Review Reports

Round 1

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

The author analyzed the extreme water level for all tide gauges along the entire Baltic Sea coast. The results have great engineering applications. There are some comments for the author to make revisions.

1.    How about sample data? Is the annual maximum and minimum from hourly tide data for a long period?

2.    How about the method of determining the parameters of extreme distribution?

3.    In the theory of extreme value analysis, the estimate of 500-year even 1000-year period is not reliable from a 60-year data length. The author may consider removing these values in table 8-10. In addition, although the estimated value of each return period is important, its 95% confidence interval is also a necessary reference in engineering decisions, and it is recommended that it be discussed.

4.    Line 169-172: The text does not show any comparison or literature on selecting the Gumbel distribution for the maximum water levels and the Pearson type III distribution for the minimum water levels.

5.    Section 3.3: Table 10 shows the differences in the heights of positive theoretical sea levels between two data sets. The author explains that it is caused by an increase in the average sea level and an intensification of the western atmospheric circulation. In extreme value analysis theory, its parameters are constant and do not change with time. Is extreme value analysis applicable under the nonstationary conditions?

6.    Line 462-464: Only two the Gedser and Kołobrzeg tide gauges have a part of the upper range of quantiles negative. This may be due to storm surges at the beginning of the 20th century [38]. Why do only the two stations located in the southwest have this phenomenon, but not other 19 stations? Whether this is related to extreme value sampling, please refer to the following papers

(1) Rantanen, M., van den Broek, D., Cornér, J., Sinclair, V. A., Johansson, M. M., Särkkä, J., et al. (2024). The impact of serial cyclone clustering on extremely high sea levels in the Baltic Sea. Geophysical Research Letters, 51, e2023GL107203. https://doi.org/10.1029/2023GL107203

7.    Figure 8 shows that the number of observations of exceedances of the theoretical water height for return periods of different lengths from 1960 to 2020. The author can discuss typhoon events that caused observations to exceed theoretical values for 100-year return period.

 

Mirror comments:

1.    Line 215: Citation mission of reference 20.

2.    The width of some tables is very different. The author can try to edit it to the same width.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

In this manuscript the authors perform a frequency analysis of the annual minimum and maximum levels, determining, with the help of probability distributions, the characteristic values ​​related to some return periods of interest. The authors' approach includes the analysis using the annual maximum and minimum data series (block maxima, annual maxima series) for 42 stations from the coasts of the Baltic Sea.

 

Regarding the presented analysis, I have the following observations:

 

First of all, the authors present, in the Introduction section, a synthesis of the different approaches and existing gaps regarding these types of analyses, thus creating, in a correct and clear way, the context and the necessity of performing the presented analysis.

 

Regarding the frequency analysis presented by the authors, it suffers from some statistical deficiencies. In Tables 8 and 9 it can be seen that the annual exceedance probabilities of interest are between 0.1% and 99%. Regarding the choice of the Gumbel distribution for forecasting the maximum levels related to these annual exceedance probabilities, I believe it is a wrong choice. The Gumbel distribution is one of the most deficient probability distributions, because it has important statistical limitations, being "captive" of a constant skewness from which it cannot escape. It was used in the past due to the simplicity of the relationships and not due to its performance, especially taking into account the average length of the number of years analyzed (n=60 years). Using the maximum likelihood method to estimate the two parameters of the distribution amplifies the uncertainties regarding the results obtained, being an estimation method strongly influenced by the variability of the lengths of the available recorded data. I think a much more stable method, such as the method of linear moments (L-moments), and a distribution with a large number of parameters should have been used.

 

The use of tests and performance indicators for the selection of the model distribution (in this case Gumbel) is not recommended if the sole purpose is to determine the model distribution only for the domain of recorded data probabilities, outside this domain (forecasting more extreme events, T=1000 years) these tests and indicators are not relevant. This was another reason for using the L-moments method, which, besides being the most stable method of parameter estimation under the influence of the variability of available data lengths, also presents clear criteria for selecting the best model, especially since important contributions have been made in this regard in recent times (Ilinca et.al. 2023, etc.). This is the main disadvantage of using incomplete dedicated programs, limited to certain estimation methods and certain distributions. 

 

General conclusion. The analysis is interesting and has a logical statistical structure, but it presents deficiencies regarding the choice of distribution and parameter estimation method, the most notable in the case of maximum level analysis. The results are characterized by important uncertainties, due to this choice. In general, these types of analyses involve a holistic approach, which involves different methods of estimating parameters and probability distributions. It is also recommended to avoid using, in a mixed way, distributions with different numbers of parameters, as they calibrate higher moments of different order, especially the Gumbel distribution. Also, the authors did not justify the choice of the maximum likelihood method for estimating the parameters. I recommend that the authors, for some of the reference stations, do a comparative analysis with the linear moments method, and the distribution choice be made according to L-moments methods, namely the selection of the distribution depending on the calibration of the L-skewness and L-kurtosis indicators.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

The authors makes good reversion following my reviewer's comments.

