Abstract

Numerical models are used to test whether the sea surface height (SSH) can be used as an indicator for the variability of Atlantic meridional oceanic mass transports. The results suggest that if the transports over the western boundary current region and those in the eastern part of the basin are considered separately, significant correlations (0.3–0.9) are found between zonal SSH differences and the meridional transports in the top 1100 m. Much weaker correlations are found for the basinwide transport, which corresponds to the surface branch of the meridional overturning circulation (MOC). For the eastern and western branches of the meridional transport, combining the SSH signal with the baroclinic structure obtained from Rossby wave theory enables calculation of a quantitative estimate of the transport variability in the top 1100 m. The results of the method are less convincing for the variability of the MOC. The reason for this is that even small relative errors in the variability of the eastern and western branches can be large compared with the MOC variability. These errors project onto the sum of the eastern and western transports and therefore onto the surface branch of the MOC. Nevertheless, being able to infer transport anomalies from SSH signals in the eastern and western parts of the Atlantic might prove useful in interpreting MOC observations from the U.K. Natural Environment Research Council Rapid Climate Change (RAPID) mooring array at 26°N, which show a large subannual variability that is mainly due to changes at the western boundary. Transports inferred from the SSH could help to identify the origin of this variability and whether transport anomalies propagate into the western boundary region from the basin interior or from other latitudes.

1. Introduction

To understand how the global climate may change under increasing greenhouse gas forcing, knowledge about the current state and evolution of the meridional overturning circulation (MOC) is of fundamental importance. Currently, the warm water masses carried northward by the upper branch of the MOC release about 1 PW of heat over the North Atlantic (Trenberth and Caron 2001), thus contributing to Europe’s moderate climate. Most estimates from numerical models suggest that the MOC is likely to weaken by about 30% during the coming century, thus modifying the spatial pattern of climate change (Alley et al. 2007; Cubasch et al. 2001). The climatic consequences linked to a changed MOC strength are far from being fully understood. Apart from the expected imprints on temperature ranging from a reduced warming to a cooling of the North Atlantic area if one considers a possible shutdown of the MOC, a changed circulation is also likely to affect processes such as the biological production and the oceanic uptake of CO2 of the North Atlantic (Schmittner 2005; Mikaloff Fletcher et al. 2006).

Most past observational estimates of oceanic transports such as the MOC or the meridional heat transport were based on hydrographic sections. Although they provide valuable information about the general ocean circulation (Ganachaud and Wunsch 2000) such observations only provide snapshots, and at a given location the transport is often based on a single hydrographic section. Even when several sections exist (e.g., Bryden et al. 2005; Palmer et al. 2004) the temporal spacing between the different observations means that inferring the variability of the meridional flow is subject to large uncertainties. The only way to reduce these uncertainties is to increase the temporal resolution of the measurements (Baehr et al. 2007). In a recent effort a mooring-based continuous MOC observing system has been deployed in the North Atlantic at 26°N in the framework of the U.K. Rapid Climate Change (RAPID; Marotzke et al. 2002) and the U.S. Meridional Overturning Circulation and Heat-flux Array (MOCHA) programs. For the first time continuous MOC time series are available, and the observations show that even on subannual (weekly, monthly, and seasonal) time scales the MOC variability is large (Cunningham et al. 2007; Kanzow et al. 2007; Johns et al. 2008). Observations from the RAPID monitoring array allow us to estimate the MOC variability at 26°N based on measurements originating mainly from the western and eastern Atlantic boundaries. However, this local information is not necessarily enough to decide whether the MOC is undergoing a large-scale reorganization. To assess the spatial coherence (e.g., Bingham et al. 2007) and possible origins of an observed MOC signal, the data from the RAPID MOC observing system will need to be complemented by additional information.

Satellite observations are available globally and provide data at high temporal and spatial resolution, which allow us to highlight the variability linked to, for example, eddy or Rossby wave activity. The impermeability of the ocean to electromagnetic radiation means that the satellite data remain confined to surface observations such as the sea surface height (SSH), η, the surface temperature, the wind speed (through the ocean roughness), or the ocean color. Based on geostrophy, η allows estimations of surface currents such as the Kuroshio or the Gulf Stream (Imawaki et al. 2001). Previous studies established possible qualitative links between η and transports at greater depths in the water column (Häkkinen 2001; Häkkinen and Rhines 2004), but η alone cannot provide a quantitative estimate. One way to explore the link between η and the flow at depth is the assimilation of satellite altimetry data into numerical models where the assimilation of observations of η leaves an imprint on the simulated deep circulation (Wunsch and Stammer 1998, 2003). A more direct approach has been proposed by Wahr et al. (2002), who suggest using gravity measurements to infer the deep circulation based on estimates of the pressure at the ocean bottom. However, the spatial resolution currently available for gravity measurements is too coarse.

For a successful estimate of oceanic meridional transports, knowledge about the vertical (baroclinic) structure of the flow is crucial. Recent work has shown that, especially on time scales longer than one month, significant differences are found between the variability of η and of the bottom pressure (Vinogradova et al. 2007). The differences between η and bottom pressure signals indicate the presence of short-term (subannual) baroclinic variability in the water column. This is consistent with the MOC variability time scales seen in the observations from the RAPID MOC monitoring array (Cunningham et al. 2007; Kanzow et al. 2007) as well as with results from numerical models (e.g., Hirschi et al. 2007). In another model-based approach, Cromwell et al. (2007) link η with the MOC through a statistical model, which can then be used to predict the MOC based on η. Whereas this method yields encouraging results on longer than interannual time scales, the MOC variability on shorter time scales cannot be inferred. Furthermore, a relatively long (10 yr) “training” period during which both the MOC and η need to be known is required in order to build the statistical model.

Recent work based on Rossby wave theory suggests that at least some of the MOC variability found on short (subannual) time scales could be linked to variability in η, which reflects fluctuations in the amplitude of the first baroclinic mode (Hirschi et al. 2007). The aim of the present study is to extend these results, and to test whether the conceptual model based on Rossby wave theory has the potential to provide a quantitative estimate of the variability found for meridional transports in numerical models on subannual to interannual time scales.

