Reconstruction of Agulhas ring vertical sections from SLA data
and ARGO profiles.
The reconstruction was possible for all 16 Agulhas rings with duration larger than 4 months
identified and tracked in the SLA data. At each time step, all ARGO profiles from 2 days before to 2
days after the SLA time when the eddy is identified and that are located less than 2.5º from an eddy
center are selected for the reconstruction. So, to each eddy corresponds a number of ARGO profiles,
between 11 and 83, that are located near the eddy center at different times. The distances between
the profile position and the eddy centers and the temperature (T) and salinity (S) anomalies are
calculated. If the time of the profile does not correspond to the exact SLA time, the eddy position is
linearly interpolated for estimation of the distance. The ARIVO climatology is linearly interpolated
to the profile position and subtracted from the T and S data to give the anomalies. So these
anomalies correspond to the deviation of the local mass field in relation to the mean state of the
years 2005 to 2008.
The way the anomalies are calculated can be influenced by the presence of Indian Ocean
waters in the climatology, carried into the South Atlantic by Agulhas rings. Such influence can
promote a bias in the resultant T and S anomalies. To estimate this influence, the South Atlantic
basin was divided in 5 regions (Figure S1): region A (20°S-40°S and 45°W-30°W), region B (20°S40°S and 30°W-15°W), region C (20°S-40°S and 15°W-0°), region D (20°S-40°S and 15°W-0°) and
region E (30°S-37°S and 0°-15°E). Considering the area of each region and the total period of four
years used in the climatology, a total value of 4.6x109 Km2day is obtained for the spatio-temporal
coverage of regions A, B, C and D, and a value of 1.6x109 Km2day is obtained for the region E.
From the diameter and the number of days that the eddies stayed in each of these regions, an
estimate impact from the Agulhas rings in the climatology can be calculated in terms of spatiotemporal coverage. The contributions of the Agulhas rings presence for the five regions are: 0.2x108
Km2day (A), 3.1x108 Km2day (B), 7x108 Km2day (C), 3.2x108 Km2day (D) and 2.5x108 Km2day
(E). The maximum relative impact in the area of the Agulhas rings formation (E) is of 5%, while
region C presented the maximum relative impact (15%) due to the longer period that the eddies
stayed in this region and the larger diameters. Since profiles from different periods of the eddy
lifetimes are taken to reconstruct the vertical sections, corresponding to different regions, the
contribution of Indian Ocean waters in the climatology is diluted in the final product. So the total
influence of the rings in the climatology should be between 5% and 15%. Based on this analysis the
impact of Indian Ocean waters transported by Agulhas rings in the climatology, although existent, is
considered as negligible in the present work. Other processes, such as direct leakage of Indian
Figure S1: Agulhas ring tracks. The region of propagation of the Agulhas rings was
divided in five subregions to estimate the impact of the rings in the climatology. The
numbers in the lower right corner of each subregion present the relative impact (%). The
black star represent the position of the reference profile used by Schmid et al. [2003],
and the black rectangle the position of the western ARGO profile used in the present
work.
Ocean waters or the contribution of cyclones and filaments are not considered here.
Another approach to obtain the anomalies is to consider a reference profile of “pure” South
Atlantic water, as in the work by Schmid et al. [2003]. However, the choice of such a reference
profile is a complicate task due to the large range of the geographical positions of the ARGO
profiles used for the eddy vertical structures reconstruction. Using as an example the position of the
reference profile taken by Schmid et al. [2003] (38°S, 001°W), the difference between the
climatological T and S values for this position and for the position of the western ARGO profile
used in the present work, with virtually no contribution from Agulhas leakage, is as large as 3.5°C
for T and 0.6 for S. These values are more than three times larger than the mean anomalies observed
in the ring centers. Thus, taking such a “pure” South Atlantic water profile as a reference would
introduce an artificial bias in our estimations simply because the climatology is variable along the
domain considered for eddy reconstruction.
The anomaly vertical profiles were subsampled in the vertical and projected into a zonal axis
with origin in the eddy center. Since the tracks of the Agulhas rings are almost zonal, this axis
corresponds to the eddy propagation direction. A symmetry in the meridional direction was
considered.
As these profiles represent different stages of the eddy structure, that suffer important
transformations during its life time as observed by Schouten et al. [2000] and others, they can not
be immediately combined to generate the eddy sections. The amplitude modification of the Agulhas
rings observed in the present study are described by Souza et al. [2011]. Although a decay in the
eddy amplitude with time was observed, the relation between the vertical mean T and the amplitude
is nearly linear (Figure S2). A linear normalization can be then applied to remove the temporal bias
from the T and S anomalies in the selected profiles (eq. 1). A similar normalization is applied to the
distances between the profile positions and the eddy centers (eq. 2).
