Editorial Type:
Article
Article Type:
Research Article

Mechanism on the Short-Term Variability of the Atlantic Meridional Overturning Circulation in the Subtropical and Tropical Regions

Lei Han aChina-ASEAN College of Marine Sciences, Xiamen University Malaysia, Sepang, Malaysia
bLaoshan Laboratory, Qingdao, China

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https://orcid.org/0000-0001-6470-4152
Online Publication:
13 Sep 2023
Print Publication:
01 Sep 2023
DOI:
https://doi.org/10.1175/JPO-D-23-0027.1
Page(s):
2231–2244
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Abstract

The continuous, moored observation revealed significant variability in the strength of the Atlantic meridional overturning circulation (AMOC). The cause of such AMOC variability is an extensively studied subject. This study focuses on the short-term variability, which ranges up to seasonal and interannual time scales. A mechanism is proposed from the perspective of ocean water redistribution by layers. By offering explanations for four phenomena of AMOC variability in the subtropical and tropical oceans (seasonality, meridional coherence, layered-transport compensation as observed at 26.5°N, and the 2009/10 downturn that occurred at 26.5°N), this mechanism suggests that the short-term AMOC variabilities in the entire subtropical and tropical regions are governed by a basinwide adiabatic water redistribution process, or the so-called sloshing dynamics, rather than diapycnal processes.

Significance Statement

The Atlantic meridional overturning circulation (AMOC) is a key component in the global climate system due to its immense power in redistributing heat meridionally, which contributes to the hospitable climate of the United Kingdom and western Europe. Therefore, any changes in AMOC can have significant impacts on both global and local climate variability. Here I propose a mechanism to explain the short-term (up to interannual) AMOC variability in the subtropical and tropical regions from the perspective of ocean water redistribution. This mechanism suggests that the short-term variability of AMOC strength is dominated by an adiabatic process, and thus, its large-amplitude variation is mostly a reversible process. In other words, AMOC may be more resilient to short-term variability than previously believed, and it could recover autonomously from the abrupt changes.

Publisher’s Note: This article was revised on 15 December 2023 to correct the author’s second affiliation.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Lei Han, lei.han@xmu.edu.my

Abstract

The continuous, moored observation revealed significant variability in the strength of the Atlantic meridional overturning circulation (AMOC). The cause of such AMOC variability is an extensively studied subject. This study focuses on the short-term variability, which ranges up to seasonal and interannual time scales. A mechanism is proposed from the perspective of ocean water redistribution by layers. By offering explanations for four phenomena of AMOC variability in the subtropical and tropical oceans (seasonality, meridional coherence, layered-transport compensation as observed at 26.5°N, and the 2009/10 downturn that occurred at 26.5°N), this mechanism suggests that the short-term AMOC variabilities in the entire subtropical and tropical regions are governed by a basinwide adiabatic water redistribution process, or the so-called sloshing dynamics, rather than diapycnal processes.

Significance Statement

The Atlantic meridional overturning circulation (AMOC) is a key component in the global climate system due to its immense power in redistributing heat meridionally, which contributes to the hospitable climate of the United Kingdom and western Europe. Therefore, any changes in AMOC can have significant impacts on both global and local climate variability. Here I propose a mechanism to explain the short-term (up to interannual) AMOC variability in the subtropical and tropical regions from the perspective of ocean water redistribution. This mechanism suggests that the short-term variability of AMOC strength is dominated by an adiabatic process, and thus, its large-amplitude variation is mostly a reversible process. In other words, AMOC may be more resilient to short-term variability than previously believed, and it could recover autonomously from the abrupt changes.

Publisher’s Note: This article was revised on 15 December 2023 to correct the author’s second affiliation.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Lei Han, lei.han@xmu.edu.my
Keywords: Atlantic Ocean; Meridional overturning circulation; Ocean dynamics; Interannual variability; Oceanic variability; Seasonal variability

1. Introduction

The meridional overturning circulation (MOC) is typically portrayed as a mapping of the full 3D ocean circulations onto the 2D plane of latitude and depth (or density), which is commonly depicted using a streamfunction. This representation effectively schematizes the characteristics of the ocean circulation in the vertical plane. The main objective of the present research is to investigate the variability of the Atlantic MOC (AMOC) in the subtropical and tropical regions.

The strength of the AMOC has an intimate relationship with the meridional heat transport in the Atlantic (Knight et al. 2005; Biastoch et al. 2008; Dong et al. 2009; Kelly et al. 2014; Dong et al. 2015; Jackson et al. 2019; Lozier et al. 2019; Smith and Heimbach 2019; Dong et al. 2021), which contributes significantly to the climate variability in the United Kingdom and western Europe (Sutton and Hodson 2005; Hirschi et al. 2007; Rhines et al. 2008; Sutton and Dong 2012; Srokosz and Bryden 2015; Lozier et al. 2017; Moffa-Sánchez and Hall 2017). The dramatic variability of AMOC strength came as a surprise as the transbasin mooring array at 26.5°N, the Rapid Climate Change–Meridional Overturning Circulation and Heatflux Array (RAPID–MOCHA), came into operation since 2004 (Srokosz and Bryden 2015). This remarkable variability has motivated numerous studies aiming to understand its controlling mechanisms on different time scales. Wind and buoyancy forcing have been deemed as the main causes of such variability, with buoyancy forcing dominating all time scales in the subpolar North Atlantic and the decadal one in the subtropics, while wind forcing dominant in the short-term variability in the subtropical area (Biastoch et al. 2008; Cabanes et al. 2008; Lozier 2012; Polo et al. 2014; Pillar et al. 2016; Kostov et al. 2019). In the context of the current research, the term “short-term” pertains to a specific time scale of interest, encompassing subannual, seasonal, and interannual time scales as defined in previous studies. (Cunningham et al. 2007; Hirschi et al. 2007). This paper aims to investigate the short-term AMOC variability in the subtropical and tropical (ST&T) Atlantic. Specifically, four phenomena/questions related to AMOC variability in this region have been examined.

