The Agulhas Current Time-series Experiment mooring array (ACT) measured transport of the
Agulhas Current at 34

The Agulhas Current system is the strongest western boundary current
in the Southern Hemisphere and transports warm tropical water southward
along the east coast of South Africa

To understand the complicated dynamics of the Agulhas Current requires
an integrated approach using numerical ocean models, satellite remote
sensing measurements, and in situ observations. Previous studies
have suggested that measuring the dynamics of the Agulhas Current
in the northern region is easier due to its stable trajectory and
its confinement to the continental slope

There is a trade-off between spatial and temporal sampling. In situ mooring observations provide high temporal observations of
the Agulhas Current throughout the water column but are spatially
coarse. In contrast, satellite observations can provide high spatial
resolution data of the surface ocean but lacks detailed information
below the surface. Hence, numerical models are needed to provide a
temporally coherent, high-resolution representation of the ocean throughout
the water column. Numerous studies aiming to monitor long-term changes
in global current systems have adopted methods to combine various
sampling tools (

This modelling study recreates the Agulhas transport proxy developed
by

The Hybrid Coordinate Ocean Model (HYCOM) is a primitive equation
ocean model that was developed from the Miami Isopycnic Coordinate
Ocean Model (MICOM)

This study used output from a one-way nested

AGULHAS was initialized from a balanced field of the parent model
interpolated to the high-resolution grid and ran from 1980 to 2014
using interannual forcing from ERA40

The ACT was established to obtain a multi-decadal proxy of Agulhas Current
transport using satellite altimeter data. The first phase of the experiment
was the in situ phase where the ACT mooring array was deployed in the
Agulhas Current, near 34

Geographical location of the ACT array with the mooring (red crosses) and CPIES (magenta circles) stations relative to the T/P, Jason-1,2,3 satellite track #96 (black line). Colour shading illustrates bathymetry (metres) obtained from GEBCO (General Bathymetric Chart of the Oceans).

Previous analyses have shown that the vertical structure of the Agulhas
Current is barotropic

Time mean cross section of the
velocity structure of the Agulhas Current across the ACT array (m s

The transport proxy created by

In order to recreate the Agulhas Current proxy in HYCOM, data corresponding to the measurements collected from the ACT mooring array were extracted from the model. To build the regression models, the transport per unit distance and sea surface slope for each of the nine mooring locations were calculated using the model data (hereafter CPIES pairs P3–P4 and P4–P5 were included as mooring positions 8 and 9).

The barotropic velocity – equivalent to an integral of the velocity
with depth – from each mooring location (A–G) and CPIES pairs P3–P4
and P4–P5

In order to reproduce the “along-track”
SSH altimeter data needed to create the proxy as in

Nine linear regression models were developed to estimate the transport per unit distance (Tx and Txsw) from the HYCOM sea surface slope during the same 3-year period over which the ACT proxy was developed (April 2010–February 2013). The 3-year time period is hitherto referred to as the reference period.

To calculate the total transport across the ACT array required continuous
Tx estimates across the current. This was achieved as in

HYCOM transport per unit distance proxy (m

Assuming that the 3-year linear relationship between SSH slope
and transport per unit distance (Tx and Txsw) from
2010–2013 remains constant, the regression models were applied to
the entire 34-year SSH model data. Thereafter, the 34-year transports
were calculated by applying the same methods that were used to calculate
the 3-year transport time series; firstly, obtaining Tx and
Txsw estimates at 1 km intervals along the array and secondly
integrating horizontally to obtain

The simulated model transports were calculated using the full-depth
velocity fields across the array. If the relationship between SSH
slope and transport is strong, there would be good agreement between
the proxy and the actual model transports. To quantify this, correlations
and transport statistics for the model and proxy were calculated from
the two time series (Table

Eddy kinetic energy (EKE) was calculated to show the surface variability
of the current coincident with averaged SSH contours used to represent
the mean surface structure (Fig.

Transport variability in HYCOM was analysed by investigating the current
structure during the residual transport events in the least- and best-performing regression models. Residual transport events were identified
as the outlying residual transport values above and below 2 standard
deviations of the estimated transport.

where

To investigate the current structure during these residual events,
composite averages of the cross-track velocity structure were analysed.
The cross-track velocity at each depth layer in HYCOM was extracted
at 12 km intervals from 0 to 400 km offshore for the 34-year model
period. Although the ACT array only reached 300 km offshore, analysis
of the current structure in HYCOM was extended further offshore. Previous
analyses have shown increased levels of offshore variability in this
HYCOM simulation

Sensitivity experiments were performed in HYCOM to test how many years of mooring data is needed to create an accurate proxy of Agulhas Current transport. With 34 years of model data the linear relationship could be tested over much longer or shorter periods.

Using the method described in Sect. 2.4.3, the proxy regression
models were built using 1, 6, 12, 18, and 34 years of HYCOM data. In
addition, the proxies were calculated over two arbitrary 3-year periods
to test the sensitivity of the proxy to current dynamics over different
years. Lastly, the regression models were calculated over the maximum
and minimum annual transport years in HYCOM, as well as during the
years the HYCOM transport standard deviation was the largest and the
smallest. Table

Sensitivity experiment time periods.

The coefficients of determination (

Two transport types, the box transport (

The 34-year mean transport and standard deviation from HYCOM for

The

This 34-year annual correlations between the box (black) and jet (blue) transport proxies against the box and jet transports extracted from HYCOM.

