Longterm observations of transport, eddies, and ... - Wiley Online Library

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, C02003, doi:10.1029/2008JC004846, 2009

Long-term observations of transport, eddies, and Rossby waves in the Mozambique Channel U. Harlander,1,2 H. Ridderinkhof,1 M. W. Schouten,1,3 and W. P. M. de Ruijter4 Received 1 April 2008; revised 27 October 2008; accepted 2 December 2008; published 11 February 2009.

[1] Data from an array of current meter moorings covering a period of two and a half

years are used to estimate the varying transport through the Mozambique Channel. The total transport during this period is small (8.6 106 m3 s1 or 8.6 Sv southward). Below 1200 m the transport is weak but a prominent deep western boundary undercurrent with cores at 1700 and 2200 m is found that transports 1.5 Sv to the north. The transport shows a large temporal variability, and neither a continuous upper layer western boundary current nor a continuous deep undercurrent is found. The variability in the upper layer is dominated by a period of 68 days and results mainly from eddies that migrate southward through the Mozambique Channel. In addition to this southward propagation, a westward-propagating signal is evident from a space-time diagram of the throughflow. The signal is interpreted as a Mozambique Channel Rossby normal mode. This interpretation is consistent with results from a Principal Oscillation Pattern Analysis (that estimates normal modes from the data) and a quasi-geostrophic channel model. A detailed inspection of a single ‘‘eddy event’’ shows that a precursor of an anticyclone is a strong southward current along the Madagascar coast that propagates westward to the center of the Channel. During the westward propagation, the current becomes unstable inducing an anticyclone. This scenario connects the westward-propagating mode with the eddy growth and explains the coincidence of the eddy and Rossby mode frequency. Still, the type of instability that leads to eddy growth could not be determined yet. Citation: Harlander, U., H. Ridderinkhof, M. W. Schouten, and W. P. M. de Ruijter (2009), Long-term observations of transport, eddies, and Rossby waves in the Mozambique Channel, J. Geophys. Res., 114, C02003, doi:10.1029/2008JC004846.

1. Introduction [2] The Agulhas Current, transporting saline Indian Ocean water into the North Atlantic, is important not only for the coastal region of South Africa but also for the global ocean circulation. In a recent book, Lutjeharms [2006] reviews the large amount of papers, dealing not only with the Agulhas Current but also with the two currents that, apart from the gyre, feed this strong flow: the East Madagascar Current (EMC) and the Mozambique Current (MC) both originating from the South Equatorial Current (SEC). The present paper focuses on the MC flowing through the Mozambique Channel that separates the island of Madagascar from Africa. Components of the global ocean circulation system in the Mozambique Channel are brought about by southward migrating eddies [Ridderinkhof and de Ruijter, 2003; Schouten et al., 2003], transporting South Indian Ocean and Red Sea water into the Agulhas 1 Department of Physical Oceanography, Royal Netherlands Institute for Sea Research, Texel, Netherlands. 2 Now at Department of Aerodynamics and Fluid Mechanics, BTU Cottbus, Cottbus, Germany. 3 Now at TNO Defence, Security and Safety, The Hague, Netherlands. 4 Department of Physics and Astronomy, Institute for Marine and Atmospheric Research, Utrecht University, Utrecht, Netherlands.

Copyright 2009 by the American Geophysical Union. 0148-0227/09/2008JC004846

Current, and the deep Mozambique Undercurrent, carrying North Atlantic Deep Water and Antarctic Intermediate Water toward the equator along the continental slope [de Ruijter et al., 2002]. [3] There are several fundamental questions that have to be addressed to understand better the role the MC plays in the global ocean circulation. Probably most important is simply to obtain reliable estimates for the MC mean volume transport and its variability. As pointed out by DiMarco et al. [2002], ‘‘Historical transports based on hydrographic data in the Channel vary from 5 Sv northward to 26 Sv southward depending on reference level and time of the year.’’ Gru¨ndlingh [1993] reviewed earlier descriptions of the Mozambique Channel flow and found that the net flow is southward. More recently, Ganachaud et al. [2000] estimated a southward throughflow of 14 Sv, and de Ruijter et al. [2002] estimated 15 Sv; DiMarco et al. [2002] and Donohue and Toole [2003] found a throughflow of 5.9 and 18 Sv. To obtain reliable estimates of the Mozambique Channel throughflow, DiMarco et al. [2002] conclude that ‘‘Direct long-term measurements of the Current are needed to quantify its magnitude and variability.’’ Such measurements are discussed in the present paper that is a follow-up of the paper by Ridderinkhof and de Ruijter [2003] in which results from a pilot experiment are presented. [4] Since 2003, after a successful pilot experiment in 2000 to 2002, an array of moorings is being maintained

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HARLANDER ET AL.: MOZAMBIQUE THROUGHFLOW

across the narrow section of the Mozambique Channel, around 17°S, as part of the Dutch LOCO programme (Long-term Ocean Climate Observations). It involves continuous current, temperature and salinity observations over the full depth and width of the Channel. In the present paper, velocity data of this cross section are analyzed for the period 25 November 2003 to 23 March 2006. Such observations give not only estimates of the total throughflow and its variability, but also more insight into the Mozambique Channel eddies and the Mozambique Channel Undercurrent. [5] In accordance with the total transport, the undercurrents along the African east coast also show a large variability. The Agulhas Undercurrent, first observed at 32°S [Beal and Bryden, 1997], was later found at sections as far north as 20°S [de Ruijter et al., 2002], transporting relatively fresh intermediate waters to the north. The associated transport of this current, at around 1500 m depth, was estimated at 2 Sv [Beal and Bryden, 1997]. Around 2500 m a secondary core of northward flow was found both at 32°S and 20°S, carrying North Atlantic Deepwater (NADW) northward into the Mozambique Channel [de Ruijter et al., 2002]. At 32°S, Beal and Bryden [1997] estimate a northward flow of about 4 Sv for this deep current. For the total equatorward transport of the Mozambique Undercurrent at 17°S, de Ruijter et al. [2002] find 5 Sv, and van Aken et al. [2004] find 2 Sv to leave the Mozambique Channel to the north across Davie Ridge at about 16°S. [6] A second fundamental question that is addressed in the present paper is whether the Mozambique Channel throughflow is continuous or discontinuous. De Ruijter et al. [2002] think it is discontinuous and we will see that the present data support this view. Inspecting MC stick plots, Ridderinkhof and de Ruijter [2003] found strong anticyclonic motions that dominate the flow variability during the period of the pilot experiment (19 months in 2000 and 2001). By adding data from satellite altimetry, Schouten et al. [2003] showed that these motions correspond with anticyclones migrating southward through the Mozambique Channel. The new LOCO data shed some light on a series of questions related to the Mozambique Channel eddies: what is the vertical structure of the eddies, and how do they typically propagate within the Channel? Where is their origin and due to which process do they grow? [7] Four to five strong anticyclones pass the Mozambique Channel each year [Schouten et al., 2003]. In a previous study, Schouten et al. [2002] suggested a remote origin of this four to five per year signal and considered Rossby waves traveling westward across the Indian Ocean as the agents that transmit this signal. Alternatively, we will propose that Mozambique Channel Rossby normal modes with periods of sixty to eighty days might destabilize the flow after an anticyclone has passed the mooring site, triggering the development of a new anticyclone. This in turn could induce eddies with a dominant frequency of four to five per year. Note that less consistently, weaker cyclonic eddies do also occur in the Mozambique Channel. [8] The paper is organized as follows. In section 2 we give a brief description of the database used. In section 3, the mean velocity field in the mooring section is discussed. In section 4, the total and regional volume transport and transport variability is described. In section 5 we focus on the main characteristics of the eddies that propagate through

