Future Response of the Wadden Sea Tidal Basins to Relative Sea-Level rise—An Aggregated Modelling Approach

Round 1

Reviewer 1 Report

General

The questions addressed are highly topical. But while the m/s starts with account of the ‘unique’ value of the Waddensee and the potential impact of sea level rise, the paper then becomes an exploration of the behaviour of a particular model, and the discussion does not really return to these issues.

Specific

#24-26 This sentence is difficult to follow – too many different equilibriums. I assume we are talking about ‘deeper than’ the original non-SLR (SLR – sea level rise) equilibrium, then developing to the new with SLR equilibrium.

#30-32 ‘These insights..’ it is not clear what the insights are nor that they are inherently generic as opposed to a specific Waddensee phenomenon.

Figure 1. The legend says Waddensee but it is not deliminated or even labelled in any way on the image. The image covers an area much larger than what I would think of as the Waddensee. Please add your boundaries AND latitude and longitude marks to locate the region.

Fig 2 – Some locating marks – lat and long, inset of showing relation of the Dutch Waddensee to the area shown in Fig 1 or the North Sea. This is an international journal and not everyone knows exactly where the Netherlands coast is. The legend should define the dotted lines explicitly.

#76- The formation of the Waddensee was due to SLR following the end of the last glaciation, the current wording of this section fails to recognise that the whole history of the Waddensee has been of a dynamic equilibrium state.

There is a lot of ‘uniques’ here – the Waddensee is unique because of the size of the area – the habitats are not unique in of themselves. The sea level measurements are not unique – the UK sea level records are also a continuous series and longer. So a little more balance would be welcomed.

#187 – That the results are generic needs to be justified and explained not just made a sweeping statement.

Model description – it is difficult to judge but my sense is much of this has previously appeared and there is scope for it to be reduced leaving the interested reader to seek the detail via the cited literature.

#380 – This would seem to be an important point and as the authors are couching this in study in terms of the climate crisis to discuss the consequences of initiatives to limit and reverse SLR… so do we have centuries to mitigate and adapt?

Author Response

Thank you for reviewing our manuscript. Your comments really helped us improving the manuscript. Please find our response to each of your comments them in italic font.

General

The questions addressed are highly topical. But while the m/s starts with account of the ‘unique’ value of the Waddensee and the potential impact of sea level rise, the paper then becomes an exploration of the behaviour of a particular model, and the discussion does not really return to these issues.

Good point. This was because the application of the analysis to Dutch Wadden Sea is discussed just before the Concluding Discussion section. We have now added a paragraph in the Concluding Discussion summarizing that part.

Specific

#24-26 This sentence is difficult to follow – too many different equilibriums. I assume we are talking about ‘deeper than’ the original non-SLR (SLR – sea level rise) equilibrium, then developing to the new with SLR equilibrium.

This sentence is revised to “As sea-level rises, there is a lag in the morphological response, which means that the basin will be deeper than the systems morphological equilibrium. However, so long as the rate of sea-level rise is constant and below a critical limit, this offset becomes constant and a dynamic equilibrium is established.”

#30-32 ‘These insights..’ it is not clear what the insights are nor that they are inherently generic as opposed to a specific Waddensee phenomenon.

‘These insights’ is modified to ‘The insights from the present study’.

Figure 1. The legend says Waddensee but it is not deliminated or even labelled in any way on the image. The image covers an area much larger than what I would think of as the Waddensee. Please add your boundaries AND latitude and longitude marks to locate the region.

The Wadden Sea is the long and narrow stretch light colored area between the barrier islands and the mainland. This is added to the caption of the figure. The figure is revised by adding the latitude and longtitude marks.

Fig 2 – Some locating marks – lat and long, inset of showing relation of the Dutch Waddensee to the area shown in Fig 1 or the North Sea. This is an international journal and not everyone knows exactly where the Netherlands coast is. The legend should define the dotted lines explicitly.

The figure is revised by (1) adding the latitude and longtitude marks; (2) changing the legend for tidal divides to dotted line (was dashed, causing confusion); (3) added labels for North Sea; and Ëms estuary” (following the suggestion of Reviewer 3).

#76- The formation of the Waddensee was due to SLR following the end of the last glaciation, the current wording of this section fails to recognise that the whole history of the Waddensee has been of a dynamic equilibrium state.

