Anomalies of Meridional Overturning: Mechanisms in the North Atlantic

Armin Köhl Physical Oceanography Research Division Center for Observations, Modeling, and Predictions, Scripps Institution of Oceanography, La Jolla, California

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Abstract

Optimal observations are used to investigate the overturning streamfunction in the North Atlantic at 30°N and 900-m depth. Those observations are designed to impact the meridional overturning circulation (MOC) in numerical models maximally when assimilated and therefore establish the most efficient observation network for studying changes in the MOC. They are also ideally suited for studying the related physical mechanisms in a general circulation model. Optimal observations are evaluated here in the framework of a global 1° model over a 10-yr period. Hydrographic observations useful to monitor the MOC are primarily located along the western boundary north of 30°N and along the eastern boundary south of 30°N. Additional locations are in the Labrador, Irminger, and Iberian Seas. On time scales of less than a year, variations in MOC are mainly wind driven and are made up through changes in Ekman transport and coastal up- and downwelling. Only a small fraction is buoyancy driven and constitutes a slow response, acting on time scales of a few years, to primarily wintertime anomalies in the Labrador and Irminger Seas. Those anomalies are communicated southward along the west coast by internal Kelvin waves at the depth level of Labrador Sea Water. They primarily set the conditions at the northern edge of the MOC anomaly. The southern edge is mainly altered through Rossby waves of the advective type, which originate from temperature and salinity anomalies in the Canary Basin. Those anomalies are amplified on their way westward in the baroclinic unstable region of the subtropical gyre. The exact meridional location of the maximum MOC response is therefore set by the ratio of the strength of these two signals.

* Current affiliation: Institut für Meereskunde, Zentrum für Meeres- und Klimaforschung, Universität Hamburg, Hamburg, Germany

Corresponding author address: Dr. Armin Köhl, Institut für Meereskunde, Zentrum für Meeres- und Klimaforschung, Universität Hamburg, Bundesstr. 53, 20146 Hamburg, Germany. Email: koehl@ifm.uni-hamburg.de

Abstract

Optimal observations are used to investigate the overturning streamfunction in the North Atlantic at 30°N and 900-m depth. Those observations are designed to impact the meridional overturning circulation (MOC) in numerical models maximally when assimilated and therefore establish the most efficient observation network for studying changes in the MOC. They are also ideally suited for studying the related physical mechanisms in a general circulation model. Optimal observations are evaluated here in the framework of a global 1° model over a 10-yr period. Hydrographic observations useful to monitor the MOC are primarily located along the western boundary north of 30°N and along the eastern boundary south of 30°N. Additional locations are in the Labrador, Irminger, and Iberian Seas. On time scales of less than a year, variations in MOC are mainly wind driven and are made up through changes in Ekman transport and coastal up- and downwelling. Only a small fraction is buoyancy driven and constitutes a slow response, acting on time scales of a few years, to primarily wintertime anomalies in the Labrador and Irminger Seas. Those anomalies are communicated southward along the west coast by internal Kelvin waves at the depth level of Labrador Sea Water. They primarily set the conditions at the northern edge of the MOC anomaly. The southern edge is mainly altered through Rossby waves of the advective type, which originate from temperature and salinity anomalies in the Canary Basin. Those anomalies are amplified on their way westward in the baroclinic unstable region of the subtropical gyre. The exact meridional location of the maximum MOC response is therefore set by the ratio of the strength of these two signals.

* Current affiliation: Institut für Meereskunde, Zentrum für Meeres- und Klimaforschung, Universität Hamburg, Hamburg, Germany

Corresponding author address: Dr. Armin Köhl, Institut für Meereskunde, Zentrum für Meeres- und Klimaforschung, Universität Hamburg, Bundesstr. 53, 20146 Hamburg, Germany. Email: koehl@ifm.uni-hamburg.de

1. Introduction

Understanding and detecting changes of the overturning rate are of paramount interest because the rate is intimately related to the meridional heat transport in the ocean and fundamentally influences the mid- and high-latitude climate in northern Europe (Hall and Bryden 1982).

Recent studies have indicated that the MOC can undergo rapid changes in association with major climate shifts. Model results suggest that the human-induced increase in the atmospheric concentration of CO2 and other greenhouse gases could lead to a measurable reduction in MOC strength in the Atlantic Ocean (Manabe and Stouffer 1993; Wood et al. 1999; Cubasch et al. 2001), which would modify substantially the climate over western Europe. Moreover, it is possible that such changes will occur over less than 20 years.

The possibility of imminent large transitions of the present day MOC has lead to major dedicated observational programs in Europe and the United States aimed at continuously monitoring and detecting changes in the MOC (e.g., NERC RAPID, online at http://www.soc.soton.ac.uk/rapidmoc/) and its drivers at high latitudes (FP5 ASOF-EC).

Causes and mechanisms for such changes are not yet well understood, nor is it obvious what the best possible observing and monitoring network would be to detect or even predict changes of the MOC. Significant work is therefore warranted to address both questions. Besides a monitoring network, it is required to identify ocean fields that can be used to forecast changes several months or years ahead of time.

The importance of the surface boundary conditions on the stability of the MOC was discussed by Stommel (1961) who found different equilibria solutions in a simple box model depending on the prescribed surface conditions. Warren (1983) describes the freshwater fluxes in the polar regions as the main characteristic that distinguishes the MOC in the Pacific Ocean from the Atlantic Ocean. Marotzke and Willebrand (1991) demonstrated the existence of multiple solutions in a general circulation model and showed that small changes in the boundary conditions can indeed lead to transitions from one state into another. More recently Spall and Pickart (2001) found that overturning is very sensitive to boundary convection, whereas a counterintuitive result is described by Marotzke et al. (1999), who find that overturning is not limited by the rate of convective mixing; which however determines essentially the deep-water properties.

Decadal variability in the North Atlantic is thought to be related to anomalies of meridional overturning (Gordon et al. 1992). Despite its importance for the regional and global climate, many basic questions related to possible causes and effects of variations in the changes in the MOC remain unanswered, such as whether changes in the thermohaline circulation are being “pulled” by slow mixing in the interior or “pushed” by convective processes (Marshall and Schott 1999). Many different studies explore mechanisms of self-sustained MOC oscillations. Kelvin wave propagation mechanisms are described by, for example, Greatbatch and Peterson (1996) and Winton (1996), whereas te Raa and Dijkstra (2002) describe propagation due to density gradients. Stochastic atmospheric forcing may also induce variability (Griffies and Tziperman 1995), which can be transiently amplified under nonnormal dynamics (Tziperman and Ioannou 2002).

The findings of Klinger and Marotzke (1999) suggest that the surface density contrast in both hemispheres directly controls the MOC rate. A methodological approach to actually monitor the MOC rate and its variability was addressed in a recent work by Hirschi et al. (2003) who demonstrated the feasibility of such a task considering model results. They found that data across the latitude where the rate is to be determined is sufficient to identify changes in the MOC.