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the mooring section. These characteristics are discussed by means of Empirical Orthogonal Functions (EOFs), Principal Oscillation Patterns (POPs), and space-time plots. Subsequently, in section 6 we compute baroclinic channel normal modes. It is suggested that such modes help to explain the predominance of the seventy day period in the Mozambique Channel flow. Finally, in section 7, conclusions will be given.

2. Data [9] The Long-term Ocean Climate Observations (LOCO) program is measuring the transient mass and heat transport across the Mozambique Channel at its narrowest section, around 17°S [de Ruijter et al., 2006]. A pilot array of instrumented moorings had been deployed in 2000 to 2002 [Ridderinkhof and de Ruijter, 2003]. In November 2003 it was refined by additional instruments (conductivitytemperature-depth (CTD) profilers, current meters (CMs), Acoustic Doppler Current Profilers (ADCPs), and a sediment trap). The mooring positions are shown by solid triangles in Figure 1 together with the mooring labels. For the present study velocity data of this cross section were analyzed for the period 25 November 2003 to 23 March 2006. Note that from 15 February 2005 to 9 March 2005 no data are available because of instrument redeployment. [ 10 ] Because of unexpected strong currents in the Mozambique Channel, varying instrument depth levels were a problem in the pilot array as discussed by Ridderinkhof and de Ruijter [2003, Figure 4]. Consequently, for the following LOCO periods thinner cables and lens-shaped floaters have been used. With this improved setup, vertical motion of the instruments is in the order of ten meters. Moreover, all ADCP observations have been averaged to standard depth levels (Dz = 25 m), that is, unwished vertical motions have been removed from the ADCP data. [11] Note further that in the period before the redeployment (called LOCO I period hereafter), the upper ADCP of mooring 4 was not working, and in the subsequent period (called LOCO II period), data from mooring 6 were not be available since this mooring could not been recovered. The distribution of the CMs and ADCPs for the LOCO period I and II are shown in Figures 2a and 2b, respectively.

3. Observed Mean Flow [12] Whereas earlier velocity observations from the Mozambique Channel cross section were hardly dense enough to allow for a detailed estimate of the Mozambique Channel mean flow and its volume transport [Ridderinkhof and de Ruijter, 2003], more reliable estimates can be expected from the present data. [13] To extract low-frequency phenomena, we first filtered the time series using a low-pass running mean filter with tapered weights wk Yt ¼

M 1 X wk Xtk ; k¼M w

wk ¼

1 kp cos þ 1 ; 2 M

¼ w

M X

wk ;

k¼M

ð1Þ

where X (Y) denotes the unfiltered (filtered) velocity components, and M is the width of the ‘‘window’’ (we used M = 168 covering a period of 3.5 days). Next, the spatially

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Figure 1. Position and labeling of the moorings. Between mooring 5 and 5A a sediment trap was mounted at the bottom. The isobaths at 200 (black), 500 (red), 1000 (yellow), 2000 (green), and 3000 m (blue) are indicated by thin lines. inhomogeneous observations were interpolated to a regular grid by applying the MATLAB function griddata with a cubic interpolation scheme. Note that during the LOCO I and LOCO II period the spatial distribution of instruments differed slightly (Figures 2a and 2b). Moreover, as already mentioned above, data from the LOCO I mooring 4, and LOCO II mooring 6 were unavailable. Nevertheless, the data coverage was sufficient to apply griddata without further assumptions, e.g., on the vertical structure of the flow for missing moorings [Ridderinkhof and de Ruijter, 2003]. In a last step, the time mean flow perpendicular to the mooring cross section was evaluated from the filtered and interpolated data. [14] This mean flow is shown in Figure 3a. Its gross features are (1) a strong poleward near-surface flow along the Mozambique coast (minimum 0.45 m/s), (2) a weaker equatorward near-surface flow along the WestMadagascar coast (maximum 0.10 m/s), and (3) a surprisingly strong and extended deep western boundary current flowing equatorward along the Mozambique coast (maximum 0.045 m/s). The ‘‘barotropic’’ component of the velocity field appears to be somewhat weaker than estimated earlier [de Ruijter et al., 2002; Ridderinkhof and de Ruijter, 2003; Schouten et al., 2003]. Eddy resolving model simulations like the one by Biastoch and Krauss [1999] capture the eddy structure qualitatively, although they still seem to overestimate the surface intensification and underestimate the typical diameter of the eddies. [15] The features 1 – 3 given above might be explained by the existence of opposing boundary currents within the Mozambique Channel. However, from the paper of Schouten et al. [2003] we know that southward propagating anticyclones dominate the flow in the Channel. Therefore we think that 1 and 2 essentially result from such anticyclones. On the other hand, there is a prominent deviation from east – west antisymmetry of the near-surface mean flow (the difference between the maximum and minimum near-surface velocity amounts 0.35 m s1). This asymmetry might for some part be related to a western boundary current [Sætre, 1985] that is superposed to the southward traveling anticyclones. Another part might be related to the self-

