  We consider the problem of large wave prediction in two-dimensional water
waves. Such waves form due to the synergistic effect of dispersive mixing of
smaller wave groups and the action of localized nonlinear wave interactions
that leads to focusing. Instead of a direct simulation approach, we rely on the
decomposition of the wave field into a discrete set of localized wave groups
with optimal length scales and amplitudes. Due to the short-term character of
the prediction, these wave groups do not interact and therefore their dynamics
can be characterized individually. Using direct numerical simulations of the
governing envelope equations we precompute the expected maximum elevation for
each of those wave groups. The combination of the wave field decomposition
algorithm, which provides information about the statistics of the system, and
the precomputed map for the expected wave group elevation, which encodes
dynamical information, allows (i) for understanding of how the probability of
occurrence of rogue waves changes as the spectrum parameters vary, (ii) the
computation of a critical length scale characterizing wave groups with high
probability of evolving to rogue waves, and (iii) the formulation of a robust
and parsimonious reduced-order prediction scheme for large waves. We assess the
validity of this scheme in several cases of ocean wave spectra.