First, although there is widespread consensus that wind forcing primarily controls the short-term AMOC variability, particularly on the seasonal time scale, in the ST&T Atlantic (Biastoch et al. 2008; Cabanes et al. 2008; Kanzow et al. 2010; Lozier 2010; Polo et al. 2014; Xu et al. 2014; Zhao and Johns 2014a,b; Pillar et al. 2016; Evans et al. 2017; Johnson et al. 2019; Kostov et al. 2021), specific dynamical interpretations vary. Take the section of 26.5°N, for example; the wind-driven process of dominance remains debated. Some studies attributed such short-term variability to the local variation at 26.5°N, such as processes at western boundary (Frajka-Williams et al. 2016; Kostov et al. 2021), eastern boundary (Chidichimo et al. 2010; Kanzow et al. 2010; Pérez-Hernández et al. 2015), or both (Polo et al. 2014). While some argued, instead of being forced locally, the short-term AMOC variability was a result of a basinwide adjustment to the changed wind (Zhao and Johns 2014a; Yang 2015; Evans et al. 2017).

Second, proof indicates that the AMOC at different latitudes in the subtropics exhibits lagged correlations, with the northern latitudes leading. This characteristic is referred to as the meridional coherence [or latitudinal covariability (Mielke et al. 2013), latitudinal dependence (Zhang 2010), latitudinal coherence (Zou et al. 2020)] of the AMOC (Bingham et al. 2007; Zhang 2010; Elipot et al. 2013; Kelly et al. 2014; Xu et al. 2014; Zhao and Johns 2014b; Yang 2015; Elipot et al. 2017; Frajka-Williams et al. 2018; Li et al. 2019; Wang et al. 2019). However, little or no coherence was identified across the subtropical/subpolar gyre boundary at 40°–50°N (Bingham et al. 2007; Biastoch et al. 2008; Lozier 2010; Zhang 2010; Lozier 2012; Kelly et al. 2014; Elipot et al. 2017; Jackson et al. 2019).

What is the cause of the coherence structure in the ST&T Atlantic? Previous studies pursued this question mainly at the western boundary of the North Atlantic because either advection [export of deep water by the deep western boundary current (DWBC)] or boundary waves there are southward, i.e., in the same direction as the phase shift of the AMOC anomaly (Roussenov et al. 2008; Zhang 2010; Elipot et al. 2013, 2014; Frajka-Williams et al. 2018; Herrford et al. 2021; Kostov et al. 2023). But it was also argued that neither wave adjustment nor DWBC advection seems able to explain the observed pattern of coherence satisfactorily (Elipot et al. 2013).

Third, right in its first year of operation, the RAPID-MOCHA array noticed a phenomenon that the cumulative transport by layers had a small variability at the middle layer compared with the layers at above and below (Kanzow et al. 2007). Longer time series afterward confirmed that the deep changes were localized in the lower North Atlantic Deep Water (NADW) within 3–5 km and were well compensated with the upper-layer (0–1 km) AMOC variations on interannual time scales, while the upper NADW (UNADW, 1–3 km) transport variability, in contrast, does not show large interannual variability (McCarthy et al. 2012; Frajka-Williams et al. 2016; Zou et al. 2019). This phenomenon becomes even more intriguing when considering that the major portion of the NADW is transported by the upper layer instead of the lower layer, as indicated by the RAPID-MOCHA array (McCarthy et al. 2012). A perturbation experiment found surface buoyancy anomaly in the subpolar North Atlantic could generate a transport anomaly at 26°N, primarily concentrated in the upper layer and the lower NADW layer (LNADW) (Kostov et al. 2023). However, the underlying mechanism behind this covariability has not been well identified yet.

Fourthly, in the winter of 2009/10, the RAPID-MOCHA array recorded a significantly weakened AMOC strength, which is commonly referred to as the 2009/10 downturn (McCarthy et al. 2012). It was believed responsible for a coinciding cooling in the upper North Atlantic (McCarthy et al. 2012). This substantial weakening event was attributed to the extreme negative North Atlantic Oscillation (NAO) phase in that winter (McCarthy et al. 2012; Cunningham et al. 2013; Mielke et al. 2013; Zhao and Johns 2014b; Srokosz and Bryden 2015; Jackson et al. 2019) via southward Ekman transport anomaly and intensification of the upper midocean geostrophic flow to the south (Zhao and Johns 2014b). The detailed dynamical process of this downturn and its rapid recovery has yet to be illustrated.

