Three forms of variability in Argentine Basin ocean bottom pressure

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi: /2006jc003679, 2007 Three forms of variability in Argentine Basin ocean bottom pressure C. W. Hughes, 1 V. N. Stepanov, 1 L.-L. Fu, 2 B. Barnier, 3 and G. W. Hargreaves 1 Received 2 May 2006; revised 11 August 2006; accepted 12 September 2006; published 26 January [1] Ocean bottom pressure data are examined from a year-long deployment of two bottom pressure recorders, separated by 417 km, in the Argentine Basin. Three forms of variability are found. At high frequencies (periods shorter than 2 hours) the signal appears to be due to gravity wave propagation with the waves preferentially coming from the west. At intermediate frequencies (periods between 2 hours and 12 days), the two records are highly coherent and in phase, reflecting large-scale coherent fluctuations which are well reproduced in a barotropic ocean model. However, the dominant mode is at a period of 20 days, with a phase lag of about between the two records, consistent with the a mode of variability previously inferred from satellite altimetry and current meters, although the slightly shorter period is consistent with the suggestion that more than one mode contributes to the altimeter observations. Comparison with altimetry demonstrates that aliasing of higher-frequency signals is not a significant source of error and confirms that a previously used altimetry mapping technique reduces the apparent amplitude of the mode. The pressure records show a transport change of about 280 Sv over one 12-day period, and altimetry suggests that regions of higher variability exist. The mode is only weakly excited in barotropic models but is strongly excited in a baroclinic model with a realistic eddy field, suggesting that it is intrinsically linked to interactions between eddies, mean flow, and topography. Citation: Hughes, C. W., V. N. Stepanov, L.-L. Fu, B. Barnier, and G. W. Hargreaves (2007), Three forms of variability in Argentine Basin ocean bottom pressure, J. Geophys. Res., 112,, doi: /2006jc Introduction [2] The Argentine Basin is, dynamically speaking, a very interesting region. It is deeper than 6 km at its southern end, where it is bounded by a very steep continental slope (Figure 1a). The continental slope to the west of the basin supports the confluence of two western boundary currents: the Brazil Current from the north and the Falklands or Malvinas Current from the south (Figure 1c). These generate a strong eddy field, clearly seen in satellite altimetry (Figure 1d), but rarely well reproduced by ocean models. [3] Near the center of the basin there is a rise in the topography called the Zapiola Drift, the peak of which is close to 5 km deep. It is now well established [Flood and Shor, 1988; Whitworth et al., 1991; Weatherly, 1993; Saunders and King, 1995] that there is a large recirculating current, the Zapiola Anticyclone, flowing anticlockwise around the Zapiola Drift. Again, most models have trouble reproducing this feature, which penetrates to the sea floor, and is thought to carry a recirculating transport of more than 100 Sv (1 Sv = 10 6 m 3 s 1 ). 1 Proudman Oceanographic Laboratory, Liverpool, UK. 2 Jet Propulsion Laboratory, Pasadena, California, USA. 3 Laboratoires des Écoulements Géophysiques et Industriels, Institut de Mécanique de Grenoble, Grenoble, France. Copyright 2007 by the American Geophysical Union /07/2006JC [4] As illustrated by de Miranda et al. [1999], and in Figure 1d, the observed region of strong eddy activity forms a C-shaped region, with low energy in the center of the basin. Most models, however, show a more amorphous region of high eddy activity, reaching into the basin interior from the western boundary (see Barnier et al. [2007] for examples). The generation of the anticyclone was investigated by de Miranda et al. [1999] using a sigma-coordinate ocean model at 1/3 resolution which did reproduce both the C-shaped distribution of eddy energy and the strong recirculation. The suggestion of Dewar [1998] that such recirculations could be the result of eddy stirring of potential vorticity over topographic features creating a high-pressure region over the topographic rise was tested by running the model with enhanced lateral friction. The magnitude of the lateral friction was sufficient to damp the eddies but should make little difference to the damping of the anticyclone, which is at a larger scale and therefore dominated by bottom friction. The anticyclone was not present when the eddies were damped out, strongly suggesting that eddies are responsible for exciting it. [5] Another interesting feature in this region was first suggested by Chao and Fu [1995], who showed using satellite altimetry that there is enhanced intraseasonal energy in this region, at length scales greater than 500 km. Their Plate 3, which also presents comparable diagnostics from a general circulation model, shows three hot spots of enhanced large-scale intraseasonal energy in the Southern 1of17

2 Figure 1. Context for the BPR deployments, showing BPR positions plotted on backgrounds of (a) Argentine Basin topography (contours at 0.5, 2, 4, 5, 5.5, and 6 km), (b) the satellite altimeter-based CEOF mode as calculated in FCQ. Contours are amplitude, normalized to a maximum value of 1. Colors are phase, each color band covering a 30 range. The natural direction of phase propagation for the mode follows the order red-yellow-green-blue (i.e., anticlockwise). Phase is only plotted where the amplitude is greater than 0.1. (c) Mean dynamic topography from Niiler et al. [2003], contour interval 5 cm, values increasing northward. (d) Eddy kinetic energy from Ducet et al. [2000]. The large dots represent the two BPRs which were recovered. A third, unrecovered instrument is represented by a small dot. Ocean. Two of these, in the southeast Pacific and southeast Indian Ocean sectors, are well reproduced by the model. The third, in the Argentine Basin, is present in the model but at much weaker amplitude than in the observations. In fact, the relative weakness of the Argentine Basin variability seems to be a generic feature of non-eddy-resolving models [e.g., see Fukumori et al., 1998; Hughes and Stepanov, 2004]. [6] This feature was investigated in more detail by Fu et al. [2001, hereinafter referred to as FCQ], who showed using Topex/Poseidon altimetry that it is dominated by a wave number 1 pattern rotating anticlockwise around the Zapiola Drift, with a period of about 25 days. This mode is illustrated in Figure 1b by the first Complex Empirical Orthogonal Function (CEOF) mode from the gridded altimetry (the plot here uses an extension of the data to the period 2of17