In this article we apply a method complementary to that of Hirschi et al. (2003) to study physical causes for and effects of a changing MOC at 30°N in the North Atlantic and analyze what is required to estimate those changes in an optimal way in a state estimation setting. Our study is based on the method of optimal observations, which is a tool for constructing observations that are optimal for the estimation of scalar quantities such as transports. Köhl and Stammer (2004, hereinafter KS) have shown that, in context of a variational data assimilation framework, such observations are well suited for solving the monitoring problem. The tool will be applied here to study anomalies of the MOC at 30°N and 900-m depth for the year 1997. The emerging patterns of required observations are complex and, in contrast to the approach of Hirschi et al. (2003), mostly point away from the latitude at which the quantity of interest is defined. As a byproduct, the method reveals the dominant processes that accompany the anomalies, which are associated with the causes and effects of the anomaly. Since this method is embedded in a linearization approach, results will be restricted to small changes, for example, present-day variability, but not regime changes.

In this paper we will mainly focus on the connection between the causes in the controlling regions and how they effect the MOC rate and the associated hydrographic changes. Therefore, the results are of greater relevance for forecasting rather than monitoring issues. The method of optimal observations and the framework of the adjoint method is presented in section 2. Optimal observations emerge as a response to optimal forcing anomalies, which are presented in section 3 in association with the decomposition of the response. A synthesis into an observing strategy is attempted in section 4. We conclude in section 5.

2. Methodology

a. Optimal observations

We provide a brief introduction into the idea of optimal observations in applications for scalar quantities. A general derivation is given by KS. Optimal observations for a specific target quantity o (in our case the MOC to 900-m depth at 30°N) are defined as those observations xobs that change o maximally when assimilated by variational data assimilation. We are thus seeking for an approximation of ∂o/∂xobs. Köhl and Stammer (2004) assumed that deviations of an ocean model trajectory δx due to parameter changes δα may be represented by a linear relation
i1520-0485-35-8-1455-e1
where 𝗙 is a linear propagator, representing the linearized model. The definition ∂o/∂xobs can then be split into two parts:
i1520-0485-35-8-1455-e2
Köhl and Stammer (2004) showed that in the limit of large observational errors and linearized models, the impact of the data xobs on the estimated parameter changes δα can be approximated from the solution of the variational data assimilation problem by
i1520-0485-35-8-1455-e3
with the weight 𝗪 for a priori information of the parameter, 𝗩 describing the inverse of the error covariance of the model data difference, and 𝗘 the observational matrix. The result
i1520-0485-35-8-1455-e4
separates then into optimal perturbations 𝗩−1𝗙T(∂o/∂x)T, which are calculated from the adjoint sensitivities and the response 𝗪𝗘𝗙 to those. The gradient ∂o/∂xobs can be calculated by one adjoint and one forward run of the linearized model or equivalently one optimization step of the adjoint method with o(x) substituting the cost function.

b. Physical interpretation of optimal observations

Although Eq. (4) is restricted to the limit of large observational errors, the two-step representation allows a physical interpretation of the result, which holds independently of this limit. First, forcing anomalies are calculated with the adjoint model. Optimal observations emerge then as the response to these anomalies. The adjoint sensitivities describe locations where the target quantity can be perturbed most easily, yet variability of the target quantity will only be observed if the forcing variability projects onto those locations. Therefore, Lee et al. (2002) used a projection on the NCEP forcing in order to verify the impact of the estimated sensitivities.

In our case the variance of the forcing is chosen as the weight 𝗩. The product with the sensitivities (the optimal perturbations) takes then both the spatial distribution of real variability and locations of potentially largest impact into consideration. The response to these perturbations thus emphasizes all processes that are associated with realistic overturning variability. Moreover, different mechanisms of variability are associated with different subsets of the control vector (e.g., wind stress vs buoyancy fluxes) and different levels of their variance yield (modulated by the individual sensitivities) the relative contribution of each of these mechanisms to the total overturning variance.

Optimal observations depend naturally on the target quantity o(x), but also the weights 𝗪 and 𝗩, and the model 𝗙δα. Since the definition is derived with the assumption of a linearized model, the linear dependency on the controls α enables a decomposition in which optimal observations result as a sum of the responses to each of the optimal perturbations. In order to study different mechanisms it is then instructive to form different subgroups such as wind stress and buoyancy forcing. The response to those will further isolate different mechanisms. More details about the decomposition are given in section 3.

c. Model framework

The design of optimal observations and the evaluation of the performance in a variational assimilation system require all components necessary for an adjoint assimilation. This is the forward model with its adjoint and an optimization procedure. The physical model is based on the primitive equations in a z-coordinate formulation. Its numerical implementation was developed at the Massachusetts Institute of Technology (MIT) and is described by Marshall et al. (1997). The numerical code (Adcroft et al. 2002) is designed to allow the construction of the adjoint by the automatic differentiation tool TAMC/TAF (Giering and Kaminski 1998). A description of the steps necessary for the construction are given by Marotzke et al. (1999), and Stammer et al. (1997) provides a first global application of an adjoint assimilation involving the MIT model. The weights 𝗪 and 𝗩 of Eq. (4) are approximated by the error profiles for temperature and salinity taken from Levitus and Boyer (1994) and Levitus et al. (1994). Error values for the forcing fields are derived from the variance of the corresponding National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) fields and were computed by Köhl et al. (2004, manuscript submitted to J. Phys. Oceanogr.). The optimization algorithm is the quasi-Newton method M1QN3 developed by Gilbert and Lemaréchal (1989).

The model setup used in this study is basically the same as the model used for the 1° global-state estimation described by Köhl et al. (2002), covering the global ocean from 80°S to 80°N with realistic topography based on the Smith and Sandwell (1997) dataset. The spatial resolution is 1°. The thickness of the 23 vertical levels increases smoothly from 10 m at the surface to 500 m below 2000 m. Vertical mixing is represented by the KPP scheme of Large et al. (1994). Background coefficients of vertical diffusion and viscosity are 10−5 and 10−3 m2 s−1, respectively. Harmonic diffusion along neutral surfaces according to Redi (1982) in association with the parameterization of Gent and McWilliams (1990, hereinafter GM) for eddy-induced tracer advection represents unresolved eddy processes. The GM advection coefficient is 103 m2 s−1. Isopycnal diffusivity and horizontal viscosity are chosen as 102 and 104 m2 s−1, respectively. The model is operated in the hydrostatic configuration with an implicit free surface.

