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On Oceanic Rogue Waves
Atmospheric and Oceanic Physics · Submitted 14 Jan 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that $h_{obs}$ nearly coincides with the threshold $h_{1/1000}\sim1.62H_s$ estimated at a point for a typical $3$-hour sea state, suggesting that the Andrea rogue wave is likely to be a rare occurrence in quasi-Gaussian seas.
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We propose a new conceptual framework for the prediction of rogue waves and third-order space-time extremes of wind seas that relies on the Tayfun (1980) and Janssen (2009) models coupled with Adler-Taylor (2009) theory on the Euler characteristics of random fields. Extreme statistics of the Andrea rogue wave event are examined capitalizing on European Reanalysis (ERA)-interim data. A refinement of Janssen's (2003) theory suggests that in realistic oceanic seas characterized by short-crested multidirectional waves, homogeneous and Gaussian initial conditions become irrelevant as the wave field adjusts to a non-Gaussian state dominated by bound nonlinearities over time scales $t\gg t_{c}\approx0.13T_{0}/\nu\sigma_{\theta}$, where $T_{0}$, $\nu$ and $\sigma_{\theta}$ denote mean wave period, spectral bandwidth and angular spreading of dominant waves. For the Andrea storm, ERA-interim predictions yield $t_{c}/T_{0}\sim O(1)$ indicating that quasi-resonant interactions are negligible. Further, the mean maximum sea surface height expected over the Ekofisk platform's area is higher than that expected at a fixed point. However, both of these statistics underestimate the actual crest height $h_{obs}\sim1.63H_s$ observed at a point near the Ekofisk site, where $H_s$ is the significant wave height. To explain the nature of such extreme, we account for both skewness and kurtosis effects and consider the threshold $h_{q}$ exceeded with probability $q$ by the maximum surface height of a sea state over an area in time. We find that $h_{obs}$ nearly coincides with the threshold $h_{1/1000}\sim1.62H_s$ estimated at a point for a typical $3$-hour sea state, suggesting that the Andrea rogue wave is likely to be a rare occurrence in quasi-Gaussian seas.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We propose a new conceptual framework for the prediction of rogue waves and third-order space-time extremes of wind seas that relies on the Tayfun (1980) and Janssen (2009) models coupled with Adler-Taylor (2009) theory on the Euler characteristics of random fields. | contribution 0.88 | 0.80 | 0.09 | asserted 0.81 |
| s1 | Extreme statistics of the Andrea rogue wave event are examined capitalizing on European Reanalysis (ERA)-interim data. | contribution 0.54 | 0.84 | 0.03 | asserted 0.96 |
| s2 | A refinement of Janssen's (2003) theory suggests that in realistic oceanic seas characterized by short-crested multidirectional waves, homogeneous and Gaussian initial conditions become irrelevant as the wave field adjusts to a non-Gaussian state dominated by bound nonlinearities over time scales $t\gg t_{c}\approx0.13T_{0}/\nu\sigma_{\theta}$, where $T_{0}$, $\nu$ and $\sigma_{\theta}$ denote mean wave period, spectral bandwidth and angular spreading of dominant waves. | background 0.39 | 0.26 | 0.11 | hedged possibility 0.93 |
| s3 | For the Andrea storm, ERA-interim predictions yield $t_{c}/T_{0}\sim O(1)$ indicating that quasi-resonant interactions are negligible. | result 0.85 | 0.84 | 0.06 | hedged possibility 0.53 |
| s4 | Further, the mean maximum sea surface height expected over the Ekofisk platform's area is higher than that expected at a fixed point. | result 1.00 | 0.74 | 0.05 | asserted 1.00 |
| s5 | However, both of these statistics underestimate the actual crest height $h_{obs}\sim1.63H_s$ observed at a point near the Ekofisk site, where $H_s$ is the significant wave height. | result 0.86 | 0.71 | 0.09 | asserted 1.00 |
| s6 | To explain the nature of such extreme, we account for both skewness and kurtosis effects and consider the threshold $h_{q}$ exceeded with probability $q$ by the maximum surface height of a sea state over an area in time. | method 0.75 | 0.61 | 0.07 | asserted 0.90 |
| s7 | We find that $h_{obs}$ nearly coincides with the threshold $h_{1/1000}\sim1.62H_s$ estimated at a point for a typical $3$-hour sea state, suggesting that the Andrea rogue wave is likely to be a rare occurrence in quasi-Gaussian seas. | interpretation 0.78 | 0.94 | 0.61 | hedged possibility 0.90 |
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The paper
Original abstract
We propose a new conceptual framework for the prediction of rogue waves and third-order space-time extremes of wind seas that relies on the Tayfun (1980) and Janssen (2009) models coupled with Adler-Taylor (2009) theory on the Euler characteristics of random fields. Extreme statistics of the Andrea rogue wave event are examined capitalizing on European Reanalysis (ERA)-interim data. A refinement of Janssen's (2003) theory suggests that in realistic oceanic seas characterized by short-crested multidirectional waves, homogeneous and Gaussian initial conditions become irrelevant as the wave field adjusts to a non-Gaussian state dominated by bound nonlinearities over time scales $t\gg t_{c}\approx0.13T_{0}/\nu\sigma_{\theta}$, where $T_{0}$, $\nu$ and $\sigma_{\theta}$ denote mean wave period, spectral bandwidth and angular spreading of dominant waves. For the Andrea storm, ERA-interim predictions yield $t_{c}/T_{0}\sim O(1)$ indicating that quasi-resonant interactions are negligible. Further, the mean maximum sea surface height expected over the Ekofisk platform's area is higher than that expected at a fixed point. However, both of these statistics underestimate the actual crest height $h_{obs}\sim1.63H_s$ observed at a point near the Ekofisk site, where $H_s$ is the significant wave height. To explain the nature of such extreme, we account for both skewness and kurtosis effects and consider the threshold $h_{q}$ exceeded with probability $q$ by the maximum surface height of a sea state over an area in time. We find that $h_{obs}$ nearly coincides with the threshold $h_{1/1000}\sim1.62H_s$ estimated at a point for a typical $3$-hour sea state, suggesting that the Andrea rogue wave is likely to be a rare occurrence in quasi-Gaussian seas.
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How the literature uses it
3 arXiv papers cite this in 8 sentences
Papers citing it · 7 sentences without a confident label
Uses its method or tool 1 paper
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The nonlinear space-time statistics can then easily processed by using the encountered spectral moments $m_ijk^(e)$ using the FST model [ref] , which is based on Eq. [ref] as described above.
The sinking of the El Faro: predicting real world rogue waves during Hurricane Joaquin · The occurrence frequency of a rogue wave by the El Faro vessel · 1.00
What it cites · 5 sentences without a confident label
Cites as background 1 paper
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First, the essential elements of Janssen's (2003) formulation for the excess kurtosis of directional or short-crested seas are presented [ref] .
On the kurtosis of deep-water gravity waves · Introduction · 0.80
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