been thoroughly recalibrated at source, but their accuracy will have varied.
Therefore, it would be very fine to read in the manuscript whether you expect that the dataset of choice contains other biases linked to the history of the tide recordings in the Netherlands. Any potential bias in the model input in the the periods 1940-1959 and 2000-2019 seems particularly relevant for the conclusions of this study. These potential biases should be named. The Discussion should also assert whether those biases, however speculative and/or undetermined, tend to strengthen or weaken the interpretation and hence the conclusions.
[12a-b] 2.2 Atmospheric Reanalysis (and Appendix A)
a. This section does not explain for which purpose and in which way you use the reanalyses. For example, the ERA5 has a “backward extension to1950”. How do you go about this? Do you consider it fit for your purposes? Waiting does not pay off either, for the subsequent section Methods does not dwell on how you pre-processed the model input either. Therefore, an early explanation of all pre-processing choices would be beneficial before diving into the Statistical Methods – either in an expanded § 2.2 or in a new § 3.1.
b. I feel that Appendix A should be either blended in the body of the manuscript or published separately as a technical note. In the former scenario, which I would endorse, the section on Data should then describe the other datasets introduced in the present Appendix.
[13] 3.1 Statistical Models 98-99
The sentence
Four statistical models were developed and used to unravel the influence of different factors on SLR and to extract the background sea-level trend.
sounds like a downplayed announcement of the novelty of the study, which had suitably been stated in the Introduction (65-). The operation of unravel-and-extract is vague without recalling the explaining power of the factors that are made explicit and of those left in the background. Also, from the logical viewpoint, the background trend is dual to the selection of influencing. (I find comfort in a later sentence at 105-106: “its exact meaning depends on the choice of the predictive variables”.)
I would probably rephrase the sentence above as
Four novel statistical models have been developed to separate the SLR signal into the time-varying influence of chosen predictive factors and the time-varying resulting background signal.
assuming I have understood correctly merit and novelty of the study. But if you developed a single model in four setups, the wording should be adjusted (and the appropriate terminology used consistently all over).
[14] 3.1 Statistical Models 100
The ‘penalised maximum likelihood’ is referred to as ‘parametric bootstrap method’ in the abstract (6) and in the introduction (73). If the relationship between ‘penalised maximum likelihood’ and ‘parametric bootstrap method’ is topical, please comment on it explicitly. In general, please make sure to use a uniform terminology across the manuscript and avoid switching between near-synonyms. A consistent terminology will help the readers to skip forwards and backwards through the sections comfortably.
[15] 3.1 Statistical Models 106-107
I find it difficult to interpret the sentence
Its smoothness is controlled by a penalty term subtracted from the log-likelihood, which is proportional to the time integral of the squared curvature of the smooth term Wood (2020).
because the “smoothness” of the smooth curve is presented as the effect of a “smooth term” not defined earlier. I would suggest to write the parametric equations, if only in a concise symbolic form, in the body of the manuscript and add a lay résumé of the attending mathematics in the Appendix (with reference to Wood 2020 for the more statistically-minded reader of OS).
[16] 3.1 Statistical Models 107-108
Re
The penalty term was assigned a weight tuned to match the variance of the smooth curve to the variance of a 30-year average.
leads to the question of how sensitive to this statistical parameter the conclusions are. Take note: this is not a general question of model sensitivity. The point that ought to be addressed is: should one revise the conclusion about the SLR in the Netherlands if the smooth curve had been tuned to the variance of a shorter/longer time window? Is 30 years a robust one-fits-all value or does it affect the model’s capability to assess multidecadal physical processes?
[17] 3.1 Statistical Models 110
I prefer this
This setup makes no assumptions about the drivers of SLR.
to the more colloquial
This setup is equivalent to assuming we do not know anything about the drivers of SLR.
I would suggest to make the terminology for drivers, factors, and predictive variables more uniform or more consistent across the manuscript.
[18] 3.1 Statistical Models 118-121
My understanding of the passage
Therefore, we decide to use a linear regression model with an undetermined phase and amplitude but a fixed period as in Baart et al. (2011) even though it might remove some additional variability around the period of nodal tides. Using this second model, the influence of the nodal cycle on the trend and variability of sea level can be studied.
is that
Therefore, we study the influence of the nodal tide constituent on the trend and variability of sea level using a linear regression model with undetermined phase and amplitude as in Baart et al. (2011). As a downside, the resulting sea level variability may not account properly for other multidecadal influences having periodic components close to the nodal cycle.
If correct, I hope that the second version is useful to review the first.
[19] 3.1 Statistical Models 122-123
In
For the third model, wind effects are included by adding u|u| (TrNcZw), where u is the zonal wind from reanalysis averaged over the closest grid cell of each tide gauge (Fig. 1a).
I resent the lack of clarity about the average of the tide gauge readings. In the case of wind, I then wonder if you meant “averaged over the cells closest to the tide gauges”. In sum, do they process only one wind signal for the zonal wind or as many signals as there are eligible wind cells?
[20] 3.1 Statistical Models 127
Why do you use Pd to label the model considering the pressure gradient? Would Pg not be a valid name considering that gradient starts with g?
[21] 3.1 Statistical Models 127
I would appreciate reading which data have been used for the “linearly detrended sea level along the Dutch coast”. This connects to the remark that the manuscript lacks a section detailing the use of model inputs.
[22] 3.1 Statistical Models 132-134
In
Then, instead of using the pressure in both boxes as predictive variables as in Dangendorf et al. (2014b), we take the difference between the southern and northern boxes. This adds only one variable to the model and is physically motivated by the fact that the meridional pressure gradient is related to the zonal wind by geostrophy.
I was puzzled by the expectation that geostrophy applies to the upper atmosphere, while the winds used as predictive variables here are taken at 10 m height. If this expectation is correct, the correlation between winds well within the atmospheric boundary layer and those well above would be another relationship not mentioned in the manuscript. Please clarify.
This concludes this comment. Thank you for your reading.
Citation: https://doi.org/10.5194/egusphere-2022-935-CC1 -
CC2: 'Comment on egusphere-2022-935 (#2)', Giordano Lipari, 02 Dec 2022
This comment #2 resumes the analysis already presented in comment #1 up and including § 3.1 (https://doi.org/10.5194/egusphere-2022-935-CC1). The numbering of the remarks continues that of the previous tranche, but I will not propose examples of linguistic editing here.