3 Figure 2. Pressure time series from Grace 2 and Grace 3. (a) The pressure at each site, and difference between the two, after removal of tides and subtraction of an arbitrary mean. (b) Running standard deviation of high-pass filtered pressure records at the two sites. Standard deviation is calculated over min samples centered on each point, for data filtered to pass only periods shorter than 2 hours but is very similar to that in FCQ). A similar mode was reproduced by FCQ as the third CEOF of a regional barotropic ocean model at 0.5 resolution and this, plus general theoretical arguments based on the length scale and frequency of the mode, was taken as evidence that the mode is a topographic Rossby wave propagating around the Zapiola Drift. Current meter measurements [Weatherly, 1993] gave supporting evidence for the existence of this mode at depth. The observed mode had a maximum peakto-trough amplitude in sea level of about 20 cm, implying transport fluctuations of about 50 Sv relative to a region of constant sea level, but the amplitude did not appear to be related to local winds. FCQ suggested that the mode might bear some relationship to the Zapiola Anticyclone and could be forced by the eddy field in the Argentine Basin. They also expressed some reservations about the capability of the altimetry data to resolve the time series, as the period of the mode is close to the Nyquist period of 20 days, and suggested that the actual amplitude might be underestimated by the altimetry. More recent work [Tai and Fu, 2005, hereinafter referred to as TF] shows that the amplitude was indeed underestimated but that a different method makes it possible to retain the complete amplitude from the altimetry. The new method produces amplitudes almost twice as large, giving a maximum peak-to-trough amplitude of almost 40 cm, or 100 Sv. [7] Recently, W. Weijer et al. (Multiple oscillatory modes of the Argentine Basin. part I: Statistical analysis, submitted to Journal of Physical Oceanography, 2007, hereinafter referred to as Weijer et al., submitted manuscript, 2007) investigated the barotropic modes in the Argentine Basin, and their relationship with Rossby wave basin modes in a flat-bottomed ocean basin. They found a number of modes with rather similar structure to that seen in the altimetry, but none with both the correct structure and 25 day period. They suggest that the dominant pattern in the altimetry might be due to a combination of two modes with periods of about 20 and 31 days. In what follows we refer to the observed variability at periods of 20 to 30 days as the mode, implying a single mode, but we will return to the possibility of there being several such modes in the discussion section. [8] In order to investigate this mode (or these modes) further, three bottom pressure recorders (BPRs) were deployed in the Argentine Basin, at the positions marked by dots in Figure 1. The timing was designed to coincide with the flight of the Gravity Recovery And Climate Experiment (GRACE) satellite mission, which is designed to detect large-scale variability of the Earth s gravity field and hence ocean bottom pressure variability. Pressure fluc- 3of17

4 Table 1. Variance Observed by the Grace 2 and Grace 3 BPRs, and Their Difference, Divided by Period, for Periods Shorter Than 16 Days, Days, Days, and Longer Than 90 Days Grace 2 Grace 3 Difference Variance, mbar <16 days days days >90 days tuations at a 25-day period are too fast for the GRACE data to clearly resolve and would produce spurious, aliased patterns of pressure variability elsewhere in the world if not corrected for. Given the apparent difficulty in modeling this mode, it seemed particularly important to have good observations overlapping the GRACE period. [9] The three BPRs, named Grace 1 3, were deployed in a triangle surrounding the amphidrome of the altimetryderived CEOF. The aim was to sample the mode at a range of different phases, with instrument positions also constrained by wishing to avoid regions of highly energetic small-scale eddies or very deep water (5500 m was estimated as the safety limit), and limiting the ship time necessary to deploy and recover the instruments. Unfortunately Grace 1 (the small dot in Figure 1) was lost, presumed flooded, but Grace 2 and Grace 3 returned good data over a 1-year period. This paper reports on the variability observed by the two BPRs, and its interpretation in comparison with model data and satellite altimetry. 2. Bottom Pressure Data: Three Forms of Variability [10] Grace 2 was deployed in 5114 m depth, at S, W, for 1 year starting on 16 May Grace 3 was deployed in 5141 m depth, at S, W, for 1 year starting on 17 May The two instruments were separated by a distance of 417 km. The pressure records from the two BPRs are shown in Figure 2, together with their difference. These data have been linearly interpolated from their original near-15 min sampling to exactly 15-min intervals, have had diurnal, semidiurnal, and some higherfrequency tides removed by least-squares fitting of 58 tidal constituents, and have had a linear trend removed. A clear oscillation is present at Grace 3, with a period of about 20 days and peak-to-trough amplitude as high as 50 mbar (1 mbar is approximately equivalent to 1 cm of sea level change). Some of the stronger oscillations are also visible at Grace 2, although with a phase shift. If we identify this 20-day oscillation with the 25-day mode of FCQ, then the stronger signal at Grace 3 is in accord with the larger amplitude of the modal spatial structure at this site, as shown in Figure 1b. [11] Table 1 shows how the energy in the observed signals is divided between frequency bands (chosen to illustrate the spectral distribution of energy). Grace 2 is not as clearly dominated by the 20-day oscillations as Grace 3 and shows higher-frequency variability as well. This is also visible at Grace 3, despite the larger 20-day signal. The higher-frequency variability is reduced, however, in the difference (Grace 3) (Grace 2). This suggests that, unlike the 20-day signal, higher-frequency signals are very similar and in phase at the two sites. A similar degree of cancelation also occurs at the longest timescales, but there is also a substantial noncanceling signal in the intermediate (30 90 day) band. [12] For a geostrophic, barotropic signal, the transport between two points is given by T = dp(h/rf), where dp is the pressure difference, H is ocean depth (taken here as 5100 m), r is seawater density (this reaches about 1050 kg m 3 at 5000 m, so we take a depth-average of about 1040 kg m 3 ), and f is the Coriolis parameter ( s 1 at the latitude of the BPRs). With these parameters, a 1 mbar pressure signal thus translates into 4.84 Sv of transport between the two BPR positions. The maximum peakto-trough change in daily mean pressure difference between the two BPRs is 57.7 mbar over a 12-day period, corresponding to about 280 Sv difference in transport. To take a less extreme scenario, the (mbar) 2 variance in pressure difference, if all due to barotropic flows, translates to a root-mean-square transport difference (from the mean) of 58 Sv, with 43 Sv in the day band alone. This is an enormous transport range, especially when it is considered that neither BPR is near the peak of the modal structure as identified in Figure 1b, and larger differences could be expected between positions which sample the mode at 180 phase difference. As an example, if we assumed the 57.7 mbar change was all due to a mode with the structure shown in Figure 1b, then a larger difference corresponding to over 350 Sv could have been measured with different positioning of the BPRs. While it is unlikely that the measured change is entirely due to this mode, it is also unlikely that the BPRs were positioned so as to measure the largest possible signal, so transport changes of this size are quite likely. For comparison with current measurements, a 100 Sv barotropic transport between the two BPRs corresponds to a mean current of about 4.7 cm s 1. [13] The spectra and cross-spectrum from the two BPRs are plotted in Figure 3. At periods longer than about 2 hours (less than 12 cycles per day), the spectra show power approximately proportional to (frequency) 2, although for the section between about 0.1 and 1 cycles per day a good fit can be made to (frequency) 3. On top of this background there is a clear significant peak at about days ( cycles per day) for Grace 3, and a less clear peak for Grace 2. There are also significant peaks at 3, 4, 5, 6, and 7 cycles per day, suggesting the presence of high harmonics of the tides, although the diurnal and semidiurnal tides have been well removed by the tidal fitting procedure. At periods shorter than 2 hours, the power spectra flatten out near a level of about (mbar) 2 (cycle per day) 1. The sharp tail-off in power near to the Nyquist frequency is the result of linear interpolation onto 15-min intervals. It is worth noting that the logarithmic scale on the y-axis reduces the apparent significance of the day mode. Power spectra plotted in variance-preserving form (not shown) show complete dominance of power at periods longer than about 12 days, to the extent that nothing else is visible in the plots. [14] The cross-spectrum shows significant coherency across almost the whole frequency range, with the exception of periods longer than 25 days, and some periods shorter than 2 hours. The phase lag is close to zero at intermediate 4of17

5 Figure 3. Power spectra and cross-spectrum for BPR records Grace 2 and Grace 3. (a) Power spectrum from each record, plus reference curves: power proportional to (frequency) 2 ; power = mbar 2 (cycles per day) 1. This is a composite of two calculations with different window widths, error bars appropriate to each window are marked. (b) Phase and (c) squared coherency for cross-spectrum between Grace 2 and Grace 3. Three different window widths are used, and the corresponding 95% and 99% significance values for squared coherency are marked. Phase values are marked with a cross where squared coherency is not significant at the 95% level. The frequencies corresponding to periods of 20 days, 12 days, 2 hours, and 1 hour are marked on the phase plot. frequencies, switching to 180 around periods of about 1 hour (24 cycles per day), and increasing to about 100 at 25 day periods (0.04 cycles per day). For comparison, the phase lag predicted by the CEOF from satellite altimetry at periods of days (Figure 1b) is about 130. [15] It therefore seems natural to split the data into three frequency bands: long period (greater than 12 days), medium period (12 days to 2 hours), and short period (less than 2 hours). The variances in these three bands are (49.00, 4.16, 0.013) mbar 2 for Grace 2, and (105.88, 3.61, 0.013) mbar 2 for Grace 3, again demonstrating the dominance of the long periods. For the short-period time series, a running standard deviation, calculated from 301 points (3.14 days) centered on each time, is plotted in Figure 2b. The two curves clearly have similarities, but also significant differences, indicating that some of the power at high frequency is derived from the same source at the two BPR sites, but some is from different sources. The correlation coefficient between these two curves is 0.46, which requires only 28 degrees of freedom to be significant at the 99% level. A calculation of the effective degrees of freedom from the autocorrelation and cross-correlation functions, following Chelton [1983], gives an estimate of 70, showing that this correlation is clearly significant at well above the 99% level. [16] The cross-correlation functions for Grace 2 and Grace 3 at the three frequency bands are shown in 5of17

