Dear Referee,



thank you very much for taking the time to review our manuscript. We appreciate the effort you put into reading our preprint and providing constructive comments. Your feedback and suggestions are very valuable to us to improve the quality of our manuscript and our research. We are taking your comments seriously and will address each one of them comprehensively in our revised manuscript. We will especially try to emphasize the motivation and impact of our study and results. In the following we will address each of your comment with a reply and our planned action. If you have any additional insights or suggestions that you believe would further improve our research, please do not hesitate to share them with us. We look forward to sharing our revised manuscript with you soon.



Greetings from Hamburg

1. There are a couple of issues with the language of the manuscript, e.g., the use (or lack thereof) of definite/indefinite articles, wrong prepositions, wrong punctuation etc. In order to improve the quality of the language, please give the manuscript to a native speaker or send it to a language editing service.

Reply: Thank you for your feedback regarding the language of our manuscript. As none of us is a native speaker, we will send the revised version of the manuscript to a language editing service before resubmitting it.

Action: The manuscript will be sent to a language editing service.

1. LL13-15: “The results show an increase of tidal range in the Elbe estuary due to SLR and further reveal, that tidal flat growth can have no effect, decrease or increase the tidal range relative to sole SLR.”
   
   
   
   The way this is written, this almost sounds like a non-result. Please describe in more detail in the abstract, which of your investigated scenarios leads to which results.

Reply: Thank you for your comment, possibly the last part of the sentence addresses your concern. The full sentence in the abstract is the following:

LL13-15: “The results show an increase of tidal range in the Elbe estuary due to SLR and further reveal, that tidal flat growth can have no effect, decrease or increase the tidal range relative to sole SLR, depending on the location and amount of tidal flat elevation.”

As it seems to be written in a confusing way and less specific, we will rewrite it.

Action: we will change the sentence to:

LL13-15: “The results show an increase of tidal range in the Elbe estuary due to sole SLR and further reveal strongly varying changes due to tidal flat growth scenarios: While tidal flat elevation until the mouth of the estuary can cause tidal range to decrease, tidal flat elevation in the entire estuary can cause tidal range to increase relative to sole SLR.”

1. LL30-32: “However, facing the future acceleration of SLR, is difficult to quantify the amount to which tidal flat growth can keep pace with sea level rise, and it remains questionable, whether present hydromorphodynamic equilibrium will be maintained in the future.”
   
   
   
   Please give a reference for the future acceleration of SLR.

Action: We will add a reference:

LL30-32: “However, facing the future acceleration of SLR (Fox-Kemper et al., 2021), it is difficult to quantify the amount to which tidal flat growth can keep pace with sea level rise, and it remains questionable, whether present hydromorphodynamic equilibrium will be maintained in the future.”

1. LL48-49: “The Elbe estuary is the part of the Elbe river extending from the weir in Geesthacht to the North Sea (Figure 5).”
   
   
   
   Normally, the figure that is referenced first in your manuscript should be Figure 1. In my opinion, a map of the study area also makes sense as Figure 1.

Reply: Thank you for this comment, Figure 1 shows the two model domains and therefore includes the Elbe estuary. We don’t want to add another map of the Estuary, as we want to keep the manuscript as short as possible. To refer to Figure 1 first, we will change the previous sentence.

Action: We will change the previous sentence to:

LL47-49: One of the main estuaries in the German Bight is the Elbe estuary (Figure 1), which contains the port of Hamburg and is therefore an important shipping route. The Elbe estuary is the part of the Elbe river extending from the weir in Geesthacht to the North Sea (Figure 5).

1. LL56-57: “Nowadays the Elbe estuary is an amplified estuary, where the tidal amplitude increases in upstream direction and reaches its maximum close to the port of Hamburg.”
   
   
   
   Is “amplified estuary” a commonly used term? At least I haven’t stumbled upon this before. What you describe sounds like a “hypersynchronous estuary” to me (see Nichols and Biggs, 1985).

Reply: Thank you for your input. The term “amplified estuary” is used e.g. by Savenije (2012) and by van Rijn (2011). To me the term “amplified estuary” is more self-explanatory and comprehensible. I therefore would prefer to use it instead of “hypersynchronous estuary”.

Action: We would like to keep using the term “amplified estuary”.

1. LL60-61: “The future of the Elbe estuary depends not only on anthropogenic measures implemented on site, but also in particular on sea level rise and its implications.”
   
   
   
   Previously, you have already used the abbreviation SLR for sea level rise. Please use the abbreviation after defining it.

Action: We will change the sentence to:

LL60-61: “The future of the Elbe estuary depends not only on anthropogenic measures implemented on site, but also in particular on SLR and its implications.”

1. LL64-66: “Understanding the future evolution of tidal dynamics due to sea level rise in heavily utilised estuaries such as the Elbe estuary is important for the development of adaptation measures, e.g. in navigation, port infrastructure and water management.”
   
   
   
   As far as I understand, this is the main motivation of your study. Accordingly, you should dedicate more than one sentence to this. Please explain in more detail, what impacts might be expected in estuaries in response to SLR. And what processes might be triggered by an amplification of tidal range (e.g., see Winterwerp and Zhang, 2013)? And please also describe in more detail, what this will mean for the future management of the estuary. It might also be useful to briefly address the recent deepening of the Elbe in order to showcase the perspective of different stakeholders on the estuary and how they might be impacted by further developments in the future.

Reply: Thank you for the feedback. There is another sentence about the importance of tidal range in estuaries, which is part of the motivation of the study:

LL90-95: “Tidal range is the double of tidal amplitude and the difference between tidal high water and tidal low water. It is an integral part of the energy flux of a propagating tidal wave. Tidal range in estuaries is closely linked with tidal current velocity, mixing, circulation, sediment transport, water quality and ecosystem communities (Khojasteh et al., 2021). Additionally, it is a parameter which has an influence on navigation in and drainage into the estuary, as well as on the dimensioning of waterfront structures and other hydraulic structures in the estuary (HTG, 2020).”

