  We review recent progress in modeling the probability distribution of wave
heights in the deep ocean as a function of a small number of parameters
describing the local sea state. Both linear and nonlinear mechanisms of rogue
wave formation are considered. First, we show that when the average wave
steepness is small and nonlinear wave effects are subleading, the wave height
distribution is well explained by a single "freak index" parameter, which
describes the strength of (linear) wave scattering by random currents relative
to the angular spread of the incoming random sea. When the average steepness is
large, the wave height distribution takes a very similar functional form, but
the key variables determining the probability distribution are the steepness,
and the angular and frequency spread of the incoming waves. Finally, even
greater probability of extreme wave formation is predicted when linear and
nonlinear effects are acting together.

Chaotic Dynamics;Atmospheric and Oceanic Physics;Fluid Dynamics