Rogue ocean waves and the St. Petersburg paradox

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.