Probabilistic Assessment of Correlations of Water Levels in Polish Coastal Lakes with Sea Water Level with the Application of Archimedean Copulas

Round 1

Reviewer 1 Report

This work revealed that correlations between the maximum annual water levels in coastal lakes and in the Baltic Sea in selected gauge stations were very strong and statistically. These results were confirmed by the synchronicity analysis carried out with the help of the Copula function. The highest relationship was detected in the case of Lake Resk Przymorskie, while the lowest was observed in Lakes Jamno and Bukowo.

However, the water level in the coastal lake is, of course, relative to the sea it connects. I am confused that what is the main aim of this study? More details should be provided in the manuscript.  

Comments for author File: Comments.doc

Author Response

Response to Reviewers: First of all, we would like to thank the reviewers for their valuable comments. Below please find the original comments and our responses (in bold) explaining how the original manuscript was amended during the revision.

Reviewer 1

This work revealed that correlations between the maximum annual water levels in coastal lakes and in the Baltic Sea in selected gauge stations were very strong and statistically. These results were confirmed by the synchronicity analysis carried out with the help of the Copula function. The highest relationship was detected in the case of Lake Resk Przymorskie, while the lowest was observed in Lakes Jamno and Bukowo.

However, the water level in the coastal lake is, of course, relative to the sea it connects. I am confused that what is the main aim of this study? More details should be provided in the manuscript.  

Response to Reviewer:

The aim of the study has been additionally described in lines 89-101.

Reviewer 2 Report

Dear authors,

The paper is very interesting. The manuscript has been reviewed, I recommended a minor revision. Some comments are as follows:

1. Figure 1 needs to be improved, such as color, lat/lon information, using different color to represent land and ocean.

2. Figure 3 are not very clear, need a figure with high resolution.

3. It is better to present with a color figure for figure 6.

4. More references should be added in introduction, especially for paragraph 1,2 and 3.

5. Copula Theory was used in this paper. So I think some words should be added to explain why select Copula Theory to conduct the analysis rather than some other mathematical tools.

6. Conclusion are too long, needs to be simplified.

7. Quantitative results should be added in abstract. In addition, the background of climate change and sea level rise can be added.

8. In the discussion, some words can be added to highlight the importance of this study in the background in a warming climate. In addition, the authors can discuss the possibility to conduct this study at a global scale. 

Author Response

Response to Reviewers: First of all, we would like to thank the reviewers for their valuable comments. Below please find the original comments and our responses (in bold) explaining how the original manuscript was amended during the revision.

Reviewer 2

The paper is very interesting. The manuscript has been reviewed, I recommended a minor revision. Some comments are as follows:

1. Figure 1 needs to be improved, such as color, lat/lon information, using different color to represent land and ocean.

Response to Reviewer:

Thank you for the positive opinion. Figure 1 has been improved accordingly.

2. Figure 3 are not very clear, need a figure with high resolution.

Response to Reviewer:

Figure 3 has been improved: the drawing markers and fonts have been enlarged.

3. It is better to present with a color figure for figure 6.

Response to Reviewer:

Figure 6 has been improved accordingly.

4. More references should be added in introduction, especially for paragraph 1,2 and 3.

Response to Reviewer:

More references have been added in Introduction (paragraphs 1, 3).

5. Copula Theory was used in this paper. So I think some words should be added to explain why select Copula Theory to conduct the analysis rather than some other mathematical tools.

Response to Reviewer:

One of the aims of our research was to compare results obtained with the use of the linear coefficient of correlation with the non-linear one - copulas are such a type of tools. Correlation coefficients have their drawbacks, for example they are not a resistant measure (what means that untypical observations can significantly affect the value of the correlation coefficient) [Gurgul, Syrek 2009]. The correlation coefficients also show no invariance towards non-linear transformations, scale-invariant. Copulas and the related measures of correlation strength have no such a drawback. They are exceptionally useful and practical statistical tools in studies on correlations between random variables. Currently, there are many researches using copulas to measure relationships between hydrological data (like runoff, precipitation, sediment transportation), but they are rarely used in analysis of limnological data.

6. Conclusion are too long, needs to be simplified.

Response to Reviewer:

Conclusions have been shortened and simplified, according to the suggestion of the Reviewer.

7.  should be added in abstract. In addition, the background of climate change and sea level rise can be added.

Response to Reviewer:

The quantitative results have been added in Abstract (lines: 24-27).

8. In the discussion, some words can be added to highlight the importance of this study in the background in a warming climate. In addition, the authors can discuss the possibility to conduct this study at a global scale.

Response to Reviewer:

Conclusions have been supplemented with the following sentences highlighting the importance of our study: “Regarding the relatively small number of studies of that kind in the world scientific literature, this research may be of great importance both at the regional and global scales. Due to the climate warming the sea level has been increasing, which may have a significant impact on the functioning of coastal lakes, including fluctuations of their water levels, chemistry and ecological status. Thus, further, more detailed studies on that issue are necessary and this research may be the starting point for such studies in the future” (lines: 408-413, 499-504).

Round 2

Reviewer 1 Report

The authors have well addressed my comments. I suggest that this manuscript can be accepted for publication in Water journal.