Millennial-Scale Oscillation of the AMOC in a Two-hemisphere Box Model

We identify a millennial-scale oscillatory eigenmode of the Atlantic Meridional Overturning Circulation (AMOC) in a conceptual two-hemisphere box model. To isolate the governing mechanism, we examine two idealized cases that represent situations where AMOC variability arises exclusively from the North Atlantic Deep Water (NADW) cell or from the Antarctic Bottom Water (AABW) cell. 

In the NADW-influenced case, the AMOC anomaly is parameterized as positively related to the north-south salinity difference. Linear analysis shows that the oscillation period increases as the mean AMOC strength decreases. Thus, a weaker mean AMOC produces slower oscillations, and the dominant time scale can shift from multicentennial to millennial. For example, when the mean AMOC strength is near 10 Sv, the model yields a dominant millennial-scale oscillation. 

In the AABW-influenced case, the AMOC anomaly arises from AABW-related processes and exhibits a negative linear dependence on the north-south salinity difference. The resulting millennial oscillation is driven by upward transport from the deep to the upper South Atlantic, a process that responds sensitively to local surface freshwater fluxes. 

Taken together, these results highlight internal ocean dynamics that can generate millennial-scale AMOC variability through two distinct pathways, associated with northern and southern overturning processes, respectively. Finally, we discuss the implications of these findings for interpreting observed millennial-scale climate variability during the last glacial period and the Holocene.