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    The leaky equatorial Pacific mechanism during an El Niño as proposed by Clarke (1991). Anomalous westerly winds blow water east across the Pacific Ocean, uniformly lowering (L) sea level in the western equatorial Pacific and along the western and southern Australian coasts. The dashed line denotes the 200-m isobath. During La Niña, the equatorial winds are easterly and the sea level in the western equatorial Pacific and around the Australian coast is anomalously high [from Li and Clarke (2004), Fig. 1].

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    Map of the western Australian coast. The black diagonal lines show the TOPEX/Poseidon, Jason-1, and Jason-2 satellite tracks, and the gray line shows the approximate position of the shelf edge (200-m isobath). Locations of the sea level measurements used in the three separate interannual EOF analyses are shown by open circles at the coast, by solid markers at the shelf edge, and by solid markers approximately 100 km offshore of the shelf edge. Tracks 90, 101, 166, 177, and 253 are labeled.

  • View in gallery

    (a) Spatial structure of the first mode EOF of the interannual sea level along the coast of southwestern Australia from 14° to 35°S at the coast (dashed, 94% of variance), shelf edge (dotted, 96% of variance), and approximately 100 km seaward from the shelf edge (solid, 84% of variance). Figure 2 shows a map of these locations. (b) Principal component time series for the first mode EOFs corresponding to (a).

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    The right-handed coordinate systems (x, y) and (n, s) where x is perpendicular to the shelf edge and seaward, y is parallel to the shelf edge, n is perpendicular and outward from the satellite tracks and shelf edge boundary of box 1 (Fig. 5) and s is distance along the boundaries of box 1. As shown in the diagram, is the angle between the x and s axes. Unit vectors in the x, y, n, and s directions are i, j, en, and es, respectively.

  • View in gallery

    Box 1 where was estimated off the southwestern coast of Australia. The solid lines correspond to the satellite tracks and the dashed line to the shelf edge (200-m isobath). Tracks 101, 166, 177, and 90 are labeled and colored. Thick colored lines denote the sections of track around Box 1 used in the estimation of . Point C indicates the crossover point of Track 166 and Track 101. Point E is the location of the intersection of Track 166 and Track 177.

  • View in gallery

    (left) Correlation and (right) least squares regression coefficients of interannual along-track SSH on interannual coastal sea level for (a),(b) tracks 101, (c),(d) 177, (e),(f) 253, and (g),(h) 166. For each track, the coastal sea level used in the calculations corresponds to the coastal sea level station nearest to where the track crosses the coast (see Fig. 2; track 101, Carnarvon; track 177, Geraldton; tracks 166 and 253, Fremantle). The colors used for each track correspond to the colors used for each track in Fig. 5 and the thickened parts of the correlation and regression coefficient plots correspond to the thickened segments of track in Fig. 5. The bold black vertical line shows the location of the shelf edge, and the vertical color-coded lines show where another track crosses the track under consideration in that panel. For example, the green vertical line in (a) corresponds to track 90 (see Fig. 5). It marks where track 90 crosses the red track 101 and corresponds to point G in Fig. 5.

  • View in gallery

    Divergence of interannual eddy momentum flux calculated with tracks 101, 177, and 166 (thick solid) and with tracks 101 and 177 (dashed) over box 1. The similarity of these curves indicates that track 166 contributes little to D′. The thin solid curve shows calculated over box 1.

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    Map of the western coast of South America from 2° to 35°S. The black lines show the TOPEX/Poseidon, Jason-1, and Jason-2 satellite tracks, and the thick gray line shows the approximate position of the shelf edge. Note that the shelf edge is quite narrow along most of the coast. The solid dots and open dots correspond to the locations of sea level measurements along the shelf edge and coast, respectively.

  • View in gallery

    (a) Spatial structure of the first mode EOF of the interannual sea level along the western coast of South America from 4° to 35°S at the shelf edge (solid, 88% of variance) and coast (dashed, 60% of variance). Figure 8 shows a map of these locations. (b) Principal component time series for the 1st mode EOFs corresponding to (a).

  • View in gallery

    Spatial structure of the first mode EOF of the interannual SSH along (a) track 39 (97% of variance), (c) track 115 (97% of variance), (e) track 191 (93% of variance), and (g) track 13 (92% of variance), and their corresponding principal component time series (b) track 39, (d) track 115, (f) track 191, and (h) track 13.

  • View in gallery

    (a) RMS (cm2 s−2) along track 101 from near the coast to point C (see Fig. 5). The thin vertical line B corresponds to the approximate location of the shelf edge. The horizontal lines indicate the approximate average level of eddy variability on the shelf (≈150 cm2 s−2) and seaward of the shelf (≈230 cm2 s−2). (b) As in (a), but now along the southern track 177 with F marking the shelf edge and E the end of the segment of track (see Fig. 5). The horizontal lines mark the approximate level of eddy variability on the shelf more than 40 km from the shelf edge (≈150 cm2 s−2) and more than about 30 km seaward of the shelf edge (≈370 cm2 s−2).

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Estimation of the Effect of Eddies on Coastal El Niño Flows Using Along-Track Satellite Altimeter Data

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  • 1 Department of Earth, Ocean and Atmospheric Science, The Florida State University, Tallahassee, Florida
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Abstract

Previous work has shown that the El Niño sea level signal leaks through the gappy western equatorial Pacific to the coasts of western and southern Australia. South of about 22°S, in the region of the Leeuwin Current, the amplitude of this El Niño signal falls. Using coastal sea level measurements and along-track altimetry data from the Ocean Topography Experiment (TOPEX)/Poseidon, Jason-1, and OSTM/Jason-2 satellites, this study finds that the interannual divergence of the eddy momentum flux D′ is correlated with the southward along-shelf sea level amplitude decay, consistent with the eddies removing energy from the large-scale sea level signal. The quantity D′ is also correlated with the interannual flow with a surprisingly short dissipation time scale of only 2 days, much shorter than the interannual time scale.

A similar analysis off the western coast of South America, site of the originally named “El Niño” current, was carried out. Interannual sea level decay along the shelf edge is observed, and the interannual southward flow along the shelf edge is found to be highly positively correlated with the along-shelf sea level decay with a dissipation time scale of a few days. Dynamics similar to the Australian case likely apply.

Current affiliation: Applied Physical Sciences Corp., Groton, Connecticut.

