The exchange of atmospheric plus oceanic mass between ocean basins is investigated using a global barotropic ocean model. We find two particular cases of exchange between two basins. At periods of 4–6 days, the exchange is between the Atlantic and Pacific basins, and represents a known oscillation forced by atmospheric pressure. This mode represents a failure of the inverse-barometer relationship due to the large scale and high frequency of atmospheric forcing, and the presence of continents. Significant exchange between Atlantic and Pacific also occurs at longer periods. The second case is most prominent at periods longer than 30 days (strongest at periods longer than 100 days), and represents a mass exchange between the Southern Ocean and the Pacific. The Southern Ocean part of this exchange is clearly related to the Southern Mode of fluctuations in Antarctic circumpolar transport, forced by Southern Ocean wind stress. The reason for the exchange being with the Pacific rather than other basins is explored, and is found to be related to the balance of wind stress by form stress in Drake Passage: exchange with the Atlantic and Indian oceans becomes dominant if Drake Passage topography is removed. While recognizing the limitations of a barotropic model, we contend that it is necessary to understand the barotropic adjustment process in order to make sense of longer timescale processes. Accordingly, we end with speculation on the possible importance of the barotropic results for global sea level and tropical dynamics.
 For many purposes, the rapid barotropic adjustment of the ocean is simply taken for granted, while attention is focussed on the baroclinic processes which are generally more important for the transport of heat and salt, and in determining the mean flow near the surface. However, it should not be forgotten that the baroclinic processes take place against the background of a barotropic adjustment process. That process is not necessarily a simple one, and can involve rapid propagation of signals on a global scale.
 The theory of barotropic adjustment within a particular ocean basin has been explored, and is conceptually quite simple. Any non-local response to a change in forcing is initially due to barotropic Kelvin waves, which rapidly set up the initial pressure response, followed by barotropic Rossby waves or basin modes, which propagate along f/H contours (f is the Coriolis parameter and H the ocean depth), setting up a topographic Sverdrup balance, equivalent to the flat-bottomed Sverdrup balance but with f/H contours as characteristics instead of f contours [Anderson and Killworth, 1977; Schulman and Niiler, 1970]. What is less clear is the nature of the barotropic adjustment between ocean basins. Since barotropic adjustment is rapid (the initial Kelvin waves travel at around 200 ms−1, and the constant forcing experiments discussed below generally reach a steady state after 30 days or less), this leads to the possibility of rapid signal propagation between ocean basins.
 Our aim in this paper is to investigate the exchange of mass between ocean basins, based on results from a global barotropic ocean model. We aim to identify the primary modes of exchange, and to understand the dynamics leading to those preferred modes. In order to do this, we first look at exchanges in a model with realistic atmospheric wind stress and pressure forcing, and use a number of methods to identify two main modes of exchange. We then investigate these modes in more detail, comparing them with modes already noted in the literature, and performing idealized model experiments to test our understanding of the associated dynamics.
 Strictly speaking, we are not considering exchange of ocean mass between basins, but of mass of ocean plus atmosphere. Whereas fluctuations of ocean mass can be calculated as an area integral of sea level anomaly (in a barotropic context), fluctuations of oceanic plus atmospheric mass are given by an integral of ocean bottom pressure. There are two reasons for concentrating on this parameter. Firstly, this is the parameter which can be derived from the gravity measurements from the GRACE (Gravity Recovery and Climate Experiment) satellites which are currently in orbit. Secondly, the main focus of this paper is on a wind-driven mode of variation which occurs most clearly on timescales longer than about 30 days. On such timescales, the ocean exhibits an “inverted barometer” response to atmospheric pressure forcing, and this represents the main cause of sea level variability, while producing no signal in bottom pressure. In order to understand the dynamics, it is therefore advantageous to concentrate on the bottom pressure signal, forced mainly by wind stress, rather than the sea level signal, which mainly reflects the inverse barometer response.
 In fact, a further complication results from the fact that the average of atmospheric pressure over the ocean is not constant in time. An increase in atmospheric pressure over the ocean, with no associated horizontal gradients, has no dynamical effect on the ocean, simply resulting in a corresponding increase in bottom pressure. For the most part, we are not interested in this global average signal, and will subtract it off, resulting in diagnostics based on ‘dynamic bottom pressure’ rather than ‘actual bottom pressure’.
2. Barotropic Model Results
 The model used is the same barotropic model as that used by Hughes and Stepanov , but now run for 20 years, producing daily-averaged values from 1985 to 2004. The model is global, at 1° resolution, and is forced by 6-hourly atmospheric winds and pressures from the European Centre for Medium-Range Weather Forecasts (ECMWF).
