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Paleoclimate proxy data suggest that the Atlantic Meridional Overturning Circulation (AMOC) was shallower at the Last Glacial Maximum (LGM) than its preindustrial (PI) depth. Previous studies have suggested that this shoaling necessarily accompanies Antarctic sea ice expansion at the LGM. Here the influence of Southern Ocean surface forcing on the AMOC depth is investigated using ocean‐only simulations from a state‐of‐the‐art climate model with surface forcing specified from the output of previous coupled PI and LGM simulations. In contrast to previous expectations, we find that applying LGM surface forcing in the Southern Ocean and PI surface forcing elsewhere causes the AMOC to shoal only about half as much as when LGM surface forcing is applied globally. We show that this occurs because diapycnal mixing renders the Southern Ocean overturning circulation more diabatic than previously assumed, which diminishes the influence of Southern Ocean surface buoyancy forcing on the depth of the AMOC.