In this research, I attempt to explain the abovementioned questions/phenomena from the perspective of sloshing dynamics. It is an approach that was used to provide a new insight into the remarkable seasonal variability of the Indian Ocean MOC (Han 2021). Here is the idea of this mechanism. When a material surface (typically represented by an isopycnal) heaves up or down in the ocean interior, it squeezes or stretches the water column above or beneath it. This process is accompanied by concurrent horizontal movements of water at both layers due to continuity. In general, such squeezing/stretching-induced horizontal movement forms an anomalous overturning cell in that the squeezed/stretched water column tends to move equatorward/poleward (for the Northern Hemisphere) to preserve its potential vorticity. This cell appears in the Lagrangian coordinate (e.g., density) as well, because the opposite transports comprising the cell are accommodated in separate density layers. This squeezing/stretching-induced water redistribution in the horizontal direction was coined “sloshing” by Schott and McCreary (2001). Han (2021) named such an overturning cell the sloshing MOC. The aim of this paper is to quantify the role of sloshing in the AMOC variability in the ST&T regions.

This paper is set out as follows. Section 2 introduces the data and the method. Section 3 demonstrates how the sloshing solution performs in explaining the abovementioned phenomena concerning AMOC variability. A summary and discussion are given in section 4.

2. Data and method

a. Data

Data used in the subsequent calculation are the Estimating the Circulation and Climate of the Ocean State Estimate version 4 release 3 (ECCO v4r3) (Forget et al. 2015; Fukumori et al. 2017). It is a data assimilation product generated by best fitting the numerical simulation of an ocean general circulation model, the Massachusetts Institute of Technology general circulation model (MITgcm) to over 1 billion observations (Rousselet et al. 2020, 2023). The ECCO v4r3 used here spans the period 1992–2015 with a monthly resolution.

ECCO products skillfully reproduce the AMOC variability, which compares favorably with observations at multiple latitudes (Cabanes et al. 2008; Baehr et al. 2009; Evans et al. 2017; Jackson et al. 2019; Smith and Heimbach 2019; Kostov et al. 2021). It is among the best datasets in the correlation with the RAPID-MOCHA observations (Jackson et al. 2019). The estimate of MOC from ECCO products is in broad agreement with several independent estimates (Cessi 2019). Comparisons between ECCO v4r3 and RAPID-MOCHA array show remarkable agreement in various aspects (Fig. 1). ECCO products have been frequently employed in the process and mechanism studies on the AMOC (e.g., Cessi 2019; Johnson et al. 2019; Rousselet et al. 2020, 2023). It is thus also adopted in the current research for the mechanism study on the AMOC variability. For simplicity, its version number is omitted hereafter when unambiguous.

Fig. 1.
Fig. 1.

Comparison of the AMOC between the RAPID-AMOC mooring at 26.5°N (orange) and ECCO v4r3 (green) at their overlapping period (April 2004–December 2015). Monthly time series are used from both datasets. (a) The overturning streamfunction, i.e., the net northward transport above a depth, across 26.5°N. Shading represents one standard deviation for the respective dataset. (b) Monthly time series of the AMOC index at 26.5°N with a correlation coefficient of 0.74. (c) As in (b), but for the 1-yr filtered time series with a correlation of 0.80. (d) The multitaper power spectrums (Wunsch and Heimbach 2013) for the two time series in (b) with annual and semiannual frequencies being indicated. The AMOC index is defined as the maximum of the overturning streamfunction in (a), or approximately the net northward transport above 1000 m (for ECCO) (Kanzow et al. 2010).

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-23-0027.1

b. Material surface, isopycnal, and heaving velocity

Movements of water parcels in the ocean interior tend to follow the surfaces of constant density, or isopycnals. That is the way how the deep water from lower latitudes rises along the tilted isopycnals to the surface at higher latitudes (Rintoul 2018). Thus, isopycnal is a well materially conserved surface unless there is diapycnal mixing. Within the scope of this research, we focus on the isopycnals below the mixed layer and above the bottom boundary layer, where neglection of diapycnal mixing is an acceptable approximation (Cessi 2019). Indeed, it is the basis of the classical physical oceanographic argument that “there is little or no mixing across buoyancy surfaces.” Below the mixed layer isopycnals are “almost impermeable barriers” (Young 2012). If ξσ(x, y, t) denotes depth of a certain isopycnal of density σ, similar to the way of obtaining the kinetic boundary condition at the free sea surface, the vertical velocity component of the water parcel on the isopycnal (written as wiso) can be obtained as
wiso=∂ξσ∂t+uH⋅∇ξσ.
The first term in the RHS of Eq. (1), which can be written as wheave=∂ξσ/∂t, represents the up-and-down movement of the water parcel alongside the isopycnal surface. The second term, which can be written as wtilt = uH ⋅ ∇ξ, represents the vertical component when the water parcel advects upslope/downslope along the tilted isopycnal.

When evaluated with the monthly data of ECCO, the depth of a given isopycnal, ξσ(x, y, t) is obtained by interpolation from the 3D density field. More technical details can be found in its application to the Indian Ocean MOC (Han 2021). Comparison of wheave + wtilt with the Eulerian vertical velocity in ECCO at about the same depth shows good agreement in the tropical/subtropical Atlantic except some boundary areas (Fig. 1 in the online supplemental material), which indicates the vertical movement of water parcel can be well represented by Eq. (1).

