Sudden stratospheric warming (SSW) events pose a major challenge for seasonal weather prediction because of their rapid, complex onset and development and sensitivity to initial conditions. Climate models also struggle to capture the long-term statistics of SSW, owing to their diversity and intermittent nature. The high impact of such rare events, including strong hurricanes and monsoons as well as SSW, motivates a general formulation for quantifying their statistics and predictability. Here we describe transition path theory (TPT), a mathematical framework originally developed for molecular simulation, and argue that it is a useful paradigm for both real-time forecasting and mechanistic understanding of rare climate events. We demonstrate the utility of TPT on a low-order, stochastically forced stratospheric model with two stable states, corresponding to radiative equilibrium and a vacillating regime conducive to SSW events. In this stochastic bistable setting, TPT provides an ideal probabilistic forecast of a transition as well as dominant transition pathways and return times. These dynamical statistics are obtained by solving partial differential equations in the model's phase space that capture the distribution of possible transition paths. We demonstrate this explicitly on a highly truncated, stochastically forced Holton-Mass model. In a low-noise regime, TPT predicts dominant transition pathways involving an eastward streamfunction phase giving way to a sudden deceleration in mean zonal wind, characteristics that are borne out by numerical experiments.
University
University of Chicago