We did not intend to indicate that the whole history of the Wadden Sea has been of a dynamic equilibrium, because we do not think that is the case. Van der Spek and Beets (1992) reported that the Wadden Sea has experienced periods of extension as well as of shrinkage depending on the SLR rate and the sediment supply. We have added the reference.

There is a lot of ‘uniques’ here – the Waddensee is unique because of the size of the area – the habitats are not unique in of themselves. The sea level measurements are not unique – the UK sea level records are also a continuous series and longer. So a little more balance would be welcomed.

The text is revised such that the word “unique” is omitted.

#187 – That the results are generic needs to be justified and explained not just made a sweeping statement.

As motivation of the statement added “when examined at the aggregated scale implicit in this type of model formulation.” to the text. Furthermore, we deleted “generic and” following the suggestion of Reviewer 3.

Model description – it is difficult to judge but my sense is much of this has previously appeared and there is scope for it to be reduced leaving the interested reader to seek the detail via the cited literature.

Yes, it is correct that the ASMITA model concept has been described in the literature. Therefore, the model description is limited to the necessary information for a single-element ASMITA model suitable for representing a tidal basin in the Wadden Sea. This succinct summary has not been given in previous publications concerning the ASMITA model.

#380 – This would seem to be an important point and as the authors are couching this in study in terms of the climate crisis to discuss the consequences of initiatives to limit and reverse SLR… so do we have centuries to mitigate and adapt?

Drowning of the tidal flats due to accelerated SLR is a long process. That means indeed that there is a long time available for mitigation and adaptation, although we cannot wait too long as significant loss of the ecological value will then be caused. Moreover, the slow process may also be dangerous if the urgency of the problem is not recognized.  We added a

“However, even though a slow drowning process implies no immediate morphological need for mitigation and adaptation, this does not reflect the ecological need and significant changes to the ecosystem may result from these pervasive morphological changes.”

Reviewer 2 Report

This paper utilizes a theoretical analysis of the underlying AMITA model to study the response of tidal inlets to SLR, with a focus on understanding thresholds of SLR rates that result in drowning of tidal inlets. This is an important topic and the information is in general clearly presented.

The underlying model and its description is mostly clear with the exception of the physical interpretation of n. A better description initially of how the power n relates to sediment fraction size and why this mathematical relationship accurately represents those physics would be helpful. This would be especially helpful in supporting the conclusions at the end of the paper in regards to sediment size. A great deal of time is spent discussing the importance of n in the model results/behavior, however, not enough time is spent understanding how it relates to the physical system (and how a manager might decide what an appropriate value might be). For something that is clearly very critical in the response of the system more details on its physical interpretation initially would be very helpful.

The abstract indicates that exceeding 80% of the critical SLR rate is some sort of threshold. As well as at line 326 there is an indication that r=0.6 is some sort of threshold. There is an inconsistency there and it is not inherently clear what these “thresholds” are based on. All the analysis shown has smoothly varying curves and while there are clear differences with different r values, what makes one a critical or threshold value is not clear. Is it based on some deviation from equilibrium depth or some change in the morphological time scale? Please clarify the basis of these identified thresholds!

Finally, it might be nice to discuss what some of these non-dimensional values might be for the inlets in question (are they clusterd in the parameter space?). Also what they are in realword dimensions! At the end you do discuss the real world values for critical sea level rise, and you allude to the fact that morphological time scales are quite long in other systems (San Pablo Bay). It leaves one wondering what are the time scales and equilibrium heights for the inlet systems that you use to motivate this work? It would be helpful to give the reader a better sense of the systems and what these percent changes in each value mean.

Smaller Q’s and comments

Why are no results shown for h(0)<1?

Line 362-363This sentence is unclear: This morphological timescale is  different to the one with respect to the morphological equilibrium (for R=0). 

Line 390: continued not continues

Although attractive Figure 9 is superfluous, no more info than in the table.

Author Response

Thank you for the useful comments which helped us to improve the manuscript. Please find our response to each of your comments them in italic font.

Comments and Suggestions for Authors

This paper utilizes a theoretical analysis of the underlying AMITA model to study the response of tidal inlets to SLR, with a focus on understanding thresholds of SLR rates that result in drowning of tidal inlets. This is an important topic and the information is in general clearly presented.