However, we agree, that the motivation of the study should be discussed in more detail. We will add some sentences about the relevance of an amplification of tidal range and other possible SLR responses, which will give an idea of how many different stakeholders could be affected.

Action: following sentences will be added before line LL64-66:

“SLR will not only simply raise water levels in estuaries, but can also cause changes in the variations of water level. The increase in water levels can help deep-drafted vessels to navigate the estuary fairway, but, at the same time, can hinder ships to pass beneath bridges due to reduced clearance. Changes in low tide levels can lead to difficulties in drainage into the estuary and can therefore impact agriculture in the hinterland, navigation in connected channels and tributaries and urban drainage systems (Khojasteh et al., 2021). Changes in water level and variations of water level (low tide and high tide levels) are moreover relevant for the dimensioning of waterfront structures and other hydraulic structures in the estuary (HTG, 2020). Changes in water level and tidal range can furthermore change the inundation time of intertidal area and can increase or decrease the location and extension of intertidal area, which can impact biodiversity and agriculture.

Other possible SLR induced changes in tidal dynamics besides an increase or decrease of tidal range are, changes in current velocities and in tidal asymmetry and therefore e.g. enhanced flood dominance, which can cause an increase in sediment import. Increase of tidal range and tidal asymmetry can cause fine sediments to be pumped into the estuary, which can reduce hydraulic drag and in turn cause an increase in tidal amplification and eventually lead to a hyper-turbid-state (Winterwerp and Wang, 2013). Such changes in sediment dynamics can impact biodiversity and create economic challenges due to the siltation of navigation channels. SLR can also increase saltwater intrusion into an estuary due to an increase in tidal prism and water depth, which can affect e.g. ecosystems, aquifers and agriculture (Khojasteh et al., 2021). Understanding the future evolution of tidal dynamics due to SLR in heavily utilised estuaries such as the Elbe estuary is therefore important for the development of adaptation measures, e.g. in navigation, port infrastructure and water management.”

We will change the paragraph LL91-95 to:

Our objective is to investigate how tidal range along the Elbe estuary is influenced by potential future SLR and tidal flat growth scenarios. Tidal range is the double of tidal amplitude and the difference between tidal high water and tidal low water. It is an integral part of the energy flux of a propagating tidal wave. As mentioned before, it is a parameter which has an influence on navigation in the estuary and drainage into the estuary, as well as on the dimensioning of bank structures. Moreover, tidal range in estuaries is closely linked with tidal current velocity, mixing, circulation, sediment transport, water quality and ecosystem communities (Khojasteh et al., 2021). We therefore focus on this parameter, which is, compared to the other mentioned parameters, a highly reliable result of hydrodynamic numerical simulations.

1. LL136-137: “Sea level rise is added at the open boundary of the German Bight Model.”
   
   
   
   Why haven’t you added the sea level rise at the boundary of the Dutch continental shelf model? Isn’t the boundary of your German Bight model in areas, where tidal constituents will already be significantly impacted by SLR? Please discuss the effect of your assumption/simplification.

Reply: Thank you for your comment. As we add SLR at the open boundary of the German Bight model, SLR induced changes at the model boundary are neglected in our study. Previous research by Jordan et al. (2021) shows large-scale changes of the M2 amplitude in the North Sea due to SLR. Referring the results of Jordan et al. (2021) to our model boundary, we neglect changes of the M2 amplitude in the range of less than ±2 cm. Ideally SLR could be added at the boundary of the shelf model to consider changes in tidal dynamics in the continental shelf seaward of the German Bight Model boundary. However, this approach is not suitable in our case, since the resolution of the DCSMv6FM is insufficient for estimating SLR induced changes (Rasquin et al., 2020). In our opinion, further research is needed regarding the required resolution of a hydrodynamic numerical model when simulating the effect of SLR in the North Sea. Such a study would require several models with increasingly higher resolution, to determine a resolution condition after which SLR induced changes remain approximately the same. Furthermore, the aim of our study is to understand effects of SLR and tidal flat elevation on tidal dynamics in the Elbe estuary. Our results might show an incomplete picture of future changes due to SLR, as we neglect large scale changes arising in the North Sea. However, this deficiency can also be an advantage as helps to understand the distinct regional changes and therefore improve a system understanding.

Action: We will add the following sentences after the line LL136-137 to explain why we added SLR at the German Bight model boundary:

“Sea level rise is added at the open boundary of the German Bight Model, therefore SLR induced changes in tidal dynamics seaward of the German Bight are neglected. Ideally SLR could be added at the boundary of the shelf model to consider changes in tidal dynamics in the continental shelf seaward of the German Bight Model boundary. However, this approach is not suitable in our case, since the resolution of the DCSM is insufficient for estimating SLR induced changes (Rasquin et al., 2020).”

We will also add the following sentences in the discussion to discuss the effect of our simplification:

In our study, SLR induced changes in tidal dynamics seaward of the German Bight model are neglected. Previous research by Jordan et al. (2021) shows large-scale changes of the M2 amplitude in the North Sea due to SLR. Referring the results of Jordan et al. (2021) to our model boundary, we neglect changes of the M2 amplitude in the range of less than ±2 cm. However, we assume the neglection of the changes at the German Bight model boundary not to be of importance for the key results of our study, which aims to improve the system understanding of SLR and tidal flat growth induced changes in the Elbe estuary.”

1. Figure 1.
   
   
   
   Please use a different colourbar for the left panel. When showing the European Continental Shelf with water depths of several thousand meters, it doesn’t make sense to limit your colourbar to 37.5 m. Furthermore, when using different panels, they should be labelled by using (a), (b), (c), etc. This also applies to most of your other figures.

Reply: You are right. We will gladly implement your comment.

Action: We will add panel labels and will replace the figure of the DCSMv6FM Model with a figure with better colourbar.