The physical interpretations on the two terms in Eq. (1) were demonstrated in Fig. 4 of Han (2021). The heaving term wheave aims to capture the vertical movement of the water parcel in order to quantify the horizontal volume transport anomaly associated with the squeezing/stretching process, i.e., the so-called sloshing transport. In contrast, the tilting term wtilt is not related with such kind of transport anomaly. Thus, only the wheave component is involved in obtaining the MOC streamfunction anomaly revealed by the isopycnal displacement, i.e., the sloshing MOC streamfunction. In fact, the sloshing MOC streamfunction (to be introduced in the next subsection) derived with wtilt is negligibly small compared with that of wheave (not shown).

c. Sloshing MOC streamfunction

MOC can be depicted by transport within either isopycnal layers or depth layers. While the mean and variation of AMOC transport from the two approaches are nearly identical in the ST&T Atlantic owing to the relatively flat isopycnal (Zhang 2010; Xu et al. 2014). So, here we adopt the customary depth-coordinate in defining the Eulerian MOC streamfunction. Apart from integrating the horizontal velocity component υ, it is equivalent to integrate the vertical velocity component w to obtain the MOC streamfunction (Han 2021). Thus, the sloshing MOC streamfunction, written as ψslo(y, z, t), can be obtained by the following integration,
ψslo(y,z,t)=ψslo(yN,z,t)−∫yyN∫xwxewheave(x,y′,z,t)dxdy′,
where wheave(x, y, z, t) denotes the heaving velocity interpolated to the standard depths and yN the northern boundary of the integration. In contrast to the Indian Ocean, the Atlantic does not have a wall boundary in the north for the integration to start from. In this study, yN is posed at 44°N, where is adjacent to the border of the subtropical and the subpolar gyres (Barrier et al. 2014; Zou and Lozier 2016; Elipot et al. 2017; Yeager et al. 2021). The value of Eulerian MOC, ψEul, at yN is used as the northern boundary condition of ψslo. The northern boundary is posed at 44°N for two reasons: first, the sloshing MOC solution can cover a larger area of the ocean if the boundary is pushed farther north, and second, the integration area should avoid the subpolar region because the extensive diapycnal mixing there undermines the isopycnal as the proxy of material surface, which leads to unforeseeable errors in Eq. (1). The solution of Eq. (2) with the boundary condition ψslo(yN, z, t) = ψEul(yN, z, t) is denoted as ψsloBC.

The relationship between sloshing and heaving can be elucidated using a metaphorical analogy involving toothpaste. Imagine heaving as the act of squeezing toothpaste normal to the tube, while sloshing can be likened to the concurrent flow of toothpaste along the tube in response to the squeezing motion. While one difference has to be noted for the ocean water movement since the isopycnal heaving is due to the horizontal movement of water (convergence or divergence) as well. That is to say, heaving is not the driving factor but the manifestation of the adiabatic sloshing transport. To test the influence of the boundary condition in the solution ψsloBC, another solution is also obtained for the sloshing MOC by setting the anomaly of ψslo(yN, z, t) as zero, i.e., assuming an artificial barrier of overturning anomaly between subtropical and subpolar regions. To differentiate with ψsloBC, this second solution is written as ψsloBC=0. Since variability is the sole concern, it is important to note that the sloshing-MOC solutions presented in the following analysis (i.e., ψsloBC and ψsloBC=0) refer exclusively to the anomaly. All the Eulerian MOC streamfunctions in this paper were calculated using the gcmfaces toolbox (Forget et al. 2015).

3. Results

a. Seasonality of AMOC

Using ECCO, one can calculate the climatological monthly mean streamfunction anomalies of the Eulerian MOC (ψEul) and the sloshing MOC (ψsloBC) with abovementioned method. Striking resemblance is found for all months of the year (see four typical months in Fig. 2, and the other eight months in supplemental Fig. 2). This similarity is remarkable given that the two streamfunctions were derived with independently variables (υ and ρ, respectively). It explains as well the observational fact that the 34.5°S section has a stronger AMOC seasonality than other latitudes in the southern Atlantic (Dong et al. 2015).

Fig. 2.
Fig. 2.

Climatological monthly anomalies of AMOC streamfunctions (Sv; 1 Sv ≡ 106 m3 s−1): (top) the Eulerian MOC (ψEul), (middle) the sloshing MOC (ψsloBC), and (bottom) their difference in four typical months (from left to right: January, April, July, and October). The sloshing MOCs in the upper levels are left out due to the inaccuracy of the solutions in this region. Positive/negative values represent clockwise/anticlockwise-overturning cells. The yellow dashed line marks 26.5°N.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-23-0027.1

In addition to the spatial similarity, the variability of the sloshing MOC also agrees well with the Eulerian one in both phase and amplitude, on both seasonal and interannual time scales, at 26.5°N (Fig. 3). The agreement becomes even better for the last 10 years when more observations become available for data constraint.

Fig. 3.
Fig. 3.