propagation of the anticyclones. Due to an interaction of an anticyclone with the African coast, an eddy can travel southward even without any background flow [Saffman, 1992], in spite of the beta and nonlinear effects that push a Southern Hemisphere anticyclone west-northwestward [Reznik, 1992]. The eddy drift velocity is variable but amounts to 0.05 m s1 for the large Mozambique Channel eddies. Thus it is probably a mixture of both effects, boundary current and vortex self-propagation, that leads to a mean southward total volume transport [Ridderinkhof and de Ruijter, 2003]. [16] The deep mean flow is dominated by the Mozambique undercurrent that corresponds quite well in strength and position with the undercurrent observed earlier by de Ruijter et al. [2002]. The undercurrent has two cores (not visible in Figure 3a), one at about 1700 m, the other somewhat deeper at 2200 m. Thus the undercurrent appears to be deeper and weaker than the Agulhas undercurrent observed by Beal and Bryden [1997], showing a center at 1200 m with a velocity of about 0.25 m/s. The deeper core of the Mozambique undercurrent transports NADW northward [Beal and Bryden, 1997] and we will find in section 4.2 that the mean undercurrent transport corresponds well with the transport found by van Aken et al. [2004] about one degree north of the mooring section. [17] The flow variability (see Figure 3b) is strongest near the surface and is mainly eddy induced [Schouten et al., 2003]. In the deeper part of the cross section the isolines of the standard deviation slope upward to the east showing that the variability is largest at the western coast, where the mean currents are strongest. [18] Concluding this section, in Table 1 we give mean velocity and the maximum and minimum throughflow velocity for the three key regions of the Mozambique Channel transport: the upper layer southward jet close to the Mozambique coast (covered by the upper ADCP at mooring 5), the deep western boundary undercurrent (covered by the lowest current meter and the bottom ADCP at mooring 5A), and the upper layer return current (covered by the upper ADCP at mooring 8). The data are shown separately for the LOCO I and II period (the numbers in

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Figure 2. (a) Positions of current meters and ADCPs during the LOCO I period (25 November 2003 to 15 February 2005). (b) Positions of current meters and ADCPs during the LOCO II period (9 March 2005 to 23 March 2006). brackets correspond to the latter period). Note that a single ADCP measurement covers a water column of about 550 m but we just give the speeds for the top, middle, and bottom value of the column. Table 1 underlines features already described above. The minimum throughflow in the western part of the Channel (1.659 m/s) differs significantly from the maximum throughflow (0.72 m/s) pointing to a superior number of anticyclones. At the eastern part, there is more

symmetry in the north and southward velocities. Note also the large maximum throughflow (0.318 m/s) related to the deep western boundary undercurrent.

4. Observed Volume Transport [19] In the following we estimate the volume transport through the Mozambique Channel. We begin by considering

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Figure 3. (a) Mean flow (m/s); (b) standard deviation (m/s). The bold dots give the locations of velocity observations. Dots in an almost connected row show the positions of ADCPs, single dots show the positions of current meters. Note that in the first and second period we do not have data from mooring 4 and 6, respectively (see Figure 2). the total transport. Subsequently, we perform a regional analysis. 4.1. Total Transport [20] The time series of total transport is shown in Figure 4a. The observation period starts at 25 November 2003 (day 1) and ends at 23 March 2006 (day 850). The instruments were redeployed in late spring 2005 where we thus do not have data for a period of 21 days. The mean transport is about 8.6 Sv. As already mentioned above, some part of this transport is probably due to a western boundary current, another part might be induced by eddy self-propagation or nonlinear wave rectification. However, large variations dominate the total transport time series: the maximum in northward transport is about 30 Sv, and in southward transport 60 Sv (see also the work of de Ruijter et al. [2005]). The standard deviation amounts ±14.1 Sv. The large variation can be attributed to energetic anticyclones

that travel southward through the channel [Ridderinkhof and de Ruijter, 2003; Schouten et al., 2003; de Ruijter et al., 2005]. The dynamic origin of the eddies is still under debate and we will come back to this issue in sections 5 and 6. [21] Note that the total volume transport is not a good measure for the eddy activity in the near-surface flow. As we will see, a regional analysis can reveal more details on the physical origin of the eddies and the transport variations. [22] To check how sensitive the transport depends on instrument failures during LOCO I (where the upper ADCP of mooring 4 did not work) and LOCO II (for which mooring 6 could not be recovered) we recalculated the transport but omitted data from mooring 6 for LOCO I and data from the upper ADCP at mooring 4 for LOCO II. The resulting transport is plotted as green dashed line in Figure 3a. Qualitatively, the original curve looks similar to the green one. However, omitting mooring 6 during LOCO I leads to higher variability and larger maxima and minima. Com-

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Table 1. Mean, Maximum, and Minimum Throughflow in Meter per Second at Different Depths of Mooring 5, 5A, and 8a Depth (m) 5

Max Mean Min

5A

50

275

550

0.243 (0.720) 0.447 (0.403) 1.659 (1.637)

0.324 (0.144) 0.169 (0.151) 0.717 (0.590)

0.158 (0.107) 0.104 (0.095) 0.517 (0.517)

Max Mean Min

8

Max Mean Min

0.837 (0.966) 0.087 (0.077) 0.642 (0.859)

0.331 (0.428) 0.048 (0.064) 0.347 (0.362)

1500

1800

2050

2350

0.318 (0.095) 0.012 (0.003) 0.208 (0.119

0.154 (0.158) 0.018 (0.021) 0.133 (0.138)

0.138 (0.159) 0.032 (0.036) 0.100 (0.152)

0.061 (0.075) 0.012 (0.010) 0.030 (0.023)

0.243 (0.294) 0.034 (0.039) 0.188 (0.256)

a

Values from the LOCO I and (in brackets) LOCO II period are shown. See Figure 1 for the position of moorings.

