Reconstructing global overturning from meridional density gradients

Abstract

Despite the complexity of the global ocean system, numerous attempts have been made to scale the strength of the meridional overturning circulation (MOC), principally in the North Atlantic, with large-scale, basin-wide hydrographic properties. In particular, various approaches to scaling the MOC with meridional density gradients have been proposed, but the success of these has only been demonstrated under limited conditions. Here we present a scaling relationship linking overturning to twice vertically-integrated meridional density gradients via the hydrostatic equation and a “rotated” form of the geostrophic equation. This provides a meridional overturning streamfunction as a function of depth for each basin. Using a series of periodically forced experiments in a global, coarse resolution configuration of the general circulation model NEMO, we explore the timescales over which this scaling is temporally valid. We find that the scaling holds well in the upper Atlantic cell (at 1000 m) for multi-decadal (and longer) timescales, accurately reconstructing the relative magnitude of the response for different frequencies and explaining over 85 % of overturning variance on timescales of 64–2048 years. Despite the highly nonlinear response of the Antarctic cell in the abyssal Atlantic, between 76 and 94 % of the observed variability at 4000 m is reconstructed on timescales of 32 years (and longer). The scaling law is also applied in the Indo-Pacific. This analysis is extended to a higher resolution, stochastically forced simulation for which correlations of between 0.79 and 0.99 are obtained with upper Atlantic MOC variability on timescales >25 years. These results indicate that meridional density gradients and overturning are linked via meridional pressure gradients, and that both the strength and structure of the MOC can be reconstructed from hydrography on multi-decadal and longer timescales provided that the link is made in this way.

1 Introduction

The meridional overturning circulation (MOC) is a large-scale global circulation of water throughout the world’s ocean. The strength of global overturning has a significant effect on climate through meridional heat transport and the ventilation of the deep ocean. However, the ocean is a highly complex system and the driving processes of, and energetic constraints on, global ocean circulation are still extensively discussed in the literature (Butler et al. 2013; Kuhlbrodt et al. 2007; Wunsch and Ferrari 2004). Nevertheless, numerous attempts have been made to scale the strength of overturning, principally in the North Atlantic, with large-scale physical properties such as vertical diffusivity (Park and Bryan 2000) and kinetic energy/potential energy conversion in the North Atlantic (Gregory and Tailleux 2011).

In particular, a robust scaling for the meridional overturning circulation constructed from large-scale hydrographic properties has been sought by physical oceanographers. The existence of such a scale would enhance our descriptive understanding of the behaviour of large-scale ocean circulation and would enable us to infer how ocean circulation might qualitatively and quantitatively respond to hypothesized changes in climatic forcing as a result of anthropogenic climate change. As well as having predictive value, reliable scaling relationships could also be used to reconstruct past variability in ocean circulation from the paleoclimate record. Previous studies have typically relied on the use of temperature and salinity proxies to constrain the distribution of water masses in the ocean (Rahmstorf 2002). From this distribution, the structure of large-scale ocean circulation can then be inferred. However, quantitative estimates of past variability in circulation strength are currently harder to obtain. Overturning scales can also be used to inform parameterizations in theoretical modelling studies, which in turn can be used to investigate how the meridional overturning circulation interacts with other oceanic and atmospheric processes (e.g. Gnanadesikan 1999).

Many previous studies have sought to relate the strength of the meridional overturning in the North Atlantic to the meridional density gradient (e.g. Rahmstorf 1996; Thorpe et al. 2001; de Boer et al. 2010; Sijp et al. 2012). The idea of a linear relationship between overturning and meridional density gradients dates back to early conceptual models of a thermohaline circulation (e.g. Stouffer et al. 2006) driven by the density difference between the high latitude and low latitude ocean. Whilst the thermohaline circulation has been shown to be highly sensitive to high-latitude surface buoyancy forcing in the North Atlantic in numerous modelling studies (e.g. Stouffer et al. 2006), certain model results suggest that this relationship is far from linear with some idealized studies finding that meridional overturning can even decrease with increasing meridional density gradient in some circumstances (e.g. de Boer et al. 2010).

However, it should be noted that horizontal flow is not simply proportional to the local horizontal density gradient at any depth. Instead, vertically integrated horizontal density gradients translate into horizontal pressure gradients (via the hydrostatic relationship) that, in turn, are able to transfer momentum. Due to the influence of the Coriolis force, the meridional geostrophic velocity is actually proportional to once-integrated zonal density gradients, as opposed to once-integrated meridional density gradients. Therefore, a direct link between meridional overturning and meridional density gradients is far from clear. Attempts to scale meridional overturning with meridional density gradients typically begin with the scaled thermal wind equation on a basin scale (e.g. de Boer et al. 2010), which implies that $V/H \sim \Delta \rho_{x}$ where V is the meridional velocity scale, H is the depth scale and $\Delta \rho_{x}$ is the basin-wide zonal density difference. In order to translate this relationship into a function of meridional density gradients, a linear relationship between zonal ($\Delta \rho_{x}$) and meridional ($\Delta \rho_{y}$) density gradients is often assumed to hold (see Sect. 2.1 for further discussion) such that $V/H \sim \Delta \rho_{y}$. This yields a meridional velocity scale $V \sim \Delta \rho_{y} H$ (e.g. for an upper overturning cell of scale depth H) and, therefore, an overturning transport $\Psi \sim VH \sim \Delta \rho_{y} H^{2}$ (e.g. de Boer et al. 2010).