2. Numerical models

We use a coarse-resolution model as well as an eddy-permitting model. The coarse-resolution simulation uses the Massachusetts Institute of Technology (MIT) ocean general circulation model as described in Hirschi and Marotzke (2007). The model domain consists of one rectangular basin of 60° width extending from 80°S to 80°N. The horizontal resolution is 2.5° in both longitude and latitude, and the vertical is divided into 19 levels with thickness ranging from 30 m at the surface to more than 500 m for the bottom level. Idealized, zonally constant temperature and salinity fields are used to force the model at the surface. The meridional temperature and salinity profiles are calculated from analytical functions and ensure a vigorous MOC cell with sinking in the Northern Hemisphere (see Hirschi and Marotzke 2007 for details). A short freshwater discharge at 67.5°N during the last 100 yr of the simulation ensures a strong temporal decrease of the MOC. The idealized model allows us to test whether a major MOC change is reflected in η.

As in Hirschi et al. (2007) the eddy-permitting model used here is a 1/4° version of the Ocean Circulation and Climate Advanced Modeling Project (OCCAM) described in Webb (1996) and Marsh et al. (2005a,b). OCCAM is a global general circulation model with realistic topography. The vertical is divided into 66 levels with thicknesses ranging from 5 m at the surface to 207 m for the bottom level. The surface forcing consists of 6-hourly National Centers for Environmental Prediction (NCEP) fluxes for wind, heat, and evaporation minus precipitation (EP; Kalnay et al. 1996). For the sea surface salinity there is an additional restoring term to monthly surface salinity values of Levitus et al. (1998). The model simulates the global ocean circulation for the years 1985–2003. In the present study we only use the North Atlantic portion of OCCAM extending from the equator to 70°N. OCCAM is eddy-permitting and the best representation of eddies is achieved at low latitudes where the Rossby radius is large. However, eddies can be simulated well up to midlatitudes. In the Agulhas region the persistence time of eddies compares well both with observations and with the results from a 1/12° version of OCCAM (Donners et al. 2004). The limitations of the 1/4° resolution become apparent in the representation of the energy cascade from larger to smaller length scales (e.g., breakup of eddies into cyclonic/anticyclonic pairs), which cannot be resolved.

In contrast to the idealized model there is no major rearrangement of the MOC during the years 1985–2003 simulated in OCCAM. However, there is a substantial short-term variability that exhibits similarities with that seen in observations of the MOC (Kanzow et al. 2007; Cunningham et al. 2007). Using OCCAM can therefore help to decide if η can be used to infer MOC fluctuations that occur on time scales similar to those seen in observations.

3. Qualitative relation between sea surface height signals and meridional transports

Variations in η are linked to density changes in the water column through the steric height

 
formula

where δ is the specific volume anomaly and pbot and ps are bottom and surface pressures, respectively (see, e.g., Gill 1982). Typically, a large fraction of η is reflected in the steric contribution ζ. Differences between η and ζ are a consequence of mass convergence or divergence, atmospheric pressure fluctuations, evaporation, and precipitation.

Seawater densities can be linked to meridional transports through the thermal wind balance

 
formula

where f is the Coriolis parameter, g the earth’s gravitational acceleration, and ρ* a reference density. Subscripts denote differentiation in the vertical (z) and zonal (x) directions, respectively.

Hirschi and Marotzke (2007) have shown that the shear obtained from zonal density gradients through the thermal wind relation can be used to infer a transport

 
formula

that captures much of the variability and vertical structure of the full meridional transport

 
formula

obtained from the full meridional velocity component v. The densities ρe and ρ(x) are the values at the eastern and western limits xe and x between which ψtw and ψ are calculated. The velocity vc ensures that there is no net mass transport for ψtw across the full longitude–depth section. Note that for the Atlantic Ocean there is a net meridional mass transport linked to the transport through Bering Strait. However, this transport has been estimated to be in the order of 1 Sv (1 Sv ≡ 106 m3 s−1; Coachman and Aagaard 1988; Woodgate et al. 2005) and is therefore neglected in our calculations.

When integrated over the full zonal width of the basin, Eq. (4) gives the meridional overturning streamfunction Ψ. At any given latitude y and depth z, Ψ is

 
formula

where xe and xw are the eastern and western margins.

Equation (3) implies that changes in the meridional transport affect the steric height ζ. To what extent changes in ζ are representative of the variability in ψ can be tested by calculating the correlation

 
formula

where n is number of time steps for which data are available and where

 
formula

is the zonal difference in ζ.

Ideally, ζ is the quantity we would want to relate to meridional transports, but satellite altimetry only provides η. Inferring ζ is more difficult. The steric height ζ can be extracted from satellite observations provided that gravity measurements of adequate accuracy and spatial resolution are available. Currently, this is only the case on basinwide scales; the distinction of different locations along longitude–depth sections as required for our purpose is not yet feasible. For this reason we will also test the correlation

 
formula
 
formula

between zonal differences in Δη and ψ in order to be able to decide how useful the existing satellite altimetry could be.

a. Application to numerical model output

In the idealized model a short freshwater pulse at 67.5°N between model years 8110 and 8120 ensures a pronounced reduction in the strength of the overturning streamfunction Ψ. This allows us to assess if a major rearrangement of Ψ is reflected in Δη. The agreement between the temporal evolution of Ψ at depths of 441, 991, and 2276 m and Δη is tested at 57° and 25°N (Fig. 1). The zonal limits for Δη are the eastern and western margins. The northern location is where the largest values of Ψ occur. The southern location at 25°N allows us to investigate the spatial coherence of the changes induced by the freshwater pulse. The levels of 441, 991, and 2276 m allow us to test to what extent Δη reflects the surface (northward) branch of Ψ.

Fig. 1.