Figure 4. (a) Time series of the total transport in Sv (black). The observation period is 25 November 2003 (day 1) to 23 March 2006 (day 850). Due to mooring deployment there is a 21 day break between 15 February and 9 March 2005. Red line gives mean, the two thin black lines mark standard deviation. The green dashed line results from a sensitivity analysis (see text for more details). (b) Mozambique Channel cross section together with defined subdomains I – IV. The total and the local transports and the corresponding standard deviations (in brackets) are given in Sv. (c) Single-sided amplitude spectrum of the total transport and the transport in subdomain I – III. (d) As Figure 4a but for subdomain I (blue) and II (black). The mean (red) and standard deviation (black) are shown for subdomain II. JJA stands for June, July, and August. 6 of 15


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Table 2. Correlations Between Volume Transports of Different Cross Section Subdomainsa Total I II III VI

Total

I

II

III

IV

1.0000

0.5930 1.0000

0.0918 0.7327 1.0000

0.5678 0.3872 0.1540 1.0000

0.1014 0.4923 0.6376 0.0228 1.0000

a

Domains I to IV are given in Figure 4b.

pared to this, the differences for the LOCO II period look rather small. However, the mean transport is affected and increases from 7.06 Sv to 5.00 Sv. For the LOCO I period the mean transport increases just from 9.81 Sv to 9.01 Sv. This very simple sensitivity analysis shows that quite likely we underestimate the magnitude of the mean transport for the LOCO I period because of the lack of data from the upper part of mooring 4. Moreover, we find that the smaller amplitudes of the transport in the LOCO II period cannot be explained by missing data from mooring 6. In a forthcoming paper that focuses solely on the transport and also includes the most recent data from the LOCO III period these issues will be discussed in more detail. 4.2. Regional Transport [23] To get insight into the local contributions of the transport through the Mozambique Channel, we subdivided the mooring cross section into four regions (see Figure 4b): region I represents the transport along the western boundary, region II the near-surface return transport that results mainly from the eastern branch of anticyclonic eddies; region III covers the area of the deep western undercurrent and region IV can be classified as an area of generally weak flow. [24] For each quadrant of Figure 4b we give the mean transport, together with its standard deviation. The sum of the local transports gives the total transport, shown in the upper left corner of Figure 4b. [25] The mean transport in region I amounts 15.7 Sv and might be partly eddy and partly boundary current induced. In contrast, the transport of 5.9 Sv in region II is mainly eddy induced. Assuming that the eddies in region I transport the same amount of water to the south (i.e., neglect of transport due to eddy self propagation), one could argue that within the Mozambique Channel, a western boundary current transports about 9.8 Sv to the south. However, it has to be noted that a continuous western boundary current does not exist. During the observational period, the transport in region I peaks seven times above +10 Sv. This result confirms findings from the pilot study by Ridderinkhof and de Ruijter [2003], who discussed the intermittency of the western boundary current and even suggested that there is no boundary current, neither along the African, nor the Madagascar shelf. [26] The volume transport by the deep western undercurrent is comparably weak (1.5 Sv) but certainly important for the distribution of water masses along the coast of Mozambique and Tanzania. Finally, we observe that the residual transport in region IV is rather insignificant. Note that the transport’s standard deviation is large in all four regions. [27] In Table 2 we show the correlation matrix spanned by the total transport and the regional transports. Several interesting features can be observed: (1) due to channel-size

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eddies, there is a strong anticorrelation between the transport in subdomain I and II; (2) there is a good correlation between the total transport and the transport in subdomain I and III; (3) there is a surprisingly weak correlation between the total transport and the transport in subdomain II; and, finally, (4) there is a surprisingly good correlation between the transport in subdomain I and III, and between II and IV. [28] In the present study, we focus mainly on the dynamics of the upper part of the cross section, that is subdomain I and II. (An analysis of the Mozambique Undercurrent will be discussed elsewhere.) We have already mentioned that the total transport is not a good measure for the eddy activity in the Mozambique Channel. One reason for this is that an ‘ideal’ slowly propagating, barotropic vortex with closed streamfunction isolines does not affect the total volume transport much. For some periods (see, e.g., day 700 to 850 in Figure 4d), the eddies correspond with ‘ideal’ vortices and the regional transports cancel. Another reason is that phase differences between the northward and southward transports can lead to insufficient cancelation and thus to a large total transport, even for rather weak eddies. For example during the first hundred days of observation, the eddy strength is overestimated because of this reason. On the other hand, following Ridderinkhof and de Ruijter [2003, Figure 8] and focusing either on region I or II, the eddies can clearly be identified in the regional transport time series, as is shown in Figure 4d. For example, in region II, strong anticyclones correspond with transports that peak above the standard deviation level, that is a transport 14.4 Sv. Note that the sum of the transport in subdomain I and II mainly determines the total transport. [29] Inspecting the time series shown in Figures 4a and 4d it is at first sight surprising that the correlation between the total transport and the transport of domain I is fairly large, but the correlation between the total transport and the one of domain II is small (see Table 2). One reason for this discrepancy is a phase lag between the time series of region I and II. With respect to a minimum in the total transport (and the transport of region I), a maximum in northward transport of region II has a delay of about two weeks. An autocorrelation shows that the correlation coefficient changes from 0.09 to 0.26 if this lag is taken into account. This phase lag cannot be explained by southward propagating eddies but points to a zonally propagating wavelike feature. Interestingly, Ridderinkhof and de Ruijter [2003] have found that during an eddy event a strong and coherent current shifts more and more to the west side of the channel. This observation is in accordance with the phase lag we found for the regional transports. A more detailed analysis (see section 5) reveals that eddies seem to be formed when there is a strong flow near the center of the Mozambique Channel, in general about one or two weeks before a developing anticyclone reaches maximum size and the southward total transport peaks. [30] The time series shown in Figure 4d are dominated by a period of 68 days. Figure 4c shows a Single-Sided Amplitude Spectrum X N ð j1Þð f 1Þ sð jÞwN jS ð f Þj ¼ 2 ; j¼1