The way in which the scaling $\Psi \sim \Delta \rho_{y} H^{2}$ is implemented and exploited varies significantly across the literature. Considering H to be fixed yields a linear relationship between overturning and density difference (Rahmstorf 1996). Alternatively, considering the density difference to be constant yields a quadratic relationship between overturning and scale depth (Gnanadesikan 1999). However, Levermann and Fürst (2010) demonstrated (using a coupled climate model) that both of these quantities vary simultaneously and considering either to be fixed is unphysical. Thus, suitable scales for both $\Delta \rho_{y}$ and H must be chosen, but the approach to this can appear ad hoc with definitions sometimes chosen empirically because they yield positive results within a particular model and experimental setup, despite a lack of cross model support. De Boer et al. (2010) carried out a methodical evaluation of a wide range of both $\Delta \rho_{y}$ and H scale candidates in an idealized GCM, finding that traditional measures of $\Delta \rho_{y}$ (e.g. the depth-averaged meridional density gradient) and H (e.g. the pycnocline depth) do not scale overturning well. The latitudinal extent over which $\Delta \rho_{y}$ is taken also has some bearing on the inferred scale. Traditional notions of thermohaline circulation based on the Stommel (1961) box model have sometimes considered the meridional density difference between the pole and the equator to be instrumental in setting the strength of meridional flow in a single basin [often resulting in a three box model featuring the high-latitude ocean, the surface low-latitude ocean, and the deep low-latitude ocean—e.g. Oliver et al. (2005)]. However, Hughes and Weaver (1994) and Rahmstorf (1996) scaled the meridional overturning circulation in the Atlantic Ocean with the meridional density difference between the northern high-latitudes and the Southern Ocean at 30°S, thus allowing changes in Southern Ocean density at the boundary to directly influence the overturning scale. It has been suggested, using idealized double-hemisphere models, that the overturning circulation might respond differently to changes in the equator-to-pole or pole-to-pole meridional density gradient, with the equator-to-pole density gradient influencing the strength of local overturning in the dominant hemisphere and the pole-to-pole density gradient determining the degree of overturning asymmetry and cross-equatorial flow (Klinger and Marotzke 1999; Mohammad and Nilsson 2006).

In this paper, we derive a scale for meridional overturning at different depths constructed using twice vertically-integrated meridional density gradients. Whilst, previous scaling studies have typically focused on steady state simulations, rectilinear bathymetry and/or the Atlantic only, in this study, we investigate the validity and robustness of this scaling approach in a general circulation model (GCM; with realistic topography) subjected to transient buoyancy forcing, testing the overturning inferred from twice-integrated meridional density gradients against model simulated overturning in both the Atlantic and Indo-Pacific basins. We explore a wide range of forcing timescales ranging from sub-decadal to millennial periods through a series of deterministic, periodically varying surface buoyancy forcing experiments in a coarse resolution GCM, allowing us to isolate the ocean’s response at each timescale. We then extend our analysis to a higher resolution, stochastic simulation forced with North Atlantic Oscillation (NAO) structured stochastic variability in all surface buoyancy and momentum forcing components.

2 Methods

In this section, we begin by deriving a scaled overturning streamfunction using twice vertically-integrated meridional density gradients. We then describe the model configuration and experimental setup that we use to test this scale in a realistic ocean GCM.

2.1 Deriving a scaled meridional overturning streamfunction

Under the assumption of geostrophic balance, the meridional velocity, v, is given by:

$$fv = \frac{1}{\rho }\frac{\partial p}{\partial x}$$

(1)

where f = the Coriolis parameter, ρ = density, and p = pressure. That is, the meridional velocity is proportional to the zonal pressure gradient. By taking the vertical derivative of this geostrophic balance and applying the hydrostatic approximation $(\partial p/\partial z = - \rho g$, in which g is the gravitational constant), we obtain the meridional component of the thermal wind equation:

$$\frac{\partial v}{\partial z} = \frac{g}{f\rho }\frac{\partial \rho }{\partial x}$$

(2)

The thermal wind equation can then be rewritten in scaled form, providing an expression for the basin-scale meridional velocity, V, in terms of the basin-scale zonal density difference, Δρ_x:

$$\frac{\partial V}{\partial z} = \frac{g}{{f_{0} \rho_{0} }}\frac{{\Delta \rho_{x} \left( z \right)}}{{L_{x} }}$$

(3)

where L _x is the zonal length scale (assuming vertical walls) and ρ ₀ and f ₀ are representative values for density and the Coriolis parameter, respectively.

In this study, we assume that basin-scale meridional and zonal pressure gradients can be related by a dimensionless constant of proportionality, c_ρ, such that $\frac{{\Delta \rho_{x} }}{{L_{x} }} = c_{\rho } \frac{{\Delta \rho_{y} }}{{L_{y} }}$ (where L _y is the meridional length scale). This relationship has been shown to hold at equilibrium in a general circulation modelling study with idealized bathymetry (Park and Bryan 2000) and has been rationalized theoretically by Wright et al. (1995) and Marotzke (1997), arguing that a meridional pressure gradient across a basin will set up an eastward zonal flow that converges at the eastern boundary, producing a zonal pressure gradient that in turn drives a meridional flow (Kuhlbrodt et al. 2007). An alternative rationalization of this relationship is to consider a meridional density gradient along the western boundary. This can be rapidly transmitted into a zonal density gradient through the propagation of boundary waves southwards along the western boundary, eastwards along the equator and then northwards up the eastern boundary (e.g. Johnson and Marshall (2002) and references therein). For further discussion, a more comprehensive overview of the different attempts to relate meridional flow to meridional density gradients can be found in Appendix 1 of Fürst and Levermann (2012).

Substituting this linear relationship into Eq. 3 yields:

$$\frac{\partial V}{\partial z} = \frac{{c_{\rho } g}}{{f_{0} \rho_{0} L_{y} }}\Delta \rho_{y} \left( z \right)$$

(4)

This relationship is most intuitively described as a scaled “rotated” form of the conventional thermal wind equation, although it may also be obtained by consideration of ageostrophic flow in the western boundary current (Gnanadesikan 1999). As explained in the Sect. 1, this equation is typically scaled directly to yield a meridional velocity scale of $V \sim \Delta \rho_{y} H$ (e.g. for an upper overturning cell of scale depth H) and an overturning transport of $\Psi \sim VH \sim \Delta \rho_{y} H^{2}$. However, this has the potential to yield misleading results where the vertical profile of horizontal density gradients has a complex structure. More generally correct is to retain the depth dependence in $\Delta \rho_{y}$ and integrate again to obtain:

$$V\left( z \right) = \frac{{c_{\rho } g}}{{\rho_{0} f_{0} L_{y} }}\left( { \frac{1}{h}\mathop \smallint \limits_{ - h}^{0} \left( {\mathop \smallint \limits_{z'}^{0} \Delta \rho_{y} \left( {z^{\prime\prime}} \right)dz^{\prime\prime}} \right)dz' - \mathop \smallint \limits_{z}^{0} \Delta \rho_{y} \left( {z^{\prime}} \right) dz^{\prime}} \right)$$

(5)

where h is the bottom depth and V is the basin-scale meridional velocity determined by local anomalies from the depth-averaged pressure gradient (Oliver et al. 2005). The constant of integration, $\frac{{c_{\rho } g}}{{\rho_{0} f_{0} L_{y} }}\left( { \frac{1}{h}\mathop \smallint \limits_{ - h}^{0} \left( {\mathop \smallint \limits_{z'}^{0} \Delta \rho_{y} \left( {z^{\prime\prime}} \right)dz^{\prime\prime}} \right)dz'} \right)$, is fixed by the constraint of zero net meridional flow.

