Stabilising millennial oscillations in large-scale ocean circulation with a delayed feedback due to a circumpolar current

TL;DR

The study tackles why millennial-scale oscillations in the global ocean circulation can arise and persist under certain continental configurations. It combines cGENIE Earth system model experiments (Drake World vs Ridge World) with a minimal three-box delay differential equation model that encodes a circumpolar-delayed salt transport around the Southern Ocean. A delayed feedback term with delay $\tau \approx 1000$ years and strength $\sigma$ can convert subcritical Hopf scenarios into supercritical ones, producing stable millennial oscillations whose bifurcation structure mirrors the EMIC results and require an open circumpolar passage. The findings link Antarctic circumpolar current dynamics to MOC stability and past ocean redox states, and they suggest that changes in ACC speed could influence the likelihood and amplitude of such oscillations in both past and potentially future climates.

Abstract

The global ocean circulation plays a pivotal role in the regulation of the Earth's climate. The specific pattern and strength of circulation also determines how carbon and nutrients are cycled and via the resulting distribution of dissolved oxygen, where habitats suitable for marine animals occur. However, evidence from both geological data and models suggests that state transitions in circulation patterns have occurred in the past. Understanding the controls on marine environmental conditions and biodiversity requires a full appreciation of the nature and drivers of such transitions. Here we present stable millennial oscillations of meridional overturning circulation in an Earth system model of intermediate complexity, cGENIE, that appear to only occur in the presence of a circumpolar current. To demonstrate that a circumpolar current can act as a driver of stable oscillations, we adapt a simple ocean box model to include a delayed feedback to represent the effect of a circumpolar current on meridional overturning circulation. We investigate the millennial oscillatory solutions that arise in the box model by bifurcation analysis and show that the model can reproduce the same bifurcation structure observed in the Earth system model. Our results provide new insights into the nature of oscillations that could have occurred under certain continental configurations in the geological past, and also highlight the potential influence of the changing Antarctic circumpolar current speed on the stability of the Atlantic meridional overturning circulation.

Figures (10)

• Figure 1: cGENIE Drake World setup. (a) Model bathymetry. Landmasses (above sea level; a.s.l.) are shaded white. (b) Zonal wind stress field used as boundary condition. (c) Barotropic streamfunction (Sverdrup, 1 Sv = 10$^6$ m$^{-3}$ s$^{-1}$) simulated at 16 times the pre-industrial atmospheric CO$_2$ concentration of 280 ppm. The boundary is periodic in the horizontal direction.
• Figure 2: cGENIE results. Meridional overturning streamfunction for Drake World at (a) 4 PAL and (b) 16 PAL. (c) Envelope of mean salinity (across the southern channel: comprising all depths, longitudes and 45--90° S) simulated at various atmospheric CO$_2$ levels, illustrating regimes of stable equilibria (where no envelope is visible) and stable oscillations (where the envelope can be seen), for Drake World (blue) and Ridge World (black). (d) Example time series of stable oscillations (legend indicates PAL) simulated using Drake World with transients (initial spin-up of 30 kyr) removed.
• Figure 3: Boxes representing regions of the ocean with salinity variables $S_{i\in\{1,2,3\}}$ with arrows representing meridional water flux of strength $m$ and zonal flux of the southern channel of strength $\sigma$. Parameters $F_1$ and $F_2$ represent freshwater fluxes.
• Figure 4: Solutions of model (\ref{['eq:titz_delay']}) depending on freshwater forcing parameter $F_1$. Solid/dashed curves represent stable/unstable solutions. Black are equilibria and blue are maxima of periodic solutions. White and black filled circles represent Hopf and fold bifurcations, respectively. (a) is without the delayed feedback (i.e. $\sigma=0$), while (b) is with $\sigma=11 \text{~Sv}$. The delay time $\tau$ is set to $900$ years. (c) shows an example time series with $\sigma=11\text{~Sv}$ and $F_1=-0.208\text{~Sv}$.
• Figure 5: Curves of Hopf bifurcations. At a Hopf bifurcation the steady-state solution loses (or gains) stability and produces a branch of periodic solutions. Where the curves are thin/thick the Hopf bifurcation produces a branch of unstable/stable periodic solutions. The colours refer to different delay times $\tau$ shown in the legend.