I confirm the impressions I gained from the the first part of the document analysis. Definitely, the study has merit and deserves to be read. This community comment contains remarks on content, to be considered whether in the positive or in the negative. Principally, however, the recurrence of muddled paragraphs and equivocal sentences amounts to a diffuse major hindrance that, it seems to me, routine copy-editing after acceptance cannot fix. I am also afraid that the current state of the manuscript would frustrate future efforts to replicate/reproduce the study. In the following the notation ‘R11’ means ‘remark 11’.
In my view and experience, fixing this drawback would require a conscious effort of the authors’ to set a comprehensive terminology and rearrange the logical order of the statements, so as to impart a definite forward dynamics to the reading experience. To justify the case for such a thorough revision, therefore, I opted for a full-size effort of scanning the text, explaining my perplexities, and sharing possibly useful interventions. I hope that the resulting long read (and long write) proves, all in all, reasoned enough and helpful enough in the interest of the general readership.
[23] 3.2 Analysis of Model Output 139-145
Regarding the passage
The wind influence on sea level can be obtained from the results of the TrNcZw and TrNcPd GAMs. Once the linear regression coefficients are obtained between 1890 and 2020, the wind influence on sea level can be extended back to 1836, the beginning of the 20CRv3 atmospheric reanalysis. We estimate the wind-driven sea-level trend using a 3rd-degree polynomial fit to the annual-mean data. Also, a spectral analysis is performed on the detrended annual-mean data. The spectra are obtained using a multitaper method (Lees and Park, 1995). To obtain the low-frequency wind influence on sea level, the detrended annual-mean sea level data is smoothed using a local polynomial regression (LOWESS, Cleveland and Devlin (1988)) with a window of 21 years that effectively removes high-frequency variability.
Firstly, have you ever defined the ‘wind influence on sea level’? I have to look at Figure 3, referenced later in Sec. 4.2, to confirm me in my mind that this quantity is a sea level excursion measured in units of length. Further, how is wind influence computed from the two model set-ups? This lack of clarity comes back in the Conclusion (R45 onwards), which may well be the section many readers read first.
Secondly, I am a bit dazzled by a linear regression, a 3rd degree polynomial, a spectral transform, and a smoothing pass showing up in the brief span of a paragraph fairly abruptly. Unravelling the paragraph, I do appreciate that you match the beginning of the wind influence series with the beginning of the wind-forcing series, filling the gap period with a linear regression. Why, though? Do you make any parallel with wind-forcing data afterwards? (Incidentally, the artefact of linear extrapolation over the period 1863-1890 is evident in the polynomial trends of Figure 3b and deserves notice IMHO.) Also, is there a difference between the ‘wind-driven sea-level trend’ and the trend of the ‘wind influence on sea level’? If so, please explain; if not, please keep the terminology consistent. Also, whose ‘annual-mean data’ are you using to draw the fit? Are the ‘detrended annual-mean sea level data’, as mentioned in the text, the same thing as the wind influence, as mentioned in Figure 3d?
Thirdly, regarding the spectrum, what do you define as ‘low’ frequency? Is it an information that emerges from the data, and hence from the specific study, or an arbitrary choice? How does this low-pass filter relate with/interact with your handling of the nodal cycle (19.8 years)? Recall RRR. How does the choice of 21 years relate to the 30-year smoothing window of § 3.1? Recall R16. Is there any wisdom about your GAM that is useful to share regarding these windows; or is it sufficient that 30 years > 21 years; or are those two time frames completely unrelated? Also, you used a clear physics-based terminology for time frames (multidecadal etc…) and it is a pity to abandon it here. (Addressing several of these points may pertain to the Discussion section.)
Finally, if the following paraphrase is a correct basis to discuss your methodology:
The GAM results obtained with the TrNcZw and TrNcPd regressors give two monthly time series of the wind influence on the sea level in the period 1890-2020. The linear-regression coefficients of these time series are then used to extrapolate the data back to the beginning of the 20CRv3 atmospheric reanalysis in 1836. Finally, the annual averages shown in Fig. 3a are used to analyse the wind influence in greater detail. Firstly, the trend of the annual averages is computed with the 3rd-order polynomial fits shown in Fig. 3b. Secondly, the multi-taper method for spectral analysis of Lees and Park, 1995 is applied to the detrended annual averages. The resulting spectra in Fig. 3c feature a clear threshold between oscillations of short and long period. Lastly, the LOWESS local polynomial regression of Cleveland and Devlin (1988) is used to draw the smoothed variations around the trend shown in Fig. 3d, where oscillations faster than 21 years have been removed.
I would then suggest to announce your intentions (why) before showcasing your toolbox (how). Please note the pointers to the figure panels. A new figure with a flow chart of your workflow could help assist the readers, also because you intend to share the code and I presume that this will contain several subroutines/modules attending to each above task.
[24] 3.2 Analysis of Model Output 146-149
Using our four statistical models, we obtain the background sea-level trend. As a next step, the rate of SLR is obtained from differentiating these estimated smooth sea-level trends. The rates of SLR resulting from the different models do not include the same physical processes. TrNcZw and TrNcPd do not include the contribution from wind and nodal effects and TrNc does not include nodal effects while Tr includes all processes.
This is another occasion to adopt a clearer distinction between model and set-ups (or equivalent). Recall R13. Then, is the ‘background sea-level trend’ a new item in addition to the quantities presented in the paragraph just above? Is such a ‘background sea-level trend’ the direct output of your four set-ups as I read now, or do you process that output exactly as described in the previous paragraph?
The paragraph should be tightened up: one tip may be ‘do not include’ → ‘exclude’.
[25] 3.3 Uncertainty Computation 151-173
These two paragraphs
To estimate our models from the data, we use a generic method for likelihood-based estimation of GAM (Wood, 2020). It treats the unknown noise terms as independent identically distributed normal random variables. However, checks of the residuals reveal that they are serially correlated, so the independence assumption is not warranted. This does not invalidate the method: since only marginal parameters are estimated, the estimator is consistent under weak assumptions on the dependence; see Section 2 of Cox and Reid (2004).