Eddy kinetic energy (EKE in m

The jet transport proxy by

The strengths and weaknesses of the box proxy are further investigated
by selecting the highest and lowest correlated years from the 34-year
annual correlations (Fig.

During the year with maximum correlation (1988) the current is stable
and inshore, whereas during the lowest correlated year (1994) and
during the proxy reference period (2010–2013) the current is meandering
and it appears that a large portion of the energy of the current has
been shifted offshore (Fig.

The model cross-track velocity changes direction with depth, specifically
for offshore mooring G and CPIES pairs P3P4 and P4P5 at the depth
of

Mean cross-track velocity profiles
(m s

As shown previously, the performance of the linear regression models
weakened moving offshore (Fig.

As shown in RM 1 (Fig.

Linear regression models
showing the relationship between HYCOM SSH and transport per unit
distance (Tx) for (

Mean SSH (metres, m) and composite
cross-track velocity structure (metres per second, m s

It was expected that removing the outlying transport events (outliers
larger than

Examination of the composite cross-track velocity structure of the
residual transport events (Fig.

The 34-year Agulhas transport proxy under analysis thus far was based
on regression models built using only 3 years of HYCOM model data.
The statistics in Table

The sensitivity of the box transport proxy was also tested using two
arbitrary 3-year periods. In comparison to the correlation obtained
during 2010–2013 the correlation decreased by 0.02 during 1980–1982
and remained the same during 2000–2002. The results obtained from
calculating the

Transport statistics and correlation results obtained from calculating the box transport proxy over a range of time periods.

The Agulhas Current transport proxies, developed by

The HYCOM transport proxies were developed using nine 3-year linear regression models between model transport and model SSH slope, and extended using 34 years of the model SSH data from 1980 to 2014. The HYCOM model provided the means to investigate the validity of the assumptions used to create the proxies, such as the constant vertical structure of the current, hence a constant relationship between SSH slope and transport per unit distance during the 3-year reference period and secondly the temporal scale of observations needed to obtain a strong linear relationship between transport and SSH slope.

Overall, results showed that the proxy was more capable of estimating
the box transport (net transport) over the 34-year model period, explaining
52 % of the transport variance in comparison to 26 % of the jet transport
(southwest transport) variance. A limitation of this study is that
HYCOM was unable to resolve all of the observed dynamics in the Agulhas
Current, specifically the mesoscale meander events. The model demonstrated
much higher levels of mesoscale variability than observed

Furthermore, although the resolution of HYCOM is able to capture the
mesoscale dynamics of eddies

The frequently impinging eddies have been found to make it difficult
to effectively estimate the accurate box transport of the Agulhas
Current in the model since the advection of these eddies is responsible
for large transport fluctuations

It was shown that removing the residual transport events, violating
the proportional relationship between SSH slope and transport as a
result of impinging baroclinic eddies, improved the proxy performance,
i.e. increased the percentage of transport variance explained. Several
studies have suggested methods to decrease the levels of EKE in numerical
simulations.

The development of the ACT transport proxy was initially tested using
a regional Nucleus for European Modelling of the Ocean (NEMO) configuration in order to evaluate the potential of
the altimeter proxy to monitor the multi-decadal transport of the
Agulhas Current

The HYCOM output in this study was used to test the sensitivity of
the relationship between transport and SSH slope over a range of time
periods. It was hypothesized that building the linear relationship
over longer time periods,

Lastly, the study showed that the transport proxy is sensitive to subsurface variability in the model, hence caution should be taken regarding the implicit assumption of a fixed vertical current structure. The accuracy of the transport proxy remains sensitive to model bias. Hence the sensitivity of the proxy should be tested in other model simulations. Sensitivity studies of this kind, using numerical ocean models, provide useful information advancing our understanding of the sensitivities and limitations of transport proxies, contributing to the improvement of long-term ocean monitoring approaches and assisting in the development and planning of future measurement programmes.

Data sets are available upon request by contacting the corresponding author.

EV conducted the data analyses and wrote up the final paper. BB provided the HYCOM model data, supervised the project, and provided financial support. JH supervised the project and provided financial support and SE assisted with the methodology of the transport proxy. All authors conceptualized ideas and contributed to writing the paper.

The authors declare that they have no conflict of interest.

This work has been funded by the National Research Foundation of South Africa and by the bilateral South Africa–Norway SANCOOP SCAMPI project. We would like to thank the Nansen-Tutu Centre in South Africa and SAEON (South African Environmental Observation Network for providing opportunities to present the project locally and internationally. We thank the Nansen Environmental and Remote Sensing Center (NERSC) in Bergen, Norway, for hosting us for a duration of the project and we wish to thank Knut-Arild Lisæter for his guidance while working at NERSC. This work also received a grant for computer time from the Norwegian Program for supercomputing (NOTUR project number nn2993k). We gratefully acknowledge Lisa Beal, Shane Elipot, and the rest of the ASCA (Agulhas System Climate Array) team from the Rosenstiel School of Marine and Atmospheric Science (RSMAS), University of Miami, for granting us permission to replicate the Agulhas transport proxy methods. Shane Elipot was supported by the U.S. National Science Foundation through the ASCA project, Award OCE-1459543.

This paper was edited by Matthew Hecht and reviewed by three anonymous referees.