The Agulhas Current Time-series Experiment mooring array (ACT) measured transport of the
Agulhas Current at 34∘ S for a period of 3 years. Using along-track
satellite altimetry data directly above the array, a proxy of Agulhas Current
transport was developed based on the relationship between cross-current sea
surface height (SSH) gradients and the measured transports. In this study,
the robustness of the proxy is tested within a numerical modelling framework
using a 34-year-long regional hindcast simulation from the Hybrid Coordinate
Ocean Model (HYCOM). The model specifically tested the sensitivity of the
transport proxy to (1) changes in the vertical structure of the current and
to (2) different sampling periods used to calculate the proxy. Two reference
proxies were created using HYCOM data from 2010 to 2013 by extracting model
data at the mooring positions and along the satellite altimeter track for
the box (net) transport and the jet (southwestward) transport. Sensitivity
tests were performed where the proxy was recalculated from HYCOM for (1) a
period where the modelled vertical stratification was different compared to
the reference proxy and (2) different lengths of time periods: 1, 3, 6, 12, 18, and 34 years. Compared to the simulated (native) transports, it was found
that the HYCOM proxy was more capable of estimating the box transport of the
Agulhas Current compared to the jet transport. This was because the model is unable to resolve the dynamics associated with meander events, for which the jet transport algorithm was developed. The HYCOM configuration in this study
contained exaggerated levels of offshore variability in the form of
frequently impinging baroclinic anticyclonic eddies. These eddies
consequently broke down the linear relationship between SSH slope and
vertically integrated transport. Lastly, results showed that calculating the
proxy over shorter or longer time periods in the model did not significantly
impact the skill of the Agulhas transport proxy. Modelling studies of this
kind provide useful information towards advancing our understanding of the
sensitivities and limitations of transport proxies that are needed to improve
long-term ocean monitoring approaches.
Introduction
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 . The
Agulhas Current, in the northern region, is known for its narrow,
fast flow conditions following the steep continental slope .
As the current continues southwestward it becomes increasingly unstable
over the widening continental shelf until it eventually retroflects,
forming an anticyclonic loop south of Africa and returning to the
Indian Ocean as the eastward Agulhas return current .
The anticyclonic loop, known as the Agulhas retroflection, contains
some of the highest levels of mesoscale variability in the global
ocean in the form of Agulhas rings, eddies and
filaments. These contribute heat, salt and energy into the Benguela
upwelling system, the Atlantic Ocean and the global overturning circulation
system , impacting the Atlantic
Meridional Overturning Circulation (AMOC) .
In the regional context, the Agulhas Current has a major influence
on the local weather systems, due to large latent and sensible heat
fluxes, which contributes to rainfall and storm events over the adjacent
land . The unique circulation
of the Agulhas Current system, in the context of regional and global
climate variability, makes it an important field of research.
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 .
However, the close proximity of the current to the coast has made
it difficult to monitor using satellite altimetry .
Newer altimetry products dedicated to coastal areas are promising
but are yet to be validated within the Agulhas Current region .
In addition, the frequent disturbances of the current in the form
of solitary meanders, also known as the Natal Pulse, and its interactions
with mesoscale features originating upstream and from the east
remain poorly resolved in many numerical ocean models ,
highlighting the challenges involved in monitoring and modelling the
dynamics in this region.
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 (),
including the recent development of the Agulhas transport proxy established
to monitor the interannual variability and long-term trends in Agulhas
Current transport .
have shown that a strong relationship exists between
surface geostrophic velocity and full-depth transport such that sea
level anomalies can be used to study the variability and dynamics
of the Agulhas Current system as has been demonstrated before (;
etc.). The 22-year transport proxy created by
assumed a fixed linear relationship between in situ transport
and sea surface slope based on in situ measurements over
the 3-year sampling period of the Agulhas Current Time-series Experiment
(ACT) . Analyses of the Agulhas
Current transport proxy time series concluded that the Agulhas Current
has not intensified over the last 2 decades in response to intensified
global winds under anthropogenic climate change ,
but instead has broadened as a result of increased eddy activity
in agreement with . This could essentially decrease
poleward heat transport and increase mixing over the continental shelf,
thereby increasing cross-frontal exchange of nutrients and pollutants
between the coastal ocean and the deep ocean .