However, serial dependence of the noise affects the covariance of the estimated model parameters, so for deriving confidence intervals and for testing hypotheses, we must account for it. Our estimator for the rate of SLR (the finite difference of the smooth spline estimate of the variation in sea level) is particularly sensitive to low-frequency components of the noise. Our error analysis must account for these subtle aspects of serial dependence. Therefore, we apply a parametric bootstrap method based on the noise spectrum, similar to the Wild Bootstrap version of the technique in Kirch and Politis (2011): we estimate the noise spectrum, using the same method as described in the previous section, and generate random instances of the gaussian process having this spectrum. From these, we obtain instances of the sea level time series by adding the estimates of the non-random terms. Then we apply the GAM-based estimator for our models to each of these instances to obtain an estimate of the rate of SLR. This sample of estimates is used to derive the error statistics and to test hypotheses.
invite substantial streamlining. It is difficult to keep track of what leads to what, also because you do not lean on equations; recall R15. I paraphrase the test closely to signal the questions that the current formulation elicits. I understood that:
- You chose to fit the GAMs to the data using a standard methodology based on the likelihood estimation (I’d say one estimates the parameters in order to fit a model to data, as opposed to estimating a model). The residuals, however, contain serially correlated noise (Do you provide any grounding for this?), whereby the i.i.d. normal random variables implied in the likelihood estimation are not well posed. You deem this to be a minor violation of the fit methodology insofar as, firstly, the parameters you estimate (Which? How many?) are marginal (Please explain what do you mean for marginal? You will have a mixed readership) and, secondly, some weak (What do you take to be weak?) dependence (Of what on what?) makes the likelihood-based estimator consistent (So what insights does consistency help retain in your explanation, in the face of this violation?).
- Nonetheless, the serial correlation of the noise terms (How many do you have by the way?) affects the covariance of the model parameters, which is needed to determine confidence intervals and test hypotheses (Are you going to do the latter? Why not to present a plan of what you aim at first?). Then, you explain incidentally how the SLR rate is computed, but this is best placed in Sec 3.2, right when you introduced the SLR rate.
- Suddenly enough, you identify another pain point in the sensitivity of SLR rates to low-frequency noise without having closed the issue of confidence intervals and hypothesis-testing, and without explaining the current threshold for low frequencies. Does it arise from a feature of statistics or from the finite differencing? Is one of the periods of 21 or 30 years you have used? Recall R13 and R23.
- Then, you say you must account for subtle effects, which sounds reasonable, while I would be keener on reading which undesired effects that you want to remove and which explaining capabilities you want to maintain. Sensitivity to correct things is not a bad thing.
- In the same paragraph, you suddenly turn to the noise spectrum (Is this noise the sum of all noise terms you spoke about earlier?). Are you using the same multi-taper methodology as the previous section or the new bootstrap method? And you reconstruct this spectrum with random instances of Gaussian processes (Are those expected to be i.i.d. too? What advantage do you expect from the bootstrap method?). Or do you perhaps generate many random time series of noise that have the same spectrum as the original serially correlated noise, and then sum this to a deterministic part borrowed from the GAM? How many time series per model set-up you are dealing here with? And do you apply the GAM once again after this latest sum, so as it looks? How many times do you run the GAMs then? Is an iterative procedure involved here?
- Then, the section finishes abruptly here. I come away with the impression that you wanted to fix a lot of relevant things without presenting in an orderly fashion the nature and facets of the issues ahead, the expected impact on the future evaluations, and the adequacy of your workflow to forestall these limitations. The exposition is too unglued to enable me to express a judgement on the ensuing discussion, let alone to encourage me to dig deeper in the code.
I suggest rephrasing the whole Section 3 by announcing first the general guarantees you want to offer and then how the methodology delivers these. On so doing, IMHO, you stimulate an effortless curiosity to look into the results coming next. Would you also mind it to add some formulas, whether in the body of the manuscript or in the Appendix (R15), and a figure with the flow chart of your methodology? This will help organize this section greatly.
[26] Figure 2.
Comparison of the annual tide gauge data averaged over 6 tide gauges along the Dutch coast with three Generalised Additive Models (Tr, TrNc, TrNcZw)
Would you make the figure wider to accommodate for all four setups? This is perhaps the first time that you say that the tide gauge data of the six stations are averaged. Recall R8.
[27] 4 Results - 4.1 Comparison of the Different GAMs 176-182
The GAM progressively better fits the data, measured by the deviance (Tbl. 1), as the complexity of the model increases (e.g., the number of predictive variables increases), measured by the number of degrees of freedom (Tbl. 1). The deviance is used to compare generalised linear models and is a generalisation of the sum of squares of residuals used to compare linear regression models (Wood, 2020). Including the nodal cycle reduces the deviance by 12%, and including the wind further reduces the deviance by an additional 37% for TrNcPd to 58% for TrNcZw iInmplying that the best fit is obtained for TrNcZw. The improved fit for TrNcZw could be explained by the fact that here the local zonal wind is used, whereas for TrNcPd, a simplification of large-scale zonal wind is used.
Another paragraph, containing interesting results, to reorganize and streamline.
[28] 4 Results - 4.1 Comparison of the Different GAMs 183-186
The resulting fits can be seen in Fig. 2. When more predictive variables for the wind are included in the model, like the meridional wind or wind taken at multiple locations in the North Sea, the deviance can be further reduced. However, the increased degrees of freedom increase the standard error in estimating the trend (not shown). Therefore, we find that using only one predictive variable for the wind is the best choice for estimating the sea-level trend.
What is the rationale of not showing (in a compact way) that more degrees of freedom worsen the quality of the trend? I imagine the scholars interested in your study and in its application to their basins of choice would appreciate a feel how an excessive quest for many regressors can let things go wrong. (A kind of overfitting, even though we do not have a training and testing set here.)
Also, does it make more sense to say that a single predictive variable is the best choice to estimate the wind influence only, rather than the sea-level trend? Recall that Tr for trend is just one of the four set-ups you are considering. So when you use the word ‘trend’ I tend to think of that particular set-up, Tr. Therefore, if you aim to improve the trend seeking good regressors (as I read), it is not correct to call the baseline model Trend too. All set-ups produce trends, as one sees in Fig.4. So please clarify your terminology (background, trend, influence, variability, etc.) and apply that consistently everywhere --- this is of paramount important for getting the message across. This remarks extends R13.
Also please recall R9, and the fact that, in a shallow coast, bathymetry is a definite driver of (tidal and wind-driven) motion, the more so in constrained basins like estuaries and fringe basins, as applicable to the Netherlands.
[29] Figure 3
Comparison of the wind influence on sea level along the Dutch coast obtained from two different regressors: average zonal wind of the 6 tide gauge stations (TrNcZw) and the pressure difference between the Northern and Southern boxes (TrNcPd) of Figure 1. (a) Time series of annual averages. (b) Trend computed using a 3rd-degree polynomial fit with linear trend values over the first half and the second half of the total period. (c) Spectra obtained using a multitaper method (Lees and Park, 1995). Both the detrended time series (solid lines) and the detrended and smoothed time series (dashed lines) are shown. Smoothing is obtained from a LOWESS method with a window of 21 years. (d) Smoothed time series.