Corresponding author address: Allan J. Clarke, Department of Earth, Ocean and Atmospheric Science, The Florida State University, Tallahassee, FL 32306-4320. E-mail: aclarke@fsu.edu

Abstract

Previous work has shown that the El Niño sea level signal leaks through the gappy western equatorial Pacific to the coasts of western and southern Australia. South of about 22°S, in the region of the Leeuwin Current, the amplitude of this El Niño signal falls. Using coastal sea level measurements and along-track altimetry data from the Ocean Topography Experiment (TOPEX)/Poseidon, Jason-1, and OSTM/Jason-2 satellites, this study finds that the interannual divergence of the eddy momentum flux D′ is correlated with the southward along-shelf sea level amplitude decay, consistent with the eddies removing energy from the large-scale sea level signal. The quantity D′ is also correlated with the interannual flow with a surprisingly short dissipation time scale of only 2 days, much shorter than the interannual time scale.

A similar analysis off the western coast of South America, site of the originally named “El Niño” current, was carried out. Interannual sea level decay along the shelf edge is observed, and the interannual southward flow along the shelf edge is found to be highly positively correlated with the along-shelf sea level decay with a dissipation time scale of a few days. Dynamics similar to the Australian case likely apply.

Current affiliation: Applied Physical Sciences Corp., Groton, Connecticut.

Corresponding author address: Allan J. Clarke, Department of Earth, Ocean and Atmospheric Science, The Florida State University, Tallahassee, FL 32306-4320. E-mail: aclarke@fsu.edu

1. Introduction

Along the western coast of Australia, the interannual sea level is highly correlated with the El Niño–Southern Oscillation (ENSO). During an El Niño, anomalous westerly winds in the equatorial Pacific push water eastward and lower the sea level in the western equatorial Pacific (Fig. 1). This drop in sea level appears along the coast of Indonesia and the western and southern coasts of Australia as the interannual signal leaks through gaps in the western equatorial Pacific. During La Niña, the sea level increases in the western equatorial Pacific as a result of anomalous easterly winds, which cause the sea level along the western Australian coast to also rise. Pariwono et al. (1986) found that the interannual sea levels along the coast of Australia were correlated with El Niño, and Clarke (1991) proposed the leaky western Pacific mechanism that drives this, as illustrated in Fig. 1. This leaked ENSO signal has a profound influence on some marine populations along the western Australian coast. The Australian western rock lobster (Panulirus Cygnus), Australia’s most lucrative single species fishery, is one such population (Pearce and Phillips 1988; Clarke and Li 2004).

Fig. 1.
Fig. 1.

The leaky equatorial Pacific mechanism during an El Niño as proposed by Clarke (1991). Anomalous westerly winds blow water east across the Pacific Ocean, uniformly lowering (L) sea level in the western equatorial Pacific and along the western and southern Australian coasts. The dashed line denotes the 200-m isobath. During La Niña, the equatorial winds are easterly and the sea level in the western equatorial Pacific and around the Australian coast is anomalously high [from Li and Clarke (2004), Fig. 1].

Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0109.1

At interannual time scales we expect the flow to be quasigeostrophic. Therefore, the interannual sea level should also be spatially constant along the coast so that there is no flow into the boundary. But surprisingly, as shown by Li and Clarke (2004) and Clarke and Li (2004), coastal interannual sea level and altimeter-estimated interannual sea level near the shelf edge are not spatially constant. Rather, south of about 22°S, especially just seaward of the shelf edge, the interannual sea level amplitude decreases.

These results were confirmed using Ocean Topography Experiment (TOPEX)/Poseidon, Jason-1, and OSTM/Jason-2 altimeter sea surface heights (SSHs) and eight monthly western Australian coastal sea level records (see Fig. 2). The SSHs were available from National Aeronautics and Space Administration (NASA)’s physical oceanography data website (http://podaac.jpl.nasa.gov) from January 1993 through July 2011 and the monthly sea levels from the Permanent Service for Mean Sea Level (PSMSL) website (http://www.psmsl.org) from January 1993 through December 2010. These records were longer than the January 1993 through April 2002 records available to Clarke and Li (2004) and Li and Clarke (2004). Monthly time series with the mean annual cycle removed were low-pass filtered with the 11-point symmetric Trenberth (1984) filter to obtain the interannual sea level estimates. The filter removes more than 90% of the amplitude of frequencies higher than 2π/(8 months) and passes through over 80% of the amplitude of frequencies lower than 2π/(2 yr).

Fig. 2.
Fig. 2.

Map of the western Australian coast. The black diagonal lines show the TOPEX/Poseidon, Jason-1, and Jason-2 satellite tracks, and the gray line shows the approximate position of the shelf edge (200-m isobath). Locations of the sea level measurements used in the three separate interannual EOF analyses are shown by open circles at the coast, by solid markers at the shelf edge, and by solid markers approximately 100 km offshore of the shelf edge. Tracks 90, 101, 166, 177, and 253 are labeled.

Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0109.1

Interannual sea level variability was examined at the coast, shelf edge, and 100 km from the shelf edge with three separate Empirical Orthogonal Function (EOF) analyses at these locations (Figs. 2 and 3). The first mode EOF in each case describes almost all the variance, the corresponding principal components all varying in time in essentially the same way. As found by Clarke and Li (2004) and Li and Clarke (2004), the interannual sea level signal amplitude about 100 km seaward from the shelf edge drops steeply south of about 22°S (thick solid curve in Fig. 3a). To a lesser extent, the interannual sea level also drops southward from about the same latitude at the coast and shelf edge (dashed and dotted in Fig. 3a). Figure 3a also shows that the sea level amplitude decreases seaward from the coast, suggesting, by geostrophy, that there is an interannual flow parallel to the coast and shelf edge. Since the sea level difference between the solid and dotted curves increases southward, the interannual flow along the shelf edge must be increasing southward. This interannual flow has been previously examined by Feng et al. (2003), Clarke and Li (2004), and Li and Clarke (2004).

Fig. 3.
Fig. 3.

(a) Spatial structure of the first mode EOF of the interannual sea level along the coast of southwestern Australia from 14° to 35°S at the coast (dashed, 94% of variance), shelf edge (dotted, 96% of variance), and approximately 100 km seaward from the shelf edge (solid, 84% of variance). Figure 2 shows a map of these locations. (b) Principal component time series for the first mode EOFs corresponding to (a).

Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0109.1

The El Niño index Niño-3.4, the monthly sea surface temperature (SST) anomaly averaged over the equatorial Pacific from 5°N to 5°S, 120°W to 170°W, is strongly negatively correlated with the principal components (Fig. 3b) of the first mode EOF of the interannual sea levels along the coast [r = −0.79; rcrit (95%) = −0.49], shelf edge [r = −0.79; rcrit (95%) = −0.42], and 100 km seaward from the shelf edge [r = −0.71; rcrit (95%) = −0.41]. Here and elsewhere the significance level of the correlation has been calculated using the method of Ebisuzaki (1997). These strong negative correlations are consistent with the mechanism shown in Fig. 1 and the previous work on the interannual shelf edge flow. Specifically, when the sea level is high off the coast of northwestern Australia during a La Niña, there is a southward interannual flow along the shelf edge where the interannual sea level decays. The opposite occurs during an El Niño.

