1. Motivation
The Atlantic Meridional Overturning Circulation (AMOC) consists of a complex set of currents in the Atlantic Ocean that move warm, saline water northward and return cold, fresh water southward. Despite this simple qualitative description, defining the AMOC quantitatively is not straightforward. Traditionally, oceanographers have defined it in depth coordinates: locate the depth where the currents shift from net northward to net southward and sum the meridional velocities above that depth. If one assumes the Atlantic/Arctic is a closed basin by considering the Bering Strait throughflow of ~1 Sv (Woodgate et al., 2018) below the detection level of the AMOC observing arrays (Cunningham et al., 2007; Lozier et al., 2019), and by neglecting net mass divergence and precipitation in the North Atlantic on timescales longer than 10 days (Kanzow et al., 2007), then the depth where the currents shift from net northward to net southward corresponds to the depth of maximum overturning, and the sum of the meridional velocity above it is equal to the maximum in the AMOC stream function.
There is historical precedent for this depth-space definition - oceanographers have measured the AMOC for decades in the subtropical North Atlantic, where strong thermal stratification provides enough baroclinicity in the water column that the warm northward limb of the AMOC can flow directly over the cold southward limb (Fig. 1). The longest direct measurements of the AMOC are from a repeat hydrographic line across 25°N that has been occupied since 1957 (Hall and Bryden, 1982), and the first continuous observations of the AMOC have been made since 2004 at the RAPID mooring array across 26.5°N (Cunningham et al., 2007). This latitude was chosen because the oceanic meridional heat transport (MHT) reaches its maximum in the subtropics (Ganachaud and Wunsch, 2003), and because much of the Gulf Stream was already being continuously measured in the Florida Straits by a defunct telephone cable (Sanford and Larsen, 1985; Barringer and Larsen, 2001).
But this focus on the subtropical North Atlantic has led to a definition of the AMOC that emphasizes its vertical dependency despite the AMOC shifting to a horizontal circulation pattern further north (e.g.Zhang and Thomas, 2021). In the subpolar North Atlantic and Nordic Seas, reduced vertical stratification does not permit opposing currents to flow directly over one another, and instead, the northward limb of the AMOC flows along the eastern side of the basin while the southward limb flows along the western side at similar depths. Here, though the northward and southward limbs are no longer differentiated in depth, their densities remain distinct. Thus when the meridional velocities are zonally summed in density classes, the northward and southward limbs remain distinct in the streamfunction, even at high latitudes where the canonical ‘conveyor belt’ lays on its side.