  We consider the problem of short-term prediction of rare, extreme water waves
in unidirectional fields, a critical topic for ocean structures and naval
operations. One possible mechanism for the occurrence of such rare,
unusually-intense waves is nonlinear wave focusing. Recent results have
demonstrated that random localizations of energy, induced by the dispersive
mixing of different harmonics, can grow significantly due to localized
nonlinear focusing. Here we show how the interplay between i) statistical
properties captured through linear information such as the waves power spectrum
and ii) nonlinear dynamical properties of focusing localized wave groups
defines a critical length scale associated with the formation of extreme
events. The energy that is locally concentrated over this length scale acts as
the "trigger" of nonlinear focusing for wave groups and the formation of
subsequent rare events. We use this property to develop inexpensive, short-term
predictors of large water waves. Specifically, we show that by merely tracking
the energy of the wave field over the critical length scale allows for the
robust, inexpensive prediction of the location of intense waves with a
prediction window of 25 wave periods. We demonstrate our results in numerical
experiments of unidirectional water wave fields described by the Modified
Nonlinear Schrodinger equation. The presented approach introduces a new
paradigm for understanding and predicting intermittent and localized events in
dynamical systems characterized by uncertainty and potentially strong nonlinear
mechanisms.