An expression for the meridional overturning streamfunction derived from meridional pressure gradients (hereafter referred to as Ψ_p) at depth z can then be obtained by integrating again (assuming vertical walls):

$$\Psi_{p} \left( z \right) = L_{x} \mathop \smallint \limits_{z}^{0} V\left( {z^{\prime}} \right)dz'$$

(6)

It follows from this expression that meridional overturning should scale with the twice-integrated meridional density difference (Hughes and Weaver 1994), as opposed to the once-integrated meridional density difference (Thorpe et al. 2001). Furthermore, Eq. 6 implicitly defines the overturning scale depth, H, sought by previous studies in a manner directly consistent with the scaling derivation: that is, the level of no meridional flow at the boundary of overturning cells given by V(H) = 0.

The barotropic contribution to Eq. 6 (resulting from the constant of integration in Eq. 5) is analogous to the bottom pressure term that features in decompositions of the meridional overturning streamfunction (e.g. Ψ* in Sime et al. (2006) and T_EXT in Kanzow et al. (2007)). This bottom pressure term provides the zonally integrated, temporally variable reference level component of the geostrophic flow (Kanzow et al. 2007). Previous studies have suggested that this bottom pressure term can make significant contributions to total overturning at certain latitudes and timescales and cannot, in principle, be ignored (Sime et al. 2006). However, its representation in the scaling presented here is primitive and has limitations. For instance, we implicitly exclude any contributions to meridional overturning associated with zonal variations in bottom topography in the translation of zonal to meridional pressure gradients. Despite such limitations, we demonstrate in this study that it remains possible to reconstruct overturning variability on multi-decadal timescales and longer using the method derived here.

2.2 Model description

In this paper, we test the veracity of this scaling across a broad range of timescales using a series of periodically forced numerical ocean simulations. These experiments were conducted using the Nucleus for European Modeling of the Ocean (NEMO) ocean general circulation model (OGCM) in the global ORCA2 configuration (Madec 2008). This configuration solves the primitive equations on a tri-polar grid (avoiding a singularity in the Arctic Ocean) with a nominal horizontal resolution of 2°, refined to 0.5° in the equatorial region. The vertical grid structure has 31 levels (varying from 10 m thick near the surface to approximately 500 m thick in the deep ocean) and uses partial bottom cells for better representation of bottom topography (see Fig. 1). The model is equipped with a full nonlinear equation of state and the effect of mesoscale eddies is parameterized using the Gent and McWilliams (1990) advective scheme with spatially varying diffusion coefficients. A no-slip lateral momentum boundary condition is applied at the coastline. Vertical mixing is parameterized using a turbulent kinetic energy closure scheme. We use an ocean-only setup in which unperturbed surface boundary conditions are computed from Coordinated Ocean-ice Reference Experiment (CORE) bulk formulae incorporating active ocean variables and prescribed atmospheric data (Large and Yeager 2004, 2009). The model is initially spun-up from rest and integrated for a 2000-year control period using atmospheric variables given by the CORE v2.0 normal year atmospheric dataset repeated annually (Large and Yeager 2009).

Fig. 1

Map of ORCA2 model bathymetry (in units of meters) with the density boundary points used in meridional density calculations marked in yellow

2.3 The control simulation

The overturning streamfunction for the Atlantic and Indo-Pacific basins at the end of the 2000-year spin-up period is shown in Fig. 2. In the Atlantic we have an upper overturning cell of strength 15.0 Sv associated with North Atlantic Deep Water (NADW) in which warm surface waters flow poleward, lose their heat to the atmosphere, sink in regions of deepwater formation and return at depth to regions of upwelling. This overlays a reverse abyssal cell associated with Antarctic Bottom Water (AABW) of strength −3.5 Sv in the North Atlantic. Meridional overturning is qualitatively different in the Pacific with a single dominant overturning cell associated with Antarctic Bottom Water (AABW) of strength −14.2 Sv in the deep ocean. Unlike in the Atlantic, there is no vigorous upper ocean overturning cell extending into the northern hemisphere. The strength and structure of global ocean circulation is in good agreement with observations in both the upper and deep ocean. Since ORCA2 is relatively coarse resolution model, there is only a small drift remaining after 2000 years (e.g. the maximum Atlantic overturning streamfunction drifts by just −0.01 Sv over the last 100 years of the control simulation).

Fig. 2

The control a Atlantic and b Indo-Pacific overturning streamfunctions (in units of Sv; 1 Sv = 10⁶ m³ s⁻¹) plotted as a function of latitude and depth, averaged over the final 50 years of the 2000 year control simulation in ORCA2. Note color scheme is saturated for near-surface wind-driven overturning cells

2.4 Experimental setup

After the initial 2000-year spin-up period, the model is then forced using periodically varying surface buoyancy forcing of different periods in the North Atlantic. In these transient experiments, a 10 m air temperature perturbation is superimposed on the normal year cycle and fed into the bulk formulae. A zonally-constant, sinusoidal perturbation is applied between the equator and 90°N, peaking in amplitude at 60°N. The prescribed air temperature perturbation is given as a function, F, of latitude, θ, and time, t:

$$F\left( {\theta ,t;A,P} \right)\text{ := }\left\{ \begin{aligned} A\sin \left( {\frac{2\pi t}{P}} \right)\sin \left( {\frac{\theta \pi }{120}} \right) & \quad if\,0^\circ N \le \theta \le 60^\circ N \\ A\sin \left( {\frac{2\pi t}{P}} \right)\sin \left( {\frac{\theta \pi }{60} - \frac{\pi }{2}} \right) & \quad if\,60^\circ N < \theta \le 90^\circ N \\ \end{aligned} \right.$$

(7)

in which the sinusoidal amplitude of oscillation, A, is set at 5 °C for all experiments and the period of oscillation, P, takes sub-decadal to millennial values: P = 8, 16, 32, 64, 128, 256, 512, 1024 and 2048 years. The shape of the forcing cycle as a function of latitude at different stages in an oscillation is depicted in Fig. 3. The forcing period is increased sequentially in a style similar to Lucas et al. (2005), such that the 2ⁿ⁺¹ year forcing cycle is applied directly after the 2ⁿ year forcing cycle has completed (see Fig. 4). Each forcing period is repeated for four cycles or a minimum of 128 years (excluding the 2048 year cycle for which just two repetitions are made) to reach a cyclostationary state in oceanic response. Aside from the background CORE seasonal cycle, no additional buoyancy forcing perturbations are applied outside of the North Atlantic.

