Bifurcation analysis of a conceptual model for the Atlantic Meridional Overturning Circulation

Abstract

The Atlantic Meridional Overturning Circulation (AMOC) is a branch of the global ocean circulation system that is driven by salinity and temperature differences. It distributes heat and salt into the Northern Hemisphere via a warm surface current toward the subpolar North Atlantic. A deep cold current returns water to the South Atlantic, forming an overturning cell. There is substantial evidence that the AMOC has slowed down over the last century. An influx of meltwater from the Greenland ice sheets could further weaken the circulation by turning off the deep ocean convection sites in the Labour and Nordic seas. We introduce a conceptual two-box model for temperature and salinity on the surface of the North Atlantic Ocean at these deep ocean convection sites. It extends a model due toWelander, and consists of two vertically stacked boxes that interact via a mixing process. This interaction may be convective or non-convective, depending on the density difference between the boxes. The model is two dimensional and depends on two main parameters: the ratio of salinity and temperature fluxes into the surface ocean box, and the threshold density between the two boxes. These parameters encode the impact of meltwater from the Greenland ice sheets on the overall mixing strength. We take a mathematical perspective and use tools from bifurcation theory to analyse two cases of the model: a limiting case, where it is linear and piecewise-smooth, and the full model, which is smooth. All possible qualitative dynamics in the two-parameter p ; q-plane are found for both cases by using analytical and advanced numerical techniques. We find that, for certain parameter ranges, there are oscillations and bistability that may be observed in the AMOC. Moreover, the mixing process may weaken under an influx of fresh water. Partial bifurcation analysis in a three-parameter space reveals that the smooth system converges to the piecewise-smooth system in a well-defined way. We also find a complete disappearance of oscillations between temperature and salinity on the surface North Atlantic Ocean when the transition between the convective and non-convective regimes is too slow. Overall, we perform a complete bifurcation analysis in the p ; q-plane, which paints a full picture of the possible dynamics exhibited by this AMOC model for any given parameters. In particular, we describe changes in the AMOC strength due to transitions in deep ocean convection in the Labrador and Nordic seas. We also find small regions in the p ; q-plane that may not have physical significance but ensure that the given description is complete.