Relation between Δη and Ψ in an idealized model: (top) Ψ (left) before and (right) after the freshwater perturbation. Units are Sv and the contour interval is 2 Sv. (bottom) Normalized time series of Ψ at fixed depths (black) and of Δη (gray) at the latitudes indicated by the vertical lines in (top): (left) 57°N and (right) 25°N. Normalization is obtained by dividing the time series by the maximum amplitude, and the evolutions are shown for the depths of 441, 991, and 2276 m.

Fig. 1.

Relation between Δη and Ψ in an idealized model: (top) Ψ (left) before and (right) after the freshwater perturbation. Units are Sv and the contour interval is 2 Sv. (bottom) Normalized time series of Ψ at fixed depths (black) and of Δη (gray) at the latitudes indicated by the vertical lines in (top): (left) 57°N and (right) 25°N. Normalization is obtained by dividing the time series by the maximum amplitude, and the evolutions are shown for the depths of 441, 991, and 2276 m.

At 57°N the temporal evolutions of Ψ and Δη are in good qualitative agreement for all depths: Ψ and Δη undergo a sharp decrease between years 8110 and 8140 and Δη is a good indicator for the evolution of Ψ over a large fraction of the water column. At 25°N the agreement between the temporal evolutions of Δη and Ψ gradually deteriorates as Δη is compared with Ψ at greater depths. The changes in Δη indicate a decrease followed by a gradual recovery after year 8140. In comparison the initial decrease is slower for Ψ and recovery does not set in before years 8160 (991 m) and 8200 (2276 m), respectively.

Hovmöller diagrams for Δη and Ψ at different depths provide a picture for the full meridional extent of the basin (Fig. 2). For Δη the largest changes are confined to latitudes north of 20°N and only small signals of about 1 cm propagate into the Southern Hemisphere. After the onset of the freshwater perturbation (year 8110), Δη shows a brief increase at the highest northern latitudes while there is a gradual decrease for the northern midlatitudes. The lowest values occur about 40 yr after the freshwater discharge, and especially between 60° and 20°N there is a slight increase in the second half of the time interval considered here. For Ψ a similar anomaly pattern is seen at 441-m depth: After a brief initial increase shortly after the freshwater discharge there is a reduction that is confined to the Northern Hemisphere. As for Δη, a slow recovery sets in 30 yr after the perturbation. For the depths of 991 and 2276 m a good qualitative agreement can be seen north of 40°N. This correspondence gradually deteriorates when moving southward: the farther south a location, the longer it takes to reach the maximum reduction in transport, and at a depth of 2276 m Ψ is still decreasing at the end of the model integration (year 8200) south of 10°N.

Fig. 2.

(a) Hovmöller diagram for anomalies in Δη. The unit is in cm and the contour interval is 1 cm. Hovmöller diagrams for anomalies in ψ at depths of (b) 441, (c) 991, and (d) 2276 m. The unit is in Sv and the contour interval is 2 Sv.

Fig. 2.

(a) Hovmöller diagram for anomalies in Δη. The unit is in cm and the contour interval is 1 cm. Hovmöller diagrams for anomalies in ψ at depths of (b) 441, (c) 991, and (d) 2276 m. The unit is in Sv and the contour interval is 2 Sv.

In summary, the results from the idealized model run suggest that north of about 40°N a major reduction of the overturning streamfunction Ψ originating from a high-latitude perturbation is in qualitative agreement with Δη. South of 40°N, Δη indicates a gradual return to pre-perturbation values, while at depths of 991 and 2276 m Ψ is still decreasing as a consequence of the freshwater discharge.

In the eddy-permitting model there is no major rearrangement of the overturning streamfunction Ψ, but the temporally varying surface forcing ensures the presence of variability on subannual to interannual time scales. As a first step we compare the zonal structure of the meridional transports at 1100-m depth with that seen for the sea surface height signals. At 1100 m Ψ reaches its largest values; that is, the top 1100 m represent the surface branch of Ψ. Hovmöller diagrams illustrate the similarities and differences between ψ, ψtw, η, and ζ at 26°N (Fig. 3). As mentioned in a recent study (Hirschi et al. 2007), anomalies of the meridional transport tend to propagate westward with a speed similar to that of the phase speed of baroclinic Rossby waves (Fig. 3). This propagation is visible for ψ and ψtw as well as in η and ζ. Some (but not all) anomalies seen in the sea surface signals coincide with transport anomalies at the same longitudes (e.g., anomalies in 1996 and 2003 between 40° and 50°W). There is good agreement between η and ζ with the largest signals occurring in the western half of the basin—a feature also found for the meridional transports.

Fig. 3.

Hovmöller diagram for ψ (MOC), the thermal wind contribution ψtw (TW), η (SSH), and ζ (steric) at 26°N. For ψ and ψtw, values are shown for a depth of 1100 m. Units are Sv (ψ, ψtw) and cm (η, ζ).

Fig. 3.

Hovmöller diagram for ψ (MOC), the thermal wind contribution ψtw (TW), η (SSH), and ζ (steric) at 26°N. For ψ and ψtw, values are shown for a depth of 1100 m. Units are Sv (ψ, ψtw) and cm (η, ζ).

