The distribution of ocean surface wave heights and the St. Petersburg paradox*

We examined over 3.5 billion ocean surface waves measured by 148 buoys across the Pacific ocean to determine the statistical distribution of wave heights. We find that the distribution of ocean surface wave heights accumulate similarly to profits in the St. Petersburg paradox, revealing that the maximum normalized wave height depends linearly on the logarithm of the number of waves. The St. Petersburg paradox model therefore appears to extend beyond material failure[1] and anomalous transport[2], providing a promising strategy to forecast rogue waves.

[1] J. Fontana and P. Palffy-Muhoray, "St. Petersburg Paradox and Failure Probability," Phys. Rev. Lett. 124, 245501 (2020).
[2] H. Scher, M. Shlesinger, J. Bendler “Time-scale Invariance in Transport and Relaxation”, Physics Today. 44: 26-34. DOI: 10.1063/1.881289