T e , Se =
D e=
Dp
Φ
Φ
T p , Sp
A
A
(1)
(2)
where De and (Te, Se) are the equivalent distance and T and S anomalies; Dp and (Tp, Sp) are the
ARGO profile distance from the eddy center and its observed T and S anomalies; Φ and A are the
eddy instantaneous diameter and amplitude. The overline indicates the mean value along the eddy
life cycle.
Although the linear approximation is a first order estimation of the relation between the
eddy amplitude and the mean T anomaly, it is effective in reducing the noise associated to the
different times and locations of the profiles used in the vertical sections reconstruction. This choice
is based on its simplicity, not introducing artificial structures in the vertical profiles that can bias the
final results.
Figure S2. Relation between the vertical mean temperature anomaly (ºC)
and eddy amplitude (m) at the same dates for all the profiles selected for
the reconstruction of the vertical structures of the Agulhas rings identified
between January 2005 and December 2008. Only the profiles located
inside the eddy cores are shown.
After the normalization, the profiles were combined in a framework referenced to the eddy
center to produce the reconstructed vertical sections. It is important to emphasize that, since the
temporal variation of the T and S anomalies with time were removed by the normalization process,
the obtained vertical sections correspond to the mean structures of the Agulhas rings during their
lifetime.
For the construction of the eddy sections a 7th order one dimensional Lagrange polynomial
was fitted in the horizontal, at each depth level, to the T and S anomalies. Although the fitting
process smooths the observed gradients, it was necessary to extract the mean structure from the
noisy profile data. The first criteria to choose the polynomial order is that it should represent the
Gaussian shape expected for the ring geometry. The higher order polynomial applicable in all depth
levels of all observed rings was selected for a proper representation of deviations from this ideal
Gaussian shape. Although overshooting was observed near the boundaries of the 2.5° region around
the eddy centers where the ARGO profiles were obtained (limits of the reconstructed vertical
section), the area under influence of the ring was not affected.
The eddy velocities are calculated through the integration of the thermal-wind equations
using a reference level of 1500m. This levels corresponds to the depth limit of the ARGO data used
in the present study. In addition, although van Aken et al. [2003] observed Agulhas rings reaching
depths of ~5000m, a depth of no motion around 1000m is described by Garzoli et al. [1999]. The
comparison between the dynamical height, calculated using the same reference depth, and the SLA
interpolated to the profiles positions shows that the method is able to reproduce the eddy shapes.
Differences in the amplitude are due to the different time periods represented by the vertical section
(mean of the eddy lifetime) and the SLA data (mean of 7 days), the choice of reference depth and
the smoothing of the gradients by the fitting process.
It is important to emphasize that the vertical sections obtained from the reconstruction are
mean representations of the eddy structures along their lifetimes. These sections show variable
structures that will result in variable contributions to the volume and heat transports from the Indian
to the Atlantic Ocean and meridional heat flux along the eddy trajectories.
To calculate this meridional heat flux, the T anomalies were multiplied by the eddy
velocities in the reconstructed section. The result was divided by the mean eddy amplitude (on the
whole eddy life) and multiplied by the instantaneous amplitudes at each time the eddy was tracked.
This approach intents to reintroduce the time variability in the heat flux calculation, inverting the
normalization of the T and S profiles. Since the section is smoothed by the polynomial fitting
process, the resultant heat flux may be underestimated.
REFERENCES
Garzoli, S. L., P. L. Richardson, C. M. D. Rae, D. M. Fratantoni, G. Goni and A. J. Roubicek
(1999), Three Agulhas rings observed during the Benguela Current Experiment, J. Geophys. Res.,
104(C9), 20971-20985.
Schmid, C., O. Boebel, W. Zenk, J. R. E. Lutjeharms, S. L. Garzoli, P. L. Richardson and C. Barron
(2003), Early evolution of an Agulhas Ring. Deep-Sea Res. II, 50, 141-166.
Schouten, M. W., W. P. M. de Ruijter and P. J. van Leewen (2000), Translation, decay and splitting
of Agulhas rings in the southeastern Atlantic Ocean, J. Geophys. Res., 105(C9), 21913-21925.
Souza, J. M. A. C., C. de Boyer Montégut and P. Y. Le Traon (2011), Comparison between three
implementations of automatic identification algorithms for the quantification and characterization of
mesoscale eddies in the South Atlantic Ocean, Ocean Sci. Discuss., 8, 483-531.
van Aken, H. M., A. K. van Veldhoven, C. Veth, W. P. M. Ruijter, P. J. van Leewen, S. S. Drijfhout,
C. P. Whittle and M. Rouault (2003), Observations of a young Agulhas ring, Astrid, during MARE
in March 2000, Deep-Sea Res. II, 50, 167-195.