This modelling study recreates the Agulhas transport proxy developed
by , within a regional HYCOM simulation of the greater
Agulhas Current system, aiming to test the sensitivity of using 3 years of in situ mooring data to develop a transport proxy
as well as the sensitivity of the proxy to changes in the vertical
structure of the Agulhas Current. The paper is structured as follows.
Section 2 describes the data and methods; it should be noted that
this section forms a key part of the paper as the methods of recreating
the proxy are an integral component of the study. Section 3 presents
the results from the HYCOM transport proxy and lastly Sect. 4 presents
the summary and conclusions.
Data and methodsThe Hybrid Coordinate Ocean Model
The Hybrid Coordinate Ocean Model (HYCOM) is a primitive equation
ocean model that was developed from the Miami Isopycnic Coordinate
Ocean Model (MICOM) . HYCOM combines the optimal
features of isopycnic coordinates and fixed-grid ocean circulation
models into one framework and uses the hybrid layers
to change the vertical coordinates depending on the stratification
of the water column. The model makes a dynamically smooth transition
between the vertical coordinate types via the continuity equation
using the hybrid coordinate generator . Well-mixed
surface layers use z-level coordinates, ρ coordinates are utilized
between the surface and bottom layers in a well-stratified ocean,
and the bottom layers apply σ coordinates following bottom
topography. Adjusting the vertical spacing between the hybrid coordinate
layers in HYCOM simplifies the numerical implementation of several
physical processes without affecting the efficient vertical resolution,
and thus combines the advantages of the different coordinate types
in optimally simulating coastal and open-ocean circulation features
.
This study used output from a one-way nested 1/10∘ model of the
greater Agulhas Current system (AGULHAS)
. The regional nested model,
AGULHAS, received boundary conditions from the basin-scale model of the
Indian Ocean and Southern Ocean (INDIA) every 6 h. The
boundary conditions were relaxed towards the outer model over a 20 grid cell
sponge layer. The nested model covered the region from the Mozambique Channel
to the Agulhas retroflection region and the Agulhas return
current, geographically extending from approximately 0 to 60∘ E
and from 10 to 50∘ S, with a horizontal resolution of ∼10 km
that adequately resolved mesoscale dynamics to the order of the first
baroclinic Rossby radius estimated to be about 30 km .
AGULHAS has 30 hybrid layers and targeted densities ranging from 23.6 to
27.6 kg m-3.
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 and ERA-Interim
. Version 2.2 of the HYCOM source code has been used
in this model and, together with the second-order advection scheme,
provides an adequate representation of the Agulhas Current .
However, limitations of the free-running model include high levels
of sea surface height (SSH) variability south of Madagascar and offshore of the Agulhas
Current, suggesting that eddy trajectories may be too regular in the
model . The data available for this study were
a weekly output of the regional HYCOM simulation of the Agulhas region
from 1980 to 2014.
The Agulhas Current Time-series Experiment
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∘ S, for a period of 3 years from 2010 to
2013 (Fig. ). From the data collected,
provided two volume transport estimates: (1) a box or
boundary layer transport (Tbox) and (2) a western boundary jet
transport (Tjet). Tbox is the net transport within a
fixed distance from the coast, while Tjet is a stream-dependent
transport that is calculated by changing the boundaries of integration at
each time step depending on the strength and cross-sectional area of the
southwestward jet. The western boundary jet transport algorithm was developed
to specifically exclude the northeastward transport during meander events,
occurring inshore of the meander . During the second phase of
the ACT, built a 22-year transport proxy by regressing the
3 years of in situ transport measurements (obtained from phase 1 against
along-track satellite altimeter data spanning the years 1993–2015.
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).
Development of the Agulhas transport proxy
Previous analyses have shown that the vertical structure of the Agulhas
Current is barotropic , implying that the relationship
between surface geostrophic velocity and full depth transport should
be strong, despite the presence of the Agulhas Undercurrent
(Fig. ). Access to the data from
the ACT allowed us to validate the velocity cross section
in HYCOM (Fig. ).
defined the Agulhas Current to be 219 km wide and 3000 m deep on average,
as is reflected in the vertical section of the in situ ACT
observations (Fig. a). In HYCOM
the current is wider, weaker, and further offshore than the observed
current, on average the current is 254 km wide and extends deeper
down to ∼3500 m, particularly inshore with a less pronounced
undercurrent (Fig. b).