Comparison of the Eulerian (orange) and sloshing (gray, the solution ψsloBC) AMOC anomalies at 26.5°N using ECCO. (a) Full period (January 1992–December 2015) of monthly time series. (b) A 1-yr filter of (a) by applying a sliding average of 12 months. (c) As in (b), but zoomed in for the last 10 years of the data [green shaded span in (a) and (b)]. (d) A 1-yr filter of (c). Also superimposed are the southward transports at the depth range of 3–5 km inferred from the sloshing MOC streamfunction (thin black) and the RAPID array (green solid). Correlations between the two AMOC indexes are indicated in subtitles. Panels (a) and (c) show the annual/subannual variability while (b) and (d) show the interannual variability in the respective periods. “Std(Eul)” and “Std(Slo)” in the subtitle of each panel denote the standard deviations of the Eulerian and sloshing MOC streamfunctions, respectively.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-23-0027.1

b. Meridional coherence

In reproducing the observed AMOC seasonality, ECCO does a good job not only at 26.5°N (Evans et al. 2017; Jackson et al. 2019; Kostov et al. 2021) (Fig. 1), but also in the South Atlantic (Smith and Heimbach 2019). For those latitudes that observations of seasonal cycle are available, such as 41°N (Willis 2010; Mielke et al. 2013), 11°S (Herrford et al. 2021), and several ones within 20°–34.5°S (Dong et al. 2015, 2021), ECCO produces the phases that are close to the observations though the amplitudes are sometimes underestimated (Fig. 4). ECCO also well reproduces the phase lag of 3 months between 41° and 26°N identified by combined observation data (Elipot et al. 2014) (Fig. 5a). Based on ECCO’s performance in these specific zonal sections, we have a certain level of confidence in its faithfully presenting a continuous image of the meridional coherence in the ST&T Atlantic.

Fig. 4.
Fig. 4.

AMOC seasonality at six typical latitudes (34.5°S, 20°S, 0°, 16°N, 26.5°N, 41°N). Solid line and the shading represent the climatological mean and the standard deviation of the strength anomalies for the Eulerian AMOC (green) and the sloshing AMOC (orange), respectively. Observational projects at relevant latitudes are indicated in subtitles. Data: ECCO v4r3.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-23-0027.1

Fig. 5.
Fig. 5.

Hovmöller diagrams of the climatological monthly anomalies of the AMOC index (Sv). (a) The Eulerian one. (b) The sloshing one. The slanted lines in parallel between 26.5° and 41°N indicate the 3-month phase difference between the two latitudes. (c) Difference between (a) and (b). Data: ECCO v4r3.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-23-0027.1

As introduced in section 1, meridional coherence refers to the lagged correlations of AMOC variabilities at different latitudes. Concerning the cause of this phenomenon, the sloshing MOC solution provides an intriguing clue as well. It shows notable resemblance with the Eulerian AMOC in seasonal anomaly throughout the entire ST&T Atlantic (Fig. 5). Besides the climatological mean shown in Fig. 5, interannual spreads between ψEul and ψsloBC are also identical by examining several selected latitudes (Fig. 4). This result suggests that the meridional coherence of the AMOC seasonality is very likely a result of the basinwide adiabatic water redistribution process.

In addition to the seasonal time scale, the meridional coherence can also be presented at the interannual time scale with the 1-yr filtered AMOC anomalies (as shown in Fig. 3b) at various latitudes. Figure 6 demonstrates that the north–south propagation of anomaly also occurs at this time scale during certain period and can be broadly explained by the sloshing dynamics. It is worth noting that the anomaly does not always propagate southward; at certain times, it can also propagate northward (e.g., during the years 2012–14). This alerts us to another possibility regarding the anomaly at the northern boundary: that anomaly may originate not only from the subpolar region but also from within the ST&T regions, e.g., from the South Atlantic. Further investigation is necessary to understand the specific dynamics that lead to the northward propagation at the interannual time scale.

Fig. 6.
Fig. 6.

As in Fig. 5, but for the 1-yr filtered time series.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-23-0027.1

Spall and Nieves (2020) utilized a two-layer model to explain the mechanism of the remotely forced MOC as a wind-forced mass imbalance adjustment. Their idea is close to the explanation of the meridional coherence in the above analysis using sloshing dynamics.

c. Layered-transport compensation as observed by RAPID

As introduced in section 1, the well compensated transports between upper layer (0–1 km) and bottom layer (3–5 km) observed by the RAPID-MOCHA array have not been ideally explained so far. Once again, the sloshing perspective offers insights into this unresolved issue.

The southward sloshing transport within 3–5 km agrees closely with the AMOC strength, i.e., the northward upper-layer transport above 1000 m, on both annual and interannual time scales in the last decade of the data (Figs. 3c,d). The correlation coefficients between the two (the orange and the thin black) are 0.71 and 0.90 as shown in Figs. 3c and 3d, respectively, even though the agreement is reduced for the earlier years (Fig. 3b). For reference, the southward transport at 3–5 km as observed by RAPID-MOCHA array is also plotted (green solid, which is the transport term, t_ld10, adapted from the RAPID transport product) and bears a close resemblance to the sloshing transport within 3–5 km. This agreement is noteworthy, especially considering the limited data available for assimilation of ECCO in the deep ocean.

The above analysis implies that the transport anomaly that occurs in the upper layer at 26.5°N is mostly accommodated in the bottom layer. That is, the LNADW layer is more squeezed/stretched than the UNADW layer when they covary with the upper layer (0–1 km). A schematic is offered to illustrate such dynamics (Fig. 7). That the correlation is higher on interannual time scale (Figs. 3c,d) is consistent with the observations (McCarthy et al. 2012; Frajka-Williams et al. 2016; Zou et al. 2019). The specific cause why the two bounding isopycnals of UNADW fluctuate in such sync remains an open question. A multilayer model may be promising in understanding its dynamics.

