the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 May 2025
Rogue Wave Indicators from Global Models and Buoy Data
Abstract. Rogue waves pose substantial risks to maritime operations and offshore infrastructure, yet their formation mechanisms and predictability remain poorly understood. This study analyses real rogue wave occurrences using in situ observations from CDIP wave buoys from the Filtered Ocean Wave Data (FOWD) dataset and model-based estimates from ERA5 reanalysis and the ECMWF CY47R1 high-resolution hindcast. Seasonal distributions, wave height comparisons, and spectral analyses reveal that models systematically underestimate extreme wave events due to spectral smoothing and spatial averaging. A key finding is that rogue waves are usually preceded by a sharp decrease in crest-trough correlation below 0.5, followed by a rapid increase above 0.6, indicating a transition to a more structured wave field. This pattern, accompanied by spectral bandwidth narrowing and increased relative energy in the 0.25–1.5 Hz range, suggests energy focusing mechanisms play a critical role. Analysis of rogue wave events at four CDIP buoy stations show that the crest-trough correlation parameter alone is not a good rogue wave indicator, but its temporal variability is. These results highlight the need for improved modelling by integrating dynamic wave field specific parameters and high-resolution numerical models to enhance rogue wave risk assessments on a global scale.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-2031', Anonymous Referee #1, 19 Jun 2025
Please find the detailed comments in the supplement.
- AC1: 'Reply on RC1', Laura Azevedo, 06 Sep 2025
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RC2: 'Comment on egusphere-2025-2031', Anonymous Referee #2, 23 Jun 2025
This study aims to evaluate rogue wave indicators from global model data and validate them with buoy data. The authors do not recognize/acknowledge that the spectral models do not predict individual maximum wave heights, as reported by the buoy observations, but make predictions for ‘the expected maximum wave envelope height’. This is a conceptual misunderstanding. Much of the work seems to replicate the work by Cicon, et al (2023-2024). The major new finding is that the temporal evolution of the crest-trough correlation is a potent rogue-wave predictor. Unfortunately, this hypothesis is tested on a very limited subset of the available data set, only.
The manuscript contains many generic statements without any supporting references or discussion. Interpretation of the results is often inconsistent with the data shown.
Ln 8, and throughout the manuscript: FOWD stands for ‘Free Ocean Wave Data’, not ‘Filtered …’.
P2, 2nd paragraph. Please note, rogue waves are individual waves and are therefore not resolved in a spectral, phase-averaged wave model like ECMWF’s CY47R model. Increasing the spatial resolution cannot resolve ‘localized transient events such as rogue waves’. The model predicts expected maximum envelope wave heights, but this parameter is not correlated with rogue wave height or occurrence. (see Cicon et al, 2024).
Ln 57/ ln773: Reference for Donelan & Magnusson is incomplete: ‘A.A., 2.2’
P3, ln 77-91: Please state clearly what are the differences/advancements of this work compared to Cicon et al 2024.
Ln 90 – 91: ‘…their ability to capture real-world extreme wave events remains unproven…” Please clarify if you specifically mean ‘rogue waves ’. If this is the case the statement is incorrect. Cicon, et al 2024 did exactly that, showing that these parameters are not reliable predictors.
Ln265-267, ln 271: It’s not obvious from Fig 1 that there are more rogue waves in winter. Contrary to the statement, the US west coast seems to have more rogue waves in summer.
Ln 281: Please define ‘unstable sea conditions’.
Ln 295-303. The discussion of Fig 2 must be revised. There is a good agreement between FOWD and ERA5, contrary to the statement in the manuscript. Surprisingly, the high-resolution ECMWF hindcast shows the strongest ‘smooth out of extremes’.
Ln 303: According to Fig2, top panel the highest median value of Hmax is ~4m (Nov – Jan, both FOWD and ERA5). There are no median values in the 5-7m range (FOWD) or 4-6m range (models) as stated in the manuscript.
