3.1. Correlation Patterns From Altimetry and Model Diagnostics
 Hughes and Meredith  demonstrate how there are coherent sea-level fluctuations running along the continental slope over the globe. Their sea level diagnostics are based upon a combined altimeter TOPEX/Poseidon and ERS-1/2 product [Ducet et al., 2000], with a high-pass filter applied, retaining periods less than one year and with annual and semi-annual cycles removed. Their diagnostics reveal a pattern of high, positive correlation between the subsurface pressure west of Scotland (averaged along a 1000 m depth isobath between 52°N to 63.7°N) and the subsurface pressure extending for several 1000 km along the continental slope of the Northeast Atlantic, as well as along the western and eastern boundaries (Figure 2a, left). This correlation pattern is retained when the altimetric data is smoothed horizontally over a 5° grid and also reveals a negative correlation over the central part of the basin (Figure 2a, right). This large scale, coherent pattern is interpreted in terms of the rapid propagation of boundary waves, a hybrid mixture of baroclinic Kelvin and topographic Rossby waves, along the continental slope around the basin.
Figure 2. (a) Observational diagnostics showing the correlation of the sub-surface pressure derived from altimetry and averaged along 1000 m isobath west of Scotland with the sub-surface pressure at each grid point. Left: updated from Figure 7 of Hughes and Meredith ; right: using a horizontally smoothed altimetry (5° × 5°). Model diagnostics showing similar correlation maps for (b) sea-surface height (SSH) and (c) bottom pressure (BP) for 0.23° and 1.4° resolution (left and right, respectively). All the correlation maps are calculated by comparing the value at each grid point with the value west of Scotland (averaged along 1000 m isobath between 52°N and 63.7°N), with a high-pass filter retaining periods less than 1 year applied; isobaths are included for 1000 and 3000 m (black lines).
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 The correlation of sea level is now investigated in the realistic model integration (0.23° resolution, ECMWF forcing from 1980–2000) using diagnostics with the annual cycle removed, a high-pass filter applied, and correlated with the same region west of Scotland. Again, there is a coherent, large-scale, positive correlation pattern extending around the North Atlantic (Figure 2b, left). This positive correlation runs along the continental slope of the northern rim and western boundary of the subpolar gyre to 40°N, as well as along the eastern boundary and west of the African coast (10–30°N). Thus an enhanced sea-surface height along the boundaries is correlated with a depressed sea-surface height over the central part of the subtropical gyre, reflecting the implied redistribution of mass within the basin. The correlation patterns only differ in detail when repeated for a coarse resolution (1.4°) (Figure 2b, right): the positive correlation extends further south in the coarser model to 28°N off Florida, suggesting that either the finer-scale dynamics or topography is acting to mask or attenuate the propagating sea-surface height anomalies.
 The variability in modeled bottom pressure shows a broadly similar correlation pattern to that of the sea-surface height (Figure 2c), reflecting how elevated sea surface increases the underlying bottom pressure in unstratified waters. Again, there is a positive correlation pattern extending along the continental slope running along the northern rim and western side of the subpolar gyre, as well as along the eastern boundary. In this case, the positive correlation along the western boundary extends more clearly further south along the continental slope to around 25°N irrespective of model resolution.
 The similarity in the bottom pressure and sea-surface height correlation patterns is to be expected where there is weak stratification. The sea-surface height and bottom pressure anomalies are the same on the shelf and along the upper part of the continental slope. However, in deeper waters, the baroclinic compensation leads to the sea-surface height and bottom pressure anomalies being of different sign, reflecting how the flow changes with depth across the main thermocline.
 These diagnostics clearly demonstrate that the model is capable of reproducing the coherent boundary signals seen in the altimetric diagnostics (Figure 2a). The model is now used to explore how these patterns are controlled and how they relate to changes in the meridional overturning.
3.2. How do the Bottom Pressure Signals Evolve?
 In order to understand how the sea-surface height and bottom pressure signals evolve, twin experiments are performed, where additional buoyancy forcing is applied over the Labrador Sea. The buoyancy forcing is applied by displacing the deep interface (depth of approximately 1500 m at 60°N), raised 50 m over 5 days over the northern relaxation zone, and then maintained at this new position. To avoid the differences in the twin experiments being masked by externally-driven variability, the experiments are integrated with constant annual mean forcing (without a seasonal cycle) for 10 years after an initial spin up of 50 years.
 The sea-surface height anomaly, disturbed minus reference, adjusts rapidly along the western boundary (Figure 3a, left). After 1 month, the negative sea-surface height anomaly extends over the shelf and the upper part of the continental slope along the western boundary, from Labrador to 25°N, with a positive anomaly elsewhere. After 4 months, the negative anomaly extends further south around the Gulf of Mexico and has crossed to the eastern boundary from typically 10°N to 40°N (Figure 3b, left). This pattern is broadly in accord with the adjustment process described by Johnson and Marshall  where baroclinic Kelvin waves propagate equatorward from a high-latitude source along the western boundary, cross the equator and generate baroclinic Rossby waves that spread westward into the basin interior. In addition to the boundary-trapped waves, there are large-scale barotropic anomalies on the scale of the barotropic deformation radius, as well as more eddy-scale variability over the extension of the Gulf Stream. After 24 months, any propagating signals are more difficult to detect and the strongest sea-surface height variations are concentrated over the Gulf Stream and its extension (Figure 3c, left), associated with perturbations in the eddy field.
