Rogue wave statistics in (2+1) Gaussian seas I: Narrow-banded distribution

Originally discussed in the context of ocean statistics for oil rig platform decks and satellite data, spatiotemporal exceeding probability distributions have recently been thought to explain the failure of second and third-order nonlinear models of distributions at a fixed point in space. To investigate this possibility, we derive a simplified model for the (2+1) exceeding probability distribution of ocean waves based on the Gaussian random...