1. Figure 2.
   
   
   
   Why are only three days shown here? Why isn’t a whole spring-neap cycle shown? Is the performance of the model better/worse during different phases of the spring-neap cycle? Even though you mention that the validation of the model is presented in another paper, it also wouldn't hurt to briefly describe the model quality here in terms of selected parameters (e.g., what is the mean RMSE across all tide gauges in the model domain).

Reply: We decided to show only three days, because the differences in the shape of the curves would not be clearly visible otherwise. However, as you mentioned, it could be of interest to see an entire spring-neap-cycle and possible variations in the performance. Therefore, we will add two figures of an entire spring-neap cycle in the appendix. We will also add information about the mean RMSE, BIAS and a skill-score after Willmott et al. (1985) of 39 tide gauges in the model domain.



Action:

Figures of an entire spring-neap cycle will be added to the appendix.

We will add the following sentence after LL156:

“A similar display for an entire spring-neap-cycle can be found in the appendix. It shows no distinctive differences in the performance during different phases of the displayed spring-neap cycle.”

We will add the following sentence before LL150:

“To compare the simulation results with observations, we simulated seven spring-neap-cycles between January and April 2013 with measured river discharge provided by the Federal Waterways and Shipping Agency (WSV, 2022). The comparison of water level between model results and observations at 39 gauges in the model domain for this period reveals a mean RMSE of 16.4 cm, a mean bias of 7.3 cm and a mean skill-score after Willmott et al. (1985) of 0.993. Further analysis on model performance can be found in Rasquin et al. (2020). Since the focus of our study is on the Elbe estuary, a brief validation of the model in this specific region is presented below.”

1. Figure 3.
   
   
   
   Apparently, the dashed-lines indicate certain cross-sections along the estuary that are shown in Figure 5. This should be explained. For readers not being too familiar with the Elbe Estuary, it could also help to use labels that highlight the location of the different sections along the river (e.g., “outer section”, “mouth section”, etc.).

Reply: I am not sure, if I understand your comment correctly. I think such labels are already displayed in most of the figures. However, they are not yet displayed in Figure 3, as the subdivision into sections is explained afterwards in 2.3.1: “[…]. Furthermore, the estuary is roughly divided into five sections, which are displayed in Figure 5 and named (from west to east): outer section, mouth section, lower section, Hamburg section and upper section.” We will also add such labels in Figure 3.

Action: Labels for the subsections will be added in Figure 3.

1. LL320-323: “The scenarios with SLR of 55 cm are not visualised and analysed in detail.”
   
   
   
   Even if the scenarios with a SLR are not visualized in detail, they should nevertheless be described/discussed in a little more detail. Otherwise, one might ask the question, why you mention the scenarios with a SLR of 55 cm at all?

Reply: Thank you for your comment. We have chosen not to visualise and describe the scenarios of SLR 55 cm in detail, as that would have strongly expanded the length of the manuscript. However, we wanted to determine, if the changes due to SLR are in principle similar for a different SLR scenario. Therefore, we show a comparison of the change of max. TR relative to reference condition for the two SLR scenarios in Table 2. The focus of this study lies on the interrelation between SLR, changes in estuarine geometry and changes in tidal dynamics. As we write in the discussion: “[…]TR shows qualitatively similar changes in the scenarios with SLR of 55 cm, those are assumingly induced by similar alterations in estuarine geometry as for a SLR of 110 cm.” We are planning to further examine the different changes due to varying SLR scenarios in future studies. We will add some more sentences regarding the SLR55 scenarios in the results part.

Action: We will edit the following parts:

LL320 following: “Hereinafter we focus on the results of the scenarios with 110 cm SLR to gain a better system understanding. The scenarios with SLR of 55 cm are not visualised and analysed in detail, but are included to determine whether the changes due to SLR are in principle similar for a different SLR scenario.”

LL336 following: “For all scenarios, the maximum value of TR along the estuary is reached in the Hamburg section. Table 2 lists the changes in max. TR relative to reference condition (max. TR = 3.87 m) for all simulated scenarios with SLR 110 cm as well as SLR 55 cm. Max. TR increases by 6.5 cm for a SLR of 55 cm and by 12.5 cm for a SLR of 110 cm, which is about 11-12% of the respective SLR. Both SLR-scenarios with 100% tidal flat elevation in scenario A (slr55t55 and slr110t110), show an increase in max. TR less than with sole SLR, while both SLR-scenarios with 100% tidal flat elevation in scenario B (slr55t55e and slr110t110e), show an increase in max. TR greater than without tidal flat elevation.

LL441 following: “As a simple explanation for these various changes of  TR in the different simulated scenarios is not apparent at first glance, changes of estuarine geometry are analysed to derive explanatory approaches. The analysis is conducted for the reference condition and all scenarios with 110 cm SLR. As shown in Table 2, max. TR shows qualitatively similar changes in the scenarios with SLR of 55 cm. It can therefore be assumed, that those changes are induced by similar alterations in estuarine geometry as for a SLR of 110 cm.

We will add in the discussion: “ We selected the SLR scenario of 110 cm with corresponding hypothetical tidal flat elevation scenarios which we analysed in detail. For scenarios with 55 cm SLR we found qualitatively similar changes in max. TR and therefore assume similar alterations in estuarine geometry. However, to ensure that our results are in principle applicable to other SLR scenarios than 110 cm, it would be necessary to simulate a range of several SLR scenarios and their corresponding tidal flat growth scenarios and analyse the changes of tidal dynamics and estuarine geometry for each of them.”

1. Figure 8.
   
   
   
   I first had to take a closer look at Figure 5 to understand why there are so few markers in the "Hamburg section". In my opinion, it would help to explain that the whole city of Hamburg is considered as one control volume (thus being relatively large in comparison to neighbouring control volumes).

Reply: We will add a sentence to explain the large control volume containing the two branches of the Elbe estuary in the region of Hamburg.

Action: the following sentence will be added after LL196:

“As the Elbe estuary splits into two branches, which reunite again close to the port of Hamburg and enclose the island of Wilhelmsburg, this region is contained in one relatively large control volume compared to the other control volumes.”