Please keep on using dashed lines for detrended-and-smoothed time series. According to the figure title, panel (d) regards detrended-and-smoothed time series, a name which does not feature in the caption. The caption can be streamlined and the repetitions with respect to the body of the text should be kept to a minimum.
[30] 4 Results - 4.2 Wind Influence on Sea Level 188-197
Figure 3a shows the resulting wind influence on sea level, where the large interannual variability stands out. From these annual-mean time series, we estimate the wind-driven sea-level trend as is shown in Fig. 3b. For the second period, 1928-2020, the wind-driven trend is 0.12 mm/yr and 0.15 mm/yr for respectively TrNcZw and TrNcPd. Long-term strengthening of the zonal wind has increased the sea level along the coast of the Netherlands. This long-term strengthening of the zonal wind is consistent with the observed northward shift and increased speed of the jet stream, which could be due to a decreasing temperature gradient between the North Pole and the equator at the height of the tropopause (Fig. 7d and 9d from Hallam et al. (2022)). A long-term influence of atmospheric drivers (zonal and meridional wind and surface pressure) was found earlier for the period 1953-2003 (Fig. 2c from Dangendorf et al. (2014a)), but our results are in contradiction with the atmospheric-driven sea-level drop over the period 1900-2011 found by the same authors. This could be due to an update in the atmospheric reanalysis (20CRv3 instead of 20CRv2).
Where is the long-term strengthening of the zonal wind evident in your study so far? If I follow the text literally, you are assuming from the outset that an explanation of your model results exists, instead of showing that your evidence correlates with the proposed explanation. I consider this argumentation, or at least the way it delivered, weak. The Discussion section, and not the Results, is the appropriate part of the manuscript to contrast your results with the existing literature in ample detail.
[31] 4 Results - 4.2 Wind Influence on Sea Level 198-206
After removing the trend from the data in Fig. 3a, a spectral analysis is performed (Fig. 3c). The spectra of the wind-impact on sea level obtained using both TrNcZw and TrNcPd have a similar shape, but the total variance is larger for TrNcZw compared to TrNcPd which is a result of the larger interannual variability of TrNcZw as shown in Fig. 3a. For both methods, there is more energy in the signal for periods larger than two decades than for smaller periods. Therefore, the signals are smoothed using a local polynomial regression (LOWESS, Cleveland and Devlin (1988)) with a window of 21 years that effectively removes high-frequency variability (dashed lines in Fig. 3c). The resulting detrended and smoothed time series, Fig. 3d, show that low-frequency wind variability can raise or drop sea level by over 2 cm over a period of 2 to 5 decades. In App. A, this low-frequency variability lags low-frequency sea-surface temperatures in the North Atlantic that have a similar pattern as the Atlantic Multidecadal Variability.
You do not need to repeat any information given in the Methods, especially its details. Again, the separate Appendix overburdens the reader with the task to walk the data-methods-results ladder once again. (R12.)
[32] Figure 4. (a–d)
The rates of SLR were obtained for four different statistical models. A window of three years is used, so the rates cannot be computed for the first and last years of the time series. The period shown here is 1891 to 2019. The dashed lines show the 5th and 95th percentiles of the uncertainty range computed from a parametric bootstrap method. Numbers in grey under the curves indicate the mean rates for four different periods ([1900-1919], [1920-1939], [1940-1959], [2000-2019]) (e) Median sea level rates. (f) Standard error of the sea level rates.
Where does this time frame of 3 years come from? Why is that necessary?
Then,in panel (e) please use the same y-axis range as panels (a-d). In the y-axis please use SLR, which you have already defined: panel (f) will benefit from the gain in typesetting space and panel (e) can accommodate for ‘median SLR’. (Although the interpretation is obvious here, you might want to use a dotted line to indicate the uncertainty range, once you have used dashed line for detrended-and-smoothed results.)
[33] 4 Results - 4.3 Rates of SLR 208-213
The rates of SLR obtained from differentiating the estimated smooth sea-level trend from each of the four models are shown in Fig. 4. Reduction of uncertainty is generally the main motivation for removing variability due to known atmospheric drivers from the sea-level trend (Dangendorf et al., 2014a). The rate of change from TrNc has lower uncertainty than the rate from Tr. Including the zonal wind (TrNcZw) as a predictive variable further decreases the uncertainty, whereas including the pressure difference (TrNcPd) increases the uncertainty again. The standard error in estimating the trend is larger at the time series’ start and end because there are fewer constraints than in the middle of the time series.
Please refer to panels of Figure 4. See R24 for an example.
[34] 4 Results - 4.3 Rates of SLR 214-225
In addition to reducing the uncertainty, the wind also influences the rate of SLR itself. Both TrNcZw and TrNcPd have lower rates in the first part of the 20th century compared to Tr and TrNc. From the 1960s onward, the rates of SLR of TrNcZw and TrNcPd increase rapidly. The TrNcZw model has the smallest standard error and estimates the largest rate of SLR over recent decades, which reached 3.0[2.4−3.5] mm/yr over the period 2000-2019. For this model, the rate of SLR over periods before the acceleration in the 1960s is 1.8[1.4 − 2.3] mm/yr over the period 1900-1920, 1.7[1.3 − 2.0] mm/yr over the period 1920-1940 and 1.5[1.1 − 1.8] mm/yr over the period 1940-1960. Table 2 shows for the different GAMs the probability (the p-value) that the estimated rate difference between the periods 2000-2019 and a previous period (1900-1919, 1920-1939 and 1940-1959) would exceed the rate difference found in this study if the sea level had changed at a constant rate. For the Tr model, we find probabilities between 5 and 23% for the different periods. Having more predictive variables in the GAM decreases these probabilities. For the TrNC model, the probability is 14% when compared with the period 1900-1919 due to the higher rates of SLR of this model at the beginning of the 20th century. However, for the other periods, we find probabilities of 1%, implying that finding these rate differences would be very unlikely if there would have been no acceleration (Mastrandrea et al., 2011).
This key paragraph is quite additive in its arrangement. Please lead the reader through it by reorganizing and streamlining its moving parts.
[35] 4 Results - 4.3 Rates of SLR 226-230
For the TrNcZw model, we find probabilities of 0% for all periods, and in the TrNcPd model, we find probabilities smaller than 5% and only 1% when compared with the period 1940-1959. These probabilities indicate that an acceleration of SLR is virtually certain (Mastrandrea et al., 2011). We conclude that along the coast of the Netherlands, the sea level has accelerated since the 1960s, but this acceleration has been masked by wind-field and nodal-tide variations. This agrees with the global mean sea level that has accelerated since the 1960s (Dangendorf et al., 2019).