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wN ¼ expð2pjÞ=N ;

f 2 ð0; 1=2Þ ð2Þ

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of the total transport (dashed line), the transport in subdomain I (solid line), and the transport in subdomain II (thick solid line). Here s( j) is the transport at day j, N = 850 is the total number of days in the time series, and f is the frequency in cycles per day. It can be seen that the spectrum of the subdomain I and II transport shows a peak at a period of 68 days that clearly stands out from AR(1) red noise. Time series of environmental data can frequently be seen as stationary stochastic processes where the current value of the time series is related to the past value (AR(1) process). 2 /(1 + a1 The AR(1) spectrum of a time series Xt is G( f )2 = sP 2 (a1 2 cos 2pf )), where s is the variance, a1 = [(Xt m)(Xt+1 m)]/s2 is the lag 1 correlation coefficient, and m is the mean [Storch and Zwiers, 1999, p. 223]. In Figure 4c, G( f ) is plotted and the area below G( f ) is filled red. Note that the peak in Figure 4c is quite sharp. The curve intersects with the AR(1) curve at 71 and 61 days, respectively. Note further that the spectra show additional peaks, the most prominent one at the 46 day period. [31] A dominance of the 50 to 80 day period in the southwest Indian Ocean and the region around Madagascar is well known. Mysak and Mertz [1984] found a 40- to 60-day oscillation in the longshore currents at the African coast between the equator and 5°S. Quadfasel and Swallow [1986] reported 50-day oscillations in current meter records off the northern tip of Madagascar. Fifty-day oscillations are also found in results of a numerical shallow-water model forced by monthly mean winds [Kindle and Thompson, 1989; Woodberry et al., 1989]. Kindle and Thompson [1989] and Schott et al. [1988] conclude that the oscillations are due to internal barotropic instabilities in the ocean. Palastanga et al. [2007] for example observes that the eddy activity in the Mozambique Channel is related to variations in strength of the South Equatorial Current. They assume that the 50 to 80 day variability at the southern tip of Madagascar can be attributed to Rossby waves generated to the east by baroclinic instability. On the other hand, Schouten et al. [2002] suggest that the 50 to 80 day period is connected to trains of Rossby waves that propagate westward across the subtropical southern Indian Ocean. The frequency of the eddies in the Mozambique Channel (4 – 6 eddies per year) appears to be connected to the frequency of the Rossby waves approaching Madagascar from the east. How this connection actually works in not clear yet. [32] In the following section we show that, in addition to the Rossby waves that can be observed to the east and south of Madagascar, Rossby waves can be observed within the Mozambique Channel as well, having a period of about 70 days. These waves seem to be connected to the Mozambique Channel eddies, as we will discuss below.

5. Eddies and Rossby Waves in the Mozambique Channel [33] The large variability of the Mozambique Channel throughflow can be attributed to energetic anticyclones traveling southward through the Channel [Ridderinkhof and de Ruijter, 2003; Schouten et al., 2003]. The explanations of the origin of these eddies range from baroclinic and barotropic instability of either the boundary current [van der Vaart and de Ruijter, 2001; Harlander, 2002], or of

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the current at the northern entry of the Channel [Schott et al., 1988], to windstress induced Kelvin-Helmholtz like instability of a surface jet starting at the northern tip of Madagascar [LaCasce and Isachsen, 2007]. In contrast to Schott et al. and LaCasce and Isachsen, Ridderinkhof and de Ruijter [2003] suggest that the eddies might not be formed upstream at the northern channel entrance but at the narrowest section of the Mozambique Channel, close to the mooring section where the African coast bends strongly to the west. To obtain more insight into the eddy variability and the vertical structure and propagation of the eddies, let us first consider the space-time structure of the flow through the mooring section. [34] From satellite altimetry data Schouten et al. [2003] found an intermittent occurrence of large-scale (channel size) eddies. This picture is consistent with results from a timelongitude (Hovmo¨ller) plot of the surface flow. Figure 5a shows such a plot for the velocity component perpendicular to the mooring cross section at a depth of 150 m. The eddies can be seen as patches of strong southward flow (blue) at the western part of the channel, and northward flow (red) at the eastern side. Obviously, there is a good correspondence between these patches and peaks of negative/positive volume transport in region I/II (see Figure 4d). [35] We have already discussed that the dominance of anticyclones is responsible for the spatial structure of the time averaged flow in the upper 1000 m of the Mozambique Channel (see Figure 3a). Let us next inspect in detail the velocity field during a single eddy event. From 5a we can deduce that three strong eddies occur between day 280 and 450. Figure 6 is a stick plot of the current velocity at mooring 6 (depth levels 50 m, 475 m, and 525 m) in the period between day 320 and day 392. The velocity vectors turn clockwise during this period at all three levels [Ridderinkhof and de Ruijter, 2003]. In between day 350 and 365 there is a prominent westward flow. Such strong zonal flow components cannot be explained in terms of varying boundary currents but have to be seen as part of the eddy motion within the Mozambique Channel [Schouten et al., 2003]. [36] In Figures 7a– 7h we display the time evolution of the eddy between day 320 and day 390 with a time increment of 10 days. The left side shows the velocity perpendicular to the cross section. The near-surface velocity vectors for the period t0 10 days t t0 + 10 days is shown on the right side, where in Figures 7a– 7h, t0 runs from day 320 to day 390. It should be noted that a correspondence between space and time exists under the assumption that the eddy moves by a constant speed preserving its structure. In general, from the figures on the right side alone it cannot be decided if the eddy transits the section because of advection/self propagation, or if the eddy develops locally at the section. [37] In Figure 7a we see a strong surface intensified southward flow along the Madagascar coast and a weak northward flow in the western half of the Channel. The maximum of the southward flow propagates westward (Figure 7b) and at day 340, a strong and deep anticyclone has developed (Figure 7c). The center of the anticyclone intensifies and seems to pass the mooring section at day 350 (Figure 7d). Then the anticyclone weakens and at day 370 we again observe westward phase propagation (Figure 7f).

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Figure 5. (a) Hovmo¨ller plot of the near-surface meridional velocity component. Blue indicates southward flow, red indicates equatorward flow. (b) POP reconstruction of the surface flow by using the least damped POP. Just the sign of the surface flow is plotted. Black corresponds to the negative and white to the positive sign. JJA stands for June, July, and August. At day 390 (Figure 7h) the ‘‘eddy event’’ is completed and the flow is basically in the same state as at day 320 (Figure 7a). Note that the strong westward flow at mooring 6 in the period between day 350 and 365 (discussed above by means of Figure 6) occurs when the northern part of the anticyclone passes the mooring section (Figures 7d– 7f). [38] The westward phase propagation might result from a southwestward propagation of the anticyclone and thus an oblique traversal of the eddy with respect to the mooring section shown in Figure 1. However, the flow reversals visible in Figures 7a, 7g, and 7h cannot be explained by this geometric effect. The cycle shown in the Figures 7a– 7h reminds more on a westward-propagating wave. We therefore suggest that this westward phase propagation is related to a Rossby normal mode of the Mozambique Channel. Ridderinkhof and de Ruijter [2003] argue that eddies are not formed at the northern entrance of the Mozambique Channel, but in the vicinity of the mooring section because of local instability. Taking up this idea it is conceivable that between day 320 and day 340 (Figures 7a– 7c) a westwardpropagating Rossby normal mode either destabilizes a