 In order to investigate mass exchange between basins, the model ocean was divided into 5 regions representing the Southern Ocean, the Atlantic, Indian, Pacific, and Arctic oceans. The division is illustrated in Figure 1. The boundaries between regions are all land or latitude lines except between the Indian and Pacific Oceans where islands have been connected in an ad hoc manner. Averages of model ocean bottom pressure anomaly (i.e. difference from the bottom pressure associated with a steady state ocean, with no wind stress forcing and a globally-uniform 1013 mbar atmospheric pressure field) were then computed for each day, averaged over each of the 5 regions, as well as globally. The global average was subtracted from each of the regional averages to produce regional dynamic bottom pressure averages.
 It could be argued that, given the importance of f/H contours in barotropic dynamics, the definition of ocean basins should be made using constant f/H contours rather than zonal sections as boundaries. However, given that all f/H contours are either closed or terminate at the equator, and the last f/H contour associated with each basin has a different value for each basin, this would lead to an extremely convoluted geometry. Furthermore, it is not clear that this geometry would be meaningful since, where f/H contours converge, especially near the equator, friction is likely to become important, making the regional separation less clear. For reasons of clarity and simplicity, we therefore decided to use the simple regions in Figure 1.
Table 1 lists some basic parameters concerning the variability seen in the different regions (for dynamic bottom pressure) and in the global ocean average. It can be seen that the annual cycle represents a significant fraction of the total variance in many of the regions. In order to avoid the results being dominated by a single, exceptional frequency, we subtracted off the annual cycle from each time series before processing the data further. The annual cycle was calculated by least squares fitting of a sinusoidal function over the 20 year time series. Standard deviations in the table are given for variability after subtracting the annual cycle. These are given both in pressure units, and in mass units (gigatonnes), representing the associated basin-integrated mass anomaly.
Table 1. Basic Parameters of Basin-Averaged Dynamic Pressuresa
Ocean Area Fraction
Annual Amplitude, Phase
% Variance Due to Global
Standard Deviation, mbar
Standard Deviation, Gt
Annual amplitudes are in mbar. Standard deviations are calculated after subtraction of the fitted annual cycle and (except for the top line) of the global mean pressure. The standard deviations are given in both pressure units (mbar) and mass units (gigatonnes), the latter representing the effect of basin area-integrated pressure. % variance due to global is the percentage of the regional mean pressure signal, after subtraction of the annual cycle, which is accounted for by the global mean pressure.
 It is clear that the correction for global ocean average pressure is important, especially for the annual cycle, but also at other frequencies. This may be important for the interpretation of in-situ bottom pressure measurements. It is also clear that, in terms of averaged bottom pressure, the Arctic signal is much larger than all others. This has the result that the mass variability associated with the Arctic is comparable with that from other oceans, despite the fact that the Arctic is between 3.9 and 12.6 times smaller than the other ocean basins in terms of area. The other basins all show similar variability in average pressure, although the Southern Ocean variability is slightly smaller than other basins.
 The power spectra of the area-averaged time series are illustrated in Figure 2. The time-averaged pressure time series have been normalized by multiplying by the fraction of ocean area occupied by each basin, so that similar amplitudes correspond to similar total mass fluctuations. The spectra are shown both as log-log plots, and in variance-preserving form. In grey on each plot is the equivalent spectrum, but based on sea level rather than bottom pressure. The Indian Ocean plots show, in addition, the spectrum for global ocean mean bottom (or atmospheric) pressure, in light grey.
 The most striking feature in these spectra is a peak centred at about 5 day period (0.2 cycles per day), seen clearly in the Pacific and the Atlantic, but not prominent elsewhere. It seems clear that the variation at this period must be dominated by an exchange of (ocean plus atmosphere) mass between the Atlantic and Pacific, since other basins contribute much less power in this interval. Furthermore, since the peak is clear in bottom pressure, but much less clear in sea level, the mass transport must be predominantly in the atmosphere, pointing to a failure of the inverse barometer relationship at this period.
 The only other interval which is dominated by two basins is at long periods, longer than about 100 days, where the Southern Ocean is the only basin showing power comparable to the Pacific, implying a dominance of mass exchange between these two basins at long periods. In this case, however, the sea level signal is much larger than the bottom pressure signal, showing that the sea level response to atmospheric pressure forcing is very close to an inverse barometer. Consideration of the bottom pressure signal must therefore take acount of the wind stress forcing for this mode.
 Another factor worth noting is the relatively red nature of the Arctic and Southern Ocean spectra in comparison with others. In particular, the Arctic has similar total power to the Indian Ocean, but the majority of the Indian Ocean power is at periods shorter than 10 days, whereas more than half of the Arctic power is at longer periods. In fact, in the Arctic, the bottom pressure spectrum contains more power than the sea level spectrum at all periods shorter than about 10 days, indicating a failure of inverse barometer in the Arctic for these periods. This may be due to the semi-enclosed nature of the Arctic, which makes it dynamically difficult for the sea level to adjust to a large scale atmospheric pressure change.