Time mean cross section of the
velocity structure of the Agulhas Current across the ACT array (m s-1)
during the in situ ACT period (2010–2013) from (a) the ACT
observations and (b) the HYCOM. Blue shading represents
the negative, southwest current flow and pink shading represents
the positive, northeast current flow. Contours are every 0.2 m s-1.
Dashed green vertical lines represent the nine locations of the mooring
and CPIES pairs, the first line representing mooring A and CPIES pair
P4P5 furthest offshore.
The transport proxy created by was initially developed
by finding a linear relationship between transport and sea surface
slope across the entire length of the ACT array, a common method used
in previous studies .
However, this method led to uncertainty in the linear regression
due to the strong, co-varying sea surface height across the current.
The preferred method was therefore to build nine individual linear
regression models, one for each mooring position and CPIES pairs along
the ACT array, which locally related transport to sea surface slope
. It is important to note that the regression models
assumed a constant, linear relationship between sea surface slope
and transport over the 3-year in situ period. The transport
variable in the regression models was defined as transport per unit
distance, i.e. the vertically integrated velocity with units in square metre per second (m2 s-1), where Tx represents the net component of the current flow and Txsw the southwestward component of the flow. The total
transports, Tbox and Tjet in cubic metre per second (m3 s-1), were calculated by integrating the Tx
and Txsw estimates, predicted from the regression models,
to the respective current boundaries.
Recreating the Agulhas transport proxy in HYCOM
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).
Model transport
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 was extracted for the 34-year model period.
Extracting the barotropic velocity component from each mooring avoided
interpolation errors that may have occurred if the model velocity
was interpolated onto the locations of each current-meter instrument
on each mooring (e.g. ). Transport per
unit distance (Tx) for each mooring was calculated by multiplying
the cross-track barotropic velocity by the respective depth at each
mooring location. The same method was employed to calculate the southwestward
transport component (Txsw) excluding the northeast cross-track
barotropic velocity values in the calculation.
Model SSH
In order to reproduce the “along-track”
SSH altimeter data needed to create the proxy as in ,
34 years of HYCOM SSH data was linearly interpolated onto the coordinates
of the TOPEX/Jason satellite track number 96 overlapping the model
ACT array. The coordinates of the along-track altimeter data were
obtained from the filtered 12 km Jason-2 Aviso satellite product.
To obtain the sea surface slope for each regression model, an optimal
pair of SSH data points was chosen such that the horizontal length
scale between them allowed for a maximum correlation between sea surface
slope and Tx. The length scales of the slopes ranged from
24 km at mooring A to 12 km at mooring G, and 48 km for the offshore
CPIES pairs, indicating an increase in the spatial scale of offshore
flow, possibly due to increased offshore variability. Results from
the in situ proxy experiment by also showed
an increasing length scale with increasing distance offshore; however,
the results varied in magnitude: 27 km at mooring B to 102 km at mooring
G. In this study the SSH slope was calculated such that a negative
SSH slope corresponds to a negative surface velocity (southwestward) according to geostrophy, whereas a positive slope would indicate positive northeastward
flow.
Building the regression models
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
by fitting a piecewise cubic Hermite interpolating
polynomial function to obtain transport estimates at 1 km intervals
from the coast to the end of the array (Fig. ).
Fitting the transport function to the coast and equating it to zero
would be equivalent to implementing a no-slip boundary condition in
the model. Before calculating the total transport the current boundaries
needed to be defined. The box transport (Tbox)
was calculated by integrating Tx horizontally to 230 km offshore,
the 3-year mean width of the current in HYCOM. The jet transport
(Tjet) was calculated using the algorithm
developed by by integrating Txsw, the southwestward
transport component, to the first maximum of Tx beyond the
half-width of the current (115 km in HYCOM) at each time step (Fig. ).
HYCOM transport per unit distance proxy (m2 s-1) for Tx (blue) and Txsw (red) at 1 km intervals at the first
model time step (solid lines) and for the ACT reference period (2010–2013,
dashed lines). The dashed grey lines represent the positions of moorings
and offshore CPIES pairs.