Fig. 7.
Fig. 7.

Schematic illustrating the layered-transport compensation at 26.5°N. The delineating isopycnals of the UNADW layer fluctuate synchronously, resulting in the bulk movement of the UNADW (represented by stippling) behaving as a “rigid body” with minimal squeezing or stretching. Meanwhile, the upper layer (0–1 km) and the LNADW layer (3–5 km) are either squeezed or stretched simultaneously, which produces compensated transport anomalies. The transport anomalies are in opposite meridional directions because of PV conservation. The gray curve represents the overturning streamfunction at 26.5°N. The lengths of arrows do not reflect the magnitude of the mean transport, but rather the magnitude of the variability. The heaving velocity (the group of black arrows) of each isopycnal is not necessarily uniform all over.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-23-0027.1

d. The 2009/10 AMOC downturn as detected by RAPID

The exceptional 2009/10 reduction in AMOC strength in the RAPID-MOCHA record is accurately reproduced in ECCO (Fig. 1b) and it is evident on both seasonal and interannual time scales (Figs. 3c,d). The complete progression of the AMOC reduction and subsequent recovery is captured in the sloshing MOC as well (Fig. 3). This suggests that this weakening event is likely attributed to an extreme basinwide water redistribution process driven by the anomalous wind.

This view is corroborated by comparing the anomalies of Eulerian and sloshing MOCs during the downturn (Figs. 8a,b). The anomalous negative Eulerian MOC cell in the subtropics is well accounted for by sloshing. This anomalous cell agrees well with the composite of the AMOC anomalies under negative NAO regime by a model study although the latter has a larger amplitude (Barrier et al. 2014). The upwelling/downwelling limb of this anomalous cell in the subtropics coincides well with the anomalous Ekman-sucking/pumping region (Barrier et al. 2014; Elipot et al. 2017), suggesting that this overturning cell is associated with the upwelling that is revealed by the isopycnal displacement. Moreover, the sloshing mechanism can also explain why the LNADW flow at depth of 3–5 km “weakened in concert with” the upper-ocean limb during the event, as observed in previous study (Srokosz and Bryden 2015). This is because the anomalous sloshing cell extends all the way to the bottom ocean, as depicted in Figs. 8a and 8b. Subpolar process is not likely the main cause of this event because the solution has undergone minimal changes when the anomaly communication across the intergyre boundary is prohibited in the solution ψsloBC=0 (red dashed in Fig. 8b).

Fig. 8.
Fig. 8.

The anomalous isopycnal depths and MOC streamfunctions in the 2009/10 AMOC downturn with ECCO. The anomalous (a) Eulerian and (b) sloshing AMOC streamfunctions (Sv) of the period August 2009–June 2010 (span between the two vertical lines in Fig. 3c) with respect to the climatology of 2006–15 show resemblance in both amplitude and extent. The black solid and red dashed contours represent solutions, ψsloBC and ψsloBC=0, respectively. The yellow vertical dashed line marks the location of 26.5°N. (c) The climatological monthly anomalies of the zonally averaged isopycnal depth of 27.5σ0, which lies at approximately 1000 m. Positive (negative) values represent shoaling (deepening) depths. April (thick blue) and October (thick red) are highlighted while all other months are shown in gray. The climatology uses the data of the last 10 years (2006–15). The depth anomaly of April 2010 is indicated by the dashed blue line.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-23-0027.1

The anomalously uplifted isopycnal between 30° and 40°N at the end of this weakening event serves as the third supporting evidence on the aforementioned explanation (Fig. 8c, marked by the ellipse). An early study drew a similar conclusion by attributing the downturn to “an adiabatic shoaling of isotherms through decreased Ekman pumping” (Evans et al. 2017). On the other hand, the reversible nature of the adiabatic sloshing process also provides a clue to why the AMOC could recover “quickly from this downturn” (McCarthy et al. 2012).

e. Dependency of the sloshing solution on the boundary condition

The above results show the sloshing solution ψsloBC well reproduces the MOC variabilities at both seasonal and interannual time scales in the ST&T Atlantic. This solution from Eq. (2) has two crucial elements, the boundary condition at 44°N (the superscript “BC”) and the adiabatic water redistribution in the ST&T regions (the subscript “slo”). What are the relative contributions from both elements, and to what extent (or over what time scales) does the solution ψsloBC depend on the boundary condition?

Contribution from the boundary condition could be evaluated by comparing the two solutions, ψsloBC and ψsloBC=0. The only difference between them is that the northern-boundary value in ψsloBC=0 is set to zero, i.e., prescribing a barrier for the overturning anomaly.

When analyzing the time series of the solution ψsloBC=0, we observe that the agreement with the Eulerian MOC has remained relatively stable on a monthly basis, but has noticeably degraded on an interannual time scale, characterized by an even larger variance (Fig. 9). To further test this result, another latitude, 11°S, is also examined (supplemental Figs. 3 and 4). While all correlations remain high, the level of agreement is likewise reduced for solution ψsloBC=0 on the interannual time scale. Recapping from the previous results, the sloshing MOC anomaly associated with the 2009/10 downturn shows no significant difference between the two solutions (Fig. 8b). Moreover, the reproduced latitudinal structure of the MOC variability in ψsloBC (Fig. 5) is entirely attributed to the sloshing factor, given that the boundary condition does not vary with latitude.

