Review of “Climate Variabilities Synergistically Influence Marine Heatwaves in the North Sea”

General comments:

This paper presents an analysis of the factors that affect the occurrence of marine heatwaves in the North Sea. A correlation-based K-means clustering approach was used to divide the North Sea into two regions that have different variability in marine heatwave cumulative intensity, and detailed analysis carried out to determine the mechanisms that cause that variability. The paper is well written and presented, and the topic and results are of strong interest.

Specific comments:

Line 97 – should Worsfold et al. (2024; https://doi.org/10.3390/rs16183358) be referenced here?

Line 157 – a minor comment, but why include November and May in the calculation of tendency but not March or September? Shouldn’t it be calculated either November -  March and May – September if including the months surrounding the season, or December – February and June – August if not?

Line 184 – I struggle to relate the text here, which says two distinct temporal patterns, to Figure 1b, which does not seem to show a strong peak at ~6 month period. Perhaps a log scale on the y axis might help?

Equation 3 – Is the left brace notation intended? The equivalent equation in the referenced paper uses square braces. Also, I’m not clear why the stationary version of the equation is used rather than the full one?

Line 185 – How was the 90% confidence interval calculated?

Line 211 – 2013 onwards seems a short period to calculate the correlation, even though it is statistically significant. Do any other similar length periods in the record have low correlation?

Figures using arrow vectors (particularly Figure 7) – Is it possible to make the arrows clearer as their direction is not easy to see?

Figure 7 – Colour bar for panels a and f uses a diverging colour scale and it would be better to use a non-diverging scale as the scale goes from 0 to 0.02.

Figure 7 – Are the MOC and ZOC calculated at a particular latitude / longitude?

Figure 7 convergence and overturning circulation colour scales - What direction do negative or positive numbers indicate?

Technical comments:

Line 400 – Should it say AMV instead of AMO?

Fig 2c and d – Series is misspelt in the titles.

Figure 7d, e, i, j – Suggest adding Latitude or Longitude labels on the x axis.

Figure 8 – budget is spelt wrong in the title.

Figure 9 – Colour bar should be labelled 

The paper by Lin and coauthors deals with marine heatwaves in the North Sea.

The contents and quality of the presentation need improvement.

I have some doubts on the methodology and clarity of the diagnosed mechanisms.

The Authors should consider the comments provided below.

I have also noticed this paper https://www.researchsquare.com/article/rs-6503093/v1

from the same authors, but with a different first author. Contents are similar but not identical.

Could you please clarify the situation?

General comments

While there may be implication for prediction, mentioning forecasting in the 

abstract can be misleading. I suggest to clarify that is a diagnostic analysis, instead.

"variabilities" in the plural form sounds strange. Suggest using singular or another noun, e.g. "modes"

depending on what you want to convey

Nonlinear quantities are computed for both atmospheric and ocean reanalysis data;

can you estimate the error made with this compared to using daily data?

I am not sure to understand your use of K-means in this work.

In other works (e.g. Vogt et al. 2022 10.3389/fclim.2022.847995, Wong et al. 2024

https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023AV001059) the procedure is meant

to identify groups of data points, while in your case two regions (Fig. 1) are identified.

And from Fig. 3, I have the impression this just means seasonality.

How can these two domains be related to MHW occurrence?

From line 201 and following I understand MHWs may happen predominantly in one or the other region

depending on the season, but more explanation is due.

Various climate indices are shown; sources for the associated data is missing.

The discussion on the mechanisms is quite poor, as results for a much larger domain is presented,

so local mechanisms are not discussed.

More details should be provided on the stratification procedure; are you using fixed or dynamic

thresholds? This should be consistent across indices, e.g. if they are all standardized already.

The level of discussion when presenting figures (which are often hard to read) is insufficient,

and the various domains used (e.g., larger in Fig. 10) complicates comparisons.

I would suggest to first analyse non-MHW variables and understand how they change over time and 

due to teleconnections, and then focus on the influence of these indices on MHWs. 

I feel like the summary of Fig. 11 is actually not aiding interpretation, as new concepts and 

indices are added. This should be semplified.

Appendix A seems unnecessary, as this has likely been done by the produces in more detail.

The work needs careful proofreading, as there are errors in the titles of most figures and references.

Only some examples are given below.

Comments by line

l21 why speaking about "prediction"?

l69 same comment as for the title

Fig. 1 typo in panel b title

l88/184 as far as I understand, cumulative intensity is a per-event quantity, and events

are discrete. How do you compute the Fourier spectrum then? Is it just SST?

l102 The data record starts in 1940. Are you using 1982-2021 as for the SSTs? Please clarify

l104 A reference and some more details, both on ERA5 and ORAS5, should be given

l113 MHWCI definition ain't very clear to me. What happens say if an event starts in Jan 27

and ends on Feb 10? Which month gets the CI? Please specify also the baseline period used.

l154 state the source of this version of the heat tendency equation.

Information on the number of levels in ORAS5 should be added, to clarify which is the accuracy

of the MLD estimated as such

eq3 I imagine these equation is also calculated with monthly mean data?

l189 so you apply K-means clustering over the whole year or individual seasons?