Fig. 3

Air temperature perturbation applied over the North Atlantic plotted as a function of latitude for an arbitrary forcing period of length T

Fig. 4

Timeseries of the 10 m air temperature forcing profile (illustrated for 60°N, the latitude of maximum forcing) and the response timeseries of the meridional overturning streamfunction, Ψ, at 1000 and 4000 m in the Atlantic (at 35°N) and the Indo-Pacific (at 10°S) ocean basins

3 Scaling the Atlantic MOC response to deterministic forcing

For conciseness, we hereafter refer to the model simulated overturning streamfunction as Ψ and the overturning streamfunction constructed from twice-integrated meridional density gradients (according to Eqs. 5, 6) as Ψ_p. The density scale is set as ρ ₀ = 10³ kg m⁻³, the gravitational constant is taken to be g = 10 m s⁻², and we define f ₀ = 10⁻⁴ s⁻¹ as a representative value of the mid-latitude Coriolis parameter. The meridional length scale, L _y , is taken to be 10,000 km. The zonal length scale, L _x , varies with latitude and depth. However, for simplicity, we choose a single zonal length scale of L _x  = 5000 km in the Atlantic. We consider the dimensionless ratio of zonal to meridional density gradients, c_ρ, to be a function of location only and, therefore, may be fitted to individual basins, depths, and latitudes, but may not be fitted to individual timescales of variability. In principle, this value should be relatively consistent between locations since large-scale variations in geometry are encapsulated in the zonal and meridional length scales.

We define our meridional density difference, $\Delta \rho_{y}$, to be that measured along the western boundary between 60°N and 30°S in the Atlantic (as illustrated by markers A and B in Fig. 1). We adopt a sloped boundary at the northern end of the basin, measuring density at the northernmost point (not exceeding 60°N) at each depth. Therefore, the northern boundary in the abyssal ocean is, in actuality, taken further south than 60°N. The western boundary is the primary region in which strong ageostrophic flow can occur and, consequently, where the potential energy associated with meridional density (strictly, pressure) gradients can be converted into kinetic energy (Gregory and Tailleux 2011; Sijp et al. 2012). Gnanadesikan (1999) also employs boundary layer theory to link meridional pressure gradients to a meridional frictional flow near the western boundary. The calculation of western boundary gradients in our experimental setup is complicated due to the configuration’s realistic topography. In order to minimize the impact of local topographic features and model resolution we avoid taking an exact western boundary value and, instead, take our western boundary quantities to be those averaged over a 10° longitude band adjacent to the western boundary. The precise width of this averaging band is not critical, but the emphasis on the western boundary is. Markedly diluting this contribution by, for example, doubling the width of the averaging band to 20° has a detrimental effect on the scaling accuracy, particularly in the abyssal Atlantic (not shown).

Another choice that must be made is the northern and southern location for the meridional density difference calculation. We use 60°N and 30°S respectively, but show that the scaling is relatively insensitive to either choice in Sect. 3.3.

3.1 Scaling steady-state overturning as a function of depth

In this subsection, we demonstrate Eq. 6’s ability to reconstruct the approximate vertical structure of model overturning as a function of depth in the control state ocean. One of the most significant advantages of the scaling proposed in Eq. 6 is that it allows the meridional overturning streamfunction to be reconstructed at all depths as opposed to providing a single scale for each basin. This is particularly relevant in the Atlantic where there are two very different overturning cells overlaid on one another (Fig. 2) that cannot necessarily be described by the same scale on a transient basis (Fig. 4). A vertical profile of Atlantic Ψ_p computed from the control simulation is shown in Fig. 5 alongside a vertical profile of basin-scale meridional overturning (taken to be the maximum magnitude of the overturning streamfunction—of either sign—between the equator and 30°N at each depth level). The free constant, c_ρ, has been constrained as the gradient of the linear fit between Ψ and Ψ_p: 0.96 (with a corresponding correlation coefficient of r = 0.994). There is an associated 2.5 Sv offset between Ψ and Ψ_p. This is, approximately, consistent with the fact that the model simulated overturning streamfunction, Ψ, integrates vertically to 1.3 Sv (not zero) in the Atlantic. This discrepancy is likely associated with Bering Strait transport (of strength 1.1 Sv in the control experiment), which is not corrected for in the model streamfunction calculation. The upper 250 m of the ocean feature shallow wind-driven overturning cells and have been excluded from this plot. Figure 5 demonstrates that the model provides a realistic estimate of the relative magnitude of overturning in both the upper and deep ocean and that the constructed depth profile is representative of the overturning simulated in the model. It is also seen that Ψ_p produces an accurate estimate of the depth scale of the upper overturning cell (in this case, approximately 3000 m) when the offset is accounted for.

Fig. 5

Vertical profile of Ψ (blue solid line) and Ψ_p (red dashed line) for the control overturning in the Atlantic. Ψ(z) is the maximum value of the overturning streamfunction at that level (whether positive of negative), taken between the equator and 30°N. Ψ_p(z) is calculated from the twice integrated, basin-scale meridional density gradient

3.2 Scaling transient overturning as a function of time

In this subsection, we investigate the ability of Ψ_p to reconstruct upper and abyssal overturning in the Atlantic as a function of time at two fixed depths: 1000 and 4000 m. These are the approximate depths of maximum overturning (associated with the NADW deep water cell) and minimum overturning (associated with the abyssal AABW cell) in the control run (see Figs. 2, 5). In order to determine the timescales over which such a scaling might be valid, we begin by exploring the series of periodic buoyancy forcing scenarios in a coarse resolution global ocean model as described in Sect. 2.4. The robustness of the scaling described in Sect. 2.1 to model resolution and the nature of forcing variability is explored in Sect. 4.

3.2.1 Upper ocean overturning at 1000 m, 35°N

The mean and range statistics of model simulated overturning, Ψ, at 1000 m at 35°N in response to the periodic buoyancy forcing scenarios are tabulated in Table 1 (calculated for the final cycle of each forcing series), the timeseries of model simulated overturning response is plotted in Fig. 4, and the spatial structure of induced Atlantic overturning variability is depicted in Fig. 6.