1. L367: “To access the rate at which cross-sectional-flow-area of an estuary decreases in upstream direction, the geometric parameter convergence length (L_a) is calculated by fitting an exponential function (Eq. (2)) to the data sets (see 2.3.3).”
   
   
   
   Do you really mean “to access” or should it be “to assess”?

Reply: Thank you for the note. We mean “to assess” not “to access”. We will correct the term in L367 as well as in L99 and we will send the manuscript to a language editing service.

Action: we will correct L367 and L99 accordingly.

1. Table 3.
   
   
   
   I don't quite understand, why you compare scenario “slr110t0” to your reference scenario and all other scenarios to “slr110t0”? Why not comparing all scenarios to the reference scenario? Otherwise one might ask, why you don't show all the possible scenario combinations (e.g., “slr110t110e” to “slr110t55e”, etc.)? Due to the presented changes in A₀ and L_a, it should still be possible to see that the differences between certain scenarios are negligible (e.g., “slr110t110e” to “slr110t0”).

Reply: Thank you for your comment. Initially we decided not to show all comparisons of all possible combinations of scenarios to keep the manuscript short and clear. In the discussion part (4.4) we try to answer the following three questions:

1. Why does sole SLR without topographic changes causes tidal range to increase in the Elbe estuary?

2.Why does SLR with tidal flat elevation in the mouth of the estuary causes no changes or a decrease in tidal range compared to sole SLR?

3. Why does SLR with tidal flat elevation in the entire estuary increases tidal range compared to sole SLR?

As these are the main questions we want to answer, we choose the combinations accordingly in the analysis of the differences in convergence length. However, after thinking about your and the other referees comment, we decided to additionally show the combination of all scenarios to reference condition.

We decided to change the paragraph LL375following.

Action: We extent Table 3 in the following way:

Action: We will change paragraph LL375ff in the following or similar way:

“The derived convergence length (La) of the Elbe estuary for the mean cross-sectional-flow area (A) of the spring-neap-cycle is 46.3 km in the reference condition and 41.4 km in the scenario slr110t0. Depending on the p-value for the difference of La between two scenarios, the null hypothesis of no change in convergence length La can, or cannot be rejected. We decided to consider a significance level of α=0.1. For the difference between La of scenarios slr110t0-ref the null hypothesis can be rejected. The detected significant decrease of La indicates a stronger convergence, hence a stronger rate of decrease of A in upstream direction due to SLR of 110 cm. The results further show, that in scenario slr110t110, convergence is significantly weakened compared to scenario slr110t0 and not significantly different compared to the reference scenario. For the difference between the scenarios slr110t55-ref we detect a significant decrease in La and hence a stronger convergence. For the scenarios slr110t55 and slr110t110e we cannot detect a significant change of La relative to the reference scenario nor to slr110t0. However, the results for La and their p-values indicate that La of slr110t110e is is larger than for slr110t0 and very similar to the reference condition while La for slr110t55 is similar to slr110t0.”

1. Figures 9 & 10.
   
   
   
   It is not described, what the different lines represent. I presume it is the mean of all control volumes in a section, right?

Reply: Thank you for your comment. Yes, the markers represent the value of each control volume, while the lines represent the mean values of the sections.

Action: we will change the Figure description in the following way:

Figure 9: Relative change of mean hydraulic depth (ht top and hc bottom) in each control volume (markers) and each section (lines) relative to reference condition for scenario slr110t0 (dark blue rhombuses), slr110t110 (light blue squares), slr110t110e (green triangles). (The results of scenarios slr110t55 and slr110t55e are not shown in the figure for better readability)

Figure 10: Relative intertidal area (top) and relative change in relative intertidal area (bottom) in each control volume (markers) and section (lines) along the estuary for scenario ref (black circles), slr110t0 (dark blue rhombuses), slr110t110 (light blue squares), slr110t110e (green triangles). (The results of scenarios slr110t55 and slr110t55e are not shown in the figure for better readability)

1. Figures 11 & 12.
   
   
   
   You use different types of lines and colours in these figures, which are not explained. In Figure 12, it also isn’t mentioned, what S_INT’ and MW’ stand for.

Reply: We will add a better Figure description; however, S_INT and MW are already defined in section 2.3.

Action: We will change the figure description in the following way:

Figure 11: Schematic display of SLR in estuary cross-sections (left) and schematic plan view of an estuary (right). For two cross-sections with large (1) and small (2) S_INT. The cross-sections show the MW as black lines for a reference scenario (dark blue), and two SLR scenarios (light blue and light green).

Figure 12: Schematic display of SLR in estuary cross-sections and its resulting change in intertidal area (S_INT) for different topographic gradients between high water (HW) and low water (LW). The left side of the figure shows a low gradient, while the right side shows a higher gradient. The black lines correspond to the MW for the reference condition (dark blue) and SLR (light blue). All parameters with an apostrophe belong to the scenario with SLR. The dashed grey lines are showing HW and LW for both scenarios, while the coloured dotted lines show S_HW and S_LW.

References

Fox-Kemper, B., Hewitt, H. T., Xiao, C., Aðalgeirsdóttir, G., Drijfhout, S. S., Edwards, T. L., Golledge, N. R., Hemer, M., Kopp, R. E., Krinner, G., Mix, A., Notz, D., Nowicki, S., Nurhati, I. S., Ruiz, L., Sallée, J.-B., Slangen, A., and Yu, Y.: Ocean, Cryosphere and Sea Level Change., In Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, 6, S.1211-1362, doi:10.1017/9781009157896.011., 2021.

HTG: Empfehlungen des Arbeitsausschusses "Ufereinfassungen" Häfen und Wasserstraßen EAU 2020: (inkl. E-Book als PDF), 12. Auflage, Ernst Wilhelm & Sohn, Berlin, 700 pp., 2020.

Jordan, C., Visscher, J., and Schlurmann, T.: Projected Responses of Tidal Dynamics in the North Sea to Sea-Level Rise and Morphological Changes in the Wadden Sea, Front. Mar. Sci., 8, 40171, doi:10.3389/fmars.2021.685758, 2021.

