3. Confusion
The AMOC streamfunction in density coordinates is confusing to non-experts - where the various cells are located in the water column is not clear, and the typical conveyor belt analogy gets convoluted when zonally-sloped isopycnals become important. Thus, how to visualize the AMOC in density space and communicate it to wide audiences is vital to facilitating its widespread adoption. This can be done by remapping the streamfunction in density space into depth coordinates at the depth of each density layer. Practically, this process involves calculating the zonal-mean depth at each latitude for each isopycnal, and then plotting the values of the density-space streamfunction at those depths (Fig. 2c and 2f; McIntosh and McDougall, 1996; Young, 2012; Xu et al., 2018; Rousselet et al., 2020). This yields a streamfunction that more accurately connects the size of the feature in the ocean with the size of the circulation feature in the figure, and makes the results more immediately understandable to a wider audience.
Further complicating this matter is the language used when referring to the AMOC – the “upper limb” is often referred to as the northward component and the “lower limb” as the southward component. But those terms are rooted in the depth-coordinate definition. Instead, it is more accurate to refer to the “northward limb” and “southward limb”.
The literature is also divided between the two definitions, which leads to confusion when results are compared. The most prominent example of this divide is that the RAPID array at 26°N has been reporting their AMOC data in depth coordinates for nearly 20 years (Moat et al., 2020), while the Overturning in the Subpolar North Atlantic Program (OSNAP) publishes their results in density coordinates (Lozier et al., 2019; see panels D-F in Fig. 2). Though the maximum AMOC value at RAPID is not sensitive to the choice of coordinate system (compare Fig. 2a with 2b at 26°N), the depth space definition diminishes the STMW cell and thus the RAPID streamfunction in depth space misses an opportunity to provide direct in situ data about the STMW cell. Similarly, many physical oceanography modeling and reanalysis papers have published their AMOC metrics in density coordinates (e.g. , Lumpkin and Speer, 2006; Lherminier et al., 2007; Marshall and Speer, 2012; Kwon and Frankignoul, 2014; Xu et al., 2016; Hirschi et al., 2020; Biastoch et al., 2021; Yeager et al., 2021), while most climate studies use depth coordinates for historical and logistical reasons (e.g. , Caesar et al., 2018; Jackson and Wood, 2018; Weijer et al., 2020; Liu and Federov, 2021). Output from the various CMIP models contain an AMOC variable that is defined in depth coordinates, and recalculating this variable in density coordinates would require accessing each models’ velocity and density fields. Repeating this calculation for tens of models each with various runs spanning hundreds of years is prohibitive for most users (Weijer et al., 2020; Jackson and Petit, 2022).
Another source of confusion between studies is the choice of AMOC metric. As evident in the density-space AMOC streamfunction (Fig. 2), the AMOC consists of multiple overturning cells that do not span all latitudes. Thus the AMOC is likely not meridionally coherent (e.g. Bingham et al., 2007; Lozier et al., 2008; Jackson et al., 2022), and it is difficult or near impossible to represent the wider North Atlantic circulation using a single metric, i.e. the traditional maximum streamfunction in depth coordinates (e.g., Vellinga and Wood, 2008; Drijfhout et al., 2012; Liu and Fedorov, 2021). In both climate models (Hirschi et al., 2020) and ocean reanalyses (Karspeck et al., 2017), the latter metric is located within the subtropics, where wind forcing dominates (Zhao and Johns, 2014). However, in density coordinates, the maximum transport is consistently found at higher latitudes (Hirschi et al., 2020), sometimes shifted northward by as much as 20° of latitude (Biastoch et al., 2021), where buoyancy forcing and horizontal gyre circulation play a dominant role (Chafik and Rossby, 2019; Zhang and Thomas, 2021). This latitudinal disconnect has confused oceanographers for decades: how can a meridionally-oriented current not be meridionally coherent? The recirculation cells depicted in the density space streamfunction illuminate the answer by identifying features that are confined to specific latitudinal ranges, and should not be expected to be meridionally coherent.
Another source of confusion in the literature is whether variability in the AMOC leads or lags variability in the dense overflow waters. The maximum AMOC in depth space at 45°N in a 600 year run of the Community Earth System Model leads variability in the overflow strength by 2-3 years (Danabasoglu et al., 2020), whereas the maximum AMOC in depth space between 27.5°N and 32.5°N in a 1600 year run of the HadCM3 coupled climate model lags variability in the overflows by 10 years (Hawkins and Sutton, 2008). Although the inconsistency between these two studies may be attributed to the overflow parametrization in the different models, it could also simply be a result of the AMOC definitions (subpolar vs. subtropical) used in these studies, and the relative importance of wind and buoyancy forcing at each of these latitudes. As the production of overflow water in the Nordic Seas is considered an important diagnostic of AMOC stability (Chafik and Rossby, 2019) and therefore could provide an early warning of future rapid changes of the broader North Atlantic circulation, avoiding such unnecessary confusion of the AMOC definition is critical.