Capturing rogue waves by multi-point statistics

As an example of a complex system with extreme events, we investigate ocean wave states exhibiting rogue waves. We present a statistical method of data analysis based on multi-point statistics which for the first time allows the grasping of extreme rogue wave events in a highly satisfactory statistical manner. The key to the success of the approach is mapping the complexity of multi-point data onto the statistics of hierarchically ordered height increments for different time scales, for which we can show that a stochastic cascade process with Markov properties is governed by a Fokker-Planck equation. Conditional probabilities as well as the Fokker-Planck equation itself can be estimated directly from the available observational data. With this stochastic description surrogate data sets can in turn be generated, which makes it possible to work out arbitrary statistical features of the complex sea state in general, and extreme rogue wave events in particular. The results also open up new perspectives for forecasting the occurrence probability of extreme rogue wave events, and even for forecasting the occurrence of individual rogue waves based on precursory dynamics.

Subjects

Stochastic process

complex systems

multi-point statistics

rogue wave

prediction

DDC Class

600: Technik

Lizenz

https://creativecommons.org/licenses/by/3.0/

Name

Hadjihosseini_2016_New_J._Phys._18_013017.pdf

Size

1.67 MB

Format

Adobe PDF

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Capturing rogue waves by multi-point statistics