6 Figure 4. Cross-correlations between pressure from Grace 2 and Grace 3, for different frequency bands. (a) Long period (longer than 12 days). (b) Medium periods (between 12 days and 2 hours). (c) Short period (shorter than 2 hours). Positive lag refers to a signal arriving at Grace 3 before Grace 2. Dashed lines are a nonlinear fit of the form c = acos[2p(t t 0 )/T]exp[(t t 0 ) 2 /W 2 ], where c is cross-correlation, t is lag, and a, t 0, T, and W are fitted parameters. Figure 4. For the short period band a section with particularly strong correlations (day of 2002) was used in order to maximize the signal strength, but all the available data were used for other correlations. Using all the data for the short period band reduces the main peak to an amplitude of 0.08 but does not much alter estimates of wave period or lag. For the long and short period cross-correlations, a fitted curve is also shown. This is a nonlinear fit of the product of a cosine wave and a gaussian, fitted for amplitude, period of cosine wave, width of gaussian, and lag (offset of center from lag zero). [17] The long period cross correlation suggests a wave with period 19.6 days, somewhat shorter than the altimetrybased estimate of 25 days, but using a much shorter data set. The highest peak occurs at a lag of 14.6 days, with a secondary peak at 5 days, suggesting that slightly more coherence is lost in the 100 degrees phase between Grace 2 and Grace 3 than in the 260 degrees back to Grace 2. The difference in period relative to the altimetry is surprising, as 6of17

7 the simple Rayleigh criterion rule of thumb suggests that a difference between 20 and 25 day period should be clearly distinguishable in a 360-day record and, indeed, the estimate of period from the data appears to be robust to a variety of simple methods, with a variability of about 1 day. [18] The medium period cross-correlation shows no clear period and a peak correlation of 0.91 at zero lag. This shows that there is a clear form for the variability at these periods, in which pressure at the two sites varies coherently with no sign of propagation. [19] The short period cross-correlation shows a wave at period close to 1 hour, and lag 0.45 hours (27 min). The waves have very short coherence length, showing that the period is not sharply defined, but the correlation function is clearly asymmetrical about zero lag, indicating a propagating wave which arrives at Grace 3 before Grace 2. This is consistent with gravity waves propagating approximately along the direction from Grace 3 to Grace 2. In water of depth 5000 m, the wave speed (gh) 0.5 is 221 ms 1, leading to a wavelength of about 800 km at the 1-hour period. A lag of 27 min then corresponds to a distance traveled of 358 km. Comparing this with the actual distance between BPRs of 417 km, this suggest a wave vector oriented at about 30 degrees to the line joining the BPRs. This is consistent with a source for the waves either along the Argentinian continental shelf or in the western boundary current region. To our knowledge, this is the first identification of such long gravity waves in the deep ocean. [20] Something similar to this was reported from the Californian continental shelf by Snodgrass et al. [1962]. Using 2 BPRs they found a white spectrum at periods shorter than about 2 hours, and a phase lag of near zero at longer periods, but 180 between about 1.4 hours and 0.6 hours. The power was also similar to that observed here, at (mbar) 2 (cycle per day) 1. Their instruments were closer together (100 km), but in shallower water (a depth of 600 m is given as that which produces the correct average wave speed between instruments). That produces a travel time between BPRs of 22 min. It is interesting how similar these observations are to ours, given the quite different oceanographic settings. This suggests that more gravity wave power is radiated into the deep ocean than one might initially expect. Snodgrass et al. interpret the 180 phase changes as evidence of standing waves, trapped on the continental shelf. In our case, this suggestion would not explain the asymmetry in the cross-correlation function, and it seems unlikely that gravity wave modes are trapped in the Argentine Basin. [21] The bottom pressure data thus clearly distinguish three forms of variability. There is a mode with period approximately 20 days, which behaves like the mode identified by FCQ from satellite altimetry, with a significant phase lag between the sites. At periods between about 12 days and 2 hours, bottom pressure at the 2 sites varies coherently with no phase lag. At a period of around 1 hour, gravity waves appear to be propagating predominantly from the west, reaching first Grace 3, then Grace 2. Most of the power is at long periods, suggesting that altimetry measurements in this region will be only weakly contaminated by higher-frequency dynamics. The 20-day mode bottom pressure signal is substantially larger than signals reconstructed by FCQ, confirming the suggestion that the mapping method reduces the apparent amplitude. However, that may not be the whole story, as the pressure signals are even larger than the amplitudes from the revised mapping of TF. In fact, for periods less than 30 days (summing and squarerooting numbers from Table 1), the standard deviation at Grace 3 is 7.9 mbar (7.5 mbar for just the day band), compared with the altimetry-derived standard deviation at the same position of less than 6 cm (Figure 3a of TF). Similarly, at Grace 2, the observed standard deviation of 5.1 mbar is somewhat larger than the altimeter-derived 4 cm (the conversion factor between pressures in mbar and free surface elevations in cm is within about 1% of 1.00). This suggests that either this is a more energetic year than the average, the altimetry is missing some variability even before gridding, or the signal is bottom-intensified. 3. Comparison With Altimetry and Model Data 3.1. Altimetry [22] Altimeter-derived sea levels from the Jason satellite were gridded onto a 1 grid as described by FCQ, using Gaussian weighting in both space and time. The time series of pressure, and of sea level at the nearest grid point, were each low pass filtered, passing periods longer than 6 days, and then sampled at 3-day intervals. Since a significant annual cycle is observed in the altimetry but not in the bottom pressure data, an annual sinusoid was also subtracted from each. The resulting time series are shown in Figure 5. Correlations between BPR and altimeter time series are 0.77 at Grace 2 and 0.80 at Grace 3. [23] It is clear that the gridding procedure does a good job of reproducing most features in the time series. As was suspected though, the amplitude of the time series is somewhat reduced by the gridding, altimeter-derived standard deviations being 87% of that from the Grace 2 BPR (standard deviation 7.2 mbar), and 73% of that from the Grace 3 BPR (standard deviation 10.5 mbar). The percentage of pressure variance explained by the gridded