Fig. 9.
Fig. 9.

As in Fig. 3, but that the sloshing solution (gray and black curves) is replaced with ψsloBC=0 (rather than ψsloBC) and the RAPID curves are omitted.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-23-0027.1

To summarize, the effectiveness of the sloshing MOC solution, ψsloBC, is minimally influenced by the boundary condition on a seasonal time scale, but is more impacted on an interannual time scale.

4. Summary and discussion

The major finding of this research is that the sloshing-MOC solution well reproduces the AMOC variability at short-term time scales in the subtropical and tropical regions. This suggests that the sloshing dynamics effectively dominates the short-term AMOC variability in those regions. The sloshing motion or the adiabatic water redistribution process can be quantified through the analysis of the isopycnal heaving, which can be likened to squeezing toothpaste out of a tube. This is because isopycnal serves as an accurate proxy for the material surface, and its heaving effectively captures the vertical movement of water parcels under adiabatic conditions. Hence, those processes that cause heaving are potential drivers of the sloshing motions.

a. Cause of heaving

Under adiabatic conditions, the heaving of isopycnals is primarily driven by wind, both locally and remotely. In fact, those factors that people found accountable for the AMOC variability are either causes or expressions of heaving. These factors include isopycnal displacement (Cabanes et al. 2008; Polo et al. 2014; Yang 2015; Buckley and Marshall 2016; Frajka-Williams et al. 2016; Evans et al. 2017), seasonal cycle of density at depth (Chidichimo et al. 2010; Dong et al. 2014), wind stress curl (Kanzow et al. 2010; Barrier et al. 2014; Zhao and Johns 2014a; Yang 2015; Elipot et al. 2017; Evans et al. 2017), coastal upwelling (Köhl 2005; Polo et al. 2014), westward-propagating Rossby waves (Hirschi et al. 2007; Polo et al. 2014; Zhao and Johns 2014a; Pérez-Hernández et al. 2015; Kostov et al. 2021), and propagation of boundary waves (Roussenov et al. 2008; Zhang 2010; Elipot et al. 2013; Polo et al. 2014; Zhao and Johns 2014a; Buckley and Marshall 2016; Kostov et al. 2023). The potential processes that can perturb the isopycnals and thus contribute to the sloshing overturning are summarized in Fig. 10. The anomalous sloshing-MOC cell (indicated by the 3D blue arrows in Fig. 10) is an overall outcome of the basinwide adiabatic vertical movement. This vertical movement can be revealed by isopycnal displacement or heaving. The AMOC variability in the ST&T regions is largely caused by the basinwide adiabatic vertical movement from both local and remote locations.

Fig. 10.
Fig. 10.

Schematic diagram of the sloshing MOC component and heaving factors in the North Atlantic. The distorted surface represents an isopycnal. The two large blue arrows in opposite directions denote the overturning component due to sloshing motions above/beneath the isopycnal. Numbers with circles indicate the potential factors causing isopycnal heaving. They include 1) remote Ekman pumping anomaly, 2) local Ekman pumping anomaly, 3) coastal Ekman upwelling/downwelling, 4) boundary waves, 5) equatorial Kelvin waves, 6) planetary Rossby waves, and 7) mesoscale eddies. Black arrows: heaving direction of isopycnal. Cloud arrows: directions of wind or wind curl.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-23-0027.1

Ekman transport has been widely recognized as an indispensable contributor to the AMOC variability (e.g., Cunningham et al. 2007; Hirschi et al. 2007; Cabanes et al. 2008; McCarthy et al. 2012; Mielke et al. 2013; Thomas and Zhai 2013; Dong et al. 2014; Xu et al. 2014; Dong et al. 2015; Frajka-Williams et al. 2016; Pillar et al. 2016; Jackson et al. 2019; Lozier et al. 2019; Smith and Heimbach 2019; Hirschi et al. 2020; Zou et al. 2020; Kostov et al. 2021), and particularly so in the 2009/10 downturn event (McCarthy et al. 2012; Roberts et al. 2013; Barrier et al. 2014; Zhao and Johns 2014b; Srokosz and Bryden 2015; Buckley and Marshall 2016; Frajka-Williams et al. 2016; Jackson et al. 2019). However, it is the convergence/divergence of the Ekman transport, i.e., the Ekman pumping, that does the job. After all, Ekman transport per se does not warrant a return flow at depth to form a closed overturning cell. Two-layer model forced with wind alone was able to reproduce the observed seasonal cycle of overturning surprisingly well given its simplicity (Zhao and Johns 2014a; Yang 2015), very much due to that sloshing is implicitly included in its limited dynamics.

Fourier analysis on the isopycnal depths reveals a notable signature of planetary waves in the ST&T Atlantic, with a general pattern similar to the Indian Ocean (Han 2021) (Fig. 11). The amplitude maximums at low latitudes may explain the occurrence of the maximum MOC anomaly in the tropical Atlantic on seasonal time scale in the model products (Hirschi et al. 2007, 2013; Xu et al. 2014; Zhao and Johns 2014a; Hirschi et al. 2020) (Figs. 2 and 5). It is also consistent with the observed larger MOC variability at the MOVE array (16°N) than at the RAPID-MOCHA array (26.5°N) (Frajka-Williams et al. 2018).