The underlying model and its description is mostly clear with the exception of the physical interpretation of n. A better description initially of how the power n relates to sediment fraction size and why this mathematical relationship accurately represents those physics would be helpful. This would be especially helpful in supporting the conclusions at the end of the paper in regards to sediment size. A great deal of time is spent discussing the importance of n in the model results/behavior, however, not enough time is spent understanding how it relates to the physical system (and how a manager might decide what an appropriate value might be). For something that is clearly very critical in the response of the system more details on its physical interpretation initially would be very helpful.

Agree. We added the explanation of the meaning of n and how it is related to sediment grain size.

The abstract indicates that exceeding 80% of the critical SLR rate is some sort of threshold. As well as at line 326 there is an indication that r=0.6 is some sort of threshold. There is an inconsistency there and it is not inherently clear what these “thresholds” are based on. All the analysis shown has smoothly varying curves and while there are clear differences with different r values, what makes one a critical or threshold value is not clear. Is it based on some deviation from equilibrium depth or some change in the morphological time scale? Please clarify the basis of these identified thresholds!

There are indeed two limits / critical levels. We revised the part about the 0.6 limit to make this clear.

Figures 4 and 7 suggest that that two indicative limits in the response of tidal basins to SLR can be identified. Below a value of r=0.6 the morphological timescale increases approximately linearly with increasing values of dimensionless SLR rate, r. In contrast, above a value of about r=0.8 the morphological timescale increases rapidly and non-linearly.  When r is above this limit, tidal basins will experience a long process of ‘drowning’. Finally, it might be nice to discuss what some of these non-dimensional values might be for the inlets in question (are they clustered in the parameter space?). Also what they are in realworld dimensions! At the end you do discuss the real world values for critical sea level rise, and you allude to the fact that morphological time scales are quite long in other systems (San Pablo Bay). It leaves one wondering what are the time scales and equilibrium heights for the inlet systems that you use to motivate this work? It would be helpful to give the reader a better sense of the systems and what these percent changes in each value mean.

The reason that we did not do this is because the issue about the morphological state of some of the tidal inlets is still under discussion in the Netherlands. However, we do agree that it is helpful to give them. Therefore we now included in Table 1 three more columns for the tidal range, the equilibrium depth and the time scale T for each of the basins.

Smaller Q’s and comments

Why are no results shown for h(0)<1?

Good question. The reason was that we only have cases with h(0)>1 in the Dutch Wadden Sea. However, we have changed one of the cases in each of the sub-plots so that h(0)<1 is captured in Fig. 6.

Line 362-363This sentence is unclear: This morphological timescale is  different to the one with respect to the morphological equilibrium (for R=0).

The sentence is revised to “This morphological timescale is different from the one with respect to the morphological equilibrium for R=0 ( i.e. no SLR).”.

Line 390: continued not continues

We meant “continuous”.

Although attractive Figure 9 is superfluous, no more info than in the table.

We agree that the figure essentially presents the same information as the table. We kept it as we think it will help the reader to understand the key message.

Reviewer 3 Report

The paper describes the important topic of tidal basin response to sea level rise using an equilibrium approach.  Overall, the paper is well written and extensively referenced.  It requires some additional description/ clarification and some minor grammatical changes. 

Fig 2, label Ems estuary Line 75, delete "ever" Line  96-97, change "the protection" to "protect" Line 163, change "suitable" to "suited" Line 177, delete "on" Line 182, change "is" to "are" Line 187, delete "generic and" Line 196, acts as "a" state Line 214, give a better definition, discussion of variable "n".  Letter you equate it to the ratio of the two time scales and relate it to gain size distribution.  Please discuss this when it is first defined. Line 226, also give more thorough explanation of the morphology time step. Lines 240-246, give the values of Rc, Hc, and T for Texel and explain how they were. Line 251, change Eq. 7 to Eq. 10 Table 1, explain constants  used to calculation Rc. Line 342, explain how you calculate that the time scales are very large. Line 358, it's not clear where the conclusion of less vulnerability is achieved with large range of grain sizes.   Line 362, change "take" to "takes" Line 364, change "different to" to "different from" Line 390, "continuous"

Author Response

Thank you for the thoughtful comments. Please find our responses below in italic fonts.

The paper describes the important topic of tidal basin response to sea level rise using an equilibrium approach.  Overall, the paper is well written and extensively referenced.  It requires some additional description/ clarification and some minor grammatical changes.