altimetry is 57% and 63% for Grace 2 and Grace 3, respectively. [24] In order to check that the amplitude reduction is a result of the gridding, along-track altimetry was also compared with the BPR data. The data used were the alongtrack gridded Jason altimetry product distributed by the Physical Oceanography Distributed Active Archive Center (PO.DAAC) at Different alongtrack smoothing distances were used (no smoothing, 100, 200, 300, 400 km), and for both Grace 2 and Grace 3, the best comparison was found with 300 km smoothing (a simple running mean). Grace 3 is close to the crossover point between altimeter tracks 213 and 254, whereas Grace 2 is between tracks, and closest to track 111. These data are compared with BPR data at the nearest 15-min sample. Note that the BPR data are averages over 15 min. For a gravity wave speed of about 220 ms 1, this translates to a spatial average over about 200 km. [25] These along-track altimeter time series are rather gappy from individual tracks and so the sampling is inadequate to resolve the day waves, but comparison between altimetry at the nearest latitude and BPR data at the nearest 15-min sample in time demonstrates the accuracy of the altimeter-bpr comparison. At Grace 3, with 300 km smoothing and 39 points to compare from the two altimeter 7of17

8 Figure 5. Comparison of altimetry and BPR pressure time series, after subtraction of arbitrary mean and a fitted annual cycle. Curves show time series after 6-day low-pass filter and 3-day sampling, solid is gridded altimetry, and dashed is BPR. Symbols compare simultaneous measurements at the BPR and the nearest passes of the altimeter, with 300 km along-track smoothing. Diamonds are for BPR measurements, and plus signs are for altimetry. tracks, the correlation between altimetry and BPR data after subtraction of a fitted annual cycle is The standard deviations of BPR and altimeter time series are 9.38 mbar and 8.57 mbar, respectively, and standard deviation of the difference is 3.28 mbar. This shows that the smoothed altimetry explains 88% of the variance observed at the BPR with a residual close to the expected noise level of the altimetry, an excellent result given that short length scale baroclinic variability is also expected to be present and cannot be completely removed by along-track smoothing. [26] As expected, the result at Grace 2 is less good, with a correlation of 0.78 only slightly higher than that from the gridded data. Standard deviations are 7.94 mbar for the pressure data and 7.59 mbar from the altimeter, with a residual of 5.14 mbar, meaning that the altimetry only explains 58% of the observed pressure variance, just slightly better than the gridded data. Here it appears that the gridding procedure reduces the variance in the altimetry without much reducing the correlated part of the signal. This suggests that the gridding procedure is well tuned for points in between altimeter tracks. [27] The comparison with altimetry thus bears out the suspicion voiced by FCQ that the gridded fields underestimate the amplitude of the day mode, by a few tens of percent. A 50% reduction in amplitude as a result of gridding, as suggested by TF, however, seems hard to justify from these results. Nonetheless, the observed amplitude in the BPR data appears to be consistent with, or slightly larger than, the amplitudes described in TF, once the BPR data have been filtered to pass only periods shorter than 30 days. The comparison between BPR and simultaneous altimeter measurements is consistent with either a completely barotropic signal, or a signal slightly amplified toward the bottom (by less than 10% in comparison with the surface signal), to within the accuracy of the altimeter Model Data [28] Data from three models will be considered here. The first is a global, barotropic ocean model (GBOM), as used by Hughes and Stepanov [2004]. This is a 1 model forced by 6-hourly winds from the European Centre for Medium- Range Weather Forecasts (ECMWF). The run considered here is from 5 January 1985 to 30 December The second model is a regional barotropic ocean model (RBOM) of the South Atlantic, at 0.25 resolution adapted from GBOM for this study, forced as for GBOM, and using GBOM sea level at the northern boundary (the equator). An artificial wall extends south of South Africa but is perforated at Drake Passage latitudes permitting periodic boundary conditions at the meridional boundaries. This model is run from 5 January 2002 to 30 December Daily average values of bottom pressure are stored, for each day. The third model is run 321 of the Modélisation des Ecoulements Océaniques à Moyenne et grande échelle (MEOM) team model as used by de Miranda et al. [1999]. This is the model which produced a realistic Zapiola Anticyclone and a realistic distribution of eddy energy. It is a sigma coordinate model of the South Atlantic, on a Mercator grid of resolution 1/3 in longitude, and 20 levels in the vertical, described in more detail by de Miranda [1996]. Brief mention is also made of another run of the MEOM model, run 257, which has 25 levels and less smoothing of the topography. The MEOM models are forced by monthly varying wind stress and heat flux: climatological averages based on ECMWF analyses between 1986 and 1988, repeated annually. The time series considered here are 5 years of snapshots of the barotropic stream function, sampled every 3 days. MEOM data have been averaged onto a 1 1 grid before analysis. As described above, in 5000 m depth, close to 45, 1 mbar of pressure difference can be translated to about 5 Sv of transport. In shallower water, however, the transport variability is proportionately smaller than the pressure variability. 8of17