Why is there a drop in interannual sea level amplitude along the coast and shelf edge? There are several possibilities, including alongshore interannual wind stress forcing, bottom friction, and energy conservation along the shelf edge as the interannual flow is generated. We consider each of these below.

Observations suggest that the decrease in interannual sea level is not a result of wind stress. Masumoto (2002) found that the correlation between the zonal wind stress and the first and second modes of the EOF of the interannual ocean dynamic heights along the western coast of Australia was insignificant. Masumoto’s result is suggestive, but since the alongshore sea level slope is associated with the alongshore wind stress rather than the zonal wind stress (see e.g., Enfield and Allen 1980), the alongshore component of the interannual wind stress should be examined. This component was calculated using wind stress data from the International Comprehensive Ocean–Atmosphere Dataset (ICOADS). The analysis for the period from January 1991 through December 2010 showed that the interannual alongshore wind stress was negligibly correlated with the interannual sea level or its slope. Therefore, the observed interannual alongshore sea level slope is not caused by the local wind stress.

The observed sea level decay in Fig. 3 is likely not a result of bottom friction either. Clarke and Van Gorder (1994) and Pizarro et al. (2001) suggested that bottom friction could result in a decrease in sea level amplitude along the coast on ENSO time scales. But this decay mechanism does not predict a seaward decay in sea level amplitude from the coast (see, e.g., Fig. 15 of Clarke and Van Gorder 1994), so it does not explain the seaward fall in SSH amplitude seen in Fig. 3.

Another possible explanation for the alongshore fall in anomalous sea level amplitude is that it is associated with conservation of energy as Bernoulli’s principle is applied to flow at the shelf edge in the presence of the Leeuwin Current. This current has a mean speed of about 50 cm s−1, is around 100 km wide, and runs parallel to the shelf edge off Western Australia (see, e.g., Tomczak and Godfrey 1994). To see how this conservation of energy mechanism works on an interannual time scale, suppose a La Niña is occurring. Then the sea level along the shelf edge north of about 23°N, where the Leeuwin Current begins, is anomalously high. As the associated higher potential energy is gradually converted to increased kinetic energy and increased flow along the shelf edge, the anomalous sea level along the coast falls. Anomalies of opposite sign occur during El Niño. But calculations based on a nonlinear model similar to that of Clarke and Li (2004) show that the interannual sea level amplitude fall because of this mechanism is only about 6% of the fall observed (see appendix A).

Although the above Leeuwin Current mechanism fails, it is curious that the decay in interannual sea level amplitude along the shelf edge coincides with the approximate 23°–34°S location of the Leeuwin Current (see Fig. 3). Another possible mechanism is that the alongshore decay in interannual sea level signal is dissipated by mesoscale eddies associated with the Leeuwin Current.

The presence of mesoscale eddies in the Leeuwin Current region is well known (Andrews 1977; Pearce and Griffiths 1991). Griffin et al. (2001) used plots of sea surface temperatures, sea level anomalies, and chlorophyll-a concentrations to show that eddies exist off the southwestern coast of Australia. Deng et al. (2008) used bimonthly along-track ocean dynamic heights from 1993–2002 to show the locations of the eddies in the region, and Feng et al. (2005) observed that the eddy field from 28° to 31°S reduces the energy in the mean flow. Feng et al. also found that the surface eddy kinetic energy in the Leeuwin Current region is stronger during La Niña years and weaker during El Niño years. But it was not clear whether this changing eddy energy converged or diverged and affected the interannual sea level slope and interannual flow.

Our analysis will use coastal and satellite-estimated sea level data to determine whether the eddies off the southwest coast of Australia in the region of the Leeuwin Current dynamically affect the large-scale interannual flow and cause the interannual sea level amplitude to fall southward. In section 2, the theory supporting this hypothesis will be discussed. We will then use coastal sea level station data and satellite altimetry data to document the interannual flow variability in section 3. In section 4, we will test the theory of section 2 and show that eddies are responsible for the interannual fall in sea level amplitude and are related to the interannual flow along the shelf edge off southwestern Australia. Section 5 examines whether the theory can describe the interannual variations in the coastal flow off Peru, the flow that originally gave rise to the term “El Niño.” Conclusions will then be presented in a final section.

2. Theory

a. Eddies, interannual flow, and alongshore fall in interannual sea level amplitude

To understand the dynamics of the interannual sea level near the eastern ocean boundary, we consider the momentum equations in Cartesian coordinates. We will use a coordinate system where is perpendicular to the shelf and is along the shelf, with positive southward as in Fig. 4.

Fig. 4.
Fig. 4.

The right-handed coordinate systems (x, y) and (n, s) where x is perpendicular to the shelf edge and seaward, y is parallel to the shelf edge, n is perpendicular and outward from the satellite tracks and shelf edge boundary of box 1 (Fig. 5) and s is distance along the boundaries of box 1. As shown in the diagram, is the angle between the x and s axes. Unit vectors in the x, y, n, and s directions are i, j, en, and es, respectively.

Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0109.1

Since the drop in sea level is southward along the shelf edge, we are interested in the -momentum equation
e1
where υ is the flow in the direction, the flow in the direction, the horizontal velocity, the vertical (upward) coordinate, the turbulent stress in the y direction, the time, the horizontal gradient operator, the acceleration due to gravity, the sea level displacement, and the mean water density. Note that the pressure gradient divided by has been approximated by since all analysis will take place at or near the surface where the fluctuating pressure is .
The flow is quasigeostrophic so
e2
Write
e3
where is the mean and seasonal cycle, the interannual signal found by low-pass filtering , and is the remainder. Our analysis will focus on the region seaward of the shelf edge where the energetic flows that are not due to or are dominated by energetic mesoscale eddies and meanders (Andrews 1977; Pearce and Griffiths 1991; Feng et al. 2005). Henceforth we will refer to as the “eddy” velocity with the understanding that in reality it is the remainder in (3).
Substituting the expression (3) into (2) gives a nine-term sum. The terms involving combinations of , , , and are directly related to large-scale flow and Bernoulli’s principal as discussed earlier in the introduction and appendix A. As shown there, the interannual contribution of these terms is too small to explain the fall in interannual sea level amplitude along the coast. Terms involving products of one seasonal or interannual term with an eddy term average to zero when an interannual filter is applied since eddy velocities occur at much higher frequencies than interannual. Consequently, the only interannual contribution to the 9-term sum that might explain the fall in interannual sea level amplitude is the eddy flux term and so
e4
where (·) denotes the interannual contribution of a variable.
As noted earlier in the introduction, the interannual wind forcing cannot explain the alongshore sea level gradient so it can be dropped from (1). Since and Clarke and Li (2004) estimate υ′ ~ 2 cm s−1, we have, for years, 1.3 × 10−9 m s−2 at interannual frequencies. But at the coast and shelf edge fall by about 1–2 cm from 22°S to 33°S (Fig. 3a), so ~ 10−7 m s−2 at the shelf edge and . Therefore (1) can be reduced to
e5
In addition, the interannual flow at the shelf edge is blocked, so is negligible there and (5) can be written as
e6
where is used for the interannual eddy momentum flux divergence for notational simplicity.
Equation (6) connects the interannual amplitude changes in the small-scale eddy variability with the large-scale interannual sea level slope. Why should the eddy variability vary interannually? Previous work (Feng et al. 2003; Clarke and Li 2004) has shown that the Leeuwin Current varies interannually. Perhaps when it strengthens during La Niña, there is more eddy variability and positive flux divergence , and when it weakens during El Niño there is less eddy variability and negative . If this hypothesis were true, then we would expect
e7
where has the dimension of time and is the eddy dissipation time. Note that if both (6) and (7) are true then
e8

To test the relationships (6) and (7), we must be able to estimate . In the next section we discuss how this might be done using along-track altimeter data.

b. Calculation of the divergence of the eddy momentum flux

The eddies are assumed to be quasigeostrophic, and so surface currents can be estimated from gradients of altimeter-estimated SSHs. Along-track SSH measurements from the Integrated MultiMission Ocean Altimeter Sea Surface Height Climate Data Record were used in the analysis (available from http://podaac.jpl.nasa.gov). This dataset combines along-track altimeter data from TOPEX/Poseidon, Jason-1, and OSTM/Jason-2 altimeter satellites by interpolating the individual Geophysical Data Records to a common reference orbit. The data were available from January 1993 through July 2011, with SSH measurements taken every 10 days. The along-track resolution of the altimeter data is excellent for mesoscale dynamics analysis and provides a measurement every 6 km or so, but the distance between tracks is around 315 km.

The satellite altimeter height is noisy, so the geostrophic velocity , which involves a gradient of SSH, is even noisier, and the divergence is even noisier still. In addition, except where satellite tracks cross, we are only able to calculate the component of perpendicular to the satellite track rather than the vector . In this section, we estimate by averaging over a box. Evidence that we were able to extract the signal from the noisy data is provided by the statistically significant correlations discussed in section 4b and the error analysis in appendix B.

Since we want to test (6) at the shelf edge, ideally our box should have a straight shelf edge as one side. The other three box edges should be satellite tracks so we can estimate velocities. The box should be as narrow as possible so that we stay close to the shelf edge. Box 1 (see Fig. 5) meets these criteria reasonably well, and so our analysis will focus on this box.

Fig. 5.
Fig. 5.

Box 1 where was estimated off the southwestern coast of Australia. The solid lines correspond to the satellite tracks and the dashed line to the shelf edge (200-m isobath). Tracks 101, 166, 177, and 90 are labeled and colored. Thick colored lines denote the sections of track around Box 1 used in the estimation of . Point C indicates the crossover point of Track 166 and Track 101. Point E is the location of the intersection of Track 166 and Track 177.

Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0109.1

Box 1 is bounded by the satellite tracks 101, 166, and 177 and the shelf edge (see Figs. 2 and 5). It follows from the divergence theorem that the average of over the box can be written
e9
where A is the area of the box, is the curve around the box, is the outward unit normal vector to that curve, and . Write
e10
where is the unit vector tangent to the edge of the box in a right-handed system of axes as in Fig. 4. Taking the dot-product of the second of the two equalities of (10) with , we have
e11
Substituting the expression for in (11) into (9) gives
e12
and thus the estimate for averaged over the area A is
e13

The “eddy” surface velocity component which is perpendicular to the satellite track, can be calculated at a given along-track measurement point every 10 days by geostrophy from the along-track “eddy” SSH estimates . At each along-track point, is found as a 10-day time series by removing the mean, seasonal cycle, and interannual and lower-frequency variability from the original 10-day SSH time series. The 10-day sea level slope time series for the geostrophic estimate was found from at a given along-track point by a least squares fit of 5 along-track points, the point itself and its two nearest neighbors on each side. We decided to use five along-track points to calculate because this corresponds to a distance of about 30 km, which is small enough to resolve the sea level slope for the eddies in the region with typical diameters of about 100 km (see, e.g., the western Australian eddy observations in Pearce and Griffiths 1991; Waite et al. 2007). Less than a 5-point fit will also resolve the eddy scale, but using more points enables a better estimate of the sea level slope.

By construction, the 10-day time series only contains relatively high frequencies, but contains a mean and may vary interannually if the amplitude of varies interannually. Thus, after removal of the mean, the interannual contribution can be nonzero and contribute to as in (13).

The along-track eddy component [see (10)] cannot be obtained from a single track but can be estimated for a given track at a location where two tracks intersect. Thus the term in (13) can only be calculated at a few points along the bounding curve . For box 1 (Fig. 5), the two relevant points are C and E. Table 1 suggests that is probably comprised mostly of “noise” since at both points C and E it is not significantly correlated with Niño-3.4 at any lead or lag. In addition (see Table 1), at both C and E it has a root-mean-squared (RMS) value smaller than and is only weakly correlated with it (r < 0.4). Since appears smaller and noisier than , we dropped the integral when calculating in (13).

Table 1.

RMS (root-mean-squared) values of and at points C and E in Fig. 5 and the correlations of with Niño-3.4 and . The lagged correlations with Niño-3.4 correspond to the lag for maximum |r|. A positive lag means that the interannual eddy variability lags Niño-3.4. Critical values of the correlation coefficients here and elsewhere in this paper are based on Ebisuzaki (1997).

Table 1.

We tried to check on the validity of this omission using the Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO) (http://www.aviso.oceanobs.com) ⅓° by ⅓° gridded weekly velocity data product. These data are based on the combination of altimeter data from satellites with different tracks and different time intervals for repeat orbits. We found that the AVISO data were not accurate enough here for this check. Correlations between and υ′ or and [see (6) and (7)] using (13) or (13) with omitted were all insignificant using AVISO data.