Figure 3. Snapshots of (left) sea-surface height and (right) bottom pressure anomalies from the twin experiment with annual mean forcing. An initial buoyancy forcing perturbation is introduced over the northern relaxation zone, and the anomaly is defined as the model difference between the perturbed and unperturbed states. The anomalies are shown after (a) 1 month, (b) 4 months, and (c) 2 years.
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 The accompanying bottom pressure anomaly again shows a very similar, large-scale pattern to that of sea-surface height along the boundary (Figure 3a, right), emphasizing how both variables are directly connected and adjust in the same manner through wave communication along the shelf and continental slope. The only important difference is that the bottom pressure anomaly pattern shows less fine-scale variability over the extension of the Gulf Stream and inter-gyre boundary.
 For the bottom pressure, an anomaly of opposing sign is formed over the Gulf Stream separation region (Figures 3b and 3c, right). This signal is consistent with the Kelvin wave study of Février et al. , where a negative thickness anomaly is formed in the vicinity of the Gulf Stream separation region; the circulation anomaly linked to the Kelvin wave forms a corresponding thickness anomaly as a consequence of potential vorticity conservation.
 The communication process is now revealed by mapping the time for the perturbed bottom pressure field to adjust to an initial perturbation of 1 mB in the Labrador Sea. Any circulation anomaly propagating equatorward has a decreasing amplitude in pressure because of compensation for the change in the Coriolis parameter. Consequently, our criterion is defined in terms of the time taken for the absolute value of the bottom-pressure perturbation to adjust to a value of 0.1 + 1.0∣sinθ∣ in mB where θ is the latitude. For the default twin experiment (Figure 4a), the bottom pressure anomaly adjusts in less than 6 months over the continental slope along the northern and western boundaries of the basin to the equator, and then propagates along the equator to the eastern boundary in less than 1 year. In the interior, there is a band of enhanced interior communication between 10°N and 30°N over several years, which reflects the westward propagation of baroclinic Rossby waves originating from the eastern boundary [Anderson and Gill, 1975; Anderson and Killworth, 1977].
Figure 4. Time of adjustment (years) for the twin experiments with annual mean forcing: time to reach a predefined (Coriolis parameter scaled) difference in the bottom pressure: (a) 0.23° default experiment, (b) 0.23° experiment with smoothed topography, and (c) 1.4° coarse experiment.
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 In order to assess the effect of the detailed topography, the twin experiments are now repeated with smooth topography at the same resolution and at a coarse resolution of 1.4°. For the smooth topography case (Figure 4b), there is a much more rapid communication of the bottom pressure anomaly southward around the western boundary, across the equator and northward along the eastern boundary of the North Atlantic in typically 6 months or less. The interior of the basin has adjusted to the perturbation in less than 5 years. Thus the fine-scale topography in the default integration is acting to inhibit the wave communication, probably through scattering.
 Finally, for a model with coarse resolution (Figure 4c), there is still a similar communication along the western boundary and along the equator, but there is less communication in the basin interior, particularly over the subpolar gyre and the central part of the subtropical gyre, and less transfer across the equator into the South Atlantic.
 In summary, the region of most rapid adjustment follows the pathways of waves as suggested by the idealized model study of Johnson and Marshall : the waves spread south from a northern source along the western boundary, east along the equator and north along the eastern boundary. Small-scale topography or coarse resolution leads to a weakening of the wave signal, perhaps because of scattering or dissipation of the topographic waves. However, the presence of boundary currents, eddy variability and fine-scale topography does not fundamentally alter the wave communication mechanism, although the anomalies might become harder to detect.
 An interesting difference though with Johnson and Marshall  is the rapid western boundary adjustment in the southern hemisphere (Figures 4a and 4b), which is not permitted in the idealized study incorporating only baroclinic Kelvin waves. Detailed snapshots of the sea-surface height anomaly over the first year (Figure 3) reveal variability emerging south of 20°S along the western boundary. This cross-equator transfer must be interpreted carefully as there might be an influence of the southern sponge layer. In our view, the signal though is formed through a rapid barotropic communication from the northern source over the entire basin: propagation of barotropic Rossby waves across the basin generates a western boundary current response in the southern basin, well before the arrival of any baroclinic Rossby waves from the northern source, which in turn eventually generates baroclinic boundary waves propagating northward toward the equator. In accord with this view, a coupled atmosphere-ocean model study reveals a rapid communication from the Southern Ocean to the tropics relying on the propagation of ocean barotropic and baroclinic waves [Blaker et al., 2006].