On box models of the North Atlantic thermohaline circulation: Intrinsic and extrinsic millennial timescale variability in response to deterministic and stochastic forcing

Abstract

Millennial timescale variability in the North Atlantic Ocean circulation is often discussed in terms of concepts that are rooted in the dynamics of simple, low‐dimensional box models. In this study we discuss possible explanatory mechanisms for the millennial timescale oscillations of the North Atlantic Thermohaline Circulation that have been revealed by the Greenland ice core record for the late glacial period. We subject three qualitatively different low‐order models to stochastic and sinusoidal perturbations: (1) a bistable model, (2) a model with a single stable equilibrium point and a single stable periodic orbit (limit cycle) corresponding to a collapse‐flush cycle in the North Atlantic circulation, and (3) a model with a single globally stable equilibrium point which nevertheless exhibits complex behavior when perturbed. We discuss both the physical nature of the model response and its parameter dependence. We conclude that the traditional definition of stochastic resonance should be expanded and that the temporal characteristics of the noise terms should be considered an integral part of model construction, as they profoundly affect the efficacy of a given explanatory mechanism.