Fig 2, label Ems estuary Line 75, delete "ever" Line  96-97, change "the protection" to "protect" Line 163, change "suitable" to "suited" Line 177, delete "on" Line 182, change "is" to "are" Line 187, delete "generic and" Line 196, acts as "a" state

These suggestions are gratefully followed.

Line 214, give a better definition, discussion of variable "n".  Letter you equate it to the ratio of the two time scales and relate it to gain size distribution.  Please discuss this when it is first defined.

We added the explanation of the meaning of n and how it is related to sediment grain size.

Line 226, also give more thorough explanation of the morphology time step.

We added “The morphological time scale is the time needed for a small deviation from the morphological equilibrium to decrease by a factor e.”

Lines 240-246, give the values of Rc, Hc, and T for Texel and explain how they were.

The values for all basins are now added to Table 1.

Line 251, change Eq. 7 to Eq. 10

These suggestions are gratefully followed.

Table 1, explain constants  used to calculation Rc.

These are given in Wang et al. (2018), where a 3-elements model was used instead of the single element model. However, we added the properties needed to calculate Rc to the table.

Line 342, explain how you calculate that the time scales are very large.

We added the reference to Kragtwijk et al. (2004) in which the morphological time scales are calculated. Furthermore, we also added the calculated time scale T in Table 1.

Line 358, it's not clear where the conclusion of less vulnerability is achieved with large range of grain sizes.  

We added the sentence “Sediment composition varies within tidal basins: fine sediment being found on the flats and coarser fractions in the channels. In order to respond to sea level rise and maintain elevations relative to the tidal frame of reference, the sediment demand of these different zones needs to be met..”

Line 362, change "take" to "takes" Line 364, change "different to" to "different from" Line 390, "continuous"

These suggestions are gratefully followed.

Reviewer 4 Report

This an interesting paper, and as it applies to the Wadden Sea will be of relevance to many researchers in NW Europe. It builds on the idea that import of sediment in relation to rate of sea-level rise determines the drowning fate of such estuarine embayments. The paper implies that most morphodynamic models are inappropriate for such systems and quantifies ASMITA to address the case of different adjacent Wadden Sea tidal systems. It makes clear the significance of the availability of sediment and the nature of those sediments.

I consider the paper suitable for publication once some minor editorial and typographic issues have been addressed. I consider the word 'unique' over-used, and sugest it be reduced (e.g. line 87). Line 45 delete 'of' after comprise; line 53 - surely winds are defined by the direction FROM which they blow - if the wind is blowing to the east, it is a westerly wind. I had anticipated the tidal range would be stated at this point. Line 57 consists = consist; grain size rather than grainssize (see line 58). Line 91 have = has. Line 163 better = more. Line 336 insights in = insights into. Line 362 take = takes. Line 387 flats is = flats are; on long = in the long. Several references need editing, ie line 404, 495/6

Author Response

Thank you for the encouraging comments. Your suggestions are gratefully followed, see our responses in italic fonts.

This an interesting paper, and as it applies to the Wadden Sea will be of relevance to many researchers in NW Europe. It builds on the idea that import of sediment in relation to rate of sea-level rise determines the drowning fate of such estuarine embayments. The paper implies that most morphodynamic models are inappropriate for such systems and quantifies ASMITA to address the case of different adjacent Wadden Sea tidal systems. It makes clear the significance of the availability of sediment and the nature of those sediments.

I consider the paper suitable for publication once some minor editorial and typographic issues have been addressed.

I consider the word 'unique' over-used, and suggest it be reduced (e.g. line 87).

Also following the comments from the other reviewers we omitted the word “unique” in the revised text.

Line 45 delete 'of' after comprise;

done

line 53 - surely winds are defined by the direction FROM which they blow - if the wind is blowing to the east, it is a westerly wind. I had anticipated the tidal range would be stated at this point.

“difference in tidal amplitude between the neighboring inlets” is changed to “eastward increase of tidal amplitude”. “eastward wind direction” is changed to “westerly wind”. Tidal range is stated later in the text. 

Line 57 consists = consist; grain size rather than grainssize (see line 58).

Changed

Line 91 have = has.

Changed

Line 163 better = more.

Following the suggestion from Reviewer 3 “better suitable” to “better suited”.

Line 336 insights in = insights into.

Changed

Line 362 take = takes.

Changed

Line 387 flats is = flats are; on long = in the long.

Changed

Several references need editing, ie line 404, 495/6

Done.