The model was forced with once-per-day surface heat flux and salinity flux as estimated from precipitation and latent heat flux, obtained from the NCEP–NCAR reanalysis project. Daily shortwave heat flux is treated separately. The vertical profile of absorption is modeled by the analytical formula of Paulson and Simpson (1977) for prescribed ocean water Type Ib after Jerlov (1968). Wind stress fields are 2 times per day. We make use of a preliminary estimation of surface flux corrections and initial conditions of the 1° global-state estimation by Köhl et al. (2002), which were available for the period under investigation, years 1992 through 2002.

3. Decomposition of the response

In order to highlight the physical mechanisms of the response to the calculated anomalies, the set of parameters was further divided into three subgroups (see Table 1 for a summary of the experiments) in which we investigate the responses to either initial conditions, wind stress, or buoyancy fluxes only. The responses can be seen as a decomposition of the full experiment. We recall that forcing perturbations were constructed to maximize the MOC response at 30°N to 900-m depth for target year 1997.

We first look into the overturning streamfunctions of the response to the four different sets of perturbations. Figure 1 shows the time evolution of a horizontal section at 900 m and a vertical section at 30°N as well as the annual mean MOC for target year 1997. First, it is reassuring that the maximum response is, indeed, as expected in 1997 at 30°N for 900-m depth. The same holds for the other experiments except for BUOYANCY. In terms of an observing strategy this corresponds to the trivial result that, if overturning is directly measurable, it is best observed at the location of interest. However, BUOYANCY shows that the maximum response can be away from this location.

Of the 5-Sv (Sv ≡ 106 m3 s−1) maximum response of the full configuration, 3.2 Sv are wind generated and an almost instantaneous response to the wind. The part of the signal that is propagating southward from between 50° and 60°N beginning with year 1993, reaching down to about 40°N in 1997, is only barely visible in the WIND response, whereas it is the main signal in BUOYANCY and about 60% of the maximum signal in INITIAL. The total response for BUOYANCY is only 0.3 Sv and is about 1.5 Sv for INITIAL. The corresponding propagation speed of INITIAL is larger than that of BUOYANCY. The streamfunctions for year 1997 demonstrate that optimally perturbing the MOC at 30° affects almost the whole basin: sinking occurs mainly between 50° and 60°N and 30° and 40°N, and upwelling around the equator and between 20° and 30°N. Most of the water in BUOYANCY is, however, upwelled north of 40°N and only 50% of the response reaches farther south, creating a secondary maximum. This secondary maximum is deeper (2000 m) and farther to the south (25°N) than in other configurations. This is, as further explained below, an expression of the limited physical processes through which MOC can be affected. The large-scale response of the other experiments is an equivalent demonstration for this. The Hovmöller diagrams show a negative response before and after year 1997, indicating the involvement of an oscillatory mode.

The response of the velocity field in 200- and 2000-m depth for the year 1997 is shown in Fig. 2 for the four experiments. In the western part of the Atlantic, all four experiments share a general pattern, albeit the different features are not equally well developed. The most important common feature is an intensification of the western boundary current, which includes the Brazil Current, Caribbean current, Antilles Current, enhanced transport through the Straits of Florida, and the Gulf Stream with recirculation eddies. However, farther north the North Atlantic current, as it separates from the coast, is not enhanced, but the response follows the continental boundary into the Labrador Sea, which weakens the Labrador and West Greenland Current. WIND shows the smallest changes of the surface currents in the western part but additionally a large signal in the eastern Atlantic, which consists of a weakening of the Canary and Guinea Current, that enhances the northward transport. At depth, enhancement of the DWBC is visible in INITIAL and BUOYANCY. In WIND most of the current that crosses the equator is fed by a current crossing the basin from the east.

a. Initial conditions

Anomalies of the temperature initial condition at the beginning of year 1992, when the model was started, are displayed in Fig. 3. The ratio of temperature and salinity sensitivities (not shown) is almost exactly represented by the ratio of the thermal and salinity expansion coefficients. The separation into the kinematic and dynamical part according to Marotzke et al. (1999) shows that the sensitivities are, as expected, entirely dynamical. The figure shows a wavelike pattern of alternating positive and negative corrections off the coast of West Africa at around 25°N. A corresponding pattern of much smaller amplitude exists in the Southern Hemisphere at around 25°S. Since the fate of the pattern and the mechanisms are analogous to the northern pattern and less clear to visualize, we limit the discussion to the northern part. Similar patterns are also visible in the buoyancy forcing during 1992 (Fig. 5). Since mechanisms are basically the same, we discuss mechanisms south of 30°N, where the effectivity of buoyancy forcing is limited by the interaction through the surface, on basis of the experiment INITIAL in this section. Mechanisms associated with the anomalies north of 30°N are discussed on basis of the experiment BUOYANCY in the following section. To illustrate the flow of information, we show time series of the adjoint, that trace the signal from the cost function to the perturbation, and time series of the forward model that show how the perturbations affect the circulation. These time evolutions are depicted in Fig. 4 along a roughly zonal section between 10° and 20°N. The sign is such that negative temperature anomalies at locations with negative sensitivities would enhance the MOC.

A negative sensitivity along the coast of Africa, visible for year 1996, leads to northward transport anomalies. We come back to the associated mechanism, which acts on time scales shorter than about 3 years, in the discussion of the wind stress anomalies. The wavelike feature of the sensitivity that originates from about 45°W and propagates eastward along 20°N while growing in amplitude sets the pattern of the perturbation to the initial condition. Following the fate of this perturbation in the forward integration along the section 22.5°N in Fig. 4 shows that the feature grows while propagating toward the southwest. It follows the direction of the mean circulation until it reaches the coast of Brazil where it creates a negative temperature anomaly along the coast. Note that only in year 1997 the positive temperature anomaly east of the negative anomaly supports a northward transport anomaly, which enhances the Brazil Current and the Straits of Florida Throughflow throughout the year 1997. The arrival of a negative anomaly in 1998 shuts off the transport anomaly thereafter.

Galanti and Tziperman (2003) found that Rossby waves of the advective type (Liu 1999) may play an important role in communicating midlatitudinal variability to the near-equatorial edge of the subtropical gyre in the Pacific. They were able to trace back the sensitivities of a cost function on the equator to a source region in the eastern Pacific at about 25°N. The authors conclude that the propagation path is along the baroclinically unstable area of the advective mode type. Our source region is at 30°N and the adjoint sensitivities follow roughly along 20°N. The wavelike pattern is only visible in the eastern part of the basin where the Rossby waves enter the baroclinically unstable area. The vertical profile of sensitivities displayed in the left panel of Fig. 4 shows clear similarity to the sensitivities in Fig. 11 of Galanti and Tziperman (2003), though the first maximum is deeper (310 m in contrast to 150 m). The forward run then shows, in accord with their findings, a propagation along the southern edge of the subtropical gyre where baroclinicity is largest. Liu (1999) suggests that buoyancy forcing most effectively produces the advective mode. Accordingly signatures are missing in the wind stress perturbations as opposed to similar patterns in buoyancy forcing and initial conditions.