 The ocean plus atmosphere mass flux balance between Atlantic and Southern Ocean, and the Pacific, is illustrated in Figure 3, which shows cross-spectra of each of these basin averages with the Pacific. In both cross-spectra, phase is close to 180° wherever the squared coherence is high (the horizontal line represents the 99% significance estimate), confirming that mass is exchanged between the corresponding pair of basins. The exchange between Southern Ocean and Pacific is not clear at short periods, but becomes significant at a period of about 30 days, becoming stronger at longer periods. Exchange between Atlantic and Pacific is clearly dominant at about 4–6 day periods, but is also significant at longer periods where, however, the energy in the Atlantic power spectrum is significantly lower than that in the Pacific, showing that other basins must also absorb some of the mass leaving the Pacific.
 In an attempt to objectively determine which pairs of ocean basins dominate the exchange of mass, we present in Table 2, two measures of exchange between pairs of basins. Below the diagonal are shown correlation coefficients c between basin-averaged time series, which should be near to −1 for a simple exchange of mass between two basins, but c contains no information about amplitudes: a large correlation does not necessarily mean a regression coefficient of −1. To address this point, we have given (above the diagonal in Table 2) a measure of exchange between basins defined as k = σ(a + b)/σ(a − b), where a and b are two area-weighted time series, and σ() represents the standard deviation. For two independent time series, k would be 1. Where mass is being exchanged between basins, k < 1 tending to zero for two time series which add to zero. Small values of k clearly represent mass exchange between two basins, as they require both anticorrelation, and a regression coefficient close to −1. The values of k and c are given for three frequency ranges: periods shorter than 6 days, between 6 and 100 days, and longer than 100 days (the different frequency ranges were selected by using complementary band pass filters on the time series, after subtraction of the mean from each).
Table 2. Exchange Parameter k (See Text) Above the Diagonal, and Correlation Coefficient c Below the Diagonal, Between Basins at (Top) < 6 Days, (Middle) Intermediate, and (Bottom) >100 Days Periodsa
Bold font highlights values discussed in the text.
 Almost all of the values of k in Table 2 lie between 0.85 and 1.15. The major exceptions represent exchange between the Pacific and the Atlantic, Indian, and Southern Ocean. There is also a positive correlation (c = 0.23) between Atlantic and Indian pressures for 6–100 day periods, and a weaker mass exhange (k = 0.82) between the Atlantic and Southern Ocean in the same frequency range. It is not clear how to determine what would be a significant correlation or value of k in these circumstances, in which mass must be exchanged between basins and the degree to which particular pairs of basins correlate depends on spatial scales of correlation patterns. Instead, we are using c and k to see whether particular exchange modes stand out. The outstanding values again represent long period exchange between the Pacific and Southern Ocean (k = 0.38), and short and medium period exchange between the Pacific and Atlantic (k = 0.45). From the point of view of balancing the mass lost from the Pacific, it is clear that exchanges with the Atlantic are dominant at periods shorter than about 30–100 days, with exchanges with the Indian ocean playing a secondary role, and some degree of exchange with the Southern Ocean. At longer periods, however, the Indian ocean becomes unimportant and it is exchange with the Southern Ocean which dominates, with the Atlantic playing a secondary role.
 If instead we ask what balances the mass lost from the Southern Ocean, we see that there is no clear answer at short periods, although the Pacific clearly contributes, and the Atlantic is also relevant, while the Indian ocean is (weakly) positively correlated with the Southern Ocean. At intermediate periods, both Atlantic and Pacific exchanges become stronger, and the Indian Ocean becomes irrelevant. At long periods, exchange with the Atlantic also becomes much less important, leaving the Pacific exchange to dominate.
 In summary, mass exchange between basins seems to be dominated at periods less than 30 days by the Pacific, Atlantic, and Indian oceans, with the Indian ocean less important perhaps because of its size, and with a particularly strong exchange at a period of about 4–6 days. At longer periods, however, the Southern Ocean becomes more important, and the dominant mode becomes an exchange between Pacific and Southern Ocean.
3. The 4–6 Day Mode
 The 4–6 day mode is actually well known, and has a long history. A strong sea level signal at about 4 day period was first noted in the equatorial Pacific at Canton Island and Ocean Island, by Groves . This mode was found to be well correlated with local meridional winds. Subsequent analysis, however [Groves and Migata, 1967], showed that there was also a separate spectral peak at about 5 days and, while there is a broad peak in atmospheric spectra at around 4–5 days, the fine structure appeared to be limited to the ocean. This led to the suggestion that either the larger scale atmospheric forcing had finer spectral structure than the local winds, or that the peaks are due to oceanic resonances. Wunsch and Gill  followed up the latter possibility by calculating the structure and frequency of equatorially trapped first baroclinic mode inertia-gravity waves in the equatorial Pacific, and showing that the (approximate) frequencies and spatial structure matched the observed distribution of energy in these two modes over a range of tide gauges within about 10° of the equator. This seemed to establish that the 4–6 day mode in the equatorial Pacific represented a resonant excitation of trapped baroclinic gravity waves within a few degrees of the equator.