The correlations Cζ,ψ and Cη,ψ illustrate at which longitudes and depths the variability in the meridional flow is reflected in zonal differences of ζ and η (Figs. 4 and 5). The correlations Cζ,ψ and Cη,ψ are based on 5-day averages and are shown for the latitudes of 10° and 26°N (Fig. 4) and 36° and 45°N (Fig. 5). For all four latitudes low correlations are found in the top 100 m. This is a consequence of Ekman transports in the top few model levels. Ekman transports account for most of variability in Ψ originating from the surface layer and they are not linked to zonal gradients of ζ and η. At depths larger than 100 m, Cη,ψ gradually increases before reaching maximum values between about 500 and 1100 m. Below 1100 m, Cη,ψ decreases to much lower values even if, in places, high correlations are found over the entire water column. The exact correlation patterns vary at different latitudes. At 10°N, correlation values between 0.6 and 0.8 are found over most of the basin width in the top 1100 m, and the area of high correlations extends to the western margin. Much lower values are found in the deep ocean where some areas show negative correlations. At 26°N, Δζ and Δη also reflect the variability of the meridional mass transports, but the correlations are lower. Apart from the top 1100 m close to the eastern continental margin, the highest correlations are now generally between 0.4 and 0.5. At 36°N, high correlations are found close to the eastern margin as well as west of 60°W where the correlation over most of the water column reaches values of up to 0.9. No significant correlation can be found in the midbasin between 25° and about 60°W. A similar picture characterizes 45°N, where large positive correlations are also confined to the eastern boundary region and the western half of the basin. Note that for 26°, 36°, and 45°N there is a sharp decrease of Cη,ψ at the western boundary. This indicates that zonal differences of sea surface height signals between the eastern and western basin margins cannot be used to infer basinwide fluctuations of the meridional flow.

Fig. 4.

Correlations between Δη, Δζ, and meridional transports ψ. The value plotted at any depth D and longitude L is the correlation of sea level/steric height gradient between the eastern boundary and L with the total meridional transport integrated from the eastern boundary to L and from the surface to D. (a) Correlations (top) Cη,ψ and (bottom) Cζ,ψ at 10°N. The contour interval is 0.1. (b) Same as in (a), but for 26°N.

Fig. 4.

Correlations between Δη, Δζ, and meridional transports ψ. The value plotted at any depth D and longitude L is the correlation of sea level/steric height gradient between the eastern boundary and L with the total meridional transport integrated from the eastern boundary to L and from the surface to D. (a) Correlations (top) Cη,ψ and (bottom) Cζ,ψ at 10°N. The contour interval is 0.1. (b) Same as in (a), but for 26°N.

Fig. 5.

Same as in Fig. 4, but for (a) 36°N and (b) 45°N.

Fig. 5.

Same as in Fig. 4, but for (a) 36°N and (b) 45°N.

Much higher correlation values are found close to the western margin if Δη and ψ are considered between the western margin and the eastern limit of the western boundary current system (Figs. 6 and 7). We chose the longitude of the eastern limit of the western boundary region to be within the area of increased correlation found close to the western boundary in Figs. 4 and 5. Changing the location of the eastern limit within this area has only a minor effect on the results (not shown). Instead of the rapid decrease in the correlation seen for the basinwide picture, the values remain between 0.6 and 0.9 in the top 1100 m for all four latitudes considered here. This suggests that the eastern and western branches of the circulation need to be estimated separately. Between the eastern continental margin and the eastern limit of the western boundary current system, Δη correlates with the meridional flow between the same longitudinal limits. The variability of the western boundary currents, on the other hand, leaves an imprint on Δζ between the western wall and the eastern limit of the western boundary currents. Note that whether Δη or Δζ is used has only a minor effect on the results. The correlation values Cζ,ψ are generally slightly higher, but especially in the top 1100 m the overall correlation patterns remain the same. For this reason and because satellite data can currently only provide η at a high spatial resolution we will restrict our considerations to variations of η in the subsequent sections.

Fig. 6.

Correlations between Δη, Δζ, and the meridional transport ψ over the western boundary regions. (a) Correlation (top) Cη,ψ and (bottom) Cζ,ψ at 10°N. (b) Same as in (a), but for 26°N. The contour interval is 0.1.

Fig. 6.

Correlations between Δη, Δζ, and the meridional transport ψ over the western boundary regions. (a) Correlation (top) Cη,ψ and (bottom) Cζ,ψ at 10°N. (b) Same as in (a), but for 26°N. The contour interval is 0.1.

Fig. 7.

Same as in Fig. 6, but for (a) 36°N and (b) 45°N.

Fig. 7.

Same as in Fig. 6, but for (a) 36°N and (b) 45°N.

The correlation between Δη and the meridional transport can be poor over the eastern part of the basin interior. However, for all latitudes studied here, the values increase close to the western boundary (Figs. 4 and 5), and η can be used as an indicator for the meridional transport ψ integrated between the eastern limit and the areas of increased correlation found close to the western boundary. Similarly, the correlations found for the western boundary region (Figs. 6 and 7) show that Δη can be used to infer the transport zonally integrated over the western boundary region as well. These transports correspond to the southward and northward components of the horizontal gyre circulation. The imbalance between the eastern and western transports corresponds to the surface branch of Ψ, which is not compensated through the thermocline recirculation, but is returned south through the deep branch.

4. Quantitative transport estimates

For a quantitative reconstruction of meridional transports we need an estimate for the baroclinic (depth dependent) structure of the flow. One way to achieve this is by assuming that the sea surface signals result from fluctuations of the density field as a consequence of internal long Rossby wave activity. We assume that the waves are of the form

 
formula

where Mz = pressure/ρ* and M is the Welander function (Welander 1959), and where λ and θ are longitude and latitude, respectively. The meridional wavenumber l is set to zero, as this makes only little difference to the solution (Killworth and Blundell 2005). The vertical structure F can be found as the solution of the eigenvalue problem

 
formula

with R and S given by

 
formula

where ū, N, a, and ω are the mean baroclinic flow, the Brunt–Väisäla frequency, the earth’s radius and the eigenfrequency, respectively. Details about the derivation of Eq. (11) can be found in Killworth and Blundell (2003). The eigenmodes (baroclinic modes) Fi(z) are proportional to the vertical velocity w(z), which for any longitude and latitude x and y can be written as a linear combination of the different eigenmodes

 
formula

Based on the definition of the Welander function, the modes Fi(z) can be linked to η by scaling them according to

 
formula

In the following we assume that the first baroclinic mode is dominant and that the impact of the remaining modes can be neglected. In this case Eq. (13) simplifies to

 
formula

The temporally changing amplitude Fz′ is associated with density anomalies δρ in the water column according to

 
formula

Across any longitude–depth section (apart from the equator), the density anomalies δρ can be used to compute a corresponding transport anomaly based on the thermal wind relation according to

 
formula

where vc′ is a spatially constant velocity correction that ensures that there is no net meridional mass transport associated with Δψ.