The commentary of Table 2 should probably take a single paragraph of its own.
A question arises about how such masking and the effect of human interventions in the Scheldt estuary, Ems estuary and Wadden Sea relate one with another. Recall R9.
[36] 4 Results - 4.3 Rates of SLR 231-236
All models indicate a decrease in the rate of SLR from the beginning of the 20th century until about 1960", with a minimum in the 1940s for Tr and TrNc and in the 1960s for TrNcZw and TrNcPd. This decreasing rate of SLR could be due to the strong Arctic warming from 1900 to 1930, followed by an Arctic cooling from 1930 to 1970 (Fig. 4, Bokuchava and Semenov (2021)).
This could have influenced sea level through glacier mass loss followed by gain or local steric sea level changes. Since the local sea-level budget is not closed before 1950 (Frederikse et al., 2020), we can only speculate about the causes of the drop in the rate of SLR.
Please mention what the physical boundaries of the budget area are. What do you mean for local/regional? Dutch coastal waters, North Sea, etc.?
[37] §5 Discussion 237-242
Estimating the trend, nodal cycle and atmospheric processes underlying the wind influence on sea level using the GAM allows for avoiding a priori assumptions about the sea-level trend, like having a linear or quadratic shape, while performing the regression analysis. Thereby, the rate of SLR can be computed as a time-evolving variable over the whole observational period contrary to being calculated as a constant over an arbitrary period as was done in Calafat and Chambers (2013); Steffelbauer et al. (2022).
Recall R28. Do you estimate one trend or as many trends as there are model set-ups?
[38] §5 Discussion 242-243
In addition, we propose a careful uncertainty analysis accounting for serially dependent unexplained fluctuations, which is used to evaluate the strength of evidence for an acceleration.
It is not clear from the passage whether this uncertainty analysis has been presented already or is coming next. There is no doubt that a recap and commentary of the uncertainly analysis are appropriate in this section on Discussion. (IMHO, the section on Results should only contain the dry results and show how they naturally proceed from the Methods. The line of reasoning then gains a strong forward dynamics.)
[39] §5 Discussion 243-248
These two elements help to avoid framing the problem of acceleration detection as binary. This is important when advising decision-makers: significance testing based on ad hoc models like a broken line trend may lead to a paradigm shift from a steady rate of SLR in one year to an accelerating rise a few years later, as demonstrated by the results in (Calafat and Chambers, 2013; Steffelbauer et al., 2022). To our best knowledge, the GAM has not been applied to estimate trends and acceleration in sea-level data before, and we believe it could help solve similar acceleration detection problems in regions other than the coast of the Netherlands.
I completely support the idea that decision makers can have great benefit from the time-varying representation of SLR that you are proposing. However, considering that you are focussing on a local/regional scale, I would suggest to put a little more effort in explaining how/where regional drivers (and, for this exercise, the situation of the Netherlands) end up to be represented in your model. This may be of general interest for the readers who start to think about the application of this method to their own coastal basins. I have commented on something close to this in R9, R28.
I also reuse a tip I often received: to the best of our knowledge is the appropriate idiomatic expression (L 246). Help to avoid (L 243) should be help avoid.
[40] §5 Discussion 249-258
When removing the wind influence from the sea-level observations, the underlying assumption is that this influence is only due to natural variability and that there is no structural change due to anthropogenic forcing. However, as we find a wind-driven trend over the entire period of study 1836-2020 from both the zonal wind and pressure difference model, the trend could also continue in the future. We do not know of any study investigating the possible cause of this trend. If it is caused by climate change due to anthropogenic forcing, it would be reasonable to expect it to continue in the future. Otherwise, if it is caused by natural variability, it might reverse. Most of the CMIP5 and CMIP6 ensembles do not show a systematic trend associated with wind influence on sea level in the North Sea, not over the historical period or in future scenarios. So, they either miss the process driving the trend in the observations, or the trend in the comments has to be attributed to natural variability. In each case, the magnitude of around 0.15 mm/yr over the historical period is small enough compared to other sources of uncertainty to neglect it when making sea level projections on time scales of more than several decades.
I presume that the essence of this paragraph is: you cannot offer guarantees as to how your model performs with predictions, principally because distinguishing the natural and anthropogenic components of the wind forcing is a known difficulty. I am not so sure I got it right, however, for example because I fear that you refer to past trend and future trend interchangeably. I found this entire paragraph hard to follow and hence to assess. Please edit.
[41] §5 Discussion 259-262
If the time lag found between North Atlantic SST and wind influence on sea level as described in App. A was found to be physical or if the SST signal could be skillfully forecasted, this relation could provide a source of predictability for the deviation between sea level along the Dutch coast and large-scale drivers (e.g. glacier and ice sheet mass loss, global steric…) at the decadal time scale.
The more I read about Appendix A in the body of the manuscript, the more score points gains the suggestion of incorporating Appendix A into the body of the manuscript. Recall R12, R31. I also understand that the focus of this section on Discussion has moved towards the subject of predictions. Why not create separate subsections on the diagnostic and predictive capabilities of your model?
[42] §5 Discussion 263-265
From the daily to the interannual time scale, the wind influence on sea level in shallow seas is well understood by the barotropic theory of the interplay between the Coriolis force, pressure gradient and surface wind stress (equation 3 from Mangini et al. (2021)).
In contrast, my understanding is that flow in shallow seas strictly requires consideration of the bed shear stress. In environmental fluid dynamics, a sea not subject to significant bed actions loses the qualification of shallowness. (Of course, there are process in shallow waters that are not shallow flows.) This motivates the care that should be taken to acknowledge at least/include at most what happened to the Dutch coastal waters in the period 1890-2000. Recall R9.
[43] §5 Discussion 265-269
On the multidecadal time scale, as investigated in this study, it is possible that the physical mechanism underpinning the relation between wind and sea level also involves steric sea level change (Chen et al., 2014). In particular, baroclinic signals in the deep ocean propagating as a volume flux on shallow seas (Bingham and Hughes, 2012; Calafat et al.,2012). However, since we use the large interannual variability to define the regression coefficient, we think these coefficients mostly reflect the barotropic wind influence.
Regarding the last concluding remark, I would appreciate, beside the sheer assertion of what you think, a short explanation of why you think that. Then, I cannot easily grasp whether you are talking about water or wind. In particular, the attribution ‘baroclinic’ seems to associate with water, while ‘barotropic’ with wind. Are you leveraging a notion that wind does not drag the deep layers of the ocean into the Dutch coastal waters, not even over the decades? Please streamline and clarify.