 Upon investigating this further, however, Luther  found that a broad peak in sea level at 4–6 day period persisted at a broader range of latitudes in the Pacific. Since the baroclinic modes are strongly trapped near the equator, this led him to suggest the existence of a barotropic planetary wave mode in the Pacific. He identified the forcing function as the 5-day atmospheric pressure mode noted by Madden and Julian . This mode has a zonal wavenumber −1 (meaning it propagates to the west), and takes the same sign at all latitudes, with midlatitude maxima of about 1 mbar. Independently of this, however, Pugh  had noted a spectral peak at about 5 day period at several islands in the Indian Ocean.
 In a model-based analysis of the accuracy of the inverse barometer assumption for sea level response to atmospheric pressure, Ponte  found substantial deviations from the inverse barometer assumption at about 5-day period in both the tropical Pacific and Atlantic. Subsequent analysis by Woodworth et al.  of tide gauge data from the Atlantic showed the signal to be clear there too, at island sites as far as almost 16° from the equator, leading them to suggest that the mode should be present in all tropical oceans. Further modelling by Ponte , forced by the 5-day atmospheric mode only, suggested that the source of this non-inverted-barometer response is due to an ocean response to the atmospheric pressure signal, in which the time taken for gravity waves to propagate between the basins leads to a lag in sea level adjustment to basin-averaged atmospheric pressure. No resonant mode is implicated, and a similar mode persists even in the absence of rotation. Further model analysis with realistic forcing demonstrated that the mode remained the dominant feature at 4–6 days in the presence of other atmospheric signals, and comparison with altimetry demonstrated that the basin-averaged sea level variations from the model are strongly correlated with reality [Hirose et al., 2001]. The model results were further confirmed, and more tide gauge analyses added by Mathers and Woodworth .
 There is clearly ample observational evidence for this 4–6 day mode in the real ocean, although there remain some interesting issues about how much of the tide gauge signal is due to the global barotropic mode and how much is due to the equatorially-trapped baroclinic mode. In Figure 4 we plot the correlation of dynamic bottom pressure at each point, with the Pacific basin average, after filtering for periods shorter than 6 days. A regression on the Pacific average is also shown. It is clear that, as for the tide gauges, the correlations are strongest in the tropics, although the regression coefficient suggests that the response is equally strong at higher latitudes. This regression coefficient compares well with what may be deduced from the amplitude and phase plot shown in Figure 9 of Ponte .
 In summary, the 4–6 day mode effectively represents a failure of the inverse barometer response to atmospheric pressure forcing. This becomes the dominant signal in our basin-average diagnostics because of the unusually large scale of the atmospheric forcing at this period. The inverse barometer failure is not complete: sea level does respond to the atmospheric pressure (more so within the ocean basins than is seen in a basin-average picture), but the 5-day period is too short for it to come into equilibrium. This means there is an exchange of mainly atmospheric mass, but also some oceanic mass, between the Atlantic and Pacific. The oceanic component of this exchange propagates as a Kelvin wave [Ponte, 1997] through the Southern Ocean south of Africa and Australia (Drake Passage acts essentially as a barrier). The response in the Southern Ocean is not small, as Figure 4 demonstrates, but takes different signs at different longitudes, tending to cancel in the basin averages presented here. As shown by Egbert and Ray  in the context of long-period tides, the forcing of which is analogous to atmospheric pressure forcing, global scale forcing can result in significant lags (around 30°) relative to the inverse barometer response even at 14 day period, and a small but discernible lag remains at 27.5 day period.
4. Southern Ocean–Pacific Exchange
 Within a barotropic ocean basin (defined by f/H contours emanating from the equator of a particular basin), the equilibrium flow and pressure gradient response to steady wind stress forcing can be calculated based on topographic Sverdrup balance. In order to calculate the pressure, however, a constant of integration is needed, which for a closed basin is given by mass conservation. For an open basin such as the Pacific, it is necessary to consider the boundary where it interacts with other basins (in this case the Southern Ocean) to determine the constant of integration. In order to understand why there is preferentially an exchange between Southern Ocean and Pacific rather than Southern Ocean and Atlantic, we must look to the dynamics in the Southern Ocean.
