  The evolution of unidirectional nonlinear sea surface waves is calculated
numerically by means of solutions of the Euler equations. The wave dynamics
corresponds to quasi-equilibrium states characterized by JONSWAP spectra. The
spatio-temporal data are collected and processed providing information about
the wave height probability and typical appearance of abnormally high waves
(rogue waves). The waves are considered at different water depths ranging from
deep to relatively shallow cases ($k_p h > 0.8$, where $k_p$ is the peak
wavenumber, and $h$ is the local depth). The asymmetry between front and rear
rogue wave slopes is identified; it becomes apparent for sufficiently high
waves in rough sea states at all considered depths. The lifetimes of rogue
events may reach up to 30-60 wave periods depending on the water depth. The
maximum observed wave has height of about 3 significant wave heights. A few
randomly chosen in-situ time series from the Baltic Sea are in agreement with
the general picture of the numerical simulations.
