  Nonlinear atmospheric dynamics produce rare events that are hard to predict
and attribute due to many interacting degrees of freedom. Sudden stratospheric
warming event is a model example. Approximately once every other year, the
winter polar vortex in the boreal stratosphere rapidly breaks down, inducing a
shift in midlatitude surface weather patterns persisting for up to 2-3 months.
In principle, lengthy numerical simulations can be used to predict and
understand these rare transitions. For complex models, however, the cost of the
direct numerical simulation approach is often prohibitive. We describe an
alternative approach which only requires relatively short-duration computer
simulations of the system. The methodology is illustrated by applying it to a
prototype model of an SSW event developed by Holton and Mass (1976) and driven
with stochastic forcing. While highly idealized, the model captures the
essential nonlinear dynamics of SSWs and exhibits the key forecasting
challenge: the dramatic separation in timescales between the dynamics of a
single event and the return time between successive events. We compute optimal
forecasts of sudden warming events and quantify the limits of predictability.
Statistical analysis relates these optimal forecasts to a small number of
interpretable physical variables. Remarkably, we are able to estimate these
quantities using a data set of simulations much shorter than the timescale of
the warming event. This methodology is designed to take full advantage of the
high-dimensional data from models and observations, and can be employed to find
detailed predictors of many complex rare events arising in climate dynamics.