Ln 318-328: Again, the discussion is not consistent with the results shown in Fig 2. E.g. The median value of Hmax in Dec – Feb is highest in the ERA5 data, and very close to the value in FOWD.
Similarly, the range of the non-outlier Hs values is highest in ERA5, contrary to the claim that FOWD has the broadest distribution of Hs.
Ln 334-346: The whisker plots do not contain any information on rogue waves. Yu would have to include distributions of Hmax/Hs or distributions of rogue wave heights or occurrence rates to infer that information. Separate distributions of Hmax and Hs are not sufficient to infer Hmax/Hs- related distribution.
Fig3: Top row: Specify that FOWD and model definitions of maximum individual wave height are not the same. The plots compare maximum individual wave heights with maximum envelope wave height (see e.g. Cicon et al 2024).
Ln 379-384: Again, the model does not predict the height of individual waves. The fact that Hmax/Hs distributions in the models are narrow indicates that the maximum envelope height is closely correlated with the significant wave height. This is not the case for truly individual maximum wave heights (as reported in FOWD).
Fig 4: Suggestion: Adjust the scale of the x-axes to better show the differences in the distributions. E.g. there is no information outside 0<=Hmax/Hs<=3, or 0<=BFI<=1.5.
Ln 419-435: Interpretation of skewness and kurtosis is incorrect. The authors state that skewness ( kurtosis) are measures of the asymmetry (peakedness) of the wave energy spectrum. Howver, thes statistical moments are related to the surface height distributions, not he wave energy. E.g. a typical wave energy spectrum (JONSAP or P-M) is always skewed. The discussion of Fig 4 needs to be rewritten. Also, the figure shows the ‘excess kurtosis’, which is kurtosis minus 3.
Ln468: suggestion “Hmax divided by Hs’ rather than ‘just one divided by the other’
Ln 482: The discrepancy between FOWD and original CDIP is very surprising. FOWD is derived from CDIP data. Particularly, that Hmax in FOWD (green) is significantly higher than in CDIP (red) is hard to explain (see Fig 5 top left panel). If anything, FOWD would reject individual Hmax value but would not amplify them. Please make sure you are comparing data from the same buoys. If the discrepancies proof to be real, do you have any explanations for them?
Ln 490 – 493: ‘… an increase in relative energy within 0.25-1.5Hz’ is contrary to ‘...redistribution of energy toward lower frequencies’. Please decide which of the two processes ‘… supports the formation of extreme, isolated waves’.
Ln 515-518: Please explain how ‘swell components reinforce the background wave spectrum’. This is a very generic statement without any physical meaning. What is the ‘background wave spectrum’? What type of wave-wave interaction would transfer energy from low frequency to higher frequencies?
Ln 530-535: If I understand the work by Hafner, et al correctly, they do not claim a threshold behaviour of rogue wave occurrences based on crest-trough correlation r>0.6. Rather, rogue-wave occurrences increase with increasing r-value; the probability for r~0.9 is about an order of magnitude greater than for r~0.1, but rogue waves are possible for any r-value.
Ln 535-571: The observation that a drop in crest-trough correlation followed by rapid increase as a precursor for rogue waves is very interesting and should be explored in more detail.
Ln 582-584: Very interesting result. Obviously, you should also check the null-hypothesis. How many ‘inverted peaks of r-values’ were NOT related to a rogue wave.
Ln 597-598: Note, you are comparing different parameters. The expression by Cicon et al give a probability, whereas your inverted peak hypothesis gives a binary result. Please rewrite.
Ln 605 – 689: The conclusions need to be completely rewritten since many of the claims in this manuscript do not hold ( see above). The main result is that the temporal evolution of the crest-trough correlation can serve as a practical predictor for rogue wave occurrence probability. This should be evaluated further.