Khojasteh, D., Glamore, W., Heimhuber, V., and Felder, S.: Sea level rise impacts on estuarine dynamics: A review, The Science of the total environment, 780, 146470, doi:10.1016/j.scitotenv.2021.146470, 2021.

Savenije, H. H. G.: Salinity and Tides in Alluvial Estuaries: Second Completely Revised Edition, 2.6th ed., 2012.

van Rijn, L. C.: Principles of fluid flow and surface waves in rivers, estuaries, seas, and oceans, Edition 2011, Aqua Publications, Amsterdam, 2011.

Willmott, C. J., Ackleson, S. G., Davis, R. E., Feddema, J. J., Klink, K. M., Legates, D. R., O'Donnell, J., and Rowe, C. M.: Statistics for the evaluation and comparison of models, J. Geophys. Res., 90, 8995, doi:10.1029/JC090iC05p08995, 1985.

Winterwerp, J. C. and Wang, Z. B.: Man-induced regime shifts in small estuaries—I: theory, Ocean Dynamics, 63, 1279–1292, doi:10.1007/s10236-013-0662-9, 2013.

Dear Referee,

as we had some problems with the formatting of our reply, please find attached our answers in a document.

Kind regards

Tara Mahavadi

Dear Referee,



thank you very much for your kind and encouraging words. We appreciate the time and effort you put into reading our preprint and providing constructive comments. Your feedback and suggestions are very valuable to us for improving the quality of our manuscript and our research. We will comprehensively incorporate all of your feedback in our revised manuscript. In the following we address each of your comment with a reply and/or our planned action. If you have any additional insights or suggestions that you believe would further improve our research, please do not hesitate to share them with us. We look forward to sharing our revised manuscript with you soon. As you had a lot of suggestions referring to the discussion part, we will put a first draft of a revised discussion chapter as a supplement.



Greetings from Hamburg

Line 20-21: Add citation(s) to support the sentence. Also, might be worth adding some examples of how SLR would affect tidal dynamics (you can just use the e.g. format and add short examples).

Action: We will change the sentence in the following way:

“Future global mean sea level rise (SLR), as it is projected for this century (Fox-Kemper et al., 2021), will not only raise water levels in the German Bight, but will also affect, for example, tidal dynamics (e.g. tidal amplitude and tidal asymmetry) in several ways (Wachler et al., 2020; Jordan et al., 2021).”

Line 23-25: Add citation.

Action: We will change the sentence in the following way:

“The Wadden Sea is a geological and ecological unique region, structured into several tidal basins with barrier islands, tidal channels and intertidal areas (Kloepper et al., 2017).”

Line 30: “…SLR, it is…”

Action: We will change the sentence as suggested:

“However, facing the future acceleration of SLR, it is difficult to quantify the amount to which tidal flat growth can keep pace with sea level rise, and it remains questionable, whether present hydromorphodynamic equilibrium will be maintained in the future.”

Line 35: “..other factors (e.g. vertical…)”

Action: We will change the sentence as suggested:

“A precise prediction of the future morphologic development of the Wadden Sea is difficult, as it does not only depend on the rate of SLR, but on several other factors (e.g. vertical sediment structure, sediment availability and potentially changing meteorology).”

Line 39: Remove “In any case”, as it makes what is said before is redundant. Also, add a space before.

Action: We will change the sentence as suggested:

“Potential tidal flat growth should be considered when studying SLR-scenarios, as it strongly affects tidal dynamics in the Wadden Sea (Wachler et al., 2020; Jordan et al., 2021).”

Line 78-79: Remove the parenthesis from the citation.

Action: We will change the sentence as suggested:

“The importance of accurate representation of bathymetry in numerical models of shallow coastal systems, is pointed out by Holleman and Stacey (2014) and Rasquin et al. (2020)”

Line 79: “Rasquin et al. (2020) found that insufficient bathymetric resolution may lead to overestimation of the tidal amplitude increase in the German Bight.”

Action: We will change the sentence as suggested:

“Rasquin et al. (2020) found that insufficient bathymetric resolution may lead to overestimation of the tidal amplitude increase in the German Bight.”

Line 90 – 100: There are two aims written down. Choose one and properly narrow the problem definition towards it. Consequently, change or adapt throughout the text (e.g. first line of the conclusion).

Lines 98-104: These lines are kind of doubled in the methods. Remove bits that do not add to the problem setting that is the main focus of the introduction.

Reply: Thank you for your comments. As you pointed out, there are two research question addressed in our study: To analyse the influence of SLR and tidal flat growth scenarios on tidal range in the Elbe estuary and to explain these changes with changes in estuarine geometry. However, the general aim is to gain a better understanding of the possible effects of potential SLR and tidal flat growth scenarios in the Elbe estuary. We will rewrite this part and reduce the sentences which are addressing the methods.

Action: We will change the sentences in the following or a similar way:

“In our study potential future sea level rise and tidal flat growth scenarios are simulated using a hydrodynamic-numerical model. The two issues we want to address in our study are the following: 1. How tidal range along the Elbe estuary is influenced by potential future SLR and tidal flat growth scenarios and 2. How these changes can be explained by changes in estuarine geometry. The general aim of this study is to gain a better understanding of the possible effects by potential SLR and tidal flat growth scenarios in the Elbe estuary.

Tidal range is the double of tidal amplitude and the difference between tidal high water and tidal low water. It is an integral part of the energy flux of a propagating tidal wave. As mentioned before, it is a parameter which has an influence on navigation in the estuary and drainage into the estuary, as well as on the dimensioning of bank structures. Moreover, tidal range in estuaries is closely linked with tidal current velocity, mixing, circulation, sediment transport, water quality and ecosystem communities (Khojasteh et al., 2021). We therefore focus on this parameter, which is, compared to the other mentioned parameters, a highly reliable result of hydrodynamic numerical simulations.

