  The evolution of crossing sea states and the emergence of rogue waves in such
systems are studied via numerical simulations performed using a higher order
spectral method to solve the free surface Euler equations with a flat bottom.
Two classes of crossing sea states are analysed: one using directional spectra
from the Draupner wave crossing at different angles, another considering a
Draupner-like spectra crossed with a narrowband JONSWAP state to model spectral
growth between wind sea and swell. These two classes of crossing sea states are
constructed using the spectral output of a WAVEWATCH III hindcast on the
Draupner rogue wave event. We measure ensemble statistical moments as functions
of time, finding that although the crossing angle influences the statistical
evolution to some degree, there are no significant third order effects present.
Additionally, we pay particular attention to the mean sea level measured
beneath extreme crest heights, the elevation of which (set up or set down) is
shown to be related to the spectral content in the low wavenumber region of the
corresponding spectrum.
