A New Method to Compute Transition Probabilities in Multi-Stable Stochastic Dynamical Systems: Application to the Wind-Driven Ocean Circulation

The Kuroshio Current in the North Pacific displays path changes on an interannual-to-decadal time scale. In an idealized barotropic quasi-geostrophic model of the double-gyre wind-driven circulation under stochastic wind-stress forcing, such variability can occur due to transitions between different equilibrium states. The high-dimensionality of the problem makes it challenging to determine the probability of these transitions under the influence of stochastic noise. Here we present a new method to estimate these transition probabilities, using a Dynamical Orthogonal (DO) field approach. In the DO approach, the solution of the stochastic partial differential equations system is decomposed using a Karhunen–Loève expansion and separate problems arise for the ensemble mean state and the so-called time-dependent DO modes. The original method is first reformulated in a matrix approach which has much broader application potential to various (geophysical) problems. Using this matrix-DO approach, we are able to determine transition probabilities in the double-gyre problem and to identify transition paths between the different states. This analysis also leads to the understanding which conditions are most favorable for transition.