Temperature anomalies of 1°C and more are observable in the Canary Basin throughout the 10-yr simulation, making an overturning response of more than 5 Sv possible. However, this estimate represents only an upper bound since patterns of natural variability are likely to be less effective in creating MOC anomalies.

b. Buoyancy flux

Time series of zonally integrated heat flux perturbations are shown in Fig. 5. The largest negative flux anomalies are at about 57°N in winter 1993 and shift northward to 60°N now slightly weaker for winter 1992. The recurrence of the wintertime anomalies persists until winter 1996. The 1993 anomaly as shown in Fig. 5 is focused over the center of the Labrador Sea with a weaker branch reaching into the Irminger Sea. For 1992 the anomaly has shifted almost entirely into the Irminger and Iceland Seas. The positive anomaly over the subtropical mode water region persists throughout 1995 and changes its sign thereafter.

The negative anomaly south of Iceland has a twofold impact: First, the eastern part enhances, together with the positive anomaly along the North Sea shelf, the inflow of the North Atlantic Current into the Norwegian Sea and thereby also the outflow though Denmark Strait (the same pattern was also observed in association with the construction of optimal observations for Greenland–Scotland Ridge heat transport by KS). Second, denser water in the Irminger Sea enhances watermass formation there, and through westward advection later, also in the Labrador Sea. Farther upstream, the enhancement of the Gulf Stream and North Atlantic Current also leads to increased inflow into the Norwegian Sea. Denser water (only heat flux shown) is generated in the region of the East Greenland Current, then advected during the following year into the Labrador Sea.

As in the previous section, we show the evolution of the adjoint sensitivities together with the response. The sensitivity signal is transfered to the subpolar region by a boundary wave. Figure 6 shows the evolution of the sensitivity to temperature perturbation along the western boundary on the isopycnal of the Labrador Sea Water (LSW σθ = 27.77). The signal could also be followed on many different depth levels. However, in the forward model (discussed below), the propagation associated with the boundary wave is most clearly visible on σθ = 27.77.

Boundary waves were already discussed by many other authors (see, e.g., Kawase 1987; Döscher et al. 1994; Gerdes and Köberle 1995; Greatbatch and Peterson 1996; Winton 1996) in context of possible mechanisms that transfer the thermohaline adjustment response from subpolar regions to midlatitudes. The phase speed of the first baroclinic mode of the Kelvin wave (typically 1 m s−1) is too fast to explain a time lag of several years between midlatitudinal overturning and the changed amount of Denmark Strait Overflow Water (DSOW) that Gerdes and Köberle (1995) found. Greatbatch and Peterson (1996) suggest that the weak stratification in the subpolar region decreases the speed of wave propagation and enables interdecadal oscillations. Conditions under which self-sustained oscillations are possible are investigated by Winton (1996). However, we find small propagation speeds also in midlatitudes. The signal emerging from 30°N reaches 40°N within about 3 months, which corresponds to a propagation speed of about 0.15 m s−1. The meridional speed decreases once the coastline turns toward the east and becomes more zonally oriented. An additional reduction farther north is in accord with the weaker stratification in the subpolar region.

The evolution of the horizontal and vertical structure of the boundary wave near the coast at 36.5°N is shown in Figs. 7b and 7c. In order to investigate the slow propagation speed, vertical modes were calculated using the density and the 23 layer thicknesses at 36.5°N, 72.5°W from the mean state of the model. Only modes higher than 10 show small amplitudes in the first 200 m below the surface, as observed for the sensitivity. Mode 13, depicted in Fig. 7d, shows the closest resemblance to the vertical structure of the sensitivities, although it is apparent from Fig. 7 that no single mode represents the time evolution. Figure 7a indicates a slowdown of the oscillation backward in time, suggesting that faster (lower) modes are followed by slower (higher) modes. The small propagation speed can be explained by two conditions: First, the signal resides mainly in the higher modes, which have a smaller Rossby radius and therefore smaller propagation speed (e.g., R13 = 3.3 km and c13 = 0.20 m s−1) than the first baroclinic mode (R1 = 35.5 km and c1 = 2.2 m s−1). Second, the propagation speed of a free Kelvin wave decreases with viscosity and alongshore wavelength according to Davey et al. (1983). At 1° resolution the baroclinic Rossby radius is not resolved; the wave speed, however, stays constant on the C grid (Hsieh et al. 1983).

Figure 6 shows a very large alongshore coherence of the signal (∼15°) that corresponds to a wavelength of about 4500 km. The time and length scales roughly fit to the observed propagation speed of 0.15 m s−1. A self propagation of the anomaly according to Marotzke et al. (1999) is not supported since all adjoint sensitivities to MOC anomalies are dynamical rather than kinematic and describe only adiabatic displacements. The adjoint Kelvin wave, once it reached the Labrador Sea, shows a surface signature in wintertime, which is shown in Fig. 5 in terms of heat flux. The propagation of the density anomaly along the west coast on σθ = 27.77 is shown in Fig. 6 for INITIAL and BUOYANCY. North of 40°N, the propagation of the density anomaly for BUOYANCY (Fig. 6, lower) corresponds well with that of the temperature sensitivity in Fig. 6. One part of the signal is reaching down to latitudes lower than 40°N in year 1997, but most of the signal travels at a much lower speed southward. This is not true for INITIAL in which most of the signal reaches down to about 30°N (middle panel of Fig. 6). However, only a small part of the response at 30°N actually propagates from the north. The mechanism of section 3a seems to be dominating. This difference corresponds to the difference in the MOC response (Fig. 1) where most of the MOC response of BUOYANCY is confined to the latitudes north of 40°N. Signals propagating from the north are therefore not a very efficient means to change the MOC south of 40°N.

In order to further investigate this conclusion and to show that the mechanisms are not specific for the latitude under consideration, optimal observations were computed for the MOC at 43°N. The general pattern of the corrections to the temperature initial condition shown in Fig. 8 is very similar to those in Fig. 3. However, the ratio of the corrections off Africa to those south of Iceland is now shifted toward larger corrections in the northern region. The ratio of the two maxima at 310-m depth, 20.5°W, either at 27.5° or at 63°N is 4.3 for the 30°N case and 0.12 in the 43°N case. A strong signal at 27.5°N leads to a stronger Brazil Current, which then requires enhanced upwelling near the equator. This shows a simple mechanism for the selection of the latitude of the maximum response. The scenario is quite different from the classical view of Rossby (1965) in which localized downwelling is balanced by broad upwelling due to diffusion. A partial answer to the question posed by Marshall and Schott (1999), whether the thermohaline circulation is “pulled” by slow mixing in the interior or “pushed” by convective processes, can be given. Pushing tends to be more important at high latitudes but, even at low latitudes where pulling becomes more important, interior mixing is not a necessary process.

c. Wind stress

The time series of zonally integrated zonal wind stress perturbations and the annual mean wind stress perturbation of the year 1997 are shown in Fig. 9. The meridional wind stress perturbations peak north of 70°N in autumn of 1992. A sharp transition is visible at the end of year 1996, as the evolution of 1996 is almost repeated in year 1997 with reversed sign. Basic features are zonal wind along 30°N and along the coast southeast and northwest of 30°N. The corrections of autumn 1992 (not shown) show cyclonic wind stress over the Labrador Sea region.