 On intraseasonal timescales, it has been clearly shown that fluctuations in transport around Antarctica are associated with a wind-driven Southern Mode of variability [Hughes et al., 1999]. In this mode, ocean bottom pressure fluctuations occur all around Antarctica in a region strongly influenced by the geometry of f/H contours. The geometry of this mode has been consistently reproduced in a number of ocean models [Woodworth et al., 1996; Hughes et al., 1999; Vivier et al., 2005; Weijer and Gille, 2005], and can also be seen from satellite altimetry [Hughes and Meredith, 2006]. Circumantarctic coherence has most clearly been demonstrated by intercomparison of data from tide gauges and bottom pressure recorders [Aoki, 2002; Hughes et al., 2003]. The latter two studies also demonstrate a correlation with the Southern hemisphere Annular Mode, or Antarctic Oscillation, the dominant mode of variability of the southern hemisphere atmosphere which manifests itself at sea level as a variation in the strength of zonal winds at the Southern Ocean latitudes.
Figure 4 shows the correlation coefficient and regression coefficient relative to the Southern Ocean long period basin mean, and it is clear from the pattern seen here (in comparison with that shown in the above-mentioned papers) that the Southern Ocean–Pacific exchange is associated with the Southern Mode.
 In the Southern Mode, an increase in eastward wind stress leads to an increased transport around Antarctica, and therefore a decreased ocean bottom pressure in the region surrounding Antarctica. Mass conservation requires an increase in bottom pressure elsewhere, and therefore a net northward flux of water out of the Southern Mode latitudes. Hughes et al.  argued that, if the Southern Mode were a true “free” mode following f/H contours, the increase in bottom pressure elsewhere would be uniform over the world ocean, and therefore small in comparison to the decrease in the Southern Mode region, reflecting the much greater area of the northern region. However, the actual Southern Mode appears to be an “almost free” mode, which must cross f/H contours in places [Hughes et al., 1999; Weijer and Gille, 2005]. The mode is almost free in the sense that its existence appears to be dependent on the presence of the closed f/H contours around Antarctica which would support a free mode. However, the actual response appears to be that of a forced mode driven by wind stress forcing. This leaves greater scope for geographical variability in the distribution of the associated positive pressure anomaly. As we see from the model results, and as was also noted by Hughes and Stepanov , the mass lost from the Southern Ocean appears to preferentially make its way into the Pacific, rather than the Atlantic or Indian oceans. Why should this be?
Egbert and Ray  found differences between Atlantic and Indian/Pacific ocean response to zonally-constant (long-period tidal) forcing which could provide one explanation. They found a sea level signal for which the in-phase component was lower than that required for equilibrium in the Pacific, and higher in the Atlantic, as a result of the time needed for water to flow geostrophically between the basins. In our case, excitation of the Southern Mode by zonal winds is accompanied by an atmospheric pressure anomaly which is low near to Antarctica and high at southern mid-latitudes. Incomplete sea level adjustment to this pressure anomaly, following the pattern seen by Egbert and Ray , would result in higher bottom pressure in the Pacific, and lower bottom pressure in the Atlantic, in addition to the wind-stress-forced flow which excites the Southern Mode. This would explain the pattern we see, were it most clear at high frequencies. However, the Southern Ocean–Pacific exchange is most clear at the lowest frequencies, suggesting that it is associated mainly with wind stress forcing, and is not a result of incomplete inverse barometer adjustment.
 A second possible explanation involves correlations of the atmospheric forcing. It could be the case that eastward wind stress in the Southern Ocean is associated with patterns of wind stress in the Atlantic and Pacific which produce differing local bottom pressure changes relative to their southern boundaries. However, correlation of atmospheric pressure with the Southern Mode shows no clear patterns in the Atlantic and Pacific other than a weak positive pressure over the southern midlatitudes, as shown for example in Figure 6 of Hughes and Stepanov .
 A third possible explanation, and our preferred one, concerns the role of form stress in the Southern Ocean. The Southern Mode is known to be (predominantly) excited by eastward wind stress at latitudes near the southern side of Drake Passage. However, since the work of Munk and Palmén , it has been known that the zonal wind stress at Drake Passage latitudes must be balanced in the mean by form stress (a pressure difference across topographic obstacles), a balance since demonstrated in numerous model studies [Wolff et al., 1991; Stevens and Ivchenko, 1997; Gille, 1997; Hughes and de Cuevas, 2001]. More importantly for the present work, it appears that this balance is achieved very quickly, in a matter of days [Ponte and Rosen, 1994; Weijer and Gille, 2005]. Such a form stress would not occur for the free mode along f/H contours, for which wind stress can only be balanced by bottom friction or time dependence. It is, instead, a reflection of the crossing of f/H contours by flow in the almost-free mode.
