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.