Wind stress anomalies are the most effective way to affect the MOC. The maximum MOC response is 3 Sv. Three different mechanisms exists, which are discussed in turn. Most prominent in the literature is the Ekman transport, which plays an important role in seasonal variations of the MOC and heat transport (Böning and Herrmann 1994) and is discussed by Jayne and Marotzke (2001). However, the zonally integrated Ekman transport (VEk = −τx/ρof ) associated with the zonally orientated band of wind stress corrections accounts only for 0.3 Sv. The limited latitudinal extension of the band to wind stress corrections implies Ekman pumping velocities that lead to up- and downwelling south and north of 30°N. The integral of the curl of the wind stress over the corresponding region north of 30°N (60°–10°W) gives again approximatively 0.3 Sv as for Ekman transport and explains the mechanism for selecting the down and upwelling regions for Ekman induced MOC anomalies. The width of the band of wind stress corrections is probably a function of the mixing parameters.

Figure 10 shows the vertical velocities, separated in upward and downward components, at 900 m. The largest signal is along the east coast of the United States north of 30°N and along the west coast of Africa south of 30°N. These are the regions where coastal up and downwelling is predominant. Note that coastal up and downwelling opposes Ekman pumping. The direct effect of this up- and downwelling reaches down only to about 300 m, inducing up- and downward movement of the isopycnals near the coast. The associated temperature signal is shown in Fig. 11a. The induced shallow frontal structure generates a relatively strong alongshore current (Fig. 11b) known as coastal upwelling jets, which have been observed, for example, off the coast of Oregon (Huyer 1983; Barth et al. 2000). The associated transports for both regions are toward the north and account for about 2 Sv for WIND. The alongshore currents drive most of the vertical transport near the coastline, visible in Fig. 10, and are the most important mechanism for changing the MOC.

The third mechanism comprises remote effects on deep-water formation. The cyclonic wind stress in the Labrador Sea preconditions wintertime convection(Marshall and Schott 1999). Moreover, the cyclonic wind stress around Iceland enhances the transport through Denmark Strait. Model studies show that enhanced overturning farther south follows with a lag of several years (Döscher et al. 1994). In order to separate the immediate response from long-term changes an additional experiment, in which the wind stress corrections were only applied in year 1997, was performed. The maximum MOC response is only 2 Sv in contrast to 3 Sv of WIND; however, the 1-Sv difference cannot be attributed entirely to the preconditioning effect. The reversal of the wind stress pattern that leads to lower MOC in 1996 indicates that an oscillatory mode might be of some importance. A negative MOC response is also noticeable in the year after 1997.

4. Synthesis: Optimal temperature observations

In this section we try to synthesize results of the previous section into a strategy for observing MOC anomalies. In terms of an observing strategy, we have to distinguish between forecasting, monitoring, and hindcasting situations. The subsequent discussion will be based on optimal temperature observations. Patterns of salinity observations are very similar to those found for temperatures and differ only because of different error specifications. We associate the different approaches with the years 1994, 1997, and 2001 and calculate optimal temperature observations for these years. The optimal observations shown in Fig. 12 represent locations of temperature observations that constrain the MOC to 900 m at 30°N in 1997 in the most effective way if they were assimilated with our setup of the adjoint procedure.

a. Forecasting

For forecasting, we seek locations that optimally predict MOC changes. Key regions (Fig. 12, year 1994) are the Labrador and Irminger Seas as well as the Iceland–Scotland overflows. The spreading of Labrador Sea Water is visible and reaches down to below 1000 m at about 33°N. The baroclinically unstable southern edge of the subtropical gyre is only marginally visible. The large temperature signal (as well as salinity signal, not shown) in the Iberian Basin is associated with enhanced outflow of Mediterranean Water that starts in autumn 1992 with a peak in March 1993 and persists throughout 1996. The core is at 1600 m northwest of the Strait of Gibraltar, but about 200 m deeper and a few degrees farther to the north than that of the salinity signal of the Mediterranean Water. The mechanism is not clear. A positive anomaly is visible south of Iceland.

b. Monitoring

Characteristics for the target year comprise downwelling off the coast of West Africa, upwelling at the east coast of North America, a negative temperature anomaly off the coast of Brazil, and an anomaly northeast of the Strait of Gibraltar as well as a positive anomaly south of Iceland. Altogether the scenario is dominated by the wind stress anomalies at the coasts and the effect of the Rossby wave at the coast of Brazil. It describes an east–west density gradient that manifests mainly along the coasts. The distribution supports the RAPID design proposal (Hirschi et al. 2003). However, larger signals are northeast and southwest of 30°. The Ekman part leaves no signature on temperature observations and remains unobservable.

c. Hindcasting

The effects of the enhanced overturning in year 1997 that are visible in 2001 are a subpolar gyre that is warmer at the surface and colder in depth. Moreover a cold signature is visible in the NADW. The buildup of signal of enhanced Mediterranean outflow persists.

5. Conclusions

In this paper we investigated factors influencing the meridional overturning in the North Atlantic by means of optimal observations with focus on the strength of the MOC at 30°N and 900-m depth. This method is embedded in a variational data assimilation system. Influences on the strengths of the MOC are limited in this approach to the controls of this assimilation system. They comprise in the present investigation the time-varying surface forcing fields (wind stress, heat, and freshwater fluxes) and initial conditions in temperature and salinity over the entire water column. The discussion therefore focuses on wind and buoyancy effects on variations of the MOC.

Optimal forcing anomalies are calculated as those perturbations that change the MOC at 30°N and 900-m depth maximally, respecting the observed forcing variance. Optimal observations were calculated subsequently from the model response to those anomalies. The approach allows one to decompose the response into contributions from individual controlling factors and thereby to study local and remote mechanisms that influence the strength of the MOC circulation at the specified location. Since our model runs are only 10 years long, we can only investigate causes of MOC variations on shorter time scales.

The investigation demonstrated that several mechanisms exists that act individually to create anomalies in the strength of the MOC. Since the patterns were optimally constructed, the relation between anomalies in forcing or initial conditions and the MOC response represents, in general, an upper limit for the effectiveness of the natural variability.