 We hypothesize that it is the association between excitation of the Southern Mode and form stress which leads to mass exchange preferentially between the Southern Ocean and the Pacific. Eastward wind stress will result in bottom pressure reducing in the Southern Mode region, and increasing elsewhere. At the same time, the form stress required to balance the wind stress will result in bottom pressure increasing on the western side of some topographic obstacle and decreasing on the eastern side. If we assume that the relevant topographic obstacle is in the vicinity of Drake Passage (the narrowest constriction of the flow, and one containing substantial topographic obstacles), then that would result in higher pressure in the Pacific sector than in the Atlantic sector. Since Southern Ocean bottom pressure can be considered as the southern boundary condition for dynamics within each of the other basins, that would explain why low pressure around Antarctica is associated with high pressure in the Pacific rather than the Atlantic. In fact, the Southern Ocean regression plot in Figure 4 shows ‘Pacific-like’ sea level at the north side of Drake Passage, suggesting that the important topography is not at the narrowest point of Drake Passage, but slightly further east (probably the Scotia island arc).
 We thus have a hypothetical explanation for the preferential mass transport into the Pacific. The hypothesis stresses the importance of topography in the Southern Ocean in order to support a form stress (pressure difference across topographic features). If our hypothesis is correct then it predicts three things. First, the form stress balancing zonal mean wind stress occurs predominantly in the Drake Passage region. Second, if that form stress were to occur elsewhere, then the dominant signal north of the Southern Mode would occur in an ocean basin to the west of the topography where the form stress occurs. Third, without topography in the Southern Ocean there would be no preferred basin. Bottom pressure in all three basins would then respond in the same way to a change in zonal wind stress at the Drake Passage latitudes.
 We have tested the hypothesis by means of a set of idealized experiments. In order to be sure that the correlations result purely from winds in the Southern Ocean, and not from global correlations in the atmospheric circulation, the idealized experiments are forced only by zonal wind stress given by a uniform wind of 5 ms−1 (leading to a stress of 0.03 Pa) at all latitudes south of 40°S. This small wind stress (the mean is about 0.2 Pa) is supposed to represent a plausible amplitude for a fluctuation, rather than the mean. Four model topographies are used. Experiment RT (Real Topography) uses the same topography as the integration using realistic wind stress. Experiment FDP (Flat Drake Passage) removes the topography in the Drake Passage region by setting to 4518 m all nonzero depths in the region 90–30°W, 45–80°S (other, deeper depths were also used, with very similar results). Experiment FSO (Flat Southern Ocean) removes all topography in the Southern Ocean, by setting to 5332 m all depths south of 25°S, but retaining land boundaries. Finally, experiment MT (Mirrored Topography) runs the model with topography reflected about a meridian (actually achieved by the mathematically equivalent method of reversing both the rotation of the earth and the direction of the wind stress). This can alternatively be thought of as an experiment in which the wind stress is reversed, and the direction of propagation of waves involved in the adjustment process is reversed.
 In order to give an estimate of the order of magnitude pressure difference which should be associated with the form stress, consider a balance between wind stress τ = 0.03 Pa at 60°S and form stress due to a pressure difference δp on an obstacle H = 3 km high: τdx = Hδp. The path length is 2 × 107 m, giving an integral wind stress of 6 × 105 Nm−1. Dividing by a depth of 3000 m, gives a pressure difference δp = 200 Pa, or 2 mbar. This is a maximum possible estimate, assuming all the pressure difference is on one obstacle (although it should be admitted that a smaller obstacle would lead to larger estimates). If other obstacles are also important, we should expect significantly smaller differences. For comparison, using a realistic mean wind stress of 0.2 Pa results in a pressure difference of 13.3 mbar, comparable to the observed mean sea level difference between Atlantic and Pacific.
Figure 5 shows the resulting dynamic pressure fields after the circulation has reached steady state, at the end of a 66-day spin-up. Inspection of individual time series from the models suggests that all presented pressures are within a few percent of the asymptotic values they would reach given longer runs of the model. As expected, the resulting mean flows are dominated by flows in the Southern Ocean, but there are differences (too small to see on these plots) between the mean pressures in the various basins north of the forced region. These differences are illustrated in Figure 6, which shows the zonal mean dynamic bottom pressure as a function of latitude and basin, for each of the three idealized experiments.
 As expected, the curves are almost flat within each basin, north of the region which is connected to the Southern Ocean by f/H contours. Slight deviations from flatness in the northern hemisphere are indicative of a small residual adjustment taking place. In fact, time dependent plots show that the small differences are proportional to the rate of change of pressure at a reference latitude, making it possible to define a lag relative to that reference (chosen here as the equator). Lags generally increase northwards, and are a fraction of a day in most places. The exception is the Arctic, where a lag of approximately 2 days occurs, relative to the Atlantic equator. This may be indicative of the effect of the relatively shallow sill between Greenland and Scotland, and the narrow gap into the Arctic (compared with a barotropic Rossby radius), making it difficult for Kelvin waves to penetrate into the Arctic. It may also account for the much lower energy at high frequencies (periods shorter than 3 days) in the Arctic, as compared with other basins (Figure 2).
