Recovery-induced tipping in Stommel’s kicked ocean box model

Ocean circulation, a key driver of global climate, is subject to recurrent disturbances including freshwater input from glacial melt. Stommel's idealized two-box model predicts two distinct stable regimes of thermohaline ocean circulation and offers a conceptual framework in which to explore the effects of salinity perturbations. A study that superimposed discrete salinity kicks onto the flow of the otherwise continuous model revealed a counterintuitive phenomenon: extending the recovery period between salinity kicks caused a trajectory to tip into an alternative basin of attraction. Here we analyze the recovery-induced tipping phenomenon in Stommel's kicked model across a broader swath of disturbance parameters, finding that the phenomenon is robust across a significant set of kick sizes. Furthermore, bifurcation analysis of flow-kick fixed points reveals that recovery-induced tipping stems from an alternative attractor migrating across an original separatrix as flow times vary. This migration also occurs in a continuous analog of salinity perturbation. Although the recovery times associated with seasonal or decadal freshwater influxes far exceed those associated with recovery-induced tipping, the qualitative dynamics we uncover in Stommel's perturbed model alert us that similar phenomena may occur in other models and real-world systems.