9 Figure 6. Power spectra and cross-spectra between BPR data and collocated pressures as modeled by GBOM. Plots are a composite of two analyses with different window widths. (a) Power spectra at the two positions. Solid curves are BPR data, dashed curves are model data. 95% confidence limits are shown for the two sections. (b) Phase lag. Squares and pluses are at the Grace 2 position, with pluses where the coherency is not significant at 95% confidence. Diamonds and times symbols are at the Grace 3 position, with times symbols where the coherency is not significant at 95% confidence. (c) Squared coherency, squares at Grace 2, diamonds at Grace 3. Solid line shows the 99% confidence limit, and dotted line shows the 95% limit. [29] Spectra and cross-spectra between the BPR data and GBOM are shown in Figure 6. These show high coherence between model predictions and measurements at periods between about 3 and 12 days, with much lower coherence for the day mode and longer periods. The correlation of model with measurements, for daily averages at periods less than 12 days, is 0.85 at Grace 2 and 0.90 at Grace 3. The model slightly underestimates amplitudes at these periods, with a linear regression suggesting that the model amplitudes should be multiplied by 1.3. Model power at day periods is about 10 times too small at Grace 2, and 30 times too small at Grace 3, although the phase lag (close to zero at shorter periods) remains quite small, and 9of17

10 Figure 7. Quantities of interest for the basin-scale mode. Correlations of GBOM model bottom pressure midway between the Grace 2 and Grace 3 positions (large black dots) with (a) model bottom pressure everywhere, (b) atmospheric pressure, (c) minus the Ekman pumping velocity w E = r(t/fr). All time series are filtered to pass periods between 2 and 12 days. Dashed contours are negative, the dot-dashed contour is zero, and solid contours are positive, with 0.4 and 0.7 thick. Contour interval is 0.1 in Figures 7a and 7b, 0.04 in Figure 7c. (d) f/h, with each shade representing a range of m 1 s 1, and a contour at m 1 s 1. Shading in Figures 7a, 7b, and 7c represents depth, with shade changes at 2500 m and 4100 m. coherence, though low, remains significant at Grace 2, and almost so (at the 95% level) at Grace Basin-Scale Variability [30] The model is clearly representing the dynamics well in the 2 12 day period band. In fact the correlation of the average of Grace 2 and Grace 3 values with observations in this band is 0.93, although the model appears to underestimate the amplitude by a factor of about 1.3. This means we can use the model dynamics to investigate the spatial scales and forcing for this mode. Figure 7a shows the correlation of model bottom pressure at each grid point, with model bottom pressure midway between Grace 2 and Grace 3, for the 2 12 day period band. The correlation is clearly high within the Argentine Basin, dropping off rapidly over the regions of shallower topography bounding the basin. We can therefore identify the coherent mode seen in the BPR data with no phase lag, with basin-scale variability. [31] This form of variability is reminiscent of modes which have been identified elsewhere in the Southern 10 of 17

11 Figure 8. Cross-spectra between GBOM model pressure at the center of the Argentine Basin and two potential forms of forcing. Squares correspond to atmospheric pressure averaged over the region of Figure 7b enclosed by the thick contour (correlation greater than 0.4). Diamonds correspond to minus the vertical Ekman pumping velocity w E = r(t/fr), averaged over the Argentine Basin (the area in Figure 7a enclosed by the innermost thick contour: correlation greater than 0.7). Calculation based on 20 years of daily model data, and the 95% and 99% significance values for squared coherency are marked. Phase is plotted with crosses where the squared coherency is below the 99% level, and the phase corresponding to lags of 0 and 1.5 days is plotted (solid lines) for comparison. Ocean: the other two hot spots of Chao and Fu [1995]. These both occur in regions of unusually homogenous planetary vorticity f/h, in the southeast Pacific and southeast Indian sectors of the Southern Ocean. Investigations into the dynamics of these modes [Fukumori et al., 1998; Webb and de Cuevas, 2002a, 2002b; Fu, 2003] show that they are barotropic, and well correlated with local wind stress curl, as would be expected from a local spin-up in response to wind stress in a region of homogenous f/h. GBOM reproduces the large-scale variability in these regions quite well [Hughes and Stepanov, 2004]. We have investigated the dynamics of the basin-scale mode by computing correlations and cross-spectra between model pressure midway between Grace 2 and Grace 3, and various parameters derived from the atmospheric forcing fields (all filtered to pass only the 2 12 day period band, in the case of correlations). [32] Correlations between bottom pressure and local wind stress curl are very small. The correlation with wind stress curl or Ekman pumping velocity integrated over the basin is somewhat better, but after calculating a variety of local and area-integrated forcing parameters, for a variety of domains of integration, and a variety of lags, by far the strongest correlation found was that shown in Figure 7b. This shows the zero-lag correlation c between the midpoint bottom pressure and atmospheric pressure at each point. The maximum correlation is 0.68 (increasing to 0.70 if atmospheric pressure is averaged over the region enclosed by the c = 0.4 contour). This is based on 20 years of model data, making the correlation required for 99% confidence less than 0.1. The same plot (not shown) based on measured bottom pressure (averaging Grace 2 and Grace 3) looks very similar, with a slightly higher peak value (0.74), but with reduced confidence due to only having one year of data, although this is still clearly significant at the 99% level. [33] The importance of wind stress curl is clearer at longer periods, as shown in Figure 8, which shows the cross-spectra of midpoint bottom pressure with both basinaveraged wind stress curl (actually, r (t/fr) = w E where t is the wind stress, and w E the vertical Ekman 11 of 17

