An official website of the United States government
Abstract Freak or rogue waves are a danger to ships, offshore infrastructure, and other maritime equipment. Reliable rogue wave forecasts could mitigate this risk for operations at sea. While the occurrence of oceanic rogue waves at sea is generally acknowledged, reliable rogue wave forecasts are unavailable. In this paper, the authors seek to overcome this shortcoming by demonstrating how rogue waves can be predicted from field measurements. An extensive buoy data set consisting of billions of waves is utilized to parameterize neural networks. This network is trained to distinguish waves prior to an extreme wave from waves which are not followed by an extreme wave. With this approach, three out of four rogue waves are correctly predicted 1 min ahead of time. When the advance warning time is extended to 5 min, it is found that the ratio of accurate predictions is reduced to seven out of ten rogue waves. Another strength of the trained neural networks is their capabilities to extrapolate. This aspect is verified by obtaining forecasts for a buoy location that is not included in the networks’ training set. Furthermore, the performance of the trained neural network carries over to realistic scenarios where rogue waves are extremely rare.
more »
« less
Are Rogue Waves Predictable From Field Measurements?
Rogue waves, which are defined as waves with a wave height, or alternatively a crest height, exceeding the significant wave height by a certain factor, continue to endanger ships and offshore infrastructure. Hence, reliable rogue wave forecasting is of utmost importance to increase the safety for maritime operations. While the occurrence of rogue waves is widely acknowledged, their emergence remains unpredictable due to the lack of a well-accepted basis for explaining their occurrence. In fact, two popular mechanisms explaining the formation of rogue waves lead to considerably different conclusions about their predictability. On the one hand, a rogue wave could be formed by a superposition of wave trains with unknown phases. With this generation mechanism, rogue wave prediction is not viable. On the other hand, nonlinear focusing leading to the Benjamin-Feir instability gives rise to slowly developing rogue waves. Hence, this rogue wave formation could be detected with significant advance time. Given this background, there is an imperative need to address the basic question: Are rogue waves predictable? In this article, the authors explore the predictability of rogue waves by constructing and parameterizing neural networks. The networks are trained on available buoy data, which allows not only for an assessment under the most realistic conditions but also for indicating the sufficiency of current ocean measurements for rogue wave prediction.
more »
« less
- Award ID(s):
- 1854532
- PAR ID:
- 10542101
- Publisher / Repository:
- American Society of Mechanical Engineers
- Date Published:
- Subject(s) / Keyword(s):
- extreme waves ocean buoys machine learning wave forecasting extreme events
- Format(s):
- Medium: X
- Location:
- Melbourne, Australia
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)Abstract General rogue waves in (1+1)-dimensional three-wave resonant interaction systems are derived by the bilinear method. These solutions are divided into three families, which correspond to a simple root, two simple roots and a double root of a certain quartic equation arising from the dimension reduction, respectively. It is shown that while the first family of solutions associated with a simple root exists for all signs of the nonlinear coefficients in the three-wave interaction equations, the other two families of solutions associated with two simple roots and a double root can only exist in the so-called soliton-exchange case, where the nonlinear coefficients have certain signs. Many of these rogue wave solutions, such as those associated with two simple roots, the ones generated by a $$2\times 2$$ block determinant in the double-root case, and higher-order solutions associated with a simple root, are new solutions which have not been reported before. Technically, our bilinear derivation of rogue waves for the double-root case is achieved by a generalization to the previous dimension reduction procedure in the bilinear method, and this generalized procedure allows us to treat roots of arbitrary multiplicities. Dynamics of the derived rogue waves is also examined, and new rogue wave patterns are presented. Connection between these bilinear rogue waves and those derived earlier by Darboux transformation is also explained.more » « less
-
Abstract Up to the third-order rogue wave solutions of the Sasa–Satsuma (SS) equation are derived based on the Hirota’s bilinear method and Kadomtsev–Petviashvili hierarchy reduction method. They are expressed explicitly by rational functions with both the numerator and denominator being the determinants of even order. Four types of intrinsic structures are recognized according to the number of zero-amplitude points. The first- and second-order rogue wave solutions agree with the solutions obtained so far by the Darboux transformation. In spite of the very complicated solution form compared with the ones of many other integrable equations, the third-order rogue waves exhibit two configurations: either a triangle or a distorted pentagon. Both the types and configurations of the third-order rogue waves are determined by different choices of free parameters. As the nonlinear Schrödinger equation is a limiting case of the SS equation, it is shown that the degeneration of the first-order rogue wave of the SS equation converges to the Peregrine soliton.more » « less
-
Abstract We show that new types of rogue wave patterns exist in integrable systems, and these rogue patterns are described by root structures of Okamoto polynomial hierarchies. These rogue patterns arise when the τ functions of rogue wave solutions are determinants of Schur polynomials with index jumps of three, and an internal free parameter in these rogue waves gets large. We demonstrate these new rogue patterns in the Manakov system and the three‐wave resonant interaction system. For each system, we derive asymptotic predictions of its rogue patterns under a large internal parameter through Okamoto polynomial hierarchies. Unlike the previously reported rogue patterns associated with the Yablonskii–Vorob'ev hierarchy, a new feature in the present rogue patterns is that the mapping from the root structure of Okamoto‐hierarchy polynomials to the shape of the rogue pattern is linear only to the leading order, but becomes nonlinear to the next order. As a consequence, the current rogue patterns are often deformed, sometimes strongly deformed, from Okamoto‐hierarchy root structures, unless the underlying internal parameter is very large. Our analytical predictions of rogue patterns are compared to true solutions, and excellent agreement is observed, even when rogue patterns are strongly deformed from Okamoto‐hierarchy root structures.more » « less
-
Abstract This study introduces an ensemble learning model for the prediction of significant wave height and average wave period in stations along the U.S. Atlantic coast. The model utilizes the stacking method, combining three base learner models - Lasso regression, support vector machine, and Multi-layer Perceptron - to achieve more precise and robust predictions. To train and evaluate the models, a twenty-year dataset comprising meteorological and wave data was used, enabling forecasts for significant wave height and average wave period at 1, 3, 6, and 12 hour intervals. The data collection involved two NOAA buoy stations situated on the U.S. Atlantic coast. The findings demonstrate that the ensemble learning model constructed through the stacking method yields significantly higher accuracy in predicting significant wave height within the specified time intervals. Moreover, the study investigates the influence of swell waves on forecasting significant wave height and average wave period. Notably, the inclusion of swell waves improves the accuracy of the 12-hour forecast. Consequently, the developed ensemble model effectively estimates both significant wave height and average wave period. The ensemble model outperforms the individual models in forecasting significant wave height and average wave period. This ensemble learning model serves as a viable alternative to conventional coastal models for predicting wave parameters.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
