2. Scientific Gain
When compressing the three-dimensional North Atlantic circulation into a two-dimensional streamfunction, the goal is to make the data more manageable and easily visualized, while retaining its essential components. In this section, we present evidence that the AMOC streamfunction in density coordinates retains more essential information than its counterpart in depth coordinates.
The depth space streamfunction (Fig. 2a), presents the AMOC as one large overturning cell covering all depths and all latitudes. In contrast, the density space streamfunction (Fig. 2b and 2c) identifies three distinct overturning cells that are important to the large-scale North Atlantic circulation:
  1. a light overturning cell in the subtropical North Atlantic (30.50-34.8 kg/m3 and 0°-40°N) that depicts the formation of Subtropical Mode Water (STMW)
  2. an intermediate overturning cell spanning all latitudes but with a peak in the subpolar gyre (35.50-37.02 kg/m3, 20°S-60°N) that depicts the formation of Labrador Sea Water (LSW) in the Labrador and Irminger Seas
  3. a dense overturning cell in the Greenland, Iceland, and Norwegian (GIN) Seas (37.02-37.20 kg/m3, 60°N-75°N) that depicts the formation of the densest water masses north of the Greenland-Scotland Ridge.
In depth coordinates, the STMW cell is only apparent in the upper 100 m between 10°N-20°N, and the incredible amount of water mass transformation (4 kg/m3 between the northward and southward limbs) in this cell is lost (Fig. 2b). This is a critical omission because the STMW cell corresponds almost exactly to the peak oceanic MHT from 0°-40°N (Ganachaud and Wunsch, 2003), implying that this cell is indeed important to the MHT, one of the most societally-relevant aspects of the AMOC. Similarly, the strength of the GIN cell (4 Sv) in depth coordinates is only a fraction of its strength in density coordinates (6 Sv), and its importance to forming the densest water masses that spill over the Greenland-Scotland Ridge and fill the deep North Atlantic is not conveyed in depth coordinates.
The AMOC streamfunction in density coordinates also produces a more continuous streamfunction that correctly positions the AMOC maximum in the subpolar North Atlantic, where the majority of the southward limb waters are formed. In contrast, the depth-space streamfunction artificially shifts the maximum of the LSW cell into the subtropical gyre and away from the regions of deep-water formation in the subpolar North Atlantic and Nordic Seas. This southward shift of the maximum AMOC is due to the inability of the depth-space AMOC to capture the horizontal circulation. For example, consider that in depth coordinates, the southward flow of cold, fresh waters in the Labrador Current is negated by the northward flow of warm, saline water in the North Atlantic Current. When these two currents meet near the Grand Banks of Newfoundland, the cold, fresh water subducts under the warm, saline waters and the two limbs start to project back onto the vertical dimension. But this process yields a sharply discontinuous AMOC streamfunction in depth coordinates north of 35°N (Fig. 2a). Instead, summing the meridional velocity fields in density classes rather than depth levels highlights the water mass transformation that occurs as the water circulates cyclonically around the subpolar North Atlantic (Desbruyères et al., 2019), and produces a more continuous AMOC streamfunction between the subtropical and subpolar North Atlantic (Fig. 2b).
The AMOC streamfunction in density coordinates also differentiates between overturning cells that are confined to one gyre and the overturning cell that crosses gyre boundaries. This differentiation becomes essential when assessing forcing mechanisms of AMOC variability. For example, the mechanisms driving the AMOC at subtropical and subpolar latitudes of the North Atlantic are different and time scale dependent (e.g. Jackson et al., 2022). In essence, while wind and buoyancy forcing are both considered important at higher latitudes on interannual-to-decadal scales, in the subtropics wind forcing alone can explain a substantial portion of the variability (Yang, 2015; Kostov et al., 2021), especially on seasonal-to-interannual timescales (Moat et al., 2020). Opposing wind stress variability induced by the NAO in the subpolar and subtropical ocean can lead to opposing decadal AMOC variations, which indeed breaks the notion of a single metric diagnosing the basin-scale overturning cell (Lozier et al., 2010). It is thus imperative to represent the AMOC in density space to gain correct insights into its latitudinal-dependent mechanisms.