Note that the curve around the edges of the box in (13) includes the 200-m isobath where no satellite data are available. However, while there may be some mesoscale exchange at the shelf edge, dynamically we expect that eddies are largely blocked at the shelf edge. In situ current meter observations made near the shelf edge during the year-long Leeuwin Current Interdisciplinary Experiment (Smith et al. 1991) support this conjecture. Table 2 in that paper shows that near the shelf edge (moorings D2 and D3) and away from the frictional bottom boundary layer, the principal axis of the subinertial variability was strongly aligned along the isobaths; the standard deviation of the subinertial flow along the isobaths was 3 to 4 times that perpendicular to the isobaths. Away from the shelf edge in 700 m of water at mooring D4, eddy variability was stronger and far less polarized along-isobath (see Table 2 and Fig. 4 of Smith et al. 1991). Based on these results, in our analysis we will assume that along the shelf edge, or is at least small enough that the shelf edge part of does not contribute substantially to the integrals in (13).

Table 2.

Based on (17), estimates of the interannual along-shelf edge flow υ′ at the northern (track 101) and southern (track 177) edges of box 1. The SSHs used in the first mode EOF calculation for tracks 101 and 177 near the shelf are marked as thick solid in Fig. 6. Also shown are the correlations and critical correlations rcrit at the 95% significance level of the principal component time series of the first mode EOF with the interannual sea level at the shelf edge, the nearest coastal station, and Niño-3.4. The maximum correlations were all found at a lag of zero months.

Table 2.

3. Interannual along-shelf flow

a. Along-track sea level structure

To check the key relationships (7) and (8), we must estimate the large-scale interannual flow . To do this, we will first analyze the along-track SSH data previously described. In the past, reliable altimeter SSH measurements were not available close to the coast, but recently the merged TOPEX/Poseidon, Jason-1, and OSTM/Jason-2 along-track data have been uniformly processed so that reliable data are available as close as 15 km from the coast. Although our focus is on for box 1 in Fig. 5, we here provide a context for this box by reporting results for in the Leeuwin Current region as a whole.

North of 22°S, Clarke and Li (2004) found that the interannual seaward SSH slope was very gentle and that the SSH is highly correlated with the coastal sea level, but south of 22°S, much larger seaward and alongshore sea level gradients and therefore stronger interannual flows were obtained. This is consistent with our results in Fig. 3, and here we concentrate on the region offshore of the western Australian coast south of 22°S.

In this region (see Fig. 2) there are three ascending satellite tracks that intersect the coast (tracks 101, 177, and 253). Tracks 101 and 177 clearly cut across the shelf edge, while Track 253 runs almost parallel to the shelf edge. Also Track 166 is a descending track that is parallel to the southwestern Australian coast about 100 km from the shelf edge.

The correlations and least squares regression coefficients of the interannual SSHs along tracks 101, 177, 253, and 166 on the nearest coastal sea level stations where the tracks cross the coast are shown in Fig. 6. In particular, just seaward of the shelf edge, especially on tracks 101 and 177 which are not parallel to the shelf edge (Fig. 2), there is a sudden drop in correlation and regression coefficients. This signifies a sharp decrease in amplitude of the coastal and shelf signal and, by geostrophy, an interannual flow component at right angles to the tracks. Surprisingly, further seaward along tracks 177 and 101 the regression and correlation coefficients of SSH on the corresponding coastal sea levels begin to rise again. For track 177 the correlation reaches more than 0.7 and the regression coefficient nearly unity about 400 km in along-track distance from the coast (see Figs. 6c,d). In other words, at this large distance from the coast the sea level is similar to that at the coast. This implies by geostrophy that the current perpendicular to the track averaged along the track between the coast and 400 km from the coast is nearly zero. But since we know that there is a geostrophic current perpendicular to the track near the shelf edge, there must be a current perpendicular to the track in the opposite direction to cancel it. This current corresponds to the positive slope in correlation and regression coefficients between about 300 km and 400 km from the coast in Figs. 6c,d. A qualitatively similar counter flow is suggested on track 101 between about 400 km and 700 km along-track from the coast (see Figs. 6a,b). Figure 2 of Clarke and Li (2004) shows a similar result.

Fig. 6.
Fig. 6.

(left) Correlation and (right) least squares regression coefficients of interannual along-track SSH on interannual coastal sea level for (a),(b) tracks 101, (c),(d) 177, (e),(f) 253, and (g),(h) 166. For each track, the coastal sea level used in the calculations corresponds to the coastal sea level station nearest to where the track crosses the coast (see Fig. 2; track 101, Carnarvon; track 177, Geraldton; tracks 166 and 253, Fremantle). The colors used for each track correspond to the colors used for each track in Fig. 5 and the thickened parts of the correlation and regression coefficient plots correspond to the thickened segments of track in Fig. 5. The bold black vertical line shows the location of the shelf edge, and the vertical color-coded lines show where another track crosses the track under consideration in that panel. For example, the green vertical line in (a) corresponds to track 90 (see Fig. 5). It marks where track 90 crosses the red track 101 and corresponds to point G in Fig. 5.

Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0109.1

The correlation and regression results for track 166 (Figs. 6g,h) reveal another surprising result. Because of the changing shelf edge direction, track 166 initially crosses the shelf and its edge near Bunbury and Fremantle but then runs approximately parallel to the shelf edge for several hundred kilometers (Fig. 2). The surprising result is that, just seaward of the shelf edge and the intersection with track 253, the regression coefficient increases (Fig. 6h). This increase means that the alongshore flow near the shelf edge is in the opposite direction to that on the adjacent shelf and at other sections along the coast where the interannual sea level amplitude falls. Farther northward along the track where it is approximately parallel to the shelf edge but about 80 km from it, changes in the slope of the SSH suggest that the large-scale interannual flow at this distance from the coast is not parallel to the shelf edge, that is, it appears to undergo large-scale meanders. Note that along track 166 in the region just seaward of the shelf edge where the flow reverses and for a large section of the track where the “meanders” occur, the correlation of the SSH with the coastal sea level is greater than 0.6, suggesting that these features are real.

b. Quantitative estimates of the interannual flow along the shelf edge

In the previous subsection we described qualitative changes in the interannual flow based on slopes in interannual SSH deduced from a correlation and regression analysis. Here we attempt to estimate those interannual flows quantitatively. In particular, to verify the theoretical relationships (7) and (8) for box 1, we will need to estimate for this box. Since the satellite tracks 101 and 177 do not cross the shelf edge at right angles (Fig. 5), we cannot calculate directly from the gradient of the sea level along the track, and we proceed similarly to Li and Clarke (2004).