To find explanatory approaches for the changes in tidal range simulated by our hydrodynamic-numerical model, we analyse three parameters of estuarine geometry (mean hydraulic depth, convergence of cross-sectional flow area and relative intertidal area). These geometric parameters, which describe the shape of the estuary in a simplified way, are (equally or in similar form) known from previously mentioned analytical models.”

Line 120: Fix citation

Action: We will change the sentence in the following way:

“The variation of the surface drag coefficient with wind speed is parametrised according to Smith and Banke (1975).”

Line 127: Here it implies that you have fixed layers in the vertical, correct?

Reply: Yes, our model has fixed vertical layers.

Action: To clarify this fact, we will change Line 127-128: “The model has vertically fixed layers with resolution of 1 m to a depth of 27.5 m and 10 m below that.”

Line 132-133: Add the source of these values for the boundaries

Reply: Thank you for your comment. I believe you are referring to the sentence: “Salinity is set to a constant value of 33 PSU at the open boundary and 0.4 PSU at the upstream boundary of the Elbe estuary.” We decided to uses these constant values for the salinity at the boundaries as a simplified assumption. We will cite two sources those assumption are based on.

Action: We will change the sentence in the following way:

“Salinity is set to a constant value of 33 PSU at the open boundary (based on BSH (2016)) and 0.4 PSU at the upstream boundary of the Elbe estuary (based on Bergemann (2009)).”

Figure 1: Re-export the Figure with thicker lines on the box and labels, it is very hard to read. Also, perhaps consider increasing (or changing) the font if thickening the lines does not improve considerably. Check other Figures for this correction as well (e.g. Figure 5).

Reply: Thank you for the remark, we will improve the figures 1 and 5 for the revised manuscript.

Action: Figures 1 and 5 will be improved with thicker lines and fonts.

Figure 2: Consider adding either a line with the residuals or a zoomed box to one tidal cycle only, where we can properly see the behaviour of sim x obs. Also, would be nice if you quantify the performance of the validation (quantification goes for Figure 3 as well).

Reply: Thank you for the remark. We got a similar comment on the validation from the other referee and will therefore add information about the mean RMSE, BIAS and a skill-score after Willmott et al. (1985) for the water level of 39 tide gauges in the model domain. We will consider adding residuals in Figure 2. To address your recommendation on the quantification of validation for figure 3, we will add RMSE and bias for tidal range and tidal mean water of the displayed gauges in Figure 3.

Actions:

- We will add the following sentence regarding the quantification of Figure 2:

“The comparison of water level between model results and observations at 39 gauges in the model domain for this period reveals a mean RMSE of 16.4 cm, a mean bias of 7.3 cm and a mean skill-score after Willmott et al. (1985) of 0.993.”

- We will add residuals or a zoom in Figure 2.

- We will add the information about RMSE and bias for tidal range and tidal mean water of

the displayed gauges in Figure 3.

Line 274: Remove “see”

Action: We will change the sentence as suggested:

“The depth over an estuary cross-section (Figure 6) can be highly variable due to deep channels and shallow intertidal areas.”

Line 275: Remove “as discussed by”

Action: We will change the sentence as suggested:

“Mean hydraulic depth of an estuary can be defined and calculated in several ways (Zhou et al., 2018).”

Line 317: Not necessarily in this line, but I miss a study area subtopic. It does not need to be large, but it is focused on the Elbe and German Bight, so it would be interesting for readers that are not familiar with the area to get a bit of general overview (it does not need to be large, and you can take some parts from the introduction if needed).

Reply: Thank you for the recommendation. We have a paragraph about the study area in the Introduction (LL47-58). We could possibly add a few lines in section 2.3.1.

Action: We will add the following sentences in the beginning of section 2.3.1:

“Our focus area is the Elbe estuary, which is the tidally influenced part of the river Elbe extending from the weir in Geesthacht to the North Sea (Figure 5). The weir in Geesthacht is the artificial tidal barrier of the estuary. The Estuary splits into two branches and reunites close to the port of Hamburg (Figure5). To allow large container ships to reach Hamburg, an artificially deepened fairway is maintained until the port. The part of the estuary upstream of Hamburg until the city Brunsbüttel includes intertidal areas, several islands and is connected to several small tributaries (Figure 5). Upstream of the city Brunsbüttel until Cuxhaven lies the dilating mouth of the estuary with large intertidal areas interfused by several smaller and larger channels.”

To avoid doubling, we will check if the introduction can be shortened regarding this topic.

Line 320: “In Figure 7, tidal…”

Action: We will add the comma.

Line 322-323: Rephrase (or remove). The way it is written can be interpreted as the authors did not look into it in detail, whereas the authors mean that it is not being presented in detail, as you are focusing only on one scenario for better system understanding.

Action: We will change the sentence in the following way:

“Hereinafter we focus on the results of the scenarios with 110 cm SLR to gain a better system understanding. The results of the scenarios with SLR of 55 cm are not shown here in detail, but still included to determine whether the changes due to SLR are in principle similar for a different SLR scenario.”

Line 350-354: I am not sure if I understood the message you tried to convey here. If it is to pave the way to further explain patterns found in TR in the following subtopic, it would be important to be more specific (e.g. cite defined examples instead of loose definitions like “some scenarios”, or “other scenarios”). I would encourage the authors to be specific here. Nonetheless, if that is the goal, one would expect that the next subtopic would continue from where you stopped here, trying to explain such patterns, which is not what happens.

Reply: Thank you for your comment. We wrote these sentences as a transition between the subtopic of tidal range to the subtopic of estuarine geometry. As it seems to be confusing and unnecessary, we will remove this part.

Action: We will remove these sentences.

Line 357: Remove “in the figure”.

Action: We will change the sentence as suggested:

“For better readability, the results of scenarios slr110t55 and slr110t55e are not shown.”

Line 366-370: Perhaps consider moving this part to the method section, so here we only focus on the results themselves.

