Multiscale dynamics and stochastic forcing of the Atlantic meridional overturning circulation in conceptual models

The Atlantic meridional overturning circulation (AMOC) is an important component of the global climate system. It serves to balance the climate in the Atlantic by transporting heat and salt from the equator northward, where the surface water sinks and flows back south to join with the other global ocean current systems. It has been shown in models ranging from conceptual box models to full numerical general circulation models that the AMOC exhibits two stable equilibrium states, one strong (as in the present-day) and one weak or nonexistent. These states and transitions between them are influenced by climatological changes, as evidenced in the past. We investigate the effects of freshwater perturbations and temperature variability on the transition between these equilibrium states within the context of simple box models. We employ a two-box single hemispheric model with slowly-varying restoring temperature conditions and analyze numerical solutions as well as multiple scales approximations produced by utilizing the different time scales involved. Our findings suggest that large temperature gradients between boxes favor a strong AMOC. For a restoring temperature that is periodic in nature, the behavior of the AMOC is less straightforward, and depends upon the relative amplitudes of temperature and freshwater flux variability. A multiscale analysis indicates that standard multiple scales techniques must be modified for this model due to the fast-slow nature of the system. Three methods are investigated which provide good approximate analytic solutions within the regions of slow dynamics provided the approximations remain uniform. Additionally, we extend the spatial resolution of the model to three- and four-box versions which include a southern hemispheric box. We analyze the effects of stochastic freshwater perturbations with constant and slowly-varying restoring temperatures and compare results to those of the original two-box model. The higher resolution models display significantly different behavior than the two-box models due to the nature of the weak equilibrium corresponding to a shutdown of the circulation in those models. The separate equilibrium states seem to be more locally stable, and inter-equilibria transitions are less likely in the higher resolution models. Stochastic horizontal diffusivity in a three-box model also indicates that the AMOC is highly sensitive to fluctuations and uncertainty in internal diffusion.