[44] §5 Discussion 270-279
We find a strong increase in the rate of SLR between the 1960s and 2000s (Fig. 4). From 2000 onward, the standard error of the rate of SLR increases strongly, and it is uncertain whether the increase of the rate persists. A potential application to this increase would be the extrapolation of the observed rate into the near future. This method was recently used as an additional line of evidence for future sea-level rise by Sweet et al. (2022). Based on Fig. 4c, assuming a constant rate of 3 mm/yr from 20000 onwards, we arrive at a rise of 0.3 m between 2000 and 2100, which is slightly higher than the rise over the 20th century. However, assuming a constant acceleration of 1.5/25= 0.06 mm/yr 2 (as inferred from the trend in sea level rate over 1975-2000 in Fig. 4c), we obtain a rise of 0.6 m, from 2000 to 2100, which is twice the rise without acceleration. Given the complexity of changes in the various drivers of global SLR, it would be naive to assume that the acceleration will remain constant during the remainder of this century. However, these crude extrapolations illustrate the practical significance of our estimates of the local rates of SLR and the importance of obtaining the evolution of these rates over time.
If you place the last sentence at the beginning of the paragraph, you have an example of how stating the paragraph topic at the outset and elaborating on it afterwards greatly helps speed reading. ‘20000’ in L274 should be 2000.
[45] §6 Conclusions 281-282
In this study, we estimate the sea-level trend and the influence of the nodal cycle and wind on sea level along the coast of the Netherlands.
I am often confused by how you use the term “influence” physically. Is this a part of the sea-level rise, thus a quantity measured in meters? Or is it another physical quantity that is an agency of sea level rise, and thus has appropriate units of measure? In other words: when you say to “estimate the influence of X and Y”, are you consistently referring to the components of sea level rise that can be explained as an effect of X and Y, that is SLRX and SLRY? Or to the statistical analysis of X and Y as the predictive variables of your model? This confusion is also sustained by the ensuing remarks.
[46] §6 Conclusions 282-283
We used the average of the observations from six tide gauges and zonal wind and atmospheric pressure at sea level from two reanalysis data sets.
This is eventually clear here, but should be announced much earlier on in the manuscript and not in the figure captions. See R8. (The sentence could also be streamlined linguistically.)
[47] §6 Conclusions 283-284
Using a set of four GAMs, we estimated the trend using B-splines functions and the wind influence using linear regression.
Did you estimate one trend or four trends? Then, do you estimate the wind influence with linear regression or with a 3rd order polynomial, as in Fig. 3b?
[48] §6 Conclusions 284-285
The four models include either no predictive variables, only the nodal cycle, and, additionally, either zonal wind or pressure gradient as predictive variables.
I would advocate again the distinction between model (one type, GAM) and set-ups (several implementations). I interpret the passage above as: The predictive variables in the four model set-ups are either none;oronly thenodal cycle;orthe nodal cycle and eitherthezonal wind orthepressure gradient.
[49] §6 Conclusions 285-287
We find that using only one predictive variable for the wind best estimates the sea-level trend. The deviance is reduced when more predictive variables are added to the GAM, reducing by 12% for adding the nodal cycle and another 37 to 59% for adding the wind.
I interpret the above as Adding predictive variables to the GAM reduces the deviance by 12% in the case of the nodal cycle and by another 37 to 59% in the case of the two wind variables. A single predictive variable for the wind estimates the sea-level trend best.
[50] §6 Conclusions 288-290
We obtain the wind influence on sea level using the two GAMs that include a wind predictive variable (TrNcZw and TrNcPd). Obtaining the wind influence with two different approaches shows the method’s robustness as both methods lead to similar conclusions.
The passage strengthens the case to distinguish models and set-ups: in the second sentence a certain one method appears to be robust because two certain methods are similar. Also, one may argue that you have two wind influences and that you aim to select one which has the most desirable statistical properties and hence is the most trustworthy. Beside terminology, I recommend to revise the use of the singular/plural number all over.
[51] §6 Conclusions 290-291
We find a long-term sea-level rise due to wind forcing of 0.12 mm/yr or 0.15 mm/yr for 1928-2020, depending on the used model.
I presume that the sea-level rise due to wind forcing is another definition of wind influence. The section on methods should present your terminology of choice once for all, so that the reader has not to wonder or backtrack the line of reasoning so often.
[52] §6 Conclusions 291-296
The long-term strengthening of the zonal wind is consistent with an observed northward shift and jet stream strengthening (Hallam et al., 2022). Also, we find a low-frequency wind variability which can rise or drop sea level by about 1 cm over 2 to 5 decades. We find that it is related to multi-decadal sea surface temperature variations in the North Atlantic with a similar pattern as the Atlantic Multidecadal Variability. The correlation between SST in the northern part of the North Atlantic and the multidecadal wind-driven sea-level variability can be understood as smaller SST values increase the meridional temperature gradient and strengthen the jet stream (Hallam et al., 2022).
See R30. The shift of the story line towards the zonal wind is quite abrupt in this paragraph that privileged sea levels. Many readers will probably read these conclusions first. A new topic probably deserves a paragraph on its own. In particular, the emphasis given to the low-frequency wind variability strengthens the case to move Appendix A into the body of the manuscript (R12, R31, R41). I value that your model unlocks new possibilities to unveil relationships between unsteady forcing and unsteady effects. However, tucking the arguments in an appendix looks a bit like “throwing the stone and hiding the hand”. Appendix A is surely worth being integrated in the bulk of the work and emphasised as these conclusions do. See also R53 next.
[53] §6 Conclusions 296-298
In summary, we find both a long-term SLR as well as a multidecadal sea-level variability due to wind forcing which are both connected to changes in the jet stream through various mechanisms (Hallam et al., 2022).
If I paraphrase this correctly, your contribution is that the changes in the jet stream have influenced, through various mechanisms, both the long-term development and the multidecadal variability of the SLR along the Dutch coast. This sounds to me as a significant contribution, which is a bit overshadowed by the title. What are such various mechanisms that you have elucidated, though? The abstract (16-18) does not announce the influence on long-term development, while it does emphasise the SST, unlike the conclusions. Please clarify what the main take-home messages are and present them with even emphasis across the manuscript.
Regarding the jet stream, please recall R30.