Table 1 Mean and range of Ψ at 1000 m (35°N) and 4000 m (35°N) in the Atlantic and at 1000 m (10°S) and 4000 m (10°S) in the Indo-Pacific, computed for the final oscillation of each forcing period series

Fig. 6

Meridional sections depicting the range of model simulated meridional overturning streamfunction in the Atlantic for each of the forcing frequencies (units: 1 Sv = 10⁶ m³s⁻¹). The solid black contour indicates the zero overturning contour (separating the NADW and AABW cell) of the control simulation overturning and the dotted black contour represents the zero overturning contour at maximum meridional density gradient forcing

The periodic forcing induces large amplitude, asymmetric oscillations in overturning, peaking in range at 13.7 Sv at 128-year timescales and declining for longer periods. This resonance-like behavior is consistent with the findings of Lucas et al. (2005) who applied a similar experimental design to an idealized, single basin ocean model and determined that this behavior in their model was linked to an interaction between the diffusive timescale and the timescale of Rossby wave anomaly propagation. The structure of the induced overturning variability also changes with forcing period (Fig. 6). High frequency overturning anomalies (8 and 16 year timescales) do not penetrate south of the equator until multidecadal (32 and 64 year) timescales, consistent with the idea of an “equatorial buffer” of high-frequency variability formalized by Johnson and Marshall (2002). At the longest timescales, the equator ceases to act as a buffer to the propagation of overturning anomalies. As a result, short timescale forcing is characterized by intense, localized overturning anomalies at high latitudes, whilst longer timescale forcing results in a broader pattern of variability that spans the equator.

The basin-scale overturning streamfunctions inferred from twice-integrated meridional density gradients, Ψ_p, are constructed for the transient experiments according to the method described in Sect. 3.1. The values of the correlation coefficient between model simulated overturning, Ψ, and Ψ_p at 1000 m are given in Table 2. Timeseries of both Ψ and Ψ_p anomalies (with the temporal mean signal for each timescale removed) are plotted together for the upper ocean in Fig. 7. The free geometric constant, c_ρ, is taken to be the gradient of the linear fit of Ψ against Ψ_p for the longest timescale forcing (in this case, 2048-year). This corresponds to 0.88 at 1000 m. Whilst it is visually apparent in Fig. 7 that there is a short lagged response between Ψ and Ψ_p in the Atlantic (in which Ψ_p precedes changes in overturning Ψ by approximately 4 years), all correlation coefficients are quoted without any lag for consistency and transparency.

Table 2 Correlation coefficients between model simulated overturning, Ψ, in the Atlantic at 35°N and inferred overturning, Ψ_p, given for each forcing timescale

Fig. 7

Timeseries depicting the variability (the signal minus the oscillation mean) of Ψ (blue) and Ψ_p (red) at 1000 m (35°N) in the North Atlantic plotted for the final oscillation of each surface buoyancy forcing period in the deterministically forced ORCA2 simulation

Ψ_p is a poor proxy for overturning at 8-year timescales with the magnitude of overturning overestimated by a factor of 5. At 16-year timescales, correlation is still weak (due to the lag described above), but the range of scaled overturning is more consistent with the model simulated Ψ at 35°N (though still overestimated by a factor 1.5). However, by the 32-year timescale both the pacing and range of overturning is accurately reconstructed. Correlation is >0.9 for all timescales longer than (and including) 64-years and >0.99 for all timescales longer than (and including) 256-years. Changes in the magnitude of induced overturning with forcing timescale are reconstructed, including the resonant 128-year forcing period.

3.2.2 Abyssal ocean overturning at 4000 m, 35°N

Unlike in previous scaling studies, Ψ_p retains a function of depth allowing us to also attempt to scale abyssal overturning in the Atlantic at 35°N at a depth of 4000 m. In contrast to the large amplitude oscillations seen at 1000 m, meridional overturning at 4000 m has a much weaker response (Table 1). Moreover, the response of abyssal overturning at 4000 m is highly nonlinear (Fig. 4). Indeed, there is a clear transition to a biharmonic signal at the intermediate 128- and 256-year forcing periods. Like in the upper ocean, there is also resonance-like behavior observed in deep ocean overturning at 4000 m, but, surprisingly, this occurs at the much shorter 32-year period (cf. the 128-year period at 1000 m). As discussed in Sect. 3.2.1, the upper overturning cell’s response to high frequency buoyancy forcing is characterized by intense, deep overturning anomalies at mid to high northern latitudes (Fig. 6). Indeed, the upper overturning cell expands to occupy the entire water column at the 32-year forcing period, penetrating through the 4000 m depth level. As a result, the greatest magnitude response at 4000 m is actually observed at timescales far shorter than that at 1000 m. Given the complex nature of the overturning response to simple periodic forcing seen here, we do not seek to understand the precise dynamics underlying this behavior, but instead only seek to test whether Ψ_p can adequately reconstruct the shape and amplitude of the response.

The values of the correlation coefficient between the model simulated overturning, Ψ, and density-gradient inferred overturning, Ψ_p, at 4000 m are given in Table 2. Timeseries of both Ψ and Ψ_p anomalies (with the temporal mean signal for each timescale removed) are plotted for the abyssal Atlantic in Fig. 8. The free constant, c_ρ, is equal to 0.27 at 4000 m. This number is significantly smaller than that observed at 1000 m. This is likely due to a reduction in the zonal length scale with depth, exacerbated by the presence of the mid-Atlantic ridge. As in the upper ocean, good correlations are seen from 32-year forcing periods onwards, but the amplitude of response is not accurately reconstructed until 256-year forcing timescales. Since the large amplitude deep ocean response seen at shorter timescales is due to high-frequency, localized incursions of the upper overturning cell through the 4000 m depth level (Fig. 6), it is possible that these narrow events are not triggered by, or reflected in, basin-scale pressure gradients at this depth and, therefore, may not be well-captured by a basin-scale scaling relationship. However, it is worth noting that the high correlations at and beyond the 128-year forcing cycle are very strong, despite the highly nonlinear nature of the signal. Furthermore, Ψ_p correctly reconstructs the transition to the biharmonic overturning signals seen at 128-, 256-, and 512-year forcing periods and the relative magnitudes of each peak within these responses.