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preexisting shear flow or becomes unstable itself [Walker and Pedlosky, 2002]. [39] From previous findings, e.g., Schouten et al. [2003], it can be expected that the fundamental pattern of typical variability within the Mozambique Channel is dominated by the southward migrating anticyclones. However, a significant part of the variability might also result from the westwardpropagating mode. Figures 8a and 8b show the first two Empirical Orthogonal Functions (EOFs) [Preisendorfer and Mobley, 1988], explaining about 49 and 21% of the total variance. As expected, EOF1 shows the typical dipole structure of a surface intensified anticyclone. (Comparing EOF1 with Figures 7c– 7f it should be noted that the sign of an EOF is arbitrary.) Interestingly, EOF2 looks like EOF1 but is phase shifted by p/2, indicating westward propagation. This pattern corresponds roughly with Figures 7b and 7g. Note that the explained variance of EOF1 is more than twice the value for EOF2. We think that in a large part EOF1 reflects the ‘‘standing’’ oscillation of the flow perpendicular to the mooring cross section that results from the southward moving anticyclones. For another part it seems to be related to the westward-propagating feature. A rough estimate is that about 50% of the variability explained by EOF1 is related to the southward propagating anticyclones and about 50% to the westward-propagating mode. With this partitioning the westward-propagating mode would be covered to equal shares by EOF1 and EOF2. [40] For a better physical understanding of the EOF structure, we estimated the Mozambique Channel normal modes by performing a Principal Oscillation Pattern (POP) analysis [Hasselmann, 1988; Storch and Zwiers, 1999; Weijer et al., 2007]. For the POP analysis, the data were interpolated on a 21 21 grid. The POPs were computed for the region with gridpoints 1 x 19, and 15 z 21. Thus in total we obtain 147 POPs. Figures 8c and 8d show the real and imaginary part of the least damped POP for the upper 800 m of the flow field. Its damping timescale is 1/log jlj = 34.9 days, where l is the POP’s eigenvalue,

Figure 6. Observed currents at mooring 6 between day 320 and day 392 at depths 50, 475, and 525 m.

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Figure 7. Velocity perpendicular to the cross section (left part of Figures 7a– 7h, blue/red indicates southward/northward flow) and near-surface velocity for the period t0 10 days t t0 + 10 days (right part of Figures 7a– 7h). Blue vectors show speed and direction, streamlines are drawn in red. In Figures 7a– 7h t0 runs from day 320 to day 390 with an increment of 10 days. The dashed green line shows the mooring section at t = t0. and its period is 68.5 days. As can be seen, there is a striking similarity between the first two EOFs and the real and imaginary parts of the least damped POP. This supports the idea that a significant part of the upper layer variability in the Mozambique Channel can be explained by a westwardpropagating Rossby normal mode. Note further that the POP’s period corresponds with the period that dominates the regional transport time series (see Figure 4c). [41] Figure 5b shows a reconstruction of the Hovmo¨ller plot by using the POP shown in Figures 8c and 8d. Note that only the sign of the reconstructed field is plotted to emphasize the westward-propagating features. The westward wave propagation is quite regular, except in northern

hemisphere summer 2004 and in August/September 2005. It is worth to mention that the EOFs as well as the POPs show a phase tilt with respect to the vertical direction pointing to baroclinic processes in the propagating mode. The mode’s amplitude is slightly larger at the African coast, indicating some growth during the propagation. The westwardpropagating waves can clearly be identified to a depth of about 1000 m. At greater depth, no clear westward wave propagation is visible. As can be seen in Figures 3a, 7d and 8a, the Mozambique Channel anticyclones also reach 1000 m depth and even deeper at the western part of the Channel. This might explain why there is a fairly good

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Figure 8. (a) EOF1 and (b) EOF2. The EOF1 explains about 49% and the EOF2 about 21% of the total variance. POP1 of the upper 800 m: (c) real part of POP1, (d) imaginary part of POP1. The period of POP1 is 68.5 days, the damping timescale is 34.9 days. correlation between the volume transport in region I and III and between region II and IV.

6. Rossby Wave Channel Modes [42] As pointed out above, in Figure 5b we see a wave with zonal wave number one (that is a wavelength of about 360 km), propagating from the east coast of Madagascar to the Mozambique coast within about 70 days. It appears natural to interpret the observed westward-propagating wave as a Rossby channel mode. For a barotropic Rossby mode, a zonal phase speed of 360 km per 70 days (4.2 m/s) is rather small. Only waves with meridional wavelength much smaller than the channel width would be so slow. In contrast, baroclinic Rossby modes are usually slower than 4.2 m/s, except waves with a very large meridional wavelength. Such elongated, north – south-oriented patterns of Rossby waves have indeed been observed in the Mascarene Basin east of Madagascar [Warren et al., 2002], but have also been found in satellite data covering the Mozambique Channel [Schouten et al., 2002]. Interestingly, Schouten et al. [2003] proposed that eddies in the central part of the Mozambique Channel can grow because of merging with elongated positive sea surface height anomalies that propagate westward. [43] What periods do meridionally elongated Rossby modes in the Mozambique Channel possess? Is the lowest natural eigenfrequency close to the dominant frequency 2p/70 days? To answer this question we use a model that was recently discussed by Harlander and Maas [2004]. The model is tailored to find elongated low-frequency quasigeostrophic channel modes for fluids with constant buoyancy frequency N and arbitrary channel profile. In the following we solve this model, first numerically for the ‘‘true’’ channel profile by using a second-order central finite

difference scheme. Then we approximate the channel profile by a half-ellipse. For this geometry, analytical solutions in the form of Mathieu functions exist. The true channel profile together with the fitted ellipse is shown in Figure 9. The nondimensional coordinates (x0, z0) and the dimensional coordinates (x*, z*) are related via [Harlander and Maas, 2004] x0 ¼ x*=2S 1=2 L;

z0 ¼ z*=2D;