[54] §6 Conclusions 299-305
After obtaining the sea-level trend using the four GAMs, we obtain the rate of SLR by differentiating the trend. This results in new insight into the evolution of the rate of SLR along the coast of the Netherlands over the observational period. The rates of SLR, excluding the influence of the wind, are lower at the beginning of the 20th century and larger at the beginning of the 21st century. Our best-fitting model yields a rate of SLR, excluding nodal and wind effects, of 3.0[2.4 − 3.5] mm/yr over 2000-2019 compared to 1.8[1.4 − 2.3] mm/yr in 1900-1919 and 1.5[1.1 − 1.8] mm/yr in 1940-1959. The probability (the p-value) of finding a rate difference between 1940-1959 and 2000-2019 equal to the one we found when there would not have been an acceleration is smaller than 1%. From these results, we conclude that an acceleration of SLR is virtually certain.
Here it is important to clarify what you mean with ‘excluding the influence of the wind’, since the previous paragraph invites one to think that you may have gained new insights into long-term and multidecadal scales separately. So, what do you exclude the wind influence (defined as...) from?
The paragraph could surely be streamlined linguistically. (Also my remarks could, admittedly, but I trust that the manuscript contains a more long-lasting contribution to the field which justifies its revision and editing.)
[55] §6 Conclusions 305-308
Also, we find, for the first time, that the acceleration of SLR along the coast of the Netherlands started in the 1960s. This aligns with global SLR observations and expectations based on a physical understanding of SLR related to global warming (Fox-Kemper et al., 2021; Dangendorf et al., 2019).
Kudos for identifying the SLR speed up. However, the point of alignment with global evidences suggests an incomplete inference. It is fine to have subtracted astronomical and meteorological influences from the sea level signal. Yet, since the water level measurements along the Dutch coast have been averaged spatially and since you overlook the influence on the local sea levels caused by considerable human interventions on the coastal bathymetry, you arguably conflate global and local contributions. These local contributions may have followed the global contributions passively, or have emphasised it, or have dampened it. Each of these outcomes may have prevailed over different time frames in the period under investigation. Perhaps, the acceleration of SLR in the Netherlands was delayed, or perhaps assisted.
In other words: an alignment of wind-and-tide-free observations with global observations does support the inference that global warming has had an effect in the Netherlands. Yet, it does not leave global warming as the only driver of change, unless companion effects are ruled out positively. Since the passage justly emphasise physical understanding, the reader should be alerted about the physics-based local circumstances lurking in your model.
[56] §6 Conclusions 308-309
Furthermore, we explain that the acceleration of SLR along the Dutch coast has been difficult to detect due to the masking of the acceleration by wind-field and nodal-tide variations.
I would appreciate to read which passage in your line of reasoning explains this. Or is this a general benefit of your methodology? Also, did you comment explicitly on the variation of the nodal tide itself, as I infer from your sentence? Recall R18.
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This completes the first analysis of the manuscript, excluding the Appendix and the supplemental material, and concludes comment #2.
Thank you for your reading.
Citation: https://doi.org/10.5194/egusphere-2022-935-CC2 -
CC3: 'Comment on egusphere-2022-935 (#3 Methodological reserve)', Giordano Lipari, 14 Dec 2022
This community comment #3 has been prompted by additional readings that, in turn, had been prompted by remarks on the manuscript R8-R11, R28, R35, R39 and R42. Their common denominator was a desire for clarity as to the peculiarities of Dutch coastal waters. In this one community comment, I digress from topical issues and set forth a case for a deeper and wider consideration of the existing literature.
A most relevant resource is the Zeespiegelmonitor (Sea Level Monitor), which is referred to as Baart et al. 2019 in the manuscript. This is a technical report of national interest, commissioned by Rijkswaterstaat, the governmental agency responsible for water management. The document is publicly available from the link provided in the manuscript but also from a permalink in the reports database of Rijkswaterstaat: https://puc.overheid.nl/doc/PUC_635781_31. The report is in Dutch and, for the benefit of the general reader, I will translate into English some passages.
In the following, “B2019, 45,56” is short for “Baart et al 2019, pages 45 and 56”. “Rn” is short for Remark n, where n is a progressive number in my previous community comments (up to 22 included in https://doi.org/10.5194/egusphere-2022-935-CC1, and from 23 up to 56 included in https://doi.org/10.5194/egusphere-2022-935-CC2).
[57a-b] Existing citations of B2019
The manuscript cites B2019 sparingly in LL 82,86 of §2.1, regarding the tide gauge observations along the Dutch coast.
a. As for the location of the tide gauges in LL 81-82, the phrase These stations are used for operational sea level monitoring because of their extended temporal coverage and uniform distribution along the Dutch coast clearly renders the phrase Dit zijn zes stations, redelijk uniform verdeeld langs de Nederlandse kust, met een lange historie aan metingen in B2019,39. I have critiqued the infelicity of the phrase ‘uniformly distributed’ stations in R9. Regardless, this confirms me in my mind that the authors have consulted B2019 closely.
b. As for the adjustment of the chart datum of 1885 in LL 85-86, B2019 also mentions successive jumps in the Dutch recordings. The manuscript reference to the adjustment of 1885 only is incomplete information; consider also R10. More important for the readers is to offer a guarantee that the datasets deposited at the PSMSL have been gauged with respect to a Revised Local Reference (see R2019,42-44 and https://psmsl.org/data/obtaining/rlr.php), which evens out all operations on the chart datum. This reassurance would also resolve a concern raised in R11.
[58a-b] Omissions in the citations of B2019
a. However, B2019 does present a methodology and an expert opinion to account for the SLR acceleration. Strangely, the manuscript does not mention this contribution, not even in the Introduction paragraph addressing the debate on acceleration along the Dutch coast (LL 32-41). In contrast, B2019, § 5 (Methoden voor de bepaling van de huidige zeespiegel = Methods for the determination of the present sea level) presents much relevant information in an orderly fashion. In particular, B2019,47-48 refers to a Generalized Linear Model being used to carry out an analysis remarkably similar to those of the manuscript. Referring to B2019 seems all the more compelling if it is correct to state that Generalized Additive Models are a type of Generalized Linear Models (according to https://en.wikipedia.org/wiki/Generalized_additive_model). Finally, also the results of B2019 display a striking similarity of those presented in the manuscript. For example, Fig. 6.1 in B2019,53 is
which should be contrasted with Figure 2 in the manuscript (below). The key for the axes labels above is hoogte: height; lineair model zonder wind: linear model without wind; lineair model met wind: linear model with wind; jaargemiddelden: yearly averages.
[59] Common-sense considerations
Not referring to this piece of previous research seems a conspicuous omission to me, at least one that justifies a textual analysis of such an extent as this. These incidents strongly suggest that the authors should peruse and credit B2019 more extensively, at a minimum. Regrettably, they leave an unpleasant aftertaste that substantial weaknesses may also lurk in the rest of the literature review.