Fig. 8

Timeseries depicting the variability (the signal minus the oscillation mean) of Ψ (blue) and Ψ_p (red) at 4000 m (35°N) in the North Atlantic plotted for the final oscillation of each surface buoyancy forcing period in the deterministically forced ORCA2 simulation

3.3 The relative roles of the northern and southern boundary

The forcing applied in our idealized scenarios is focussed on high northern latitudes. It is, thus, a valid question as to what proportion of the variability in the overturning streamfunction comes from density variations at the northern and southern boundary points respectively and, consequently, whether the veracity of the proposed scaling relationship has actually been successfully demonstrated in a transient scenario in which we also have variability at the southern boundary. Furthermore, can we determine how sensitive our results are to the choice of latitude of the northern and southern boundary points?

Temporal anomalies in Ψ_p are decomposed into northern and southern contributions at 1000 m (Fig. 9) and 4000 m (Fig. 10) by using a fixed, time-mean density profile at the opposing boundary. Density variations at the southern boundary point make a negligible contribution to Ψ_p until 256- and 512-year forcing periods. This is, in part, because there is little propagation of induced variability beyond the equator at decadal timescales (Fig. 6). Moreover, adjustment of the low-latitude pycnocline in response to overturning anomalies is determined by the filling of the deep ocean with dense water and, consequently, occurs over long, centennial timescales. By 2048-year timescales, northern and southern contributions to the variability in Ψ_p at 4000 m are equal in magnitude. At the longest forcing timescales, the anomalies in Ψ_p at 1000 m due to northern and southern boundary variability appear out of phase. This is because when upper ocean overturning is strong, the deep ocean fills with dense water, the low latitude pycnocline shoals, southern boundary density increases and the meridional density gradient decreases. It then follows that Ψ_p due to southern boundary variability decreases as a consequence of this. However, due to the timescale associated with this process, the northern and southern contributions only appear to occur out of phase at multi-centennial timescales.

Fig. 9

Temporal anomalies of Ψ_p in the Atlantic at 1000 m constructed using a both a variable northern and southern boundary (bold black), b a fixed northern boundary corresponding to the temporal mean profile of ρ_N (red) and c a fixed southern boundary corresponding to the temporal mean profile of ρ_S (blue)

Fig. 10

Temporal anomalies of Ψ_p in the Atlantic at 4000 m constructed using a both a variable northern and southern boundary (bold black), b a fixed northern boundary corresponding to the temporal mean profile of ρ_N (red) and c a fixed southern boundary corresponding to the temporal mean profile of ρ_S (blue)

In our analysis, we have chosen to use a northern boundary of 60°N and a southern boundary of 30°S. The corollary of the above paragraph is that the scaling used here is largely insensitive to the choice of latitude of the southern boundary point in our decadal to centennial timescale forcing scenarios. At millennial timescales, the choice of this latitude becomes more important, particularly in the abyssal Atlantic where the southern boundary contribution is largest. Highest correlations are found when the southern boundary is set to 30°S (not shown). Whilst horizontal pressure gradients at low latitudes in the subsurface ocean are typically weaker [as discussed by Griesel and Maqueda (2006)], the northern boundary point does not need to be pinned to a latitude of 60°N either. When scaling overturning at 1000 m, the northern boundary point can be moved southwards through the subpolar gyre to a latitude of 50°N without having a detrimental effect on the scaling (not shown). However, in order to capture the nonlinear dynamics of the overturning signal at 4000 m, the northern boundary must be taken no further south than 55°N. The topographic barrier between the Atlantic and the Arctic at approximately 65°N (Fig. 4) acts as a northern limit to northern boundary latitude. Intervening topography disrupts the maintenance of large-scale meridional pressure gradients between the northern and southern basin boundaries in the deep ocean and the fundamental principles of the scaling then break down.

4 Scaling the Atlantic MOC response to stochastic forcing

Scaling relationships are typically used to help improve our general understanding of ocean behavior or used in simple box models to parameterize large-scale flows governed by unresolved dynamics. However, little practical usage has been demonstrated previously in the real ocean (or in high resolution ocean models). Whether a basin-scale meridional density gradient measure can be used to reconstruct accurate timeseries of meridional overturning variability from hydrography remains an open question. In the previous section, we demonstrated that Ψ_p is a good proxy for meridional overturning at 1000 m for timescales of 16 to 32-years and longer under sinusoidal buoyancy forcing. However, such periodic forcing scenarios (incorporating variability in just one atmospheric variable) are clearly idealized. Therefore, we extend our analysis to test the ability of twice-integrated meridional density gradients to infer upper Atlantic overturning in the higher resolution, stochastically forced simulation used in Mecking et al. (2014). This simulation was conducted using the global ORCA05 configuration of NEMO with a nominal horizontal resolution of 0.5° and forced by North Atlantic Oscillation (NAO) inspired stochastic forcing. NAO based forcing fields were produced by regressing the CORE v2.0 interannually varying forcing fields onto the observed NAO index. A stochastic NAO index was generated with a white-noise spectrum in each month, normally distributed with mean and standard deviation taken from monthly-averaged observational data. The regression fields are then multiplied by the monthly NAO index and superimposed on the CORE v2.0 normal year forcing dataset. In contrast to the deterministically forced ORCA2 experiments, there is variability in all atmospheric variables, including both 10 m air temperature and wind velocity. For further details, the model setup and simulation is described in full in Mecking et al. (2014). Since deep ocean circulation is still drifting in this simulation, we only test Ψ_p in the upper Atlantic Ocean at a depth of 1000 m at 35°N. We make use of 1800 years of model simulation allowing us to explore comparable timescales to many of those tested in the deterministic experimental setup (up to 600 year timescales) using a series of band pass filters to separate out the corresponding signal components (see Table 2). The scaled overturning streamfunction in ORCA05 is calculated in the same way as in ORCA2, according to the method set out in Sect. 3.

The correlation coefficients (r) between the model simulated overturning, Ψ, and Ψ_p are given in Table 2. The free geometric constant, c_ρ, is again taken to be the gradient of the linear fit of Ψ against Ψ_p for the longest timescale forcing (in this case, the 325–600 year band): 0.69. Despite the differences in resolution and forcing, this figure is comparable to that fitted to the ORCA2 control simulation depth profile in Sect. 3.1 (0.96) and at 1000 m in the transient ORCA2 experiments in Sect. 3.2 (0.88). Timeseries of both Ψ and Ψ_p anomalies for each different frequency band are plotted in Fig. 11. As in the periodically forced coarse resolution experiments, we see good correlations at short multi-decadal timescales (the 25–50 year band) with a correlation coefficient ≥0.9 at the 80–180 year band and longer, explaining at least 81 % of the observed variability. Moreover, the amplitude of overturning anomaly across these timescales is also well modeled. As a result, the unfiltered Ψ and Ψ_p timeseries correspond remarkably well (with an unfiltered correlation coefficient of 0.73). Northern boundary variability makes the largest contribution to Ψ_p at all timescales. As in Sect. 3, the effect of southern boundary point variability for the forcing scenario applied here is largely negligible on decadal timescales, but becomes increasingly significant at centennial timescales (not shown).