 Our predictions are mostly borne out. The case with real topography results in higher pressure in the Pacific than the Atlantic, with the Indian Ocean in between. Indeed, in this case, the Atlantic mean is slightly negative, in agreement with Table 2, which shows a slightly positive correlation between Southern Ocean and Atlantic pressures at long periods. The pressure difference between Atlantic and Pacific is about 0.2 mbar, or 10% of our maximum possible estimate. Scaling this up by a factor 0.2/0.03 to represent mean winds rather than fluctuations gives a pressure difference of 1.33 mbar, just a little smaller than the pressure difference seen in the mean state of the experiment with real wind stress forcing.
 After removing the Drake Passage topography, we would expect the main form stress to move to the next most important obstacle: the series of ridges south of Australia and New Zealand. That would result in higher pressure in the Indian and Atlantic Oceans, and lower in the Pacific, which is what we see. The mirrored topography case retains Drake Passage as the main obstacle, but makes the Pacific the downstream basin, so we expect a mirroring of the roles of Pacific, Indian, and Atlantic, which is what we see. For the Flat Southern Ocean case there can be no form stress at the Drake Passage latitudes, only bottom and lateral friction, hence the large transport which results. We predicted that there would be no preferred basin in this case. That turns out to be partially true: the pressure differences between basins are smaller than in the other cases, but the Pacific pressure is clearly higher than the Atlantic and Indian pressures. With hindsight, this is to be expected, since friction acts preferentially near to Drake Passage where the flow is most constricted, and some form stress must occur on the continents to the north and south of Drake Passage.
 Determining which obstacle produces the greatest form stress turns out to be rather more difficult. The form stress exerted by a piece of topography is defined as abpb∂ H/∂ x dx, integrated from a to b where the depth H is the same at both a and b. We have chosen a reference depth of 4000 m, and calculated the form stresses on each ridge which penetrates above this depth, and on each basin deeper than this, for the range of latitudes open at Drake Passage. Form stresses were calculated as a percentage of the total form stress, for the three major topographic obstacles: the Drake Passage region, Kerguelen Plateau, and the Pacific-Antarctic Rise (Figure 7). Drake Passage is clearly the most significant obstacle, accounting for 29.4% of the total form stress, with 19.5% at the Pacific Antarctic Rise, and 16.3% at Kerguelen, but the remaining topography still accounts for 34.8% of the total. This is in line with the results of Weijer and Gille , who found that topography deeper than 4000 m is important in determining the behaviour of the almost-free mode. Taking deeper reference depths, however, makes it more difficult to separate one obstacle from another, as the valley between the Kerguelen Plateau and the Pacific Antarctic Rise becomes shallower than the reference depth at the southernmost Drake Passage latitude.
 In performing these experiments, we have assumed that the steady state is an adequate guide to the response at periods greater than about 30 days (100 days for the clearest response). We have tested this by performing a range of experiments forced by zonal winds south of 40°S, varying sinusoidally in time with periods ranging from 3–150 days. The northward transport into the Atlantic and the combined Pacific and Indian oceans (not shown) confirms that a smooth approach to the equilibrium solution begins at periods of about 20–30 days. The Pacific and Indian responses individually are more complicated when seen in terms of northward transports rather than sea level or bottom pressure, because of the Indonesian Throughflow, which can result in a net northward transport into one basin with no resulting sea level change, as long as there is a compensating throughflow with a balancing southward transport in the other basin. In fact, the behaviour of the Indonesian Throughflow is particularly simple at periods longer than about 15–20 days in these experiments, being determined by the Pacific-Indian sea level difference, which produces a flow of about 1.5 Sv per cm of sea level difference with a lag of about 1.5 days (the exact response depends on the region of averaging for sea level and the form of Southern Ocean topography used, but very similar relationships occur with both real topography and Flat Drake Passage topography). Incidentally, the flow through Bering Straits was quite negligible (of order 10−4 Sv in these experiments), consistent with Figure 6 in which it is clear that Arctic sea level is in equilibrium with the Atlantic, and barely affected by the Pacific.
 These results from the idealized experiments demonstrate the value of calculating flow across sections in addition to basin-averaged mass. Unfortunately it is impossible to diagnose the relative importance of Bering Straits or Indonesian throughflows for the response to wind stress forcing in the realistic model run, since mass exchanges between basins are dominated by the inverse barometer response to atmospheric pressure. To investigate these throughflows in more detail it would be necessary to rerun the model with no atmospheric pressure forcing.
5. Summary and Discussion
 Large-scale (ocean plus atmosphere) mass exchange between ocean basins occurs in our model between all basins, but two particular exchanges stand out most clearly: exchange between the Atlantic and Pacific, and exchange between the Southern Ocean and Pacific.