For sure, the authors should exercise much more caution in not sailing inadvertently towards the rocks of plagiarism by implicitly portraying steps ahead as strides ahead. For the sake of prudence, claims of novelty such as LL 246-248 -- To our best knowledge, the GAM has not been applied to estimate trends and acceleration in sea-level data before, and we believe it could help solve similar acceleration detection problems in regions other than the coast of the Netherlands -- may well apply and be well deserved (as I am still inclined to believe), but should attract more scrutiny from the community.
IMHO, as a Dutch saying goes, er is werk aan de wikel, there’s work (to do) in the shop. I hope this commentary will help the manuscript develop a strong backbone and gain it the unconditioned appreciation of many readers.
Citation: https://doi.org/10.5194/egusphere-2022-935-CC3 -
AC1: 'Reply on CC3', Iris Keizer, 03 Mar 2023
We thank Giordano Lipari for his interest in our work. By this reply, we'd like to comment on the three extensive community comments he made on our preprint. It really shows that our paper will be of interest to people outside of the academic field of physical sea level. We thank him for his beneficial comments which will make our paper more readable for a broader audience which is very valuable. Many of his suggestions and the extensive explanations he provided with his comments are very useful to improve our manuscript and to learn from as a starting scientist.
Some remarks on his final comment:
We do not understand the worry about plagiarism of Baart et al. 2019 because we already cite this work in the paper. We dot not want to discuss the differences between our paper and Baart et al. 2019 in depth because it is written in Dutch which means that many readers of this paper will not be able to read it. Baart et al. 2019 use two fully parametric models for the trendline (linear+quadratic trend, or broken linear trend), whereas our GAM model uses a representation of a smooth trendline of unspecified shape, which is much more general. Both our GAM and the models in Baart et al. 2019 are examples of GLMs, but GLM is a very general category of models, and therefore practically meaningless for distinguishing models. Furthermore, our estimation of the uncertainty of the trendline is completely different from Baart et al (2019), employing less restrictive assumptions. We will add the information that the PSMSL data is gauged to the Revised Local Reference.Citation: https://doi.org/10.5194/egusphere-2022-935-AC1
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AC1: 'Reply on CC3', Iris Keizer, 03 Mar 2023
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CC4: 'Comment on egusphere-2022-935', Riccardo Riva, 10 Jan 2023
This is a nice piece of work. Especially intersting is the use of GAMs, which as far as I know is not yet very common in the Earth sciences.
I would only like to make a comment about the chocie of the authors to estimate amplitude and phase of the nodal cycle, rather than prescribing it as recommenden by Woodworth (2012, J. Coast. Res. 28) and confirmed by Frederikse et al. (2016, GRL 43). An empirical estimation seems particularly risky, considering that sea level in the North Seas shows a large decadal oscillation with periods close to 20 years (see, e.g., Fig.2 in Frederikse et al., 2016).
That said, the approach proposed by the authors might still work. However, it would be nice if they added some proof of its robustness.
First of all, they could compare their estimated nodal cycle with the equilibrium tide discussed by Woodworth (2012): the resulting amplitude could be different (which in itself would be a valuable result), but I would expect the phase to remain close to the theoretical value (if not, a physical justification should be provided).
Secondly, in case the estimated nodal cycle were indeed significantly different from the theorietical one, it would be interesting to test how using the theoretical value would affect the conclusions of this study (by, e.g., adding a new experiment analogous to TrNCZw).Hope this helps,
Riccardo Riva
Citation: https://doi.org/10.5194/egusphere-2022-935-CC4 -
AC2: 'Reply on CC4', Iris Keizer, 03 Mar 2023
We thank Riccardo Riva for his compliments and beneficial comments on the manuscript. As stated in our manuscript, section 3.1, there are indeed different ways to estimate the influence of the nodal cycle on sea level in the North Sea. Using a closed budget, as Frederikse et al. (2016) do, suggests that there is no indication that the nodal cycle deviates from the equilibrium tide. However, we find that assuming the equilibrium tide leaves a large amount of energy in the spectrum close to the period of the nodal cycle. Our estimate for the nodal cycle resulting from the regression suggests an amplitude almost three times as large as the amplitude of the equilibrium tide and a phase lag of three years compared to the equilibrium tide (see attached figure). Our hypothesis for the deviation (which we will study further) is that this deviation is due to the influence of nodal tide on steric sea level. The modulation of high-frequency tides by the nodal tide might drive vertical-mixing processes that drive steric sea level. We formulate this hypothesis based on the recent paper by Joshi et al. (https://egusphere.copernicus.org/preprints/2022/egusphere-2022-151/). Since Frederikse et al. (2016) use a budget study, these nodal-driven effects are classified as steric effects in the budget, making the equilibrium tide a perfect fit. Since we don't have steric sea level in our model, the effect of nodal tide on sea level also includes steric effects which motivates us to use a statistical estimate of the nodal tide. We will expand our paper with an appendix comparing our estimates of the nodal tide to the equilibrium tide as well as the spectra of their residuals (observed sea level minus reconstructed sea level). Also, we will briefly discuss these results in the discussion section. However, discussing the physical mechanisms of the relation between the nodal tides and sea level is outside of the scope of this paper. Please, find attached a figure of (a) the nodal tide resulting from the statistical estimation in our three GAMs as well as the equilibrium tide and (b) the spectra of the residuals of three models. The model TrW only includes trend and zonal+meridional wind but no tides, the model TrNcW includes trend, nodal tide and zonal and meridional wind and the model TrEtW includes the trend and zonal+meridional wind but the sea level is corrected for the equilibrium tide. This shows that there is a lot of energy remaining around the nodal tide period using the correction for the equilibrium tide. From the plots of the nodal tide it can be seen that the statistical estimation gives a nodal tide with an amplitude more than 2.5 times larger than the amplitude of the equilibrium tide and a 3-year phase shift.
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AC2: 'Reply on CC4', Iris Keizer, 03 Mar 2023
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RC2: 'Comment on egusphere-2022-935', Anonymous Referee #2, 24 Jan 2023
Please see attached PDF for the referee report.
- AC4: 'Reply on RC2', Iris Keizer, 03 Mar 2023
Peer review completion
Journal article(s) based on this preprint
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NetherlandsSeaLevelAcceleration Dewi Le Bars, Iris Keizer https://github.com/KNMI-sealevel/NetherlandsSeaLevelAcceleration
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NetherlandsSeaLevelAcceleration Dewi Le Bars, Iris Keizer https://github.com/KNMI-sealevel/NetherlandsSeaLevelAcceleration
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