First note that the gradient of along the shelf edge is about 1 cm in 1000 km (see, e.g., the dotted curve in Fig. 3 from 22° to 32°S) or 10−8, whereas calculations of interannual sea level gradients along the edges of box 1 are of order 10−7 (order 1 cm in 100 km), an order of magnitude larger. Since can be written as
e14
by taking the dot product of both sides of the second equality with es we obtain
e15
where is the angle between the x and s axes (see Fig. 4). Because and therefore , from (15) we have
e16
Hence
e17

The along-track gradients for the northern and southern edges of box 1 were obtained by calculating an EOF of the interannual SSH estimates along each of these edges and then estimating from the first EOF structure function in each case. This procedure is justifiable because the first EOF describes most of the SSH variance, specifically 94% for Track 101 and 80% for Track 177. Also, an EOF analysis is appropriate if all the interannual SSHs are in phase in time, and calculations showed that this is indeed the case—maximum lag correlations between the interannual SSH measurements used in the calculations along each track occurred when the lag was zero months.

c. Interannual flow on the shelf

Our main focus is on the verification of the theory of section 2. However, interannual flow on the continental shelf is of interest in its own right since even weak interannual flows can transport particles hundreds of kilometers and profoundly affect marine populations (see, e.g., Li and Clarke 2004; Clarke and Dottori 2008). Interannual flow on the southwestern Australian continental shelf is considered below, beginning with an examination of the spatial structure of the SSH and coastal sea level across the shelf.

Figure 6 shows that the correlation of interannual SSHs on the shelf with the nearest interannual coastal sea level measurement is very high for all tracks considered, and that, particularly for track 101 and track 253, there is a small but discernible fall in the regression coefficients across the shelf. Also noticeable in all tracks in Fig. 6 is that even though the correlation of the closest SSH measurement to the coastal sea level is very high, the corresponding regression coefficient of SSH on coastal sea level is only between 0.8 and 0.9. Therefore, at least close to the coast, interannual SSH estimates appear to be systematically slightly underestimating the real interannual sea level.

Estimates of on the shelf can be obtained from (17) using an EOF analysis in the same way the results at the shelf edge were obtained in Table 2. The results are shown in Table 3. The interannual flows are weaker than those at the shelf edge. However, by itself is still strong enough to induce an anomalous particle transport of hundreds of kilometers along the shelf.

Table 3.

Estimates of υ′ on the shelf obtained using a least squares fit slope of the first mode structure function of the EOF of the interannual along-track SSH and the correlations and regression coefficients of υ′ with the nearest interannual coastal sea levels for tracks 101 [Carnarvon), 177 (Geraldton), 166 (Fremantle), and 253 (Fremantle).]

Table 3.

4. Testing the theory

a. Introduction

Using coastal sea level data and along-track SSH measurements, we have shown that there is a drop in interannual sea level amplitude along the shelf edge and the coast of Western Australia south of 22°S. We have also observed an interannual flow along the shelf edge that spatially coincides with the Leeuwin Current. Since bottom friction, wind stress, and Bernoulli effects on the interannual sea level in the region are negligible, we will now check to see whether Leeuwin Current eddies are causing the observed drop in interannual sea level along the shelf edge by dissipating energy interannually.

In section 2 we established that if eddies are responsible for the fall in sea level amplitude along the shelf edge, then in accordance with (6), the interannual divergence of the eddy flux should be correlated with and have the same amplitude. In addition, the interannual divergence of the eddies is likely caused by interannual variations of the Leeuwin Current, and so we expect that should be proportional to as in (7). Equations (6) and (7) can be combined to form (8), and in this section we will test all three of these relationships.

b. Results

As discussed in section 2, can be estimated near the shelf edge for box 1 (Fig. 5) using (13) with the integral in that equation dropped and the integral along the shelf edge put to zero since there. Under such approximations, calculations show that in accordance with (7), averaged over box 1 is correlated [r = 0.59, rcrit (95%) = 0.37] with estimated from an average of at the northern and southern edges of the box using tracks 101 and 177 (see Fig. 5).

The and time series are calculated from noisy data, and in such circumstances the standard least squares regression of and is not the reciprocal of on . A better regression coefficient when the noise in both variables is unknown is the ratio of the standard deviations (Clarke and Van Gorder 2013). This gives a dissipation time of only 3.1 days! This is much shorter than the interannual time scale and indicates that the interannual flow is strongly dissipated by the eddies. Figure 7 shows a plot of the ′ time series calculated over box 1 and the time series calculated with tracks 101, 166, and 177 (thick solid) and with only tracks 101 and 177 (dashed). The thick and thin solid plots are nearly the same because track 166 is nearly parallel to the coast and so, for this track, in (13).

Fig. 7.
Fig. 7.

Divergence of interannual eddy momentum flux calculated with tracks 101, 177, and 166 (thick solid) and with tracks 101 and 177 (dashed) over box 1. The similarity of these curves indicates that track 166 contributes little to D′. The thin solid curve shows calculated over box 1.

Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0109.1

The correlation of the divergence of the eddy flux over box 1 with the along-shelf interannual sea levels as in (6) was also calculated and found to be positively correlated [r = 0.41, rcrit (95%) = 0.34]. In addition, the root-mean-square (RMS) values of and were almost equivalent (5.4 × 10−6 cm s−2 and 5.5 × 10−6 cm s−2, respectively), that is, the appropriate regression coefficient is nearly unity.

Finally, the relationship (8) was analyzed. The correlation of with was very strong [r = 0.91, rcrit (95%) = 0.48]. The dissipation time scale from this analysis was 3.2 days, practically the same as calculated from (7).

5. Western coast of South America analysis

During an El Niño when the anomalous westerly winds lower the sea level in the western equatorial Pacific and around Australia (Fig. 1), they also raise it in the eastern equatorial Pacific and along the western coastlines of the Americas. Anomalies of opposite sign occur during La Niña. As in the western Australian case, we expect the sea level to be spatially constant along the coast and shelf edge, but Li and Clarke (2007) demonstrated that the interannual amplitude falls southward and is associated with a strong interannual flow along the shelf edge.

Similar to the results of Li and Clarke (2007) but using a longer altimeter sea level record from January 1993 through July 2011, the first mode EOF structure function of the interannual altimeter SSH along the shelf edge of South America shows a sharp drop in interannual amplitude from 6°S to around 16°S (Fig. 9). The principal component time series of the first mode EOF has a strong positive correlation with Niño-3.4 [r = 0.75; rcrit (95%) = 0.44]. Since the 1997/98 El Niño dominates the principal component, we checked that interannual sea level and Niño-3.4 are strongly correlated [r = 0.73; rcrit (95%) = 0.39] when this event is excluded.