ð3Þ

where L and D is the horizontal and vertical length scale, S = N2D2/f 20L2 is the nondimensional stability parameter, N buoyancy frequency, f0 = 2W sinF the Coriolis parameter, W the earth’s rotation frequency, and F latitude. For L we use the width of the Mozambique Channel at F = 17° (360 km), and for D the depth of the channel (2700 m). N generally depends on z. Here we use N = 0.01 s1, corresponding to the mean of the buoyancy frequency in the upper 500 m of the water column, where the amplitude of the westward-propagating waves is large. [44] In Figure 10 we show the streamfunction of the Rossby mode with the lowest frequency. This streamfunction is related to the geostrophic velocity components (u, v) as well as the ageostrophic velocity components w and ua (see equations (A4) – (A6)). The Rossby mode is given for the numerical model (a – d) and the analytical model (e – h) at time t = (0, T/8, T/4, 3T/8), where T is the period. Numerically we find T = 82.5 days, and analytically T = 79.5 days. Thus in spite of the differences in channel geometry, the frequency and structure of the lowest mode does not change much. This is not too surprising since it is known that solutions of standard elliptic boundary value problems are not sensitive to small changes in boundary geometry. Nevertheless, it is comforting to see that the numerical and the explicit method give results that match

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Figure 9. Mozambique Channel cross section in nondimensional (x0, z0) coordinates as defined in the text. The cross section is approximated by a half-ellipse. Corresponding coordinates are also shown. well. The period of the first Rossby mode is somewhat larger than the period of the wave we see for example in Figure 5. However, taking all the simplifications used in our model into account, a deviation between model and observed period in the order of 10% seems to be acceptable. [45] The width and depth the Mozambique Channel varies in the meridional direction and also the fluid’s buoyancy deviates from the ideal value assumed above. It is thus important to address the question of robustness of the found mode and its period to changes in N, D, and L. To obtain the sensitivity of the modes on these parameters explicitly, we consider an even simpler geometry for the Channel’s cross section than a half ellipse. Assuming a rectangular cross section, the modes are given in terms of trigonometric functions instead of Mathieu functions. Using trigonometric functions the mathematical analysis of the mode’s robustness becomes particularly simple. We find (see Appendix for more details) that a 10% increase of L leads to a 7% decrease of T. A 10% change of N or D leads to a 3% change in T. In summary, the bimonthly period found for the first Mozambique Channel mode shown in Figure 10 is quite robust with respect to slight changes in N, D, and L. [46] We end this section with a comment on the neglect of forcing and friction in our Rossby mode analysis. Warren et al. [2002] and Weijer [2008] recently explained oscillations observed in the Mascarene Basin (northeast of Madagascar) also by Rossby normal modes. Warren et al. neglected any meridional wave structure too, but they included forcing and friction into their mathematical analysis. For realistic values of Rayleigh damping r (3 109 s1 < r < 107 s1, w r) they found that the resonant waves are essentially the normal basin modes, justifying the neglect of friction to first order.

7. Summary and Discussion [47] In the present study we analyzed recent current measurements from a mooring section at 17°S across the

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narrowest part of the Mozambique Channel. The data cover the period 25 November 2003 to 23 March 2006. We found a mean volume transport of 8.6 Sv with a standard deviation of ±14.1 Sv. In the upper 1200 m, a southward transport of 15.7 Sv is found in the western part of the Channel and a northward transport of 5.9 Sv in the eastern part. Along the Mozambique shelf, a deep equatorward undercurrent of 1.5 Sv was observed. The variability of the total and regional transports is large and the standard deviation is in the order of magnitude of the mean transport. There is no continuous boundary current and the Mozambique Channel throughflow is governed by channel-size eddies migrating southward. The existence of eddies can be deduced from the upper layer regional transport time series (Figure 4d), current vector plots (Figure 6), and from spacetime plots of the near-surface flow (Figure 7). However, the total transport in contrast is not a proper measure for the eddy activity. [48] The current variability at the mooring section is dominated by a period of 68 days. This period results from the southward migrating anticyclones (about five eddies per year). However, we also found a westward-propagating signal with a similar period. It is suggested that this signal results from a baroclinic Rossby normal mode with zonal wave number one and a much smaller meridional wave number. An EOF analysis reveals that 70% of the variability within the Channel can be explained by a dipole pattern corresponding to the eddies and a phase shifted pattern that is attributed to the westward-propagating mode. This finding is supported by an estimation of the Channel normal modes applying a POP analysis. The least damped POP has a period of 68 days and is able to qualitatively reconstruct the near-surface flow and the westward-propagating signal. Finally, using a quasi-geostrophic model we showed that the first Mozambique Channel Rossby normal mode with an infinite meridional extension has a period of about 80 days, not too far away from the observed period (in view of the model simplifications). [49] By analyzing the passage of an anticyclone in detail (see Figure 7) we suggest the following scenario for the quasi-regular development of eddies in the Mozambique Channel: Before an anticyclone develops, there is a strong southward flow in the eastern part of the Channel. This anomaly propagates westward toward the center of the Channel where the flow becomes unstable. An anticyclone develops. Basically due to self-propagation [Saffman, 1992; Reznik, 1992], the vortex migrates southward. The speed of the eddy depends on its lateral extension. An eddy with a diameter that equals the Channel’s width can become stuck since the self-propagation mechanism does not work for a vortex that has contact with the east and west coast. Later the eddy is shifted to the western part of the Channel and moves southward. After the eddy has passed the mooring site, a strong southward current is found again at the eastern part of the Channel, and the ‘‘eddy-cycle’’ is completed. The Rossby normal mode propagation is visible mainly during the buildup and the decay period of the eddy. [50] Note that this scenario points to a local eddy generation close to the mooring site at 17°S, where the African coast bends to the west. Other authors suggested that eddies are generated at the northern Channel entrance [Schott et al., 1988; LaCasce and Isachsen, 2007]. Our observations are

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Figure 10. Streamfunction of the first Mozambique Channel Rossby normal mode. The first mode possesses the shortest period and the largest eigenfrequency of all Rossby modes in the channel. (a– d) Numerical solution of the mode at t = (0, T/8, T/4, 3T/8) with T = 82.5 days. (e – h) Analytical solution for the half-ellipsoidal cross section at t = (0, T/8, T/4, 3T/8) with T = 79.5 (see text for more details). not appropriate to exclude this possibility. It is likely that both types of eddies exist within the Mozambique Channel. [51] The type of instability that leads to the eddy growth in the Mozambique Channel is not determined so far. Horizontal shear (barotropic) instability is one option [van der Vaart and de Ruijter, 2001]. The baroclinic Rossby normal modes we obtained from the analytical and numerical models (that do not consider a mean current) are neutral. However, it should be noted that a meridional mean flow with arbitrary vertical shear is unstable [Walker and

Pedlosky, 2002]. This stands in contrast to the zonal flow case where the meridional change of the Coriolis parameter, b, stabilizes the flow for weak shear. Walker and Pedlosky [2002] infer for an idealized channel flow oriented in north – south direction that there is a ‘‘strong connection between the instability occurring at weak shears and the existence of Rossby normal modes’’. Our findings suggest that the Mozambique Channel seems to be a region for which this connection is likely.