Reply: This part is meant to be a short repeat of the methods for this section. A detailed description can be already found in the method section. We will shorten this part in the result section.

Action: We will shorten the paragraph in the following way:

“The geometric parameter convergence length (La) is calculated by fitting an exponential function (Eq. (2)) to the data sets (see 2.3.3). To evaluate, if La significantly changes between two scenarios a multiple regression is performed. The results of the weighted multiple non-linear least square regression are displayed in Table 3.”

Line 379: correct the value of alpha.

Line 382: What is the rationale used for changing the alpha from 0.05 to 0.1 when comparing scenario slr110t110 and slr100t0? I would expect consistency between the alphas.

Reply: Thank you for your remark. You are right, there is no reason to mention two different alphas. We will change the text and only use alpha=0.1.

Action: We will change the text and use alpha=0.1 consistently

Tables 4 and 5: As you present the mean, add also some estimates for data spread (e.g. std or Qt).

Reply: Thank you for your recommendation. We will add the standard deviation for each value in tables 4 and 5.

Action: We will add the standard deviation in tables 4 and 5:

Table 4: Mean hydraulic depth of the entire cross-section (h_t) and of the channel (h_c) in the Elbe estuary in m

Table 5:  in the Elbe estuary

Figure 8: For readability, change the numbers on the y-axis.

Action: we will change the numbers from e.g. 8e+04 to 80000

Lines 385 – 420: When showing and discussing the data for Figures 8 and 9, the authors are focusing only on the mean values. While I understand and agree with this approach as a first, the authors should also discuss the spread of the data here, as looking only at the mean can be misleading. For example, the relative change in ht in the mouth section has a mean close to zero for slr100t0, but the data has two main components, being higher closer to the mouth with a sharp decrease towards the lower section. The lower section, even though without a pattern, also shows a very large spread. The same holds for the relative intertidal area, where the spread is very visible, and should be quantified and presented here in the results (and it must be discussed in the discussion as well).

Reply: Thank you for the feedback. We agree that the spread of data needs to be described in the results and discussed in the discussion. We will discuss the reasons for the data spread and if there are distinguishable changes between the scenarios despite the data spread.

Action: We will change some sentences in the discussion chapter, which can be found at the end of our answers to you. We will also change the following paragraphs in the result section:

LL399following:

“The results indicate, that SLR of 110 cm (slr110t0) does not in general cause an increase in mean hydraulic depth along the estuary. As shown in Figure 9, the relative change of ht and hc is strongly scattering with an increase in some control volumes and a decrease in others. In the mouth section ht increases upstream of km 20 and decreases downstream. Averaged over sections, slr110t0 causes no distinct changes of ht in the mouth section, and lower section and an increase in the Hamburg section and the upper section. In scenarios slr11t110 and slr110t110e mean hydraulic depth clearly increases in the regions where tidal flats are elevated and scattering is reduced in these regions. The changes of hc are qualitatively similar to ht. Mean hydraulic depth excluding intertidal area (hc) shows a stronger decrease due to sole SLR and in the mouth section.”

LL416following:

“ϙ𝑆_𝐼𝑁𝑇 as well as the change of ϙ𝑆_𝐼𝑁𝑇 strongly varies between the control volumes along the estuary. Due to SLR of 110 cm (slr110t0) ϙ𝑆_𝐼𝑁𝑇 is decreased in the largest part of the mouth section (downstream km 25) and mostly increased in the lower section (downstream of km 85) and in the upper section. Tidal flat elevation counteracts the changes of SLR in the sections where tidal flats are elevated (mouth section and lower section) and results in a ϙ𝑆_𝐼𝑁𝑇  close to the reference scenario for these sections”.

Lines 423-435: This might be more on style, but this chunk of text is just repeating what has been said. The subtitle suggests that you would discuss the limitation, but rather most of what is written has been said elsewhere in the paper. So, I would rather discuss the limitations or just erase this part and go directly to the main discussion.

Reply: Thank you for your recommendation, we will remove the sentences which are repeating the methods and aim of the study. We will only talk about the limitation and move this part to the end of the discussion. 

Action: As you had a lot of suggestions referring to the discussion part, we will put a first draft of a revised discussion chapter as a supplement.

Lines 437-445: Consider removing or considerably reducing this. It does not add anything new and also does not help the reader follow your thoughts. In these lines, you just re-interact what you said in the results, without discussing anything on TR (which you only do later on page 22). One suggestion would be to remove the 4.1 and 4.2 subtopics, write one introduction sentence for the discussion instead and properly start from 4.3 onwards.

Reply: Thank you for your suggestion. We will revise the structure of the discussion chapter accordingly. Please find a first draft of the revised discussion chapter as supplement.

Line 460: Add space before “This”.

Action: We added a space.

Line 460: Do you have a hypothesis of why Tidal flat elevation counteracts the effect in scenario slr110t110?

Reply: Yes, tidal flat elevation causes a decrease in cross-sectional-flow area in the regions of elevation. Therefore, an elevation of tidal flats in the mouth but not further upstream, can cause a weaker overall convergence of the estuary.

Action: We will change the sentence in the following way:

“Tidal flat elevation decreases A regionally and seems to significantly counteract SLR induced changes of the convergence in scenario slr110t110, but not in the other scenarios.”Line 471-473: Would be interesting to add in the text what exactly it means physically instead of only the citation as it is an important part of your discussion. You can add one sentence from the same reference from Friedrichs et. al. (1990) explaining (i.e. what does it mean physically for previous channels to be part of the wider channel after SLR?). It can help the reader follow your thoughts here.

Reply: Thank you for the comment, unfortunately I am not sure if I understand it correctly. We will add two sentences to explain the statement in Line 471-473.

Action: We will add the following sentences:

“A decrease of hc due to SLR can be explained by shallow areas next to the previous channels becoming part of the now wider channel (Friedrichs et al.,1990). Due to SLR some previously intertidal areas next to the channel become subtidal areas and therefore part of the channel (Figure 12). The relatively small water depth over this new part of the channel will cause a decrease in hydraulic depth averaged over the channel cross-section. A decrease of ht can be in addition explained by shallow previous supratidal areas becoming intertidal areas (see Figure 12).”