On a time scale of a few months, wind stress forcing is dominant and two primary mechanisms could be identified that are responsible for changes in the MOC. The first is the Ekman drift previously discussed also by (Jayne and Marotzke 2001; Hirschi et al. 2003). However, in our model run, the more important effect is actually the northward transport associated with the heaving of isopycnals due to wind-driven coastal up- and downwelling. The up- and downwelling is created by anomalies in the local wind stress along the coasts: Through this process more than 70% of the total wind-generated variations in the MOC amplitude can be explained. This is the most important mechanism by which the model MOC is adjusted by wind stress corrections. Different from the Ekman drift, the coastal wind stress leaves a signature on the hydrography. It is not clear, however, whether the latter mechanism, revealed here from relatively coarse-resolution model results, is also dominant in the real ocean.

On time scales longer than a few years buoyancy forcing over the subpolar North Atlantic starts to play a dominate role in setting the strengths of the MOC at 30°N and, even more important, farther north. This is in contrast to the suggestion of Wunsch (2002) who argued that buoyancy fluxes do not drive the MOC. The difference may be related to the fact that only transient MOC changes are considered here whereas Wunsch (2002) most likely refers to the equilibrium state only.

Two sources of propagating density anomalies are being observed.

  1. Anomalies created in subpolar basin originating from air–sea interaction in the Labrador or Greenland, Icelandic, and Norwegian (GIN) Seas. Those can be created through buoyancy forcing (net heat or net freshwater fluxes) or through cyclonic wind stress. The southward spreading of the density signal of the associated signal—for example, the enhanced Labrador Sea Water production—is governed by an internal Kelvin wave. The propagation of the corresponding adjoint signal with the largest signal below 100 m suggest that mostly higher vertical modes are involved, which agrees with the slow propagation of about 0.15 m s−1.

  2. Anomalies in eastern basin are propagating westward. In the real life such an anomaly can be created through advection of subtropical mode water (Klein and Siedler 1989) or Mediterranean Water (Käse et al. 1986). Other mechanisms include baroclinic instability of the Cape Verde Frontal Zone (Onken and Klein 1991). Temperature and salinity anomalies in the Canary Basin off the west coast of Africa propagate as baroclinically unstable long Rossby waves southwestward and are amplified in the region of high baroclinicity of the subtropical gyre similar to a mechanism suggested by Galanti and Tziperman (2003). They reach the coast of Brazil and generate northward transport anomalies. This mechanism to adjust the MOC is required in order to explain the selection of the latitude at the maximum MOC response occurs: The proportioning between the strength of this signal and of the anomalies propagating from the north sets the latitude of the maximum MOC response.

The results suggest that different strategies for observing the MOC have to be pursued depending on whether pure monitoring or actually forecasting of MOC changes is the goal. In agreement with Hirschi et al. (2003), we find that monitoring is best done along the zonal section, essentially by monitoring the cross-basin density contrast; that is, the key regions are the boundaries. As can be expected, the goal of forecasting MOC variations involves observing larger and remote regions. Crucial areas then include the Canary Basin and most of the subpolar region, including the overflows and possibly the GIN Seas.

The same is true for estimating the MOC in a state estimation context, which likewise makes use of past and future observations and the propagation of the respective information in the dynamical model system. Since it can be expected that a full synthesis and forecast system will rely heavily on state estimation efforts, we can conclude that for the problem of early detection of MOC changes the most important information will actually come from temperature, salinity, and surface buoyancy information over the subpolar basin of the North Atlantic. For lower latitudes the Canary Basin becomes important.

Acknowledgments

Detlef Stammer read the manuscript and provided helpful comments and suggestions for improvement. Reanalysis surface forcing fields from NCEP–NCAR were obtained through a computational grant at NCAR. Computational support from the National Partnership for Computational Infrastructure (NPACI) and NCAR is acknowledged. We were supported through ONR (NOPP) ECCO Grant N00014-99-1-1049. This is a contribution of the Consortium for Estimating the Circulation and Climate of the Ocean (ECCO) funded by the National Oceanographic Partnership Program.

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Fig. 1.
Fig. 1.

Sections through the spatiotemporal evolution of the MOC calculated from the response to the four different sets of forcing perturbations as described in Table 1. The total response is close to a sum of the parts; nonlinear interactions are negligible.

Citation: Journal of Physical Oceanography 35, 8; 10.1175/JPO2767.1

Fig. 2.
Fig. 2.

Velocity response (m s−1) at 200- and 2000-m depth to the optimal forcing perturbations for the total and the decomposition in which only a subset of the forcing is perturbed. Sensitivity of the KPP mixed layer model to small changes introduces eddylike noise, especially in the Gulf Stream region, that dominates the signal. In order to increase the signal-to-noise ratio, a secondary set of experiments of INITIAL and BUOYANCY were performed for which the parameter changes were enhanced by a factor of 5. Velocities are calculated from these experiments. The MOC response of these experiments is close to 5 times the response of the original experiments.

Citation: Journal of Physical Oceanography 35, 8; 10.1175/JPO2767.1

Fig. 3.
Fig. 3.

Perturbations to the temperature initial condition for 310-m depth (°C). The layer shows the largest corrections after scaling with profiles of typical variability.

Citation: Journal of Physical Oceanography 35, 8; 10.1175/JPO2767.1

Fig. 4.
Fig. 4.

(top) Evolution of the initial temperature anomaly at 310-m depth along the section from 20°N, 20°W to 10°N, 50°W, which is roughly along the direction of propagation. Contour interval (CI) is 0.2°C. (bottom) Sensitivity to temperature perturbations in 310-m depth as function of time and longitude along 22.5°N. Contour interval is 0.001 Sverdrups per degree Celsius per gridbox volume. The size of the grid box at 310 m is 1° × 1° × 100 m. (right) Vertical structure of temperature sensitivity at 23.5°N, 25.5°W. Values are divided by the vertical spacings and units are 10−6 Sverdrups per degree Celsius per gridbox area.

Citation: Journal of Physical Oceanography 35, 8; 10.1175/JPO2767.1

Fig. 5.
Fig. 5.

Time series of (top) zonally averaged heat flux anomalies and spatial patterns of heat flux anomalies for (middle) winter 1992 and (bottom) winter 1993. The largest amplitudes of buoyancy forcing occur in wintertime and precede the maximum overturning by 4–5 years.

Citation: Journal of Physical Oceanography 35, 8; 10.1175/JPO2767.1

Fig. 6.
Fig. 6.

Sensitivity to temperature perturbations along the west coast (vertical axis is in degrees latitude) on the density surface (top) σθ = 27.77. Contour interval is 0.005 Sverdrups per degree Celsius per gridbox volume. Density response along the west coast on the density surface σθ = 27.77 for (middle) BUOYANCY and (bottom) INITIAL. The contour interval is 0.001 and 0.002, respectively.

Citation: Journal of Physical Oceanography 35, 8; 10.1175/JPO2767.1

Fig. 7.
Fig. 7.