 The Atlantic-Pacific exchange is clearest at 4–6 day period, where it can be clearly identified with a known mode forced by a global atmospheric pressure oscillation. The response in dynamic bottom pressure results from the fact that the inverse barometer adjustment to this pressure forcing takes some time, limited by the propagation speed of gravity waves, given the large distance between Atlantic and Pacific oceans. The exchange does persist, however, at longer timescales.
 The Southern Ocean–Pacific exchange is clearest at longer timescales (periods longer than about 30 days, becoming clearer still at periods longer than 100 days). This exchange is clearly associated with the Southern Mode of Antarctic circumpolar transport fluctuations, driven by zonal winds in the Southern Ocean. We have traced the preference for the Pacific over other basins in this mode, to an association between the Southern Mode and the form stress in Drake Passage. We find that this near-equilibrium or lagged equilibrium response to wind stress starts to emerge at periods longer than about 20 days.
 We must acknowledge that the barotropic model has its weaknesses. Particularly at the longer periods associated with the Southern Ocean–Pacific exchange, we would expect baroclinic interactions to become important. Certainly this should be the case in the tropics, where baroclinic Rossby waves propagate rapidly, although it is not clear how much the baroclinic modes would affect bottom pressure (particularly basin-averaged bottom pressure), except via an influence on the Indonesian throughflow. It is probably reasonable, however, to suggest that the model replicates the Southern Mode (and fluctuations in Antarctic circumpolar transport) well at periods up to 100 days or more. Indeed, the mode was first identified from a combination of eddy-permitting baroclinic ocean models and in-situ observations as the dominant feature between periods of 10 and 220 days [Hughes et al., 1999], and the barotropic model reproduces the transport fluctuations of the baroclinic model, and the observed Southern Mode pressures, extremely well in this band [Hughes et al., 2003; Hughes and Stepanov, 2004].
 Having identified the dynamics associated with the main global barotropic adjustment mode at long periods, what are the possible ramifications for this of interest to long term dynamics? One possibility relates to the sea level difference between the Atlantic and Pacific oceans. The barotropic model would predict, for a mean wind stress of 0.2 Pa, that the Pacific pressure should be higher than Atlantic pressure by 1.33 mbar, although the pressure difference could be up to ten times greater if the form stress all occurs in Drake Passage, and even greater if topographic barriers shorter than 3000 m are involved. It is well known [e.g., Reid, 1961] that density differences result in the Atlantic mean sea level being lower than that of the Pacific by an amount measured in tens of centimetres. While the barotropic dynamics will not be relevant in detail to the long-term mean circulation, the wind stress is still balanced by form stress at long timescales, and it is quite plausible that Drake Passage and a narrower range of depths become relatively more important as baroclinic effects become significant. This mechanism could therefore account for a significant proportion of the total mean sea level difference between Atlantic and Pacific oceans.
 A second possibility relates to a recent paper by Ivchenko et al. , in which a salinity anomaly was introduced over the topography on the western side of Drake Passage, in an idealized model simulation. Within 15 days, a response in surface temperature was seen at the western boundary of the Pacific, as far as the equator. Over a period of several months, the temperature anomaly grew and spread across the tropical Pacific. These rapidly-occurring temperature anomalies were found to be due to interaction between rapidly-propagating barotropic Kelvin and Rossby waves and the stratification near the boundary. In a more realistic coupled ocean-atmosphere general circulation model, Richardson et al.  observed a similar rapid response of the Pacific to a circum-Antarctic imposed salinity anomaly, followed by a global response (particularly in the northern North Atlantic) which they attribute to atmospheric teleconnections driven by the tropical Pacific temperature anomaly.
 The intriguing thing about these results is that they should not depend in detail on the source of the initial barotropic disturbance. In the cited papers it is due to a salinity anomaly causing a density change which interacts with topography to produce a barotropic signal, but a change in wind stress could equally produce the barotropic signal which propagates into the Pacific, and subsequently interacts with stratification to produce temperature anomalies. This leads to the possibility that Southern Ocean winds could influence sea surface temperature in the tropical Pacific, and hence global climate.
 These examples are clearly quite speculative, being extrapolations based on barotropic model results. However, what seems clear from these results is that global scale interactions occur rapidly in the barotropic mode, leading to local pressure fluctuations which may be influenced by global scale processes. We need to understand these interactions if we are to correctly interpret pressure and sea level measurements within each basin.
 Thanks to Ag Stephens of the British Atmospheric Data Centre for help with the atmospheric forcing fields, and to Wilbert Weijer and an anonymous referee for comments which resulted in an improved paper. This work was funded by the U.K. Natural Environment Research Council as part of the Proudman Oceanographic Laboratory's “Sea Level, Bottom Pressure, and Space Geodesy” program.