Saulo Matusalem da Silva Mendes , Alberto Scotti , Maura Brunetti , Jerome Kasparian 

Non-equilibrium evolution of wave fields, as occurring over sudden bathymetry variations, can
produce rogue seas with anomalous wave statistics. We handle this process by modifying the
Rayleigh distribution through the energetics of second-order theory and a weakly non-stationarity
reformulation of the Khintchine theorem. The probability model in unsteady conditions is then
probed against well-known unidirectional wave tank experiments. We find good agreement and
reproduce the enhanced tail of the probability distribution, describe why the peak of rogue wave
probability appears atop the shoal and explain variations in peak intensity for different depths.
Furthermore, a novel interpretation is proposed to investigate rogue wave likelihoods in finite depth
through the H − σ diagram, allowing a quick prediction of abrupt depth change effects apart from
the probability distribution.