(a) Time series (at 2000 m and 72.5°W), (b) zonal sections (at 2000 m), and (c) vertical profiles (at 72.5°W) of sensitivities to temperature perturbations at 36.5°N. Sections and profiles start Nov 1997 and are shown for four different times earlier, each 4 months apart. Units are 0.001 Sverdrups per degree Celsius per gridbox volume. (d) The vertical structure of the vertical derivative of the normal modal solution ψ for mode 13. According to Galanti and Tziperman (2003), the vertical derivative ψz corresponds to temperature as ψzαT, with α the thermal expansion coefficient, and can be compared with the adjoint sensitivity.

Citation: Journal of Physical Oceanography 35, 8; 10.1175/JPO2767.1

Fig. 8.
Fig. 8.

Anomalies of the temperature initial condition for 310-m depth. The figure is analogous to Fig. 3 but optimal for perturbing the MOC at 43°N and 900-m depth.

Citation: Journal of Physical Oceanography 35, 8; 10.1175/JPO2767.1

Fig. 9.
Fig. 9.

Time series of (left) zonally averaged wind stress anomalies and (right) spatial pattern of wind stress, for the year 1997. The largest anomalies are in 1997 and with reversed sign in 1996. The along-shore wind off North America and West Africa as well as the zonally oriented wind reverses the sign from 1996 to 1997.

Citation: Journal of Physical Oceanography 35, 8; 10.1175/JPO2767.1

Fig. 10.
Fig. 10.

Vertical velocities (m day−1) at 900-m depth from expt TOT split into upward and downward parts.

Citation: Journal of Physical Oceanography 35, 8; 10.1175/JPO2767.1

Fig. 11.
Fig. 11.

Annual mean temperature anomaly at 20°N of the year 1997 from (a) expt TOT (CI = 0.2°C) and (b) the associated meridional velocity signal (CI = 0.2 cm s−1).

Citation: Journal of Physical Oceanography 35, 8; 10.1175/JPO2767.1

Fig. 12.
Fig. 12.

Isosurfaces of the nondimensionalized gradient of the MOC at 900 m at 30°N for the year 1997 with respect to annual mean temperature observations for the years 1994, 1997, and 2001 embedded in the bathymetry of the North Atlantic. Red and green surfaces correspond to positive and negative values with an absolute value of 3 Sv °C−1. The gradient with respect to salinity observations shows a similar pattern with reversed sign. The zonal line is in 900 m at 30°N.

Citation: Journal of Physical Oceanography 35, 8; 10.1175/JPO2767.1

Table 1.

Parameter configuration of the performed experiments. Stars denote the set of controls (optimal perturbations) that were active in the corresponding experiment. All other perturbations were set to zero. The set of experiments assumes that the response of TOT is decomposable into a sum of the response of WIND, BUOYANCY, and INITIAL. Details of the perturbations are presented in section 3.

Table 1.
Save
  • Adcroft, A., J-M. Campin, P. Heimbach, C. Hill, and J. Marshall, cited. 2002: Mitgcm Release 1. [Available online at http://mitgcm.org/sealion/.].

  • Barth, J A., S D. Pierce, and R L. Smith, 2000: A separating coastal upwelling jet at Cape Blanco, Oregon, and its connection to the California Current System. Deep-Sea Res., 47 , 783810.

    • Search Google Scholar
    • Export Citation
  • Böning, C W., and P. Herrmann, 1994: Annual cycle of poleward heat transport in the ocean: Results from high-resolution modeling of the North and equatorial Atlantic. J. Phys. Oceanogr., 24 , 91107.

    • Search Google Scholar
    • Export Citation
  • Cubasch, U., and Coauthors, 2001: Projections of future climate change. Climate Change 2001: The Scientific Basis, J. T. Houghton et al., Eds., Cambridge University Press, 525–582.

    • Search Google Scholar
    • Export Citation
  • Davey, M K., W H. Hsieh, and R C. Wajsowicz, 1983: The free Kelvin wave with lateral and vertical viscosity. J. Phys. Oceanogr., 13 , 21822191.

    • Search Google Scholar
    • Export Citation
  • Döscher, R C., C W. Böning, and P. Herrman, 1994: Response of circulation and heat transport in the North Atlantic to changes in forcing in northern latitudes: A model study. J. Phys. Oceanogr., 24 , 23062320.

    • Search Google Scholar
    • Export Citation
  • Galanti, E., and E. Tziperman, 2003: A midlatitude–ENSO teleconnection mechanism via baroclinically unstable long Rossby waves. J. Phys. Oceanogr., 33 , 18771888.

    • Search Google Scholar
    • Export Citation
  • Gent, P R., and J. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20 , 150155.

  • Gerdes, R., and C. Köberle, 1995: On the influence of DSOW in a numerical model of the North Atlantic general circulation. J. Phys. Oceanogr., 25 , 26242642.

    • Search Google Scholar
    • Export Citation
  • Giering, R., and T. Kaminski, 1998: Recipes for adjoint code construction. ACM Trans. Math. Software, 24 , 437474.

  • Gilbert, J C., and C. Lemaréchal, 1989: Some numerical experiments with variable-storage Quasi-Newton algorithms. Math. Program., 45 , 407435.

    • Search Google Scholar
    • Export Citation
  • Gordon, A L., S E. Zebiak, and K. Bryan, 1992: Climate variability in the Atlantic Ocean. Eos, Trans. Amer. Geophys. Union, 73 , 161165.

    • Search Google Scholar
    • Export Citation
  • Greatbatch, R J., and K A. Peterson, 1996: Interdecadal variability and oceanic thermohaline adjustment. J. Geophys. Res., 101 , 2046720482.

    • Search Google Scholar
    • Export Citation
  • Griffies, S M., and E. Tziperman, 1995: A linear thermohaline oscillator driven by stochastic atmospheric forcing. J. Climate, 8 , 24402453.

    • Search Google Scholar
    • Export Citation
  • Hall, M M., and H L. Bryden, 1982: Direct estimates and mechanisms of ocean heat-transport. Deep-Sea Res., 29 , 339359.

  • Hirschi, J., J. Baehr, J. Marotzke, J. Stark, S. Cunningham, and J-O. Beismann, 2003: A monitoring design for Atlantic meridional overturning circulation. Geophys. Res. Lett., 30 .1413, doi:10.1029/2002GL016776.

    • Search Google Scholar
    • Export Citation
  • Hsieh, W W., M K. Davey, and R C. Wajsowicz, 1983: The free Kelvin wave in finite-difference numerical models. J. Phys. Oceanogr., 23 , 13831397.

    • Search Google Scholar
    • Export Citation
  • Huyer, A., 1983: Coastal upwelling in the California Current System. Progress in Oceanography, Vol. 12, Pergamon, 259–284.