Citation: https://doi.org/10.5194/egusphere-2025-2031-RC2 - AC2: 'Reply on RC2', Laura Azevedo, 06 Sep 2025
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CC1: 'Comment on egusphere-2025-2031', Leah Cicon, 27 Jun 2025
A big problem I see in this manuscript is the Hmax from the ECMWF wave model which include ERA5 simulations is used as an individual wave height estimate which is not the case. It is a expected maximum wave envelope height as such it cannot be compared to the observations from buoys as in Fig 2-4. The sharp decrease and sharp recovery of crest-trough correlation preceding rogue waves is a very interesting finding and should be explored further although the extent of the research in this work is not sufficient in my opinion to substantiate the claims in this manuscript. Only a very small subset of the dataset was used for this analysis and they do not explore how many inverted peaks do not correspond to rogue wave events. I have some further, more specific comments below.
ln 22: 2Hs is considered a conservative estimate for rogue waves. Normalized wave heights only begin deviating from Rayleigh distribution at around 2.2Hs which indicates a shift to a different wave regime. I believe this should be mentioned at some point in your intro or discussion.
ln 91: By now there is a decent body of literature that has shown that wave skewness, kurtosis, and the Benjamin-Feir Index are not viable parameters to predict real world rogue waves.
ln 121: Free Ocean Wave Dataset
ln 166: Should smaller be smallest?
Fig 1: Please consider changing the colormap to a sequential colormap. It is not obvious that purple is more than green. From the map currently I can not really tell in which seasons there are more rogue waves. And include which months are considered for winter, spring etc.
ln 265 and beyond: I am not confident in your seasonal assessment stating that there are more rogue waves in the winter months. The FOWD removes Hs sample of 1m and below. Perhaps you have simply removed your summer (low seas) rogue wave samples with that filtering and the occurrence rate is consistent but there are simply higher rogue wave events in the winter showing a more dominant signal. This is the challenge with using the definition that we do but this should be addressed.
ln 270: "to nonlinear wave interactions that form rogue waves". This statement could be construed as nonlinear interactions, like MI, cause rogue waves.
ln 281: "... which generate unstable sea conditions, large wave fields and steep wave conditions favorable for rogue wave formation." Where have you shown (or elsewhere) that "unstable" sea conditions and large wave fields and steep wave conditions are favourable for rogue waves?
ln 331-345: The whisker plots do not provide information on rogue wave probability you have to look at the ratio Hmax/Hs.
ln 349: Having the same symbol r for crest-trough correlation and person correlation coefficient could be confusing.
ln 438: "These are signatures of asymmetric, steep, and strongly peaked wave groups, conditions known to precede rogue wave events." This statement should have citations.
ln 483: "When using the raw, non-filtered, data, we sometimes see rogue waves peaks (when data goes above 2 on the Hmax/Hs graphs) that were not present on the filtered data." I see more of the opposite happening in Fig 5, that the FOWD shows a much stronger rogue wave signal that the raw CDIP. The large discrepancies between the FOWD and CDIP is a bit concerning. Maybe it is caused by the computation window of the FOWD compared to the raw CDIP. In FOWD they use a 10 min, 30 min, and a dynamically sized window so perhaps the time isn't consistent between the FOWD and CDIP.
ln 535 "... above 0.6 due to wave groupness and focusing, this alone does not serve as an effective predictor." No one has suggested using a fixed threshold of 0.6 as a rogue wave prediction but as a general regime in which more rogue wave occur. This is mentioned multiple times (ln 569, ln 581) as if it has been proposed as such. Both Cicon et al 2023 and 2024 suggest a probabilistic function of r and other parameters to predict rogue wave probability.
ln 596: Change correlation-based to crest-trough correlation based.
ln 597: It seems you are comparing the 0.72 predictive power from the empirical function for rogue wave probability in Fig 3 in Cicon et al., 2024 using buoy observations to the 75.3% statistic you compute. These are not the same thing and can not be compared. See Cicon et al., 2024 for definition of predictive power.
Citation: https://doi.org/10.5194/egusphere-2025-2031-CC1 - AC3: 'Reply on CC1', Laura Azevedo, 06 Sep 2025
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