Line 479: Remove this sentence as it is re-stating what is in the method.

Action: We will remove the sentence.

Line 486: Add: “Our results suggest that sea level…”. Or, a suggestion for rephrasing would be something like: “Our results suggest that changes in Sint on SLR scenarios depend on the local topographic gradient above LW and a potential change in TR.” (So to remove the SLR as the subject considering the conclusion of the sentence).

Action: we will rewrite the sentence in the following way:

“Our results suggest that Sea level rise can in general cause an increase, decrease, or no change in S_INT, depending on the local topographic gradient above LW and a potential change in TR (see Figure 12).”

Line 523-525: I am not sure if I follow the rationale here. For example, slr110t55 and slr110t55e have different behaviours in terms of TR. The authors argue that the main reason for both is the increase in mean hydraulic depth (lines 515 and 525). For the first, it compensates for the increase in Sint, whereas for the second, it follows the decrease in Sint. Considering that for both an increase in mean hydraulic depth is seen (despite different behaviours on TR), why would the main reason for the increase in TR in these scenarios be the change in mean hydraulic depth? Perhaps is a matter of wording (the use of “main reason” may mislead the reader). Also, the authors mention that no significant change in convergence is detected (line 523) but later state that convergence is increased in these scenarios (line 526).

Reply: Thank you for your comment. In scenarios slr110t55 and slr110t110 tidal flats are elevated only in the estuary mouth which causes mean hydraulic depth to increase in the mouth. Whereas in scenario slr110t55e and slr110t110e tidal flats are elevated in the mouth and lower section of the estuary, which causes mean hydraulic depth to increase in both of these sections. This means that in scenario slr110t55e and slr110t110e mean hydraulic depth increases in a much larger part of the estuary and therefore most likely has a much stronger effect on TR. Additionally the changes in Sint might compensate the effects of changed mean hydraulic depth in the mouth in slr110t55 and slr110t110, but might increase them in the lower section in slr110t110e.

We cannot for sure say, which is the main reason for the different behaviours in TR but we assume that it is the increase in mean hydraulic depth in a much larger part of the estuary. The reason for our assumption is, that the decrease of Sint in the lower section is notable in slr110t110e but very small in slr110t55e.

Regarding the changes in convergence we were reffering to a change relative to slr110t0 in line 523, but to a change relative to reference condition in line 526. We now realise that we were not fully accurate and clear in those sentences. Also, we will show and discuss additional combinations of scenarios in the results and discussion part, following a suggestion of the first referee. We will revise the discussion part and you can find a first draft of the revised chapter in the appendix.

Action: A first draft of the revised discussion chapter can be found as appendix.

Line 530: As a reader, I was expecting a deeper discussion relating to these different scenarios. For example, I was expecting a certain level of discussion with other authors (such as those you mentioned in lines 25-45), or other studies that pointed a bit on the topic (such as Stark et al., 2016-2017 in the Scheldt estuary). Also, it is cool to separate the discussion into subtopics, but there must be a bit more discussion between the scenarios. For example, you could explore a bit more the difference between increasing flats only in the outer part vs. everywhere. The authors have such nice data, it would be interesting to add a deeper discussion here.  

Reply: Thank you for your comment. We will extend the discussion regarding the comparison between the scenarios. Furthermore, we will try to put our results in context with other studies. Please find a first draft of our revised discussion in the appendix.

Action: A revised discussion regarding your suggestions can be found in the appendix.

Line 535-536: Consider removing, as it does not add much to the text (you reiterate it in the following lines).

Action: We will remove the line 535-536

Line 549: Add a short paragraph after this line, where the authors add the conclusion of the study itself and wrap it up with the aim itself. Without it, the conclusion seems more of a summary.

Action: We will add the following sentences after line 549:

“The results of this study show, that future development of TR in the Elbe estuary is not only dependent on future SLR, but also on the development of tidal flats. The results further show varying changes in estuarine geometry for the different scenarios, which can explain the differing changes in TR and improve understanding of the system in the context of SLR.”

References

Bergemann, M.: Salzgehalt am Wehr Geesthacht, personal communication, 2009.

BSH: Nordseezustand 2008-2011, Bundesamt für Seeschifffahrt und Hydrographie, Hamburg und Rostock, Berichte des BSH, 54, 2016.

Jordan, C., Visscher, J., and Schlurmann, T.: Projected Responses of Tidal Dynamics in the North Sea to Sea-Level Rise and Morphological Changes in the Wadden Sea, Front. Mar. Sci., 8, 40171, doi:10.3389/fmars.2021.685758, 2021.

Kloepper, S., Baptist, M. J., Bostelmann, A., Busch, J. A., Buschbaum, C., Gutow, L., Janssen, G., Jensen, K., Jørgensen, H. P., de Jong, F., Lüerßen, G., Schwarzer, K., Strempel, R., and Thieltges, D.: Wadden Sea Quality Status Report: https://qsr.waddensea-worldheritage.org/?_gl=1*1lhw65f*_ga*MTk4MTkxMDczLjE2OTcwMTU4Njc.*_ga_W7PEFV8FMW*MTY5NzAxNTg2Ni4xLjAuMTY5NzAxNTg2Ni4wLjAuMA., last access: 11 October 1023.

Wachler, B., Seiffert, R., Rasquin, C., and Kösters, F.: Tidal response to sea level rise and bathymetric changes in the German Wadden Sea, Ocean Dynamics, 70, 1033–1052, doi:10.1007/s10236-020-01383-3, 2020.

Willmott, C. J., Ackleson, S. G., Davis, R. E., Feddema, J. J., Klink, K. M., Legates, D. R., O'Donnell, J., and Rowe, C. M.: Statistics for the evaluation and comparison of models, J. Geophys. Res., 90, 8995, doi:10.1029/JC090iC05p08995, 1985.