Fig. 11

De-trended timeseries of Ψ (blue) and Ψ_p (red) at 1000 m (35°N) in the North Atlantic for the stochastically forced ORCA05 simulation and band pass filtered for timescales comparable to the deterministic variable buoyancy forcing experiments (units: 1 Sv = 10⁶ m³ s⁻¹)

5 Scaling Indo-Pacific overturning

Whilst there are no direct variations in buoyancy forcing applied outside of the North Atlantic, variability induced in the Atlantic propagates internally throughout the global ocean. Idealized theoretical models suggest that transport anomalies can be transmitted globally (on timescales shorter than the advective timescale) via a combination of coastal and equatorial Kelvin waves, which are then conveyed into the ocean interior via Rossby waves propagating from the eastern boundary (Huang et al. 2000; Johnson and Marshall 2004). The mean and range of Indo-Pacific overturning are given in Table 1 and response timeseries are plotted in Fig. 4 for both 1000 m and 4000 m at 10°S (a latitude at which we find strong overturning in the abyssal ocean and non-negligible overturning in the upper ocean—see Fig. 2). At this latitude, mean overturning is approximately −4 Sv at 1000 m and −10 Sv at 4000 m, whilst the MOC response to remote buoyancy forcing has a maximum range of 4.4 Sv at 1000 m and 4.7 Sv at 4000 m. We do not see significant propagation of variability until 64-year timescales; consistent with the idea of an “equatorial buffer” on the global propagation of MOC variability described by Johnson and Marshall (2004) in which the equator effectively acts as a low-pass filter on MOC anomalies, confining anomalies on multidecadal (and shorter) timescales to their basin of origin. At the longest forcing timescales we see that about 30–40 % of the high-latitude Atlantic MOC variability propagates to the Indo-Pacific basin at 10°S. This is in good agreement with the asymptotic fraction predicted by Johnson and Marshall (2004) for centennial periodic forcing of a simple two basin model of MOC anomaly propagation, though the timescales of intermediate propagation appear to be somewhat longer in our GCM experiments. As in the Atlantic, we see a resonant response in the Indo-Pacific. However, the resonant period of the Indo-Pacific basin is significantly longer at 512 years (compared with 128 years at 1000 m in the North Atlantic) suggesting that it is not simply a propagation of the resonant Atlantic signal and could be linked, at least in part, to the differing basin geometry.

A number of previous studies have attempted to scale Indo-Pacific overturning according to measures of meridional density gradient or meridional pressure gradient, typically using models with idealized topography. For example, de Boer et al. (2010) represent the Indo-Pacific basin as a simple rectangular box. Whilst Schewe and Levermann (2009) represent the Indian and Pacific oceans with more realistic geometry, the low latitude Indonesian connection between the Indian and Pacific oceans is closed and the Indonesian throughflow is prescribed so the two basins could be regarded as distinct. The more realistic geometry of ORCA2 (Fig. 1) makes scaling analysis in this region far less trivial. For instance, there is no immediately obvious definition of the western boundary of the combined Indo-Pacific basin along which to calculate the meridional density difference. Depending on whether we consider the upper or abyssal ocean, the southern extent of a continuous western boundary will either be in the Indian Ocean or the Pacific Ocean.

Therefore, we construct two different measures of Ψ_p based on a meridional density difference defined along the western boundary between the North Pacific at 40°N and (a) the southern Indian Ocean off the northeast tip of Madagascar at 25°S and (b) the South Pacific at the northeast tip of New Zealand at 39°S (see Fig. 1). The precise location of each southern boundary point is chosen such that we have sufficiently deep bathymetry to scale overturning throughout the water column. Irrespective of the boundary definition, we take the zonal length scale, L _x , of the Indo-Pacific basin to be 15,000 km (three times that of the Atlantic) and leave the remaining scale parameters unchanged (see Sect. 3). The Indonesian connection facilitates the maintenance of zonal pressure gradients across the entire Indo-Pacific basin and the propagation of upper ocean overturning anomalies (Johnson and Marshall 2004) making scaling (a) physically more appropriate for upper ocean overturning. However, this is not the case in the abyssal ocean in which we have an intervening topographic barrier. At 4000 m, Indo-Pacific overturning is dominated by the Pacific contribution making scaling (b) physically more appropriate at this depth. Correlations between Indo-Pacific overturning Ψ and the two different Ψ_p scalings for Indo-Pacific overturning are shown in Table 3. No information is given for 8, 16, and 32-year forcing cycles as Indo-Pacific overturning failed to reach equilibrium during these forcing cycles and the amplitude of the response was very small (see Fig. 4; Table 1 respectively).

Table 3 Correlation coefficients between Ψ_p and Ψ for Indo-Pacific overturning at 10°S

In line with our expectations, method (a) effectively reconstructs upper but not deep ocean overturning, whereas method (b) effectively reconstructs deep but not upper ocean overturning (Table 3). The progression in amplitude increase up to the resonant timescale of 512 years is also seen (Fig. 12), but the observed correlation drops markedly for the upper ocean at 2048-year forcing timescales. This coincides with a marked change in overturning at this timescale to a weak 1.1 Sv biharmonic signal that is not understood here. Whilst Ψ and Ψ_p are not perfectly correlated at this timescale, Ψ_p does well predict this transition to a biharmonic signal.