  • Jayne, S R., and J. Marotzke, 2001: The dynamics of ocean heat transport. Rev. Geophys., 39 , 385411.

  • Jerlov, N G., 1968: Optical Oceanography. Elsevier, 194 pp.

  • Käse, R H., J F. Price, P L. Richardson, and W. Zenk, 1986: A quasi-synoptic survey of the thermohaline circulation and water mass-distribution within the Canary Basin. J. Geophys. Res., 91 , 97399748.

    • Search Google Scholar
    • Export Citation
  • Kawase, M., 1987: Establishment of the deep ocean circulation driven by deep-water production. J. Phys. Oceanogr., 17 , 22942317.

  • Klein, B., and G. Siedler, 1989: On the origin of the Azores Current. J. Geophys. Res., 94 , 61596168.

  • Klinger, B A., and J. Marotzke, 1999: Behavior of double-hemisphere thermohaline flows in a single basin. J. Phys. Oceanogr., 29 , 382399.

    • Search Google Scholar
    • Export Citation
  • Köhl, A., and D. Stammer, 2004: Optimal observations for variational data assimilation. J. Phys. Oceanogr., 34 , 529542.

  • Köhl, A., Y. Lu, P. Heimbach, B. Cornuelle, D. Stammer, and C. Wunsch, 2002: The ECCO 1 degree global WOCE Synthesis. ECCO Rep. 20, 34 pp. [Available online at http://www.ecco-group.org/reports.html.].

  • Large, W G., J C. Williams, and S C. Doney, 1994: Ocean vertical mixing: A review and a model with a nonlocal boundary layer parametrization. Rev. Geophys., 32 , 363403.

    • Search Google Scholar
    • Export Citation
  • Lee, T., I. Fukumori, D. Menemenlis, Z. Xing, and L-L. Fu, 2002: Effects of the Indonesian Throughflow on the Pacific and Indian Oceans. J. Phys. Oceanogr., 32 , 14041429.

    • Search Google Scholar
    • Export Citation
  • Levitus, S., and T P. Boyer, 1994: Temperature. Vol. 4, World Ocean Atlas 1994, NOAA Atlas NESDIS 4, 117 pp.

  • Levitus, S., R. Burgett, and T P. Boyer, 1994: Salinity. Vol. 3, World Ocean Atlas 1994, NOAA Atlas NESDIS 3, 99 pp.

  • Liu, Z., 1999: Forced planetary wave response in a thermocline gyre. J. Phys. Oceanogr., 29 , 10361055.

  • Manabe, S., and R J. Stouffer, 1993: Century-scale effects of increased atmospheric CO2 on the ocean–atmosphere system. Nature, 364 , 215218.

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  • Fig. 1.

    Sections through the spatiotemporal evolution of the MOC calculated from the response to the four different sets of forcing perturbations as described in Table 1. The total response is close to a sum of the parts; nonlinear interactions are negligible.

  • Fig. 2.

    Velocity response (m s−1) at 200- and 2000-m depth to the optimal forcing perturbations for the total and the decomposition in which only a subset of the forcing is perturbed. Sensitivity of the KPP mixed layer model to small changes introduces eddylike noise, especially in the Gulf Stream region, that dominates the signal. In order to increase the signal-to-noise ratio, a secondary set of experiments of INITIAL and BUOYANCY were performed for which the parameter changes were enhanced by a factor of 5. Velocities are calculated from these experiments. The MOC response of these experiments is close to 5 times the response of the original experiments.

  • Fig. 3.

    Perturbations to the temperature initial condition for 310-m depth (°C). The layer shows the largest corrections after scaling with profiles of typical variability.

  • Fig. 4.

    (top) Evolution of the initial temperature anomaly at 310-m depth along the section from 20°N, 20°W to 10°N, 50°W, which is roughly along the direction of propagation. Contour interval (CI) is 0.2°C. (bottom) Sensitivity to temperature perturbations in 310-m depth as function of time and longitude along 22.5°N. Contour interval is 0.001 Sverdrups per degree Celsius per gridbox volume. The size of the grid box at 310 m is 1° × 1° × 100 m. (right) Vertical structure of temperature sensitivity at 23.5°N, 25.5°W. Values are divided by the vertical spacings and units are 10−6 Sverdrups per degree Celsius per gridbox area.

  • Fig. 5.

    Time series of (top) zonally averaged heat flux anomalies and spatial patterns of heat flux anomalies for (middle) winter 1992 and (bottom) winter 1993. The largest amplitudes of buoyancy forcing occur in wintertime and precede the maximum overturning by 4–5 years.

  • Fig. 6.

    Sensitivity to temperature perturbations along the west coast (vertical axis is in degrees latitude) on the density surface (top) σθ = 27.77. Contour interval is 0.005 Sverdrups per degree Celsius per gridbox volume. Density response along the west coast on the density surface σθ = 27.77 for (middle) BUOYANCY and (bottom) INITIAL. The contour interval is 0.001 and 0.002, respectively.

  • Fig. 7.

    (a) Time series (at 2000 m and 72.5°W), (b) zonal sections (at 2000 m), and (c) vertical profiles (at 72.5°W) of sensitivities to temperature perturbations at 36.5°N. Sections and profiles start Nov 1997 and are shown for four different times earlier, each 4 months apart. Units are 0.001 Sverdrups per degree Celsius per gridbox volume. (d) The vertical structure of the vertical derivative of the normal modal solution ψ for mode 13. According to Galanti and Tziperman (2003), the vertical derivative ψz corresponds to temperature as ψzαT, with α the thermal expansion coefficient, and can be compared with the adjoint sensitivity.

  • Fig. 8.

    Anomalies of the temperature initial condition for 310-m depth. The figure is analogous to Fig. 3 but optimal for perturbing the MOC at 43°N and 900-m depth.

  • Fig. 9.

    Time series of (left) zonally averaged wind stress anomalies and (right) spatial pattern of wind stress, for the year 1997. The largest anomalies are in 1997 and with reversed sign in 1996. The along-shore wind off North America and West Africa as well as the zonally oriented wind reverses the sign from 1996 to 1997.

  • Fig. 10.

    Vertical velocities (m day−1) at 900-m depth from expt TOT split into upward and downward parts.

  • Fig. 11.

    Annual mean temperature anomaly at 20°N of the year 1997 from (a) expt TOT (CI = 0.2°C) and (b) the associated meridional velocity signal (CI = 0.2 cm s−1).

  • Fig. 12.

    Isosurfaces of the nondimensionalized gradient of the MOC at 900 m at 30°N for the year 1997 with respect to annual mean temperature observations for the years 1994, 1997, and 2001 embedded in the bathymetry of the North Atlantic. Red and green surfaces correspond to positive and negative values with an absolute value of 3 Sv °C−1. The gradient with respect to salinity observations shows a similar pattern with reversed sign. The zonal line is in 900 m at 30°N.

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