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 Tbox
and Tjet.
Comparison of the transport proxy to actual model transports
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 ).
These provided insight into which processes the proxy may have failed
to capture, which were then further investigated in HYCOM. Statistics
are deemed significant at the 95 % significance level.
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. ). EKE was
calculated over the 3-year mean reference period, and over the highest
and lowest correlated years. In order to evaluate the subsurface current
structure along the ACT array, vertical velocity profiles were analysed
for each mooring and CPIES pair over the 3-year mean reference period
as well as over the highest and lowest correlated years.
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.
e=Txi-Txi‾,
where e is the estimated residuals, Txi is the HYCOM transport
per unit distance value and Txi‾ is the estimated transport
per unit distance value according to the linear regression models
(i.e. the transport proxy).
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 ,
which therefore made it interesting to study the subsurface structure
during the offshore current meanders and the influence these could
have on the transport proxy. To further investigate the effect of
the residual transport values on the transport proxy, all corresponding
transport events exceeding plus or minus 2 standard deviations were
removed from each linear regression model during development of the
proxy (Fig. ).
R2 statistics
from the linear regression models showing the relationship between
HYCOM SSH slope and HYCOM transport per unit distance for each mooring
(A–G) and CPIES pair (P3P4 and P4P5) over the 3-year reference period
(2010–2013). Tx is represented by the solid blue line and Txsw by the solid red line. The dashed blue line represents
the results of Tx after the removal of the residual transport
events (see Sect. 3.4). Sites A to CPIES pair P4P5 are shown by the
faint green lines.
Sensitivity tests
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 shows the time
range over which the sensitivity experiments were performed.
Sensitivity experiment time periods.
Time range (years)Model dates1January 2011–December 20113April 2010–February 20136January 2009–December 201412January 2003–December 201418January 1997–December 201434January 1980–December 20143*January 1980–December 1982;January 2000–December 2002Max (min)2003 (1982)HYCOM transportMax (min)2013 (1980)HYCOM transport SD
*Corresponds to the two additional 3-year periods.
ResultsHYCOM linear regression models
The coefficients of determination (R2) from the
regression models highlight how well the linear relationship predicts
the transport in HYCOM (Fig. ).
R2 ranged from 0.86 at mooring A (30 km offshore)
to 0.49 at the last CPIES pair P4P5 (275 km offshore) for Tx
and 0.86 at mooring A to 0.37 at P4P5 for Txsw (P values <10-3). Results from showed
an increase in the R2 statistics in the regression
models ranging from 0.51 at mooring A and 0.81 for CPIES pair P4P5
for Tx, indicating that the in situ observation-based regression models had poorer skill inshore, whereas in HYCOM
the regression models have poorer skill offshore. The results from
the Txsw regression models in HYCOM showed similar results
to for the inshore mooring locations (A, B, C, E)
with slightly higher correlations for offshore moorings F, G, and CPIES pair
P3P4 but a lower correlation for D and the furthest CPIES pair P4P5.
Proxy validation
Two transport types, the box transport (Tbox)
and the jet transport (Tjet), were
extracted from HYCOM in order to validate the relative proxies. The
Tbox (Tjet)
proxy explained 57 % (14 %) of transport variance during the 3-year
reference period (2010–2013) (Table b).
Using 34 years of model data (1980–2014), assuming the fixed 3-year
relationship between SSH slope and transport, Tbox
(Tjet) explained 52 %
(26 %) of the transport variance (Table b).
Results from also showed that Tbox
explained a higher percentage of variance (61 %) during the ACT period
than the jet transport proxy (Tjet: 55 %).
(a) Summary of the transport
statistics of the ACT observations over the 3-year in situ
period and the HYCOM model transports and HYCOM proxy transports over
the 3-year and extended 34-year time periods. Negative values denote
transport in the southwest direction. 1 Sv =106 m3 s-1 (sverdrup).
(b) Correlations between the HYCOM model transport and HYCOM proxy
transport for the box transport and jet transport with the percentage
of variance shown in brackets. All correlations were significant.
The 34-year mean transport and standard deviation from HYCOM for Tbox
and Tjet were -84±47 Sv and -110±38 Sv, respectively (Table a).