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[52] Finally, we point out that the significance of the present study lies not alone in a better understanding of the processes that determine the transport through the Mozambique Channel. The data are also well suited for benchmarks of numerical models.

Appendix A [53] For a rectangular channel with the nondimensional depth and width as the channel shown in Figure 9, the nondimensional normal modes and eigenfrequencies of the ageostrophic streamfunction c read 0 x c sin k2S 1=2 px0 sinðn2pz0 Þ cos þ wt 0 ; 2w w2 1=2 2 ¼ 2S p k þð2p nÞ2 ; 4

ðA1Þ

ðA2Þ

where k = 1, 2, . . . and n = 1, 2, . . . denote nondimensional wave numbers. Turning then to the dimensional period, we obtain T¼

1=2 p k2 n2 f02 þ ; b0 L2 N 2 D2

ðA3Þ

where b0 = 2Wcosf0/a (a is the earth’s radius). Assuming b 0 and f0 to be fixed at f0 = 17°S, this formula shows how the period of the lowest mode depends on the choice of N, D, and L. For the lowest mode with k = n = 1, N = 0.01 s1, D = 2700 m, and L = 360 km, we obtain T 70.28 days. [54] Let us now address the question if Rossby channel modes can lead to variations of the total transport. Note that Figure 10 shows the ageostrophic streamfunction c in the Mozambique cross section. The corresponding geostrophic flow has no zonal component but just a x and z dependent along channel velocity v. We can compute the geostrophic flow vg = (0, v) as well as the ageostrophic zonal and vertical velocity components ua and w from the geostrophic and ageostrophic streamfunctions y and c using the definitions [Harlander and Maas, 2004] 1 v ¼ 2S 1=2 yx0 ;

ðA4Þ

w ¼ bS 1=2 yt0 z0 ¼ cx0 ;

ðA5Þ

ua ¼ S 1=2 cz0 ;

ðA6Þ

where U is the velocity scale and b = b 0L2/U. Finding y from equation (A5) and insert this into equation (A4) we obtain v¼

1 @ 2b @x0

Z Z

@c 0 0 dz dt : @x0

ðA7Þ

Note that the vertical structure of v is given by a cosine in contrast to the sine in the streamfunction (equation (A1)).

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Thus v shows surface intensification but also a prominent opposing flow close to the bottom. For some periods we can also find opposing flows in the observations but they have a much smaller amplitude than the near-surface flows. Computing the volume transport from equations (A1) and (A7) we find zero transport for any time. This holds not only for the rectangular channel modes, but also for the modes shown in Figure 10. Thus because of their spatial symmetry, Rossby channel modes cannot explain the large variations of volume transport in the Mozambique Channel. However, the situation might be different when spatial inhomogeneity of the background conditions weakens the symmetry of the modes. A more complete model, including a varying N(x, z) and an along channel mean flow V(x, z) is necessary to add inhomogeneity to the Mozambique Channel modes. The model by Darby and Willmott [1990], formulated for Rossby waves in a meridionally stratified channel, might be a candidate for such a more complete analysis. [55] Acknowledgments. We thank Janine Nauw for help with the data, Leo R. M. Maas for helpful comments on an early draft of the manuscript, Jianping Li for providing the West Indian Ocean monsoon index, Jenny Ullgren for providing Figure 1, and two anonymous referees for many suggestions that improved the clarity of the paper. We further thank the crew of the RRS Discovery for deploying the instruments. U. H. thanks Ulrike Fallet and Gert-Jan Brummer for discussions on geological aspects of the Mozambique Channel flow. U. H. was supported by a research grant by NWO. The LOCO program is supported by investment grants by NWO.

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Storch, H. V., and F. W. Zwiers (1999), Statistical Analysis in Climate Research, 484 pp., Cambridge Univ. Press, New York. van Aken, H., H. Ridderinkhof, and W. P. M. de Ruijter (2004), North Atlantik deep water in the south-western Indian Ocean, Deep Sea Res. Part I, 51, 755 – 776. van der Vaart, P. C. F., and W. P. M. de Ruijter (2001), Stability of western boundary currents with an application to pulslike behavior of the Agulhas current, J. Phys. Oceanogr., 31, 2625 – 2644. Walker, A., and J. Pedlosky (2002), Instability of meridional baroclinic currents, J. Phys. Oceanogr., 32, 1075 – 1093. Warren, B. A., T. Whitworth III, and J. H. LaCasce (2002), Forced resonant undulation in the deep Mascarene Basin, Deep Sea Res. Part II, 49, 1513 – 1526. Weijer, W. (2008), Normal modes of the Mascarene Basin, Deep Sea Res. Part I, 55, 128 – 136. Weijer, W., F. Vivier, S. T. Gille, and H. A. Dijkstra (2007), Multiple oscillatory modes of the Argentine Basin. part I: Statistical analysis, J. Phys. Oceanogr., 37, 2855 – 2868. Woodberry, K. E., M. E. Luther, and J. J. O’Brien (1989), The wind-driven seasonal circulation in the southern tropical Indian Ocean, J. Geophys. Res., 94, 17,985 – 18,002.

W. P. M. de Ruijter, Department of Physics and Astronomy, Institute for Marine and Atmospheric Research, Utrecht University, Princetonplein 5, NL-3584 CC Utrecht, Netherlands. U. Harlander, Department of Aerodynamics and Fluid Mechanics, BTU Cottbus, Siemens-Halske-Ring 14, D-03046 Cottbus, Germany. (haruwe@ tu-cottbus.de) H. Ridderinkhof, Department of Physical Oceanography, Royal Netherlands Institute for Sea Research, P.O. Box 59, NL-1790 Texel, Netherlands. M. W. Schouten, TNO Defence, Security and Safety, P.O. Box 96864, NL-2509 JG The Hague, Netherlands.

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