How big are the big waves?

K. Podgórski, I. Rychlik, J. Rydén, E. Sjö

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338

We discuss various aspects of statistical distributions for large waves. Spatial waves evolving in time are considered. We call such a wave extremal if its crest height attains a local maximum in time. For extremal waves, the joint distribution of the wave length and the crest height is obtained. Generally, it is observed that taking into account time dynamics of spatial characteristics results in distributions different from those obtained for static records. Some other statistical issues for large waves are also discussed including, the Rayleigh model for the crest height, the evolution of wave groups, and the myth of the seventh wave.
Key words:
Gaussian fields, local extremes, wave period, wave length, extremal waves