12 pumping velocity), and atmospheric pressure averaged over the high correlation region in Figure 7b. Bottom pressure appears to respond to wind stress curl with a 1 2 day lag, but clearly other factors become important at higher frequencies, as captured by the pressure correlation. [34] This does not simply represent a failure of the inverse barometer adjustment of the ocean, since the power in the atmospheric pressure (not shown) is around 10 times that in the bottom pressure at all periods from 2 to 100 days, and the phase lag remains close to zero throughout this range. The most surprising aspect of Figure 7b is the fact that the maximum correlation is with atmospheric pressure significantly to the east of the bottom pressure measurement and not centered over either the measurement or the Argentine Basin, as would be expected for a relationship between the basin-scale mode and either wind stress curl or an inverse barometer failure. It seems clear that something more complicated is going on, although it is well captured by the barotropic model. A clue to the source of the complication may be given by the pattern of correlation of bottom pressure with zero lag w E shown in Figure 7c. The correlations are weaker, ranging between 0.19 and +0.21, and are situated over the two northern entrances to the Argentine Basin. The significance of this can be seen from the geometry of the f/h contours in Figure 7d. The Argentine Basin is practically enclosed by a contour which enters the basin from the northeast, passes clockwise around the basin edge, and leaves to the north, so high pressure in the Argentine Basin occurs when the Ekman pumping is downward where the contour enters the basin, and upward where it leaves the basin. This makes sense if we consider the steady, linear, inviscid vorticity equation written in terms of pressure: rp r H ¼ r t ¼ rw E ; ð1þ f f where p is subsurface pressure (equivalent to bottom pressure for deviations from the time average). Physically, downward Ekman pumping results in a downward geostrophic flow across f/h contours, balanced by a pressure gradient which causes pressure to increase to the left (in the southern hemisphere) along f/h contours, when facing downhill. If we integrate from east to west along the contour marked in Figure 7d, the pattern of Ekman pumping in Figure 7c results in the pressure increasing as the contour enters the Argentine Basin and decreasing as it leaves the basin, resulting in pressure along the basin boundary being higher than outside the basin. So, while local forcing within the basin is probably responsible for the difference between bottom pressure anomalies at the center and at the boundary of the basin, the basin as a whole must also respond to the boundary value of bottom pressure, which is not locally forced. [35] This may well, however, be an overinterpretation of the correlation patterns. In fact, at a lag of 2 days (bottom pressure signal lagging forcing), the equivalent of Figure 7c shows stronger correlations (up to almost ±0.3) in a pattern which is almost the reverse of Figure 7c. Interpretation of these patterns is further complicated by the fact that there are strong correlations among the potential atmospheric forcing fields, which are dominated by the eastward propagation of pressure systems across the northern half of the basin. The correlation pattern with atmospheric pressure, seen in Figure 7b, probably therefore represents the pressure pattern best related to the combination of local and nonlocal forcing functions, potentially with different lags, which combine to determine bottom pressure in the center of the basin. [36] Ultimately, what the accuracy of the model tells us is that the basin-scale pressure is the product of linear, barotropic dynamics. Given the semienclosed nature of the Argentine Basin, and the degree of homogeneity of f/h in the basin, it is perhaps surprising that nonlocal effects appear to be significant for this balance, meaning that we require the full equations to describe it. However, no simplified forcing function that we have investigated has been able to explain more than 50% of the variance in bottom pressure at the basin center, so we must conclude that a variety of regions and mechanisms are contributing significantly to the basin-scale pressure signal at 2 12 day periods The Day Mode [37] While GBOM is doing a good job for the basin-scale pressure, it is clearly failing to capture the power in the day mode. This is consistent with the fact, noted in section 1, that many models produce weaker high-frequency variability in the Argentine Basin than is seen in satellite altimetry. Two possible reasons for this seem likely: the barotropic model may have too low resolution and/or too high friction, damping the mode excessively, or the mode might be excited by interactions with the eddy field and/or mean flow, which are absent from a barotropic model, and poorly represented in many baroclinic models. [38] In order to investigate the first of these possibilities, a regional version (RBOM) of the model was constructed at 0.25 resolution and was run with a variety of bottom friction values. Atmospheric forcing was the same as for GBOM, and sea level from GBOM was used for the boundary condition at the equator. Bottom friction is more limiting than lateral friction, and the weakest value of the quadratic bottom friction coefficient is , 30 times smaller than the standard value. [39] Like GBOM, Argentine Basin pressure in the various runs of RBOM is dominated by a uniform mode over the whole basin, modeled rather less well in RBOM than in GBOM. After subtracting off this mode, the remainder (or the difference between pressure at the Grace 2 and Grace 3 positions) has slightly more power in RBOM than in GBOM, though still well below that seen in the observations. Correlations with observations at periods longer than 12 days are no better in RBOM than in GBOM. We conclude that friction and resolution are not the reason why the mode is not strongly excited in this barotropic model. [40] This conclusion is strengthened by the fact that the model appears capable of reproducing this mode but with weak excitation. Figure 9 shows the first CEOF calculated from various model data sets. In both GBOM and RBOM, the main mode of variation is a uniform pressure perturbation, in phase over the Argentine Basin. This has been subtracted off before calculating the CEOF. In addition, for GBOM, the domain for the CEOF calculation is limited to depths greater than 2000 m, to avoid the large signals which 12 of 17