As shown in section 3, significant correlations are found for the eastern and western branches of the horizontal gyre circulation if they are considered separately. Therefore, rather than estimating the meridional streamfunction Ψ directly by zonally integrating over the full basin extent, the basinwide meridional transport is split into an eastern and western branch (see schematic in Fig. 8). Equation (16) can then be applied to the eastern and western parts of the basin:

 
formula
 
formula

where xe, xm, and xw are the eastern and western limits of the eastern (ψe) and western (ψw) transport branches, respectively (Fig. 8).

Fig. 8.

Schematic illustrating the calculation of quantitative estimates for the meridional transports in the eastern and western parts of the North Atlantic in the top 1100 m [transports ΔTe and ΔTw; Eqs. (17)(19)]. The vertical structure of the flow is estimated from the density field by calculating the first baroclinic mode F′(z). Meridional transports are obtained by scaling F′(z) with η. The temporal evolution of meridional transports ΔTe and ΔTw is set by the zonal SSH differences Δηe and Δηw, respectively (see text).

Fig. 8.

Schematic illustrating the calculation of quantitative estimates for the meridional transports in the eastern and western parts of the North Atlantic in the top 1100 m [transports ΔTe and ΔTw; Eqs. (17)(19)]. The vertical structure of the flow is estimated from the density field by calculating the first baroclinic mode F′(z). Meridional transports are obtained by scaling F′(z) with η. The temporal evolution of meridional transports ΔTe and ΔTw is set by the zonal SSH differences Δηe and Δηw, respectively (see text).

In the following we will consider the transport anomalies ΔTe and ΔTw:

 
formula

where overbars denote the time mean. The sum

 
formula

provides an estimate for the variability of Ψ at 1100-m depth.

The quantitative method can provide continuous transport estimates without the need for continuous measurements of the vertical density structure. All that is needed is at least one measurement of the vertical density structure so that the baroclinic mode can be calculated. The large number of observations from hydrographic sections, moorings, or Argo floats means that the method has the potential to be applied at many different locations. The quantitative method relies on two main assumptions: 1) the first baroclinic mode is dominant and 2) the mode’s vertical structure remains constant on at least interannual time scales, and the only temporally changing quantity is the mode’s amplitude which according to our method should be reflected in η.

a. Zonally and vertically integrated transports

We apply the quantitative method to the eddy-permitting model. The first baroclinic mode needed for estimating the vertical structure of the meridional transports is obtained from the density field in the first 5-day average of the 19-yr model run. Initially, the first baroclinic mode was computed using the full theory of Killworth and Blundell (2003), that is, including mean flow and sloping bottom topography. However, whereas eigenmodes can be computed for the eastern part of the basin, solutions are not always found close to the western margin. For this reason we decided not to include the bottom slope and the mean flow for the mode calculation, thus reverting to “classical” Rossby wave theory. Note that in the eastern part of the basin, where solutions can be found with and without including the bottom slope and the mean flow, the resulting transports ΔTe are similar (not shown).

Figures 9 and 10 show the theoretical transports ΔTe and ΔTw in the top 1100 m and those obtained from the full meridional velocity in the model. The degree of agreement between the transport curves is summarized in Table 1, which lists the correlations and the explained variances. Since it can be difficult to assess for what frequencies there is most agreement/disagreement between the theoretical and actual transports from Figs. 9 and 10, we performed a wavelet coherence analysis that highlights the periodicities and times for which high correlations are found between the theoretical and the actual transports (Fig. 11).

Fig. 9.

Transport anomalies ΔTe, ΔTw (red) compared with actual transports (black). Thin lines are values based on 5-day averages; thick lines represent values smoothed with a 5-month Parzen filter (note that the 5-day resolution available for the model data is higher than the 10-day repeat cycle typical for satellite altimetry data). All values are zonally integrated transports over the top 1100 m. (a) Theoretical transport estimate ΔTe and transports from full model velocities at (top) 10°N, (middle) estimate ΔTw and actual western transport, and (bottom) ΔTe + ΔTw compared with Ψ. (b) Same as in (a), but for 26°N.

Fig. 9.

Transport anomalies ΔTe, ΔTw (red) compared with actual transports (black). Thin lines are values based on 5-day averages; thick lines represent values smoothed with a 5-month Parzen filter (note that the 5-day resolution available for the model data is higher than the 10-day repeat cycle typical for satellite altimetry data). All values are zonally integrated transports over the top 1100 m. (a) Theoretical transport estimate ΔTe and transports from full model velocities at (top) 10°N, (middle) estimate ΔTw and actual western transport, and (bottom) ΔTe + ΔTw compared with Ψ. (b) Same as in (a), but for 26°N.

Fig. 10.

As in Fig. 9, but for (top) 36°N and (bottom) 45°N.

Fig. 10.

As in Fig. 9, but for (top) 36°N and (bottom) 45°N.

Table 1.

Correlations between theoretical and actual transports, and explained variances (in parentheses). Correlations and variances are listed for the eastern/western transports and for their sum. The values are either based on the highest available temporal resolution for the numerical model output (5-day averages) or on time series smoothed with a 5-month Parzen filter. Correlation values higher than 0.1 and 0.3 are significant at the 99% (5-day averages) and 95% (5-month smoothing) levels, respectively.

Correlations between theoretical and actual transports, and explained variances (in parentheses). Correlations and variances are listed for the eastern/western transports and for their sum. The values are either based on the highest available temporal resolution for the numerical model output (5-day averages) or on time series smoothed with a 5-month Parzen filter. Correlation values higher than 0.1 and 0.3 are significant at the 99% (5-day averages) and 95% (5-month smoothing) levels, respectively.
Correlations between theoretical and actual transports, and explained variances (in parentheses). Correlations and variances are listed for the eastern/western transports and for their sum. The values are either based on the highest available temporal resolution for the numerical model output (5-day averages) or on time series smoothed with a 5-month Parzen filter. Correlation values higher than 0.1 and 0.3 are significant at the 99% (5-day averages) and 95% (5-month smoothing) levels, respectively.
Fig. 11.

