Tipping points induced by parameter drift in an excitable low-order model of the wind-driven ocean circulation

A quasi-geostrophic, low-order model of the wind-driven ocean circulation is used to illustrate tipping points induced by time-dependent forcing in excitable chaotic systems. When the wind stress amplitude G is constant in time, our model has a bifurcation from low-amplitude oscillations to high-amplitude relaxation oscillations (ROs) at a wind intensity value G_c. In the presence of time-dependent wind stress, the corresponding tipping point time t_tp is defined as the time at which ROs arise. Numerical experiments are carried out using ensemble simulations in the presence of different drift rates of monotonically increasing forcing. Additional experiments include small periodic perturbations of such forcing. The results indicate substantial sensitivity of t_tp and G(t_tp) Rate-induced tipping, coexisting pullback attractors and total independence from initial states are found for subsets of parameter space. Besides, nonlinear resonance occurs in the presence of periodic perturbations for periods comparable to the RO time scale. The small periodic perturbation can be thought of as the seasonal-to-interannual variability in the wind stress, while the monotonically increasing component stands for the effect of amplification in the midlatitude winds due to anthropogenic warming.