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Rare events arising in nonlinear atmospheric dynamics remain hard to predictand attribute. We address the problem of forecasting rare events in aprototypical example, Sudden Stratospheric Warmings (SSWs). Approximately onceevery other winter, the boreal stratospheric polar vortex rapidly breaks down,shifting midlatitude surface weather patterns for months. We focus on two keyquantities of interest: the probability of an SSW occurring, and the expectedlead time if it does occur, as functions of initial condition. These\emph{optimal forecasts} concretely measure the event's progress. Directnumerical simulation can estimate them in principle, but is prohibitivelyexpensive in practice: each rare event requires a long integration to observe,and the cost of each integration grows with model complexity. We describe analternative approach using integrations that are \emph{short} compared to thetimescale of the warming event. We compute the probability and lead timeefficiently by solving equations involving the transition operator, whichencodes all information about the dynamics. We relate these optimal forecaststo a small number of interpretable physical variables, suggesting optimalmeasurements for forecasting. We illustrate the methodology on a prototype SSWmodel developed by Holton and Mass (1976) and modified by stochastic forcing.While highly idealized, this model captures the essential nonlinear dynamics ofSSWs and exhibits the key forecasting challenge: the dramatic separation intimescales between a single event and the return time between successiveevents. Our methodology is designed to fully exploit high-dimensional data frommodels and observations, and has the potential to identify detailed predictorsof many complex rare events in meteorology.

Learning forecasts of rare stratospheric transitions from short simulations