Rogue ocean waves and the St. Petersburg paradox

TL;DR

This paper analyzes an extensive dataset of ocean waves and finds that the statistical distribution of the largest rogue waves aligns with the St. Petersburg paradox, aiding in better modeling and forecasting of ocean surface behavior.

Contribution

It demonstrates that the distribution of rogue wave heights follows the St. Petersburg paradox, providing a novel statistical insight into their behavior.

Findings

Largest wave distribution matches the St. Petersburg paradox

Analysis of over 3.4 billion waves

Improves understanding of rogue wave statistics

Abstract

Powerful rogue ocean waves have been objects of fascination for centuries. Elusive and awe-inspiring, with the ability to inflict catastrophic damage, rogue waves remain unpredictable and imperfectly understood. To gain further insight into their behavior, we analyzed 3,441,188,683 ocean surface waves in order to determine the statistical height distribution of the largest waves. We found that the distribution of rare events which resolves the St. Petersburg paradox also describes the relative height distribution of the largest waves. This result will contribute to the modeling of ocean surface dynamics and improve the accuracy of marine weather forecasts.