The proxy Tbox and Tjet were
-87±34 Sv and -92±31 Sv, respectively (Table a).
According to the ACT observations, the mean transport and standard
deviation were -77±32 Sv for Tbox
and -84±24 Sv for Tjet.
A higher jet transport was expected considering it excludes northeast
counterflows that decrease the box transport . The
differences between the standard deviations of HYCOM and the proxy
indicate that transport in HYCOM experiences more variability compared
to the proxy. The proxies only capture a portion of the transport
estimate from HYCOM, suggesting it also only captures a portion of
the model variability. The positive minimum transport values for Tbox during
both time periods also appear to be peculiar, suggesting a current
reversal during those events (Table a).
The Tjet annual correlation varies
greatly from year to year with a significant maximum correlation of
0.82 (2014) and a minimum correlation of 0.00 (2003) (Fig. ).
In contrast, the correlations for Tbox
vary much less and are always significant with a maximum correlation
of 0.88 (1988) and minimum correlation of 0.50 (1994) (Fig. ).
The box transport has higher correlations for most of the 34-year
time period except during two single years where the jet transport
has a higher correlation, 0.78 versus 0.70 during 1991 and 0.54 versus
0.50 during 1994. These results indicate that the proxy is generally
better suited in HYCOM to estimate the box transport rather than the
jet transport.
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 m2 s-2)
and sea surface height (SSH in metres) contours during (a) the reference
period (2010–2013) (b) the highest (1988), and (c) lowest (1994) correlated
years. The black line representing the ACT array.
The jet transport proxy by was developed to estimate
the transport of the Agulhas Current during mesoscale meander events,
which generally causes the current to manifest as a full-depth, surface
intensified, cyclonic circulation out to 150 km from the coast with
anticyclonic circulation farther offshore . The
Agulhas meanders in the HYCOM simulation occur in association with
large anticyclonic eddies predominantly located at the offshore edge
of the current, with a narrow, southwest stream close to the coast
. In some instances anticyclonic eddies span
the length of the entire array. Therefore, considering that the model
is unable to resolve the dynamics associated with meander events,
for which the jet transport algorithm was specifically developed,
further analysis only focuses on the box transport proxy.
Evaluating the box transport proxy
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. ), and evaluated
by plotting the current structure in the model over the respective
years (Figs. and ).
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 narrow
spacing of the SSH contours for all three periods indicates a strong
gradient inshore and hence a strong mean geostrophic current; however,
the wide spacing between the SSH contours offshore suggests that the
variability in the model is confined to the offshore side of the current.
It is assumed that high levels of mesoscale variability in the model
could bias the current position and hence the transport estimate.
However, based on the analysis there were approximately five anticyclonic eddies
during the highest correlated year (1988) and approximately seven anticyclonic
eddies during the lowest correlated year (1994) which does not explain
the difference in the accuracy of the proxy for those years.
The model cross-track velocity changes direction with depth, specifically
for offshore mooring G and CPIES pairs P3P4 and P4P5 at the depth
of ∼2000 m (Fig. ), thereby
defining the depth of the Agulhas jet. During the 3-year reference
period the velocity changes direction at moorings B and G (∼1200 and ∼2000 m, respectively) and at sites P3P4 (∼2000 m)
and P4P5 (∼300, ∼2000 m). During 1988, sites F–P4P5
experience a change in direction (≳2000 m). Lastly, during
1994 mooring G and sites P3P4 and P4P5 exhibited a change in direction
(≳2000 m). An explanation for the offshore subsurface countercurrents
may be due to the impinging baroclinic eddies continuously propagating
downstream , affecting the entire water column
by changing the direction of flow at certain depths. This directly
impacts the accuracy of the proxy and explains why the transport proxy
fails to capture current reversals (Table ),
because the SSH slope does not capture the subsurface countercurrents
associated with the impinging baroclinic eddies.
Mean cross-track velocity profiles
(m s-1) during (a) the 3-year reference period (2010–2013), (b) during the highest correlated year (1988),
and (c) the lowest correlated year (1994). Each colour represents
the different moorings (A–G) and CPIES pairs (P3P4 and P4P5). Negative
values indicate southwestward flow.
Investigating the transport variability
As shown previously, the performance of the linear regression models
weakened moving offshore (Fig. ).