Coastal sea level data from the University of Hawaii Sea Level Center (http://uhslc.soest.hawaii.edu/) from February 1994 through December 2006 were used to analyze the coastal interannual sea level along the western coast of South America and compare it to the interannual shelf edge SSH. The sea level data available along this coast are limited, but an EOF of the interannual sea levels at the locations (see Fig. 8) with the most complete time series was taken. The EOF spatial structure (Fig. 9a) shows a drop in sea level similar to that along the shelf edge, and the principal component time series (Fig. 9b) is highly positively correlated with Niño-3.4 [r = 0.85; rcrit (95%) = 0.55]. The interannual coastal sea level data are also strongly positively correlated with the interannual altimeter SSHs along the shelf edge [r = 0.95; rcrit (95%) = 0.64].

Fig. 8.
Fig. 8.

Map of the western coast of South America from 2° to 35°S. The black lines show the TOPEX/Poseidon, Jason-1, and Jason-2 satellite tracks, and the thick gray line shows the approximate position of the shelf edge. Note that the shelf edge is quite narrow along most of the coast. The solid dots and open dots correspond to the locations of sea level measurements along the shelf edge and coast, respectively.

Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0109.1

Fig. 9.
Fig. 9.

(a) Spatial structure of the first mode EOF of the interannual sea level along the western coast of South America from 4° to 35°S at the shelf edge (solid, 88% of variance) and coast (dashed, 60% of variance). Figure 8 shows a map of these locations. (b) Principal component time series for the 1st mode EOFs corresponding to (a).

Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0109.1

What causes the fall in interannual sea level amplitude along the coast? As mentioned in the introduction, Pizarro et al. (2001) suggested that bottom friction can cause a decrease in sea level amplitude along the coast at ENSO time scales, but it does not explain the seaward fall in sea level amplitude seen in Fig. 10. Coastal alongshore wind stress can also be discounted, since Pizarro et al. (2001) showed that coastal alongshore wind stress and bottom friction have negligible influence on the interannual sea levels along the western coast of South America. Also, an analysis in section 2 of appendix A shows that the interannual sea level fall along the coast is much too steep to be explained by conservation of energy and the observed interannual shelf edge flows of Li and Clarke (2007) and mean flows of Chaigneau and Pizarro (2005b). Can the sharp fall in interannual shelf edge SSH and coastal sea level be explained by eddies as in the Australian case?

Fig. 10.
Fig. 10.

Spatial structure of the first mode EOF of the interannual SSH along (a) track 39 (97% of variance), (c) track 115 (97% of variance), (e) track 191 (93% of variance), and (g) track 13 (92% of variance), and their corresponding principal component time series (b) track 39, (d) track 115, (f) track 191, and (h) track 13.

Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0109.1

Eddies and small-scale flows do exist in this region. Using surface drifters, Chaigneau and Pizarro (2005a) found that eddies generated from the Chile–Peru Current propagate seaward with a speed of 6 cm s−1 north of 15°S and 3 cm s−1 south of 30°S. These eddies have a typical diameter of order 30 km, which is considerably smaller than the eddies off Australia. The smaller diameter, lower latitude, and faster propagation of these eddies made it much more difficult to calculate this variability from altimeter data, and in the South American case it was not possible to calculate the interannual eddy divergence well enough, even with along-track data. However, it is still possible to estimate from the shelf edge sea level gradient and using (8). To do this, we need to estimate .

Previous along-track altimeter estimates of have been given by Li and Clarke (2007) for the 11-yr period from January 1993 to December 2003. They showed that the coastal interannual flow is southward (northward) during an El Niño (La Niña) when the sea level is higher (lower) than normal at the coast and shelf edge. Li and Clarke based their analysis on separate EOF first mode structure functions of SSHs along tracks 39, 115, 191, and 13 (see Fig. 8). Figure 10 shows similar along-track analyses but for the much longer January 1993 through December 2010 record available to us. As found by Li and Clarke, the first EOF explains almost all of the variance, and the seaward drop in along-track interannual sea level along tracks 39, 115, and 191 implies that there is an interannual alongshore flow at the shelf edge (Fig. 10).

The method of calculating here was similar to that of the calculations along the southwestern coast of Australia in Section 3. Figure 10 shows the EOF spatial structure and principal component time series of the interannual SSHs along tracks 39, 115, 191, and 13. Along tracks 39, 115, and 191, the interannual sea level amplitude decreases from the coast and shelf edge for about 100 km and then flattens out. Note that the shelf is quite narrow where tracks 39 and 13 cross but much wider where track 191 crosses. The slopes of the interannual SSH along tracks 39, 115, and 191 were calculated using a least squares fit of the spatial function of the first mode EOF of the interannual SSHs along each track in their respective regions of decreasing SSH seaward of the coast and shelf. For each track, the sea level amplitude flattens at around 75–100 km from the shelf edge. Equation (17) was used with each of the along-track interannual sea level gradients to find . The resulting interannual along-shelf flow amplitudes at tracks 39, 115, and 191 were highly correlated with Niño-3.4 as shown in Table 4. The alongshore flow appears to be approximately 100 km wide from around 6° to 14°S. There also seems to be an opposing weak northward flow seaward of the coast at track 13.

Table 4.

Estimates of interannual alongshore flow amplitudes off South America for tracks 39, 115, 191, and 13 based on the first EOF of the interannual SSH for each track. Column 2 shows flow amplitudes for the whole record and column 2 when the large 97/98 El Niño is not included. Column 3 shows the correlation of the first principal component time series, and therefore υ′, with Niño-3.4 for the whole record and column 5 the corresponding results when the 97/98 El Niño is removed. A positive lag means that υ′ lags |Niño-3.4|.

Table 4.

The correlation of with shelf edge for the tracks 39, 115, and 191 (see Table 4) is very high [r = 0.99; rcrit (95%) = 0.49] in the main region of interannual sea level drop along the shelf edge off the western coast of South America. Note that track 13 was not used to calculate because begins to flatten there. The dissipation time scale from (8) was found to be 1.8 days, even shorter than calculated for southwestern Australia in section 4. The correlation and dissipation scale were also checked with the 1997/98 El Niño event removed from the data. The correlation was found to be r = 0.98 [rcrit(95%) = 0.46], and the dissipation time scale was 2.4 days.

6. Conclusions

Along the coast and shelf edge off Western Australia the interannual El Niño sea level amplitude decreases poleward. Our analysis showed that this fall in amplitude corresponds to a surprisingly short dissipation time scale of only a few days, much shorter than the El Niño interannual time scale. Using along-track altimeter data and theory, it was shown explicitly that this interannual dissipation was likely due to interannual variations in small scale, high-frequency eddy variability. These interannual changes in eddy variability are correlated with the large-scale shelf edge flow in the way one might expect. Specifically, during a La Niña when the western Australian coastal and shelf edge sea levels are higher than normal, the Leeuwin Current is anomalously strong, the loss of energy owing to eddies is greater than normal, and the shelf edge and coastal anomalous sea levels fall southward. Opposite conditions apply during El Niño; the coastal and shelf edge sea levels are lower than normal, the Leeuwin Current is anomalously weak, there is less loss of energy owing to eddies, and the sea level does not fall as rapidly southward, that is, the negative along-coast and along-shelf edge sea level anomaly dissipates.