Fig. 2 typos in titles, and no units in Fig c and d; how are time series normalized?

l247 anomalies from what? Is this is stratified according to some indices? How?

l266 with units m2/s2, this is geopotential (not height)

l269 why this value? Why not using some significance threshold?

Fig 7 cannot be understood. Why are arrows colored? They are hard to see. What are the black arrows on the right side?

Missing labels on axes

l277 is this some sort on average on some sub-domain?

l318 "telecommunications"?

l340 "predominated"

l342 and otherwise? Some climatological maps should be presented.

Fig. 9 why do arrows look quite different? And what is the box in the maps?

l400 is it because some versions of the AMO index are influenced by trends?

l425 why the West Med now?

l662 incomplete citation, also l681, l700...

Fig. B1 what are the units of the ordinate?

The manuscript examines the spatio-temporal variability of marine heatwaves (MHWs) in the North Sea and explores how different large-scale climate variabilities interact to shape their occurrence and characteristics. The authors use long-term SST observations, identify two main regional patterns of MHW variability, and relate these patterns to different atmospheric and oceanic climate modes, with a primary focus on seasonal differences.

Overall, the topic is important and highly relevant, especially given the increasing frequency and impacts of marine heatwaves in shelf seas. The focus on the North Sea is well chosen, and the approach of examining the combined influence of climate modes, rather than treating them independently, is interesting. The study appears scientifically sound, and the results are clearly relevant to the community.

However, I believe the manuscript still requires major revisions. My main concern the lack of several methodological details and the presentation, particularly in the results section, which makes it difficult to follow the main results and understand them. With significant improvements in clarity and structure, the paper could be much stronger.

Introduction

1. The introduction provides useful background, but the aim of the study is not clearly stated. I strongly recommend rewriting the objectives part of the introduction to clearly state the goal(s) of the work and the main research questions.
2. Additionally, since the analysis relies heavily on different climate modes, it would be helpful to define these climate modes early on, either in the introduction or in the data/methodology section. And add a brief explanation of how the positive and negative phases of these modes could affect SST variability in the North Sea.
3. One minor point: the manuscript sometimes refers to the Atlantic Multidecadal Oscillation as AMO and sometimes as AMV. Please use only one term throughout the manuscript, as switching between them is confusing.

Data and Methods

This section requires the most attention, primarily because important details are missing or not clearly described.

1. The data section is not sufficiently clear. I suggest rewriting it in a more straightforward manner, listing the datasets used, their sources, temporal and spatial resolution, and how they are used in the analysis. Currently, it is difficult to understand exactly which products are used and why.
2. The SST analysis is limited to 2021, but high-resolution SST products are available at least until the end of 2024. It is unclear why the study stops at 2021. If this limitation is due to other variables or datasets, it should be clearly stated. Otherwise, extending the analysis to include the most recent years would strengthen the study, especially since recent years include strong extremes that could affect the statistics.
3. Regarding the marine heatwave definition, the authors use the standard Hobday et al. method, but the climatology period used to define the MHW threshold is not mentioned. It must be included in the methodology. Also, please clarify whether the same climatology baseline period is used when computing other anomalies in the study, as this is not currently clear.
4. Another confusing aspect is the detrending or trend removal. In lines 109–110, the manuscript refers to trended and detrended data, but it is not clearly explained: how the detrending is performed? and how it affects the results? This needs a clearer explanation, as detrending choices can influence both clustering and correlations with climate modes.

1. I also recommend a minor change in the subsection title in the methods (line 106). The subtitle is “Cumulative Intensity of Marine Heatwaves,” but the section actually describes the overall MHW calculation and detection method and includes multiple metrics. A title such as “Marine Heatwave Calculation” would be more accurate and clearer.
2. I was confused by the calculation of the “cumulative intensity anomaly.” Since MHWs are already defined as anomalous events, it is not clear why an additional anomaly is needed. If the authors choose to keep this variable, they need to clearly explain its importance and what additional information it provides.
3. Since the analysis relies heavily on seasons, the seasonal divisions should be clearly stated and justified. Currently, there is no clear explanation of why these particular seasonal divisions are chosen or what they represent physically for the North Sea.

Results

For me, the Results section is currently difficult to follow, not because the figures are unclear, but because the text does not clearly describe the results shown in the figures. In many paragraphs, the text moves directly to interpretation and discussion without first explaining what is actually being observed. As a result, the reader must go back and forth between the figures and the text to understand what is being claimed.

1. I strongly recommend rewriting the Results section to be more descriptive: each figure should be clearly explained first (what pattern is shown, what changes occur, what differences appear), and only after that should the interpretation be introduced. This would make the manuscript much easier to read.
2. Additionally, in lines 355–361, the manuscript separates the analysis into periods before and after 2013, but it is not clear why 2013 was chosen as a breakpoint. Where is this significant in the results? What evidence supports this split? This section needs more explanation.

Minor Comments

L26–27: The sentence is long and somewhat difficult to understand; consider splitting it for clarity.

L106–112: Please clarify the detrending approach and its spatial application.

L118–124: Seasonal definitions should be explicitly stated.

L194: The sentence structure is heavy; consider rephrasing.