the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Quantifying Tropical Cyclone-Generated Waves in Extreme-Value-Derived Design for Offshore Wind
Abstract. Wave extreme values, such as significant wave height, peak period, and crest height, are central to design and operation practices for offshore wind structures. However, the most suitable methods for deriving these extremes, both statistically and from numerical models, is not straightforward. This is especially acute in mixed-type climates, as in the Atlantic coast of the US, where tropical cyclones (hurricanes) and extra-tropical cyclones (winter storms) occur at the same locations with varying frequency and intensity. Limited guidance is provided in major offshore wind energy standards for the minimum requirements of these ocean models and methods used for determining accurate design and operational metocean conditions for regions with tropical cyclones and mixed-type environments. This study investigates the representation of extreme significant wave heights on the US Atlantic coast generated by mixed storm types, as represented in numerical simulations and univariate extreme value analysis. Notable differences between N-year design values are found, as projected by the two different modeled conditions with both block maxima and peaks-over-threshold methods. Attributing factors include hindcast duration, proximity of design location to historical track storm centers, and single analysis of mixed-type distributions. This paper is the first of its kind to propose a methodology for defining extreme significant wave heights due to tropical cyclones for offshore wind design and operation in Mid- and North-Atlantic waters. Recommendations for achieving accurate and representative extreme values for offshore design on the US Atlantic coast are provided.
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AC1: 'Comment on wes-2024-129', Sarah McElman, 04 Nov 2024
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Please note that there is a plotting error in the wave roses in Figures 6, 7, and 8: the correct orientation is shifted 90 degrees counter-clockwise. While this does not have any influence on the paper conclusions, it will be updated in a subsequent revision of the manuscript.
Citation: https://doi.org/10.5194/wes-2024-129-AC1 -
AC2: 'Comment on wes-2024-129', Sarah McElman, 04 Nov 2024
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Please note that there is a clerical error in Appendix B, Table B1. The numbers in the 4th row ("MAB HiRes (BM)") correspond to the yellow dash-dotted line in Figure A1b (N-year Hs by peaks-over-threshold with a Gumbel distribution of the tropical subset of the MAB high-resolution results).
The proper values corresponding to the "MAB HiRes (BM)" case (blue solid line, Figure 3b) are:
50-year 100-year 1,000-year 10,000-year 10.75 m 11.68 m 14.77 m 17.87 m
The 4th row of Table B1 will be corrected in a subsequent version of the manuscript.Citation: https://doi.org/10.5194/wes-2024-129-AC2 -
RC1: 'Comment on wes-2024-129', Anonymous Referee #1, 07 Nov 2024
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General comments
The article looks into differences in estimates of significant wave height extremes due to tropical and extra-tropical storms at two offshore locations in the eastern coast of the United States.
The article is poorly written and some of the analyses are not sound. For example:
- There is no motivation being given for the type I tail assumption being made when fitting the Gumbel instead of the Generalized extreme value distribution to the annual maxima. Furthermore, and as can be read in a wealth of extreme value theory publications, for instance the cited book of Coles, the Weibull and the Gumbel distributions are not the asymptotic distributions of data sampled using the peaks-over-threshold approach. This does not mean that they cannot be used but their use should be justified.
- Also, the authors confuse the directional spreading of a wave system or sea state with the variability of the mean wave direction during a storm.
Specific comments
Lines 82-83: What is the rational for fitting the Weibull (of minima, I assume) and the Gumbel distribution to POT data? Can you justify why you are deviating from the Generalized Pareto distribution?
Lines 136-138: Please indicate whether there is corresponding between the storms leading to the annual maxima in both GF and hindcast datasets.
Lines 159-161: Please rephrase of remove. The estimates are obtained using the likelihood method? If so, it suffices to state it.
Section 2.2.1: Please motivate why the Gumbel instead of the Generalized extreme value distribution is being fitted to the data.
Lines 170-171: Why is p called “probability period”? Please add that when computing the return values p is substituted by 1/n with n being the return period in years. In the tables and text only n is being given, not p.
Line 178: Why does the storm list given in Appendix C only starts in 1991?
Figure 3: 1)The data to which the distributions were fitted need to be added to the figure. (If not possible in absolute scale, then in relative scale as in Figure 4.) 2) Preferably also the 95% confidence intervals of the estimates should also be given. 3)The legend should contain for each of the lines the periods covered by the data or the sample size (number of considered annual maxima).
Line 91: There are only 15 samples in the ‘GF-EC. Trop.’ fit? Please comment on the uncertainty of the estimates.
Section 3.1.2: In my opinion this section can be removed. What is its purpose? Why are the plots of the significant wave height (even if normalised) not shown?
Section 3.1.3: The contents of this section are incorrect. First, how can the authors not be aware that the waves in the roses in Figure 7 are from the coast and therefore not realistic. Second, the authors present the variation in the mean wave directions during the consider storms (may wave systems, sea states) and analyse with reference to the article of Forristall and Ewans on directional spreading of a wave system or sea state.
Section 3.2: This section needs also to be completely redone. When comparing statistical estimates the sample sizes and confidence intervals should be given. Furthermore, when making assumption in terms of the tail of the data these should be justified.
Technical corrections
Line 46: Please specify which are the variables being considered in the univariate and bivariate analyses you are referring to. Why is this relevant for this article?
Line 69: Specify which 3 models and models of what?
Line 78: What does “Return period results” mean? Should it be “Return value estimates”?
Line 96: You mean Appendix C instead of B?
Line 104: Is the magnitude of Cds correct? Please introduce the meaning of the symbols it wanting to give the values.
Line 110 and elsewhere: Explain what you mean with “most “at-risk” turbine location” and how this has been defined.
Lines 114-118, …: Provide references for SWAN, Delft3D, Westhuysen, WAM, OWI3G,...
Line 117: Define acronyms throughout the text. For instance, what does YSU mean?
Lines 124: State also model depth for the considered output location.
Citation: https://doi.org/10.5194/wes-2024-129-RC1 -
RC2: 'Comment on wes-2024-129', Anonymous Referee #2, 06 Dec 2024
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The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2024-129/wes-2024-129-RC2-supplement.pdf
Data sets
Wave hindcast data [high-resolution models] at 40.8N, 70.7W and 36.2N, 75.0W Sarah McElman https://doi.org/10.5281/zenodo.13884957
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