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

The authors have inserted in the manuscript the necessary additions and explanatory information for the frequency analysis performed (advantages, disadvantages, etc.). 

 

My decision is to accept the manuscript in this form.

 

However, it is necessary to mention that in general such analyses also involve a subjective component (preferential choice of a distribution or parameter estimation method) which should have a reduced weight as much as possible, and the analysis should be made according to the most rigorous statistical/mathematical/hydrological criteria, so that the results obtained are characterized by minimal uncertainties.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

A review of “Application of the probability of extreme sea levels at selected 2 Baltic Sea tide gauge stations” by  Wolski et al. 

 

This paper reports a study of water level data in the Baltic Sea. The aggregation of data from the many surrounding countries is impressive.  Two types of data sets are used. One is hourly measurements (corrected for vertical land movement) at 42 stations between 1960 and 2020. The other is annual max and minima for 1900-1960 at 21 stations. 10 stations were chosen, and the extreme values were used to estimate the return interval levels of positive and negative surges.  Figure 1 shows the station locations. I note that the caption has [17-changed] which I don’t understand.

The results of the return interval analyses are then interpolated with a GIS system across the study area using Kriging.  Extreme water levels from several countries are then assembled to justify the choice of thresholds for further analyses. These should be removed or used more directly.   

Table 8 & 9 summarizes the levels for return intervals at the 10 stations studied for the 1960-2020 interval. I think Figure 4 (a and c) is supposed to show the similarity between the patterns of the interpolated 200 year return level and the observed record-long maxima at the stations (but I confess that I am not entirely sure). That the pattern in the open waters is simply interpolated with no constraints imposed by the ocean and atmosphere dynamics leaves the value in doubt and the speculation about the mechanisms that determine the patterns uninformative.   

The comparison in Table 10 of the return level estimated using the 1900-1960 data and then 1960 -2020 records is more interesting.  But the reference to “maximum theoretical water levels“ should be removed. I don’t see why the levels estimate by fitting a function to observations are called “maximum theoretical” values. The differences should be presented with uncertainty estimates so the significance of the changes can be assessed. Figure 5 would also be improved by adding data and the uncertainty bounds.  It would also be useful to report the best estimates of the parameter of the functions. The attribution of the changes to mean sea level rise is plausible but the argument here is unconvincing. It also brings into question the return interval methodology. Was the long-term trend in the data removed before the annual maxima (or peaks) were selected. The description of the method should make that clear.  

The section of the paper that estimates the area and shoreline extent of the study area impacted by changes is uninformative. It is largely driven by the interpolation process. And Tabel 14 is full of empty cells and the caption “The number of exceeding of maximum, the theoretical, water for different return periods determined on the basis of an hourly observation series of sea levels from the period 1960-2020” is unintelligible.    

 

Miscellaneous comments. 

The description of the approach to return interval estimation is very superficial. I would like to know why different functions were chosen for the positive and negative surges. That the parameter estimates (obtained by maximum likelihood methods) were not accompanied by uncertainty estimates is an important failing. Some dotted lines appear in Figure 3 but the caption doesn’t describe what they represent. This is an unacceptable failing. Further, the many assumptions that underlie this approach were unaddressed. For example, it is unclear whether they used the annual maximum approach, or the peak over threshold method. Only self-citations are used in this section. 

The interpolation uses Kriging but there are no details on how the parameters required are chosen. Were they picked to make a nice smooth map I wonder? And how is the presence of the capes and bays included. Are the water levels just interpolated across land and then screened out? 

 

Conclusion

I don’t recommend publication of this manuscript. The assembly of data is valuable, and I expect that the impact of sea level rise on the return interval of extreme events would be of interest to those in the study region. But the technical details of the approach are inadequately reported, and the spatial interpolation and superficial discussion of the dynamics responsible for the patterns it creates is uninteresting… it is not a significant contribution to science. The absence of estimates of the significances of differences is unacceptable.  Finally, the paper is poorly written and edited. There are many repetitions and ambiguities. A professional editor may be needed to make the text coherent and concise.  The references to the data sources are unhelpful. They seem to be places where the data is described and not easily accessed. Putting what they used in a repository would be more in keeping with the policy.

 

Comments on the Quality of English Language

The writing is poor. It is repetitive and often ambiguous. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

 Some parts of the paper cannot be understood. Please rewrite them.

 

1)     Line 20; part of o   >>>  What is “o”?

2)     In the Baltic Sea, D.L. is the same in the total area?

3)     The same D.L.(Datum Line) is applied in the all countries surrounding the Baltic Sea?

4)     Why the alarm is necessary when the maximum low tide?

5)     What type of tide gauge is widely used in the target basin? Please dd the information.

6)     What is the sampling time (time interval) of original observed data employed in the analysis?

7)     Line 585; The maximum sea level 275cm in Parunu includes the influence of the bay seiche?

 

Author Response

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Author Response File: Author Response.pdf