Off South America, analysis showed that a similar fall in interannual sea level amplitude near the coast and shelf edge is associated with anomalous alongshore flow and a similar dissipation time scale of a few days. It is likely that the signal dissipation along this coast is also due to the interannual divergence of the eddy momentum flux, as energetic eddies have been documented off this coast. However, in this case an explicit eddy flux divergence calculation could not be done successfully even with the high-resolution along-track altimeter data. The eddies in this region are of smaller horizontal scale and nearer to the equator so, by geostrophy, the SSH signal is smaller and the eddy velocities not accurate enough to calculate interannual variations of the eddy flux divergence. Nevertheless, it is likely that the along-track satellite data analysis used to analyze the effect of eddies on the large scale flow is not limited to the Leeuwin Current example.

Acknowledgments

We gratefully acknowledge the support of the National Science Foundation (Grants OCE-0850749 and OCE-1155257) and the helpful comments of Dr. Ken Brink and two reviewers on the first draft of this manuscript.

APPENDIX A

Energy Conservation and Sea Level Fall along the Shelf Edge

a. Western Australian case

Observations show that the interannual sea level amplitude falls along the shelf edge and the interannual shelf edge flow increases (see Fig. 3 and accompanying discussion in the text). To see if the fall in interannual sea level amplitude (and potential energy) along the shelf edge can be explained by conservation of energy and increasing kinetic energy (through increasing amplitude), consider the y-momentum equation,
ea1
At the shelf-edge there is no flow into the boundary so , and at interannual and lower frequencies is negligible. Therefore (A1) simplifies to
ea2
which is equivalent to
ea3
As in the main text the alongshore low-frequency flow υ can be written as . Substituting this into (A3) gives
ea4
Since is small compared to , it may be dropped from (A4). Looking at the interannual anomalies only, (A4) becomes
ea5
It follows from (A5) that at a northern location is equal to at a southern location and so
ea6
The drop in interannual sea level along the western coast of Australia begins at around 22°S where . Hence the fall in interannual sea level is
ea7

Assuming an average alongshore mean flow of 50 cm s−1 and an interannual flow of 2 cm s−1, 0.1 cm. This drop in sea level is much smaller than the observed interannual sea level decay of 1.5 cm and therefore cannot account for the drop along the western Australian coast.

b. Western coast of South America case

For the South American case (see Table 4) and, from Chaigneau and Pizarro (2005b), . If denotes the anomalous change in along the coast, then according to (A3) we should have
ea8
where from Fig. 9 . Since has a maximum and a minimum of 0 m s−1,
eq1
We therefore conclude that energy conservation of the large-scale flow cannot explain the alongshore fall in interannual sea level.

APPENDIX B

Evaluation of the Level of Noise in the Data

As mentioned in section 2b of the main text, obtaining involves calculating gradients of noisy altimeter SSH. Even though we calculate geostrophic flows at each along-track altimeter grid point every 10 days using a physically appropriate 5-point least squares fit to get the gradient, and even though we only require the interannual signal so we can filter heavily in time, and even though we can average scores of along-track estimates to obtain averaged over the box in Fig. 5, it is not clear a priori that we can extract the signal from the noise. The statistically significant correlations reported in section 4b suggest that we can. We provide further supporting evidence here.

In situ current meter observations by Smith et al. (1991) show that the subinertial variable flow on the shelf is wind-driven and less energetic than that in the eddy field seaward of the shelf edge. The along-track root-mean-squared RMS amplitude of estimated interannual should not vary along the track if our estimates were dominated by noise because of measurement error, because we can expect this error to be similar all along the track provided that we are not too close (less than about 40 km) from the coast. But because of the strong eddy variability seaward of the shelf edge, if the signal can be seen in the data, RMS should increase seaward of the shelf edge.

Figure B1a shows a plot of RMS along track 101 (see also Fig. 5 and note the location of B (shelf edge) and C at end of section). RMS on the long section of track on the shelf, beginning at about 35 km from the coast to near the shelf edge is noisy but, as marked by the horizontal line on the plot, averaged about 150 cm2 s−2. Seaward of the shelf RMS is larger, averaging about 230 cm2 s−2, consistent with the above idea that we are seeing an eddy signal in RMS seaward of the shelf edge. According to Fig. B1a, the transition between shelf and slope variability is of order 30 km on either side of the shelf edge.

Fig. B1.
Fig. B1.

(a) RMS (cm2 s−2) along track 101 from near the coast to point C (see Fig. 5). The thin vertical line B corresponds to the approximate location of the shelf edge. The horizontal lines indicate the approximate average level of eddy variability on the shelf (≈150 cm2 s−2) and seaward of the shelf (≈230 cm2 s−2). (b) As in (a), but now along the southern track 177 with F marking the shelf edge and E the end of the segment of track (see Fig. 5). The horizontal lines mark the approximate level of eddy variability on the shelf more than 40 km from the shelf edge (≈150 cm2 s−2) and more than about 30 km seaward of the shelf edge (≈370 cm2 s−2).

Citation: Journal of Physical Oceanography 43, 6; 10.1175/JPO-D-12-0109.1

The interannual variability along the southern track 177, where the shelf edge is approximately 100 km from the coast at point F and ends at point E (see Figs. B1b and 5) is noisier. The track is shorter, but on the shelf and more than about 40 km from the shelf edge, RMS is about 150 cm2 s−2, similar to the shelf RMS seen on track 101. This is what we would expect if this were mostly noise. Seaward of the shelf edge by more than about 30 km, RMS is about 370 cm2 s−2 on average, again substantially more than that on the shelf, qualitatively consistent with our hypothesis that we can see the interannual eddy amplitude signal seaward of the shelf edge. However, Fig. B1b shows that there is enormous variability near the shelf edge, and our results are not as “clean” as those for the longer track 101. Note also that seaward of the shelf edge, average RMS for track 101 is about 370 cm2 s−2, considerably larger than the corresponding 230 cm2 s−2 for track 171. Therefore it is likely that seaward of the shelf edge there is a real difference in eddy amplitude between the tracks. This suggests that the calculation of , which essentially involves a subtraction of the means of these tracks, will contain some signal. This is consistent with the correlation result of section 4b of the main text.

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