Rogue waves and large deviations in deep sea

Giovanni Dematteis, Tobias Grafke, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review


The appearance of rogue waves in deep sea is investigated by using the modified nonlinear Schrödinger (MNLS) equation in one spatial dimension with random initial conditions that are assumed to be normally distributed, with a spectrum approximating realistic conditions of a unidirectional sea state. It is shown that one can use the incomplete information contained in this spectrum as prior and supplement this information with the MNLS dynamics to reliably estimate the probability distribution of the sea surface elevation far in the tail at later times. Our results indicate that rogue waves occur when the system hits unlikely pockets of wave configurations that trigger large disturbances of the surface height. The rogue wave precursors in these pockets are wave patterns of regular height, but with a very specific shape that is identified explicitly, thereby allowing for early detection. The method proposed here combines Monte Carlo sampling with tools from large deviations theory that reduce the calculation of the most likely rogue wave precursors to an optimization problem that can be solved efficiently. This approach is transferable to other problems in which the system’s governing equations contain random initial conditions and/or parameters.

Original languageEnglish (US)
Pages (from-to)855-860
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number5
StatePublished - Jan 30 2018


  • Intermittency
  • JONSWAP spectrum
  • Laplace method
  • Monte Carlo
  • Peregrine soliton

ASJC Scopus subject areas

  • General


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