Regression model RM8 (CPIES pair P3P4, Fig. a)
captured the least transport variance at 46 % and RM 1 (mooring A,
Fig. b) explained the
most transport variance at 86 %. According to our methods, a negative
SSH slope in HYCOM corresponds to a negative (southwestward) surface velocity; and if the current structure were barotropic, a negative (southwestward)
transport and vice versa.
As shown in RM 1 (Fig. b),
all the data points are clustered such that the negative SSH slope
relates to a negative Tx value, in the absence of northeast
counterflows. Careful analyses of RM 8 indicates that eight of the
nine residual transport events violate the proportional relationship
between SSH slope and Tx (Fig. a).
Some of which have a negative SSH slope relating to a positive Tx
value where others show a positive SSH slope with negative Tx
value. Therefore the SSH slope does not always reflect the direction
of flow at depth, and thus the correct sign for Tx.
Linear regression models
showing the relationship between HYCOM SSH and transport per unit
distance (Tx) for (a) RM 8, capturing the least transport
variance (46 %), and (b) RM 1, capturing the most transport variance
(86 %). Txi (blue crosses) represent the Tx values from
HYCOM and Txi‾ (red line) represents the Tx estimates
from the linear regression model. The bold crosses highlight the residual
transport events with transport values greater or less than 2 standard
deviations of the transport estimate. The coefficient of determination
(R2) quantifies the amount of variance
explained by the regression model; β0 is the slope coefficient
and β1 the intercept with 95 % confidence intervals. Note
the different scaling on the x and y axes.
Mean SSH (metres, m) and composite
cross-track velocity structure (metres per second, m s-1) of the residual transport
events from RM 8 (a, b) and RM 1 (c, d). Blue shading represents the negative, southwest current flow and red represents the positive,
northeast current flow. Contours are every 0.2 m s-1. Dashed
vertical lines represents the nine locations of the mooring and CPIES pairs,
the first line representing mooring A and CPIES pair P4P5 furthest
offshore.
It was expected that removing the outlying transport events (outliers
larger than ±2 standard deviations) would increase the statistical
performance of the linear regression models (Fig. ).
However, it is noteworthy that the improvement was remarkably better
for the offshore regression models since the baroclinic eddies responsible
for breaking down the linear relationship between SSH slope and transport
frequently effected the offshore edge of the current.
Examination of the composite cross-track velocity structure of the
residual transport events (Fig. )
shows that there is a change in the direction of velocity in the bottom
layers at the location of RM 8 (CPIES pair P3P4). The cross-track
flow in the surface layers (∼0–700 m) of the current is southwestward,
whereas below ∼700 m the flow is northeastward. Therefore, the
vertically integrated flow (Tx) is positive (northeastward)
and in the opposite direction implied by the SSH slope. In contrast,
at mooring A (RM 1), the composite velocity field is always southwestward,
consistent with the SSH slope.
Sensitivity tests
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 show
the results obtained from building the linear regression models and
deriving the transport proxy using 1, 3, 6, 12, 18, and 34 years of
model data. We find that the correlation between proxy box transport
and model box transport is not improved by using more years of model
data to build the proxy. Using data from 2010 to 2013 the correlation
of 0.72 changes by no more than 0.01 when extending the number of
years of model data (Table ).
Similarly, building the proxy with 1 year of model data decreases
the correlation by only 0.01 (Table ).
The only difference was the decrease in standard deviation.
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 Tbox proxy during
the maximum (minimum) transport and standard deviation years in HYCOM
showed no improvement or decrease in the skill of the proxy either.
Transport statistics and correlation
results obtained from calculating the box transport proxy over a range
of time periods.
Net transportTransport (Sv)SD (Sv)RMSE (Sv)rMODEL-84.3247.2301.001-year-87.2635.4733.360.713-year-87.2134.0932.760.726-year-87.0435.9133.040.7212-year-86.9132.5132.830.7218-year-88.7131.2832.950.7234-year-88.1529.7433.140.721980–1982-87.8626.8034.140.702000–2002-94.8030.3132.870.72Summary and conclusions
The Agulhas Current transport proxies, developed by ,
were based on nine linear regression models, each assuming a constant
linear relationship from 3 years of observations between in
situ