Wavelet coherence analysis between the unsmoothed theoretical and actual transport time series depicted in Figs. 9 and 10 using the package of Grinsted et al. (2004). Results are shown for 10°, 26°, 36°, and 45°N for the (top) eastern and (middle) western transports as well as for (bottom) their sum. The shading shows the highest correlations between the time series (black contours: 95% confidence level). Arrows indicate the lag at which they occur. An arrow pointing to the right corresponds to lag zero. The deflection of the arrows indicate the lag (e.g., a 90° clockwise deflection for a period of 1 yr means that the actual transport is leading its theoretical counterpart by 3 months).

Fig. 11.

Wavelet coherence analysis between the unsmoothed theoretical and actual transport time series depicted in Figs. 9 and 10 using the package of Grinsted et al. (2004). Results are shown for 10°, 26°, 36°, and 45°N for the (top) eastern and (middle) western transports as well as for (bottom) their sum. The shading shows the highest correlations between the time series (black contours: 95% confidence level). Arrows indicate the lag at which they occur. An arrow pointing to the right corresponds to lag zero. The deflection of the arrows indicate the lag (e.g., a 90° clockwise deflection for a period of 1 yr means that the actual transport is leading its theoretical counterpart by 3 months).

At 10°N the volume transport in both the eastern and western branches consists of a seasonal cycle overlaid by higher-frequency variability (Fig. 9a, top and middle). These features are also found for the theoretical transport estimates, but for the seasonal signal the model transports are not in phase with their theoretical counterparts. The coherence analysis reveals two bands with high correlations between the theoretical transport estimates and the actual transports of more than 0.8 centered around periods of 1 and 0.125 yr (Fig. 11). It also confirms the phase shift between the theoretical and the actual transports seen on seasonal time scales. The phase difference is indicated by the direction of the arrows in Fig. 11. The arrows are pointing to the right for the short periods centered around 0.125 yr, which means that the theoretical and actual transports are in phase. For the periods centered around 1 yr the arrays are deflected clockwise by 25°–30° (eastern transports) and 70°–120° (western transports). This corresponds to time lags of 1 month (eastern transports) and 2–4 months (western transports). At 10°N, the sum of the theoretical estimates for the eastern and western transport shows a seasonal cycle that is also found for the upper branch of Ψ (Fig. 9, bottom, red). The low correlation and explained variance (Table 1) are due to the time lag between the theoretical and actual transport. The coherence analysis shows that for periods centered around 1 yr the correlation between the two transports is more than 0.8, but Ψ lags its theoretical counterpart by 5 weeks (counterclockwise deflection of phase arrow by 35° in Fig. 11, bottom). Only little coherence is found for periods shorter than 6 months.

From the four latitudes studied here, 26°N shows the lowest correlations between the theoretical and actual transports in the top 1100 m with values of 0.31 and 0.56 for the eastern and western transports, respectively (Fig. 9b, top and middle; Table 1). Even though significant, these correlations reflect that time intervals with good agreement (e.g., peaks/troughs around years 1995 and 2001) alternate with times where little agreement is found between the time series. The highest coherence for the eastern transport ΔTe is found for periods around 4 yr. For periods shorter than 4 yr, there are only short phases where the coherence is high (Fig. 11). For ΔTw, longer coherent phases occur for periods between 0.25 and 0.5 yr as well as for periods longer than 4 yr. There is generally little agreement between the theoretical transport Δψ1100 and the actual transports, which is reflected in both a low correlation (0.15, Table 1) and coherence (Fig. 11).

Of the four latitudes considered in this study, the highest correlations (0.9 or higher) between the eastern/western transports and their theoretical estimates occur at 36°N (Fig. 10a). All the main peaks and troughs in the transports have a counterpart in their theoretical estimates. The amplitude is largely reproduced as well even if there is an underestimation of the variability amplitude for the western boundary contribution ΔTw. At 36°N, the variability is much larger than for the other three latitudes, and the peak-to-peak differences can be as much as 80 Sv. The theoretical and actual transports for the eastern and western branches are coherent and in phase for all periods longer than 0.125 yr (Fig. 11). Even though both the eastern and western transports can be reproduced to a large extent, the resulting estimate of the surface branch of Ψ is poor (Fig. 10a, bottom). The theoretical estimate of the basinwide transport is characterized by a much larger variability than the model transports, and their time series show a small anticorrelation (−0.24; Table 1).

At 45°N the general evolution of the eastern and western transport is captured by the theoretical estimates (Fig. 10b, top and middle). However, for the eastern branch the theoretical transport overestimates the short-term variability. This overestimation of the high-frequency variability is a consequence of fluctuations in η linked to the rapid succession of atmospheric high and low pressure areas typical for 45°N. The spatial scale of synoptic weather systems means that fluctuations are generally coherent over the western boundary region but not across the entire basin. Therefore, variations of the sea level pressure are more likely to affect Δηe, which spans a large fraction of the zonal basin extent, than Δηw, which only covers the western boundary region. The high-frequency signal is not seen in the theoretical estimate of the western transport estimate and explains the higher correlation of 0.71 compared with 0.53 for the eastern branch. Removing the short-term variability by smoothing the time series with a 5-month running average yields similar correlations of 0.82 and 0.81 for the eastern and western transports, respectively (Table 1). A high coherence is found for periods longer than 4 (east) and 2 (west) yr with correlations of more than 0.8 and there is no lag between the theoretical and actual transports (Fig. 11). As for the other latitudes, the basinwide transport cannot be reproduced, which is reflected in both a low correlation and explained variance (Table 1).