Fig. 12

Temporal anomalies of Ψ (blue) and Ψ_p (red) at a 1000 m (10°S; constructed using a meridional density gradient between the northern Pacific Ocean boundary and the southern Indian Ocean boundary) and b 4000 m (10°S; constructed using a meridional density gradient calculated across the Pacific Ocean only) in the Indo-Pacific basin for the 64, 128, 256, 512, 1024, and 2048 years timescale experiments in the ORCA2 simulation

Time series of Ψ and Ψ_p(a) (for 1000 m) and Ψ_p(b) (for 4000 m) are illustrated for selected forcing periods in Fig. 12. As before, the free constant, c_ρ, is taken to be the gradient of the linear fit of Ψ against Ψ_p at the longest timescale forcing: 0.81 at 1000 m for Ψ_p(a) and 0.93 at 4000 m for Ψ_p(b) (consistent with c_ρ = 0.88 in the Atlantic at 1000 m). Due to the weak correlation of Ψ_p(a) at 2048-year timescales, c_ρ is estimated from the 1024-year forcing cycle for greater accuracy. The relative contributions of northern and southern boundary point variability to Ψ_p(a) and Ψ_p(b) are depicted in Fig. 13. Despite the propagation of overturning variability from the Atlantic via the southern boundary, it can be seen that density variations at both the northern and southern boundaries make significant contributions to the overall streamfunction. Therefore, the meridional density difference is critical to reconstructing Indo-Pacific meridional overturning. Considering either northern or southern boundary density variability alone is insufficient.

Fig. 13

Temporal anomalies of scaled Indo-Pacific overturning, Ψ_p, at a 1000 m (10°S; inferred from a meridional density gradient between the northern Pacific Ocean boundary and the southern Indian Ocean boundary) and b 4000 m (10°S; inferred from a meridional density gradient calculated across the Pacific Ocean only). Ψ_p anomalies are constructed using (1) both a variable northern and southern boundary (bold black), (2) a fixed northern boundary corresponding the temporal mean profile of ρ_N (red) and (3) a fixed southern boundary corresponding to the temporal mean profile of ρ_S (blue)

The results here demonstrate that the scaling law does hold in the Indo-Pacific basin and supports the notion that this is a general physical principle that holds throughout the global ocean and not simply a coincidence of Atlantic overturning. In doing so, however, we have also highlighted the topographic difficulties in applying such a scaling law to the Indo-Pacific basin under realistic geometric configurations.

6 Discussion and conclusions

In this study, we have presented a scaling for meridional overturning in terms of twice-integrated meridional density gradients, constructed from meridional pressure gradient anomalies and the hydrostatic relationship. We have demonstrated that this scaling is a good proxy for overturning in the upper Atlantic Ocean across a broad range of timescales under deterministic buoyancy forcing scenarios and in response to stochastic atmospheric variability in global ocean models using realistic bathymetry. Furthermore, this scaling retains depth dependence, allowing both the upper and abyssal ocean overturning to be reconstructed in the same basin. Nonlinear elements of the overturning response to simple, periodic buoyancy forcing in a coarse resolution model are well reconstructed by Ψ_p, including the resonant timescale of upper Atlantic overturning at 1000 m and the biharmonic response of abyssal Atlantic overturning at 4000 m. In a higher resolution 0.5° stochastically forced simulation, both the pacing and magnitude of overturning variability at multidecadal (and longer) timescales is accurately modelled with correlations ≥0.8 observed at multidecadal timescale and correlations >0.9 observed at centennial timescales.

The timescale at which the derived relationship between meridional overturning and twice-integrated meridional density gradients is physically justified is determined by the timescale at which the governing assumption of a linearly proportional relationship between basin-scale zonal and meridional pressure gradients holds. In principle, buoyancy anomalies can propagate around a basin boundary (via Kelvin waves) in matter of months (Johnson and Marshall 2002). However, basin-scale interior adjustment is determined by the propagation of Rossby waves from the eastern boundary (taking place over a number of years) and advective processes acting on decadal timescales. Consequently, the inferred overturning streamfunction is a poor proxy for model-simulated overturning at sub-decadal 8-year timescales. However, this scaling becomes a very good proxy for meridional overturning variability at multi-decadal through millennial timescales. The shorter timescales in this spectral band are directly relevant to contemporary climate change discussions.

It has previously been argued by de Boer et al. (2010) that meridional density gradients do not inevitably correlate well with meridional overturning. It is important to stress that our results are not in conflict with these findings. This paper attempts to reconcile the issues raised therein, arguing here that meridional overturning is well reconstructed by meridional pressure gradients that can then be expressed in terms of integrated meridional density gradients via the hydrostatic relationship. Indeed, when de Boer et al. (2010) use a $\Psi \sim\Delta \rho H^{2}$ scaling relationship with the scale depth, H, determined by the depth at which the north–south pressure gradient anomaly is zero (the implicit solution of V(H) = 0 in the framework presented here) then a reasonable scale of Atlantic overturning strength is obtained (see Eq. 8 of de Boer et al. 2010). It is not a goal of this paper to demonstrate the presence or absence of causality in the relationship between meridional pressure gradients and meridional overturning. However, we now briefly consider the causal link in light of the fact that density, pressure gradients and circulation are strongly coupled. The conceptual arguments detailed in Sect. 2.1 present the relationship as emerging from the response the meridional circulation to meridional density gradients, either via the creation of zonal pressure gradients or through ageostrophic flow. A reversed cause-and-effect, with the relationship emerging from the response of density gradients to the circulation, is not consistent with the success of the scaling on short timescales, or with a linear positive correlation (in a stable system, stronger meridional overturning erodes rather than enhances meridional density gradients). Our results cannot be used to rule out the possibility that a hypothetical third process causes well-correlated variability in meridional pressure gradients and overturning by independent mechanisms. However, the interpretation that is simplest, and is underpinned by theoretical studies, is that large-scale meridional velocities respond approximately linearly to meridional pressure gradients.

One of the suggested explanations in de Boer et al. (2010) for why meridional density gradients failed to explain changes in meridional overturning in their experiments was because their experimental setup was strongly influenced by remote forcing (e.g. Southern Ocean winds and Antarctic Bottom Water formation). Although our deterministic experimental setup is focussed on directly forced, high latitude variability in the Atlantic Ocean, we have demonstrated that remote changes in density at the southern boundary do make an important contribution to the overturning scale at the longest timescales and the accuracy of the scaling law is maintained. Indeed, southern boundary variability is critical to the maintenance of this accuracy, particularly in the abyssal ocean.

We conclude by observing that the scaling relationship proposed here has obvious applicability at centennial and millennial timescales in paleoclimate modeling studies, particularly in the Atlantic Ocean. This relationship has also been verified at far shorter timescales. In principle, our results suggest that multidecadal variability in real ocean Atlantic overturning could be reconstructed in much the same way, only requiring knowledge of the vertical density profile at the northern and southern boundaries. There is, thus, the potential that autonomous hydrographic profilers (such as Argo floats) can play an active role in the monitoring of Atlantic overturning (with the caveat that a full-depth profile would be required).