Fig. 11.
Fig. 11.

Components of the isopycnal-depth seasonal variability. (left) Amplitudes, (center) variances, and (right) phase angle are shown for (top) annual and (bottom) semiannual components. Isopycnal 27.5σ0 whose mean depth is around 1000 m is chosen for illustration. Data: ECCO r4v3.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-23-0027.1

b. AMOC shows resilience to short-term variations

A highly informative inference drawn from the current study is that the AMOC shows resilience to short-term variations. Thanks to the reversibility of the adiabatic sloshing process, the AMOC is able to effectively recover from short-term variations regardless of the magnitudes, including those that occur at interannual time scales. The quicker the variation occurs, the more probable it is for the AMOC to recover autonomously due to the larger dominance of the sloshing process over shorter time scales. The adiabatic nature of the sloshing dynamics may also account for the observed higher-frequency AMOC variability, such as daily time scale, at 26.5°N (https://rapid.ac.uk/).

The ability of the AMOC to recover autonomously from short-term variations necessitates the long-term monitoring of the AMOC in detecting its irreversible change. Since the AMOC anomalies resulting from the ST&T processes are predominantly reversible, it is essential to closely monitor the subpolar region if the detection of any irreversible AMOC changes is of concern.

c. Open questions

This paper presents an initial effort toward understanding the complex variability of the AMOC from a novel perspective. However, it is only a first step, and there are still many outstanding questions. Specifically, I highlight four such questions that invite further inquiry.

1) Subpolar impact on the subtropical AMOC

The sloshing-MOC solution ψsloBC=0 discussed in section 4e, represents a situation when the subtropical–subpolar exchange of overturning anomaly is blocked by an artificial barrier. Such anomaly barrier has two effects on the AMOC strength in the ST&T regions. On the one hand, the open boundary that permits the sloshing-MOC anomaly generated in the interior of the ST&T regions to freely radiate out to the north (or into the subpolar region) is blocked. On the other hand, the transport anomaly produced by the subpolar processes are unable to propagate into the subtropical region to impose an impact. Unfortunately, these two effects are entangled in the current solution, implying that the subpolar impact on the subtropical AMOC variability cannot be evaluated separately from this solution.

However, according to the discussion in section 3e, this barrier condition has minimal impact on the seasonal variability of the AMOC in the ST&T regions though its influence becomes evident on an interannual time scale. As a result, the best answer to the question of subpolar impact on the ST&T AMOC so far is that the subpolar processes have little influence on the ST&T AMOC variability on seasonal time scale, but may become gradually important on longer time scale.

2) Regional climate predictability

Early studies identified high correlation between the North Atlantic sea surface temperature and the upper-ocean heat content (e.g., Moat et al. 2019), whose variability may be well associated with the upper-ocean water redistribution, i.e., the sloshing process. This process is similar to the case discussed in the Indian Ocean (Han 2021). Thus, the subtropical wind, perhaps in combination with the AMOC anomaly at an intergyre latitude (e.g., 44°N as studied in this research) seems a better predictable source of the short-term variation of the subtropical North Atlantic sea surface temperature than the AMOC strength at the RAPID-MOCHA array (Duchez et al. 2016; Alexander-Turner et al. 2018; Carvalho-Oliveira et al. 2021).

3) Eddy’s role in sloshing

Eddies are parameterized in ECCO and show trivial contribution to the AMOC variability in the tropics/subtropics (not shown). While it is acknowledged that the eddies parameterized in ECCO are underestimated compared to satellite altimetry (Rousselet et al. 2023), recent studies tend to believe that eddies do not dominate the AMOC variability signal, particularly in the low to midlatitudes (Johnson et al. 2019; Rousselet et al. 2023). However, since eddies also perturb the isopycnals in a largely adiabatic way (thus also included in the schematic Fig. 10), it could be instrumental to study how eddies modulate AMOC strength from the sloshing perspective.

4) Sloshing for the subpolar MOC

Sloshing may impact the AMOC variability in the subpolar region as well, although its impact may be less dominant due to the emergence of intensive diabatic processes in the subpolar region compared to the ST&T regions. The OSNAP time series, which has released a 6-yr dataset so far, shows strong AMOC variability on short time scales (https://www.o-snap.org/; Fu et al. 2023). It is possible that this variability is somehow associated with the sloshing motion, either through a propagating-in sloshing-MOC anomaly originating from the subtropical region or even-higher-latitude region, or through local forcing. For the latter, it remains an open question whether it is feasible to study the sloshing impact on the subpolar overturning circulation with the current approach.

Acknowledgments.

The author is deeply grateful for the constructive feedback and insightful questions provided by Yavor Kostov and the other reviewer. This work was supported by Grant XMUMRF/2022-C9/ICAM/0009 from the Xiamen University Malaysia Research Fund.

Data availability statement.

The ECCO reanalysis dataset adopted in this study, version 4 release 3, is available at the website ecco.jpl.nasa.gov for open access. Data from the RAPID AMOC monitoring project are funded by the Natural Environment Research Council and are freely available from www.rapid.ac.uk/rapidmoc.

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