The theoretical transport estimates shown in Figs. 9 and 10 illustrate that sea surface height signals allow estimations of the eastern and western branches of the meridional circulation in the top 1100 m of the ocean. The correlations are between 0.31 and 0.9 (between 0.33 and 0.96 for smoothed time series). One might argue that, rather than using the first baroclinic modes obtained from Rossby wave theory, the same results would be obtained if transports were calculated from zonal differences in Δηe and Δηw through geostrophy. Whereas it is true that the correlation values would remain the same, directly computing meridional velocities from Δη through geostrophy at the sea surface and then extending the values downward would result in a large overestimation of the variability amplitude (not shown). Using the first baroclinic mode obtained from Rossby wave theory allows an estimation of the vertical structure of the meridional flow, which is crucial for a quantitative reconstruction of the variability found in the meridional transports.

b. Vertical flow structure

In the following we examine how well the theoretical estimate ΔTe captures the vertical variability structure of the flow in the top 1100 m. This is illustrated in Figs. 12 and 13 with the standard deviations of ΔTe (z) at 10°, 26°, 36°, and 45°N. For both the theoretical and the actual transports the variability sharply increases in the top few hundred meters and gradually flattens with increasing depth. Especially at 10° and 26°N the theoretical transport (solid lines) variability is too low in the top few hundred meters. This is due to the Ekman transport, which is not included in the theoretical transports. Removing the Ekman contribution from the model transport leads to a better agreement in the top few hundred meters (short dashes). We remove the Ekman contribution from Ψ by assuming that the Ekman transport occurs in the top few model layers and is compensated by a depth-independent (barotropic) return flow (e.g., Jayne and Marotzke 2001; Hirschi and Marotzke 2007; Killworth 2008). The best agreement between the theoretical and actual vertical transport structures is found at 10° and 36°N (Figs. 12a,c), where the differences at 1100 m between the theoretical and actual transports (Ekman removed) are 0.5 and 1 Sv, respectively. At 26°N the theory overestimates the variability with a standard deviation of 6 Sv at 1100 m compared with 4.5 Sv for the model transport without Ekman contribution. A large part of the overestimation found at 45°N (10 instead of 6.2 Sv) is due to the presence of the short-term variability of η mentioned in the previous section. Standard deviations for the transports smoothed with a 5-month Parzen filter reduce this difference (7.2 instead of 5.5 Sv; Fig. 13). For the other latitudes the differences between the smoothed theoretical and actual transports (Ekman removed) are typically 1 Sv so that the variability is over- or underestimated by 20% (10°N), 30% (26° and 45°N), and 5% (36°N).

Fig. 12.

Standard deviation as a function of depth for the transport ΔTe from theory (solid), meridional model velocities (long dashes), and from model velocities without Ekman contribution (short dashes). Results are shown for (a) 10°, (b) 26°, (c) 36°, and (d) 45°N.

Fig. 12.

Standard deviation as a function of depth for the transport ΔTe from theory (solid), meridional model velocities (long dashes), and from model velocities without Ekman contribution (short dashes). Results are shown for (a) 10°, (b) 26°, (c) 36°, and (d) 45°N.

Fig. 13.

Same as in Fig. 12, but with standard deviations based on transport values smoothed with a 5-month Parzen filter (see thick lines in Figs. 9 and 10).

Fig. 13.

Same as in Fig. 12, but with standard deviations based on transport values smoothed with a 5-month Parzen filter (see thick lines in Figs. 9 and 10).

Note that the variability found for the eastern and western branches in the actual and theoretical transports is much larger than that found for Ψ. For the numerical model used here the standard deviation of Ψ at 1100 m at the four latitudes studied here is between 3 and 4.4 Sv (Hirschi et al. 2007)—less than the 4.5–21 Sv found for the eastern and western transports ΔTe and ΔTw.

5. Discussion

Using the zonal difference Δη(x) = η(xe) − η(x) as a transport indicator assumes that η(x) and η(xe) have the same weight in the transport reconstruction. This need not be true and the best agreement between signals in η and the meridional transports may be obtained if ηe and ηw are considered separately according to ψ (x, z, t) = a(x, z)η(x, t) + b(xe, z)η(xe, t). We use a multiple regression to calculate the coefficients a and b and find similar results for 10°, 26°, 36°, and 45°N (illustrated for 10°N in Fig. 14). For most longitudes and depths the coefficients a and b are of opposite sign and their absolute values are similar (Figs. 14a,b). The explained fraction of the transport variance is only slightly higher than when it is based on Δη (Figs. 14c,d). In the real ocean a multiple correlation can only be used at locations where continuous measurements of both η and meridional transports are available (e.g., RAPID). At locations where data are temporally sparse, using the zonal difference Δη is the only choice. In principle the coefficients needed for the regression model could also be obtained from a numerical model, provided that the simulated statistics of the meridional transports are realistic.

Fig. 14.

Illustration of multiple regression vs theoretical approach at 10°N. (a) Western coefficient a (x, z). (b) Eastern coefficient b (xe, z). (c) Explained transport variance based on multiple regression. (d) Explained transport variance by assuming that meridional transports are proportional to Δη. Contour interval is 0.1.

Fig. 14.

Illustration of multiple regression vs theoretical approach at 10°N. (a) Western coefficient a (x, z). (b) Eastern coefficient b (xe, z). (c) Explained transport variance based on multiple regression. (d) Explained transport variance by assuming that meridional transports are proportional to Δη. Contour interval is 0.1.

