Capturing rogue waves by multi-point statistics

TL;DR

This paper introduces a novel multi-point statistical method using stochastic cascade processes and Fokker-Planck equations to analyze and predict rogue waves in ocean systems, enhancing understanding and forecasting of extreme events.

Contribution

It presents the first application of hierarchical multi-point statistics and stochastic modeling to capture and forecast rogue wave events from observational data.

Findings

Successfully models rogue wave statistics with a Fokker-Planck equation.

Generates surrogate data sets for detailed statistical analysis.

Provides a basis for predicting individual rogue wave occurrences.

Abstract

As an example for complex systems 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 grasping extreme rogue wave events in a statistically highly satisfactory 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 allowing 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.