13 Figure 9. First CEOF from various data sets, plotted as amplitude contours with phase in color, as in Figure 1b. (a) From GBOM bottom pressures, over the region shown, excluding depths shallower than 2000 m. (b) From RBOM bottom pressures, over the region shown, excluding depths shallower than 5000 m. (c) From run 321 of the MEOM model, barotropic streamfunction over the region shown. (d) From mapped altimetry, as in Figure 1b. occur on the shelf. For RBOM, to reduce the influence of boundary conditions, the domain is limited to depths greater than 5000 m. [41] GBOM does not reproduce anything like the day mode seen in the altimetry. The first CEOF (explaining 46.9% of the variance) has two amplitude maxima, 180 out of phase, in the southwest and northeast of the region, with no rotating mode. The first CEOF in RBOM (explaining 55.4% of the variance) however, captures the phase pattern from the altimetry quite nicely, although the amplitude is highest in the eastern basin. This suggests that RBOM is capable of representing this mode but that it is excited only weakly by signals from the east. [42] The alternative possibility is that the mode is excited by eddy activity, either the energetic mesoscale eddies, or as a large-scale instability of the mean flow. To investigate this possibility, barotropic streamfunction from the MEOM model used by de Miranda et al. [1999] was examined. A time series of the difference in streamfunction at Grace 2 and Grace 3 positions is shown in Figure 10. Long period variability is seen, but the dominant variability is an intermittent oscillation with period about 20 days. Curvefitting to the autocovariance function suggests 22 days. This appears as a clear peak in the power spectrum (Figure 11), and a peak in the squared coherency in the cross-spectrum between streamfunction at Grace 2 and Grace 3. The lag at this frequency is about 100, with Grace 2 leading. This looks very similar to the pressure measurements, and the amplitude of the oscillation is close to that determined from the measurements, with a peak-to-trough difference reaching almost 400 Sv at one time. Furthermore, the first CEOF of the streamfunction (which naturally downweights shal- 13 of 17

14 Figure 10. Time series of the barotropic streamfunction difference between Grace 2 and Grace 3 positions as simulated in run 321 of the MEOM model (mean value subtracted). low regions in comparison to pressure but has been filtered to pass only periods shorter than 60 days to emphasize the day mode) looks very similar to that determined from altimetry (Figure 9c). The amplitude of the CEOF (explaining 23.6% of the variance) follows a similar pattern to the mode from altimetry, and phase where the amplitude is large is also similar. The main difference is that the model CEOF does not show phase propagation to the east, south of the Zapiola Drift where amplitude is small. [43] Since the MEOM model is forced by monthly winds, linear dynamics would be incapable of producing an isolated peak in the frequency spectrum near 20-day period. The only way such a peak can arise is as a result of nonlinear current interactions within the model. The strong excitation of the day mode in this model therefore provides strong support for the hypothesis that the mode is excited by instability, rather than being directly forced. [44] A second run of the MEOM model was also considered: run 257 which has less-smooth topography and slightly higher vertical resolution. This version of the model produced an unrealistically large Zapiola Anticyclone and did not capture the day mode as clearly, with the first CEOF amplitude concentrated more in the western half of the basin, and a dominant period of 36 days, although a day signal also appeared to be present. Both the Zapiola anticyclone and the day mode are clearly very sensitive to model details, indeed a recent model intercomparison has shown that small changes can lead to large differences in the circulation in this region [Barnier et al., 2007]. The success of the DRAKKAR project s ORCA- R025 model in this comparison suggests that the detailed representation of topography together with conservation of energy and enstrophy are critical factors. A careful model investigation will clearly be necessary to understand the details of the interactions which occur in the Argentine basin. 4. Discussion and Conclusions [45] Measurements of ocean bottom pressure in the Argentine Basin demonstrate the existence of three forms of variability at subseasonal timescales after tides have been removed. [46] At periods close to 1 hour, there is weak variability (about 0.1 mbar) which is consistent with propagation of gravity waves preferentially from the west. The amplitude is close to that seen by Snodgrass et al. [1962] on the Californian shelf, and the propagation direction suggests a source either on the continental shelf, or in the western boundary current. [47] At periods between about 2 hours and 12 days, the basin responds coherently to forcing, producing bottom pressure variability with large spatial scales and a rootmean-square amplitude of about 2 mbar. This mode of variability is well-modeled by a 1 barotropic ocean model forced by atmospheric wind stress and pressure. Although it is similar to other modes known in the Southern Ocean, occurring as these modes do in a region of homogeneous f/h and responding to wind stress curl over the basin, the response to basin-integrated wind stress curl is clearest at the longer periods for which the model-data comparison is poorer. At higher frequencies, a more complicated response appears, in which a variety of both local and nonlocal forcing fields are important. [48] The dominant mode in the observations occurs at a period of about 20 days and longer. At these periods, there is a strongly excited day mode with rootmean-square amplitude about 4.4 mbar at the Grace 2 position and 7.5 mbar at Grace 3. Including longer-period variability in the day band increases the standard deviation of pressure difference between the two sites to 11.6 mbar. This implies a root-mean-square transport fluctuation of about 58 Sv between the two positions, with a peakto-trough difference reaching 57.7 mbar (280 Sv) in one case. Given the 417 km separation of the BPRs, and a water depth of 5000 m, this corresponds to a root-mean-square areaaveraged current of 2.7 cm s 1. [49] The cross-spectrum between BPR records reveals a phase lag of about 100, with the Grace 3 position lagging the Grace 2 position. While this is consistent with the 25-day wave identified from satellite altimetry by FCQ, the period for these positions and this year appears to be closer to 20 days, and fluctuations at longer periods up to 90 days appear to have a similar character. [50] Comparison of the BPR data with simultaneous along-track altimetry is very good for Grace 3, which is situated close to an altimeter cross-over point, confirming 14 of 17