Our results show that good estimates of the meridional transport variability in the eastern and western parts of the Atlantic basin in the top 1100 m are not sufficient to infer the variability of Ψ. Only for one of the four latitudes considered here (10°N) do we obtain a reasonable theoretical estimate of Ψ. For the other three latitudes there is only little (26° and 45°N) or no (36°N) agreement between Ψ and its theoretical estimates. The reason for this lies in the nature of the flow components ΔTe and ΔTw (i.e., the eastern and western branches of the horizontal gyre circulation). Both quantities exhibit a much larger variability than Ψ. This means that the values for Ψ are obtained from the difference between two numbers that are generally larger than Ψ both in terms of absolute values and of variability. Given a perfect knowledge of both transports, the surface (northward) branch of Ψ can be reproduced. However, only a small error in either the eastern or western transport can result in errors that are as large as Ψ itself. At 36°N, the correlation between the theoretical and actual transports is high (0.9), but for the western transport ΔTw the amplitude of the variability is underestimated by about 30%. The underestimation of the variability amplitude for the western transport means that a large mass imbalance is found for the sum of the eastern and western transports. This imbalance projects onto the inferred value of the surface branch of Ψ and introduces an excessive variability (Fig. 10a, bottom). A successful reconstruction of Ψ variability is only possible if very accurate estimates of the variability are available for both the eastern and western transports. Achieving this accuracy seems beyond the method presented here.

The differences between the eastern and western transports are also the reason why the correlation values shown in Figs. 4 and 5 decrease abruptly in the western boundary region. Fluctuations of both the cumulative transports and of η increase from east to west (Fig. 3). The locations of the largest cumulative transport fluctuations therefore coincide with areas of high η variability. This is generally the case at the eastern edge of the western boundary currents. As the zonal integration is extended into the western boundary region, both the amplitude and the variability of the cumulative transport decrease since the western boundary current largely compensates the eastern branch of the horizontal gyre circulation. At the same time there is no similar decrease for the error made by estimating the meridional transport from η and Rossby wave theory. This results in a decrease in the signal-to-noise ratio and reduces the ability of η to be used as an indicator for the basinwide meridional transport. A possible cause preventing an exact reproduction of meridional transports based on our method is the assumption that most of the variability in the water column can be explained with the first baroclinic mode [Eq. (14)] and that contributions from higher modes can be neglected. A recent study suggests that the contribution of higher modes can be important in certain locations (Maharaj et al. 2007). Nevertheless, being able to reproduce the amplitude of the fluctuations found in the eastern and western parts of the meridional flow is encouraging. Our results suggest that a quantitative estimate of the transport variability is possible in the top 1100 m of the eastern and western branches of the horizontal gyre circulation. Large changes are known to occur in the horizontal gyre circulation (e.g., Palmer et al. 2004; Häkkinen and Rhines 2004). These changes can be much larger than those found for Ψ, and the results shown in this paper suggest they are not only detectable but also quantifiable based on η and Rossby wave theory. The high temporal resolution of available data for η means that the strength of ocean gyres could be monitored and more could be learned about their short-term variability. Note that the meandering of the western boundary current outside the area defined by the western limit xm would result in a change of the estimates of both the eastern and western transports and might wrongly be interpreted as a change of the gyre strength. However, such a meandering of the western boundary current is detectable in η and can therefore be recognized as such.

Inferring meridional transport fluctuations from η signals might also prove useful for understanding signals in Ψ observed by the RAPID mooring array in the North Atlantic (Cunningham et al. 2007; Kanzow et al. 2007). The first results of the MOC monitoring campaign have shown that Ψ exhibits a large variability—even on subannual time scales. These short-term signals are far from being fully understood yet. The possibility of using the sea surface height η to quantify fluctuations of the meridional flow even over parts of the total zonal extent of the Atlantic opens the prospect of learning more about the origins of the short-term variability of the overturning streamfunction Ψ. A previous model study has shown that such short-term fluctuations could be linked to Rossby wave activity (Hirschi et al. 2007). The presence of fluctuations in η at the deployment locations of moorings could be linked with the changes found in the vertical density structure of the same sites. Additionally, η could also indicate whether meridional transport anomalies do propagate into the western boundary region as Rossby waves or eddies from the basin interior or from other latitudes. The use of η could therefore be a promising attempt to put the local information retrieved by the RAPID array at 26°N into a basinwide context.

6. Conclusions

A highly idealized coarse-resolution model as well as an eddy-permitting model with realistic geometry have been used to test the potential of η as a qualitative and quantitative indicator for the variability of meridional transports in the North Atlantic. Based on our results we conclude

  • In an idealized coarse-resolution model a large decrease of the meridional overturning streamfunction Ψ over several decades leads to a gradual decrease of the basinwide zonal SSH difference Δη. In this case η is a good qualitative indicator for Ψ.

  • For the eddy-permitting model, significant correlations (0.3–0.9) are found between the zonal SSH difference Δη and the meridional transports if the eastern and western branches of the horizontal gyre circulation over the top 1100 m are considered separately. Much lower correlations are found between basinwide values of Δη and the variability in Ψ.

  • Quantitative estimates of the transport variability can be obtained in the eastern and western branches of the horizontal gyre circulation. These theoretical estimates are obtained by scaling the first baroclinic mode obtained from one snapshot (5-day average) of seawater density with the temporally varying values of Δη found over the eastern and western branches of the gyre circulation.

  • If the sum of the eastern and western transports is considered (i.e., the surface branch of Ψ) even small relative errors in the theoretical estimates of both components lead to errors that can exceed the amplitude of the variability of Ψ. In the eddy-permitting model this prevents an estimate of the variability of Ψ based on Δη.

  • Even if the variability in Ψ cannot be reproduced, the ability of η to be used as a quantitative indicator of meridional transport variability in the eastern and western parts of the Atlantic could be a first step in putting local observations of Ψ such as those obtained with the RAPID MOC monitoring array at 26°N into a broader spatial context.

Acknowledgments

We thank Andrew Coward and Beverly de Cuevas for their help with the OCCAM model. We also thank two anonymous reviewers whose comments helped to improve the paper. This work was supported by the Natural Environment Research Council as part of the RAPID program and by the University of Southampton. The authors J. H., J. B., and D. C. would also like to acknowledge that this work owes much to Peter Killworth who died before completion of the manuscript. It was his breadth of interest and enthusiasm—an enthusiasm he maintained until the very end—that led to the present study.

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Footnotes

Corresponding author address: Joël J.-M. Hirschi, National Oceanography Centre, Southampton, European Way, Southampton SO14 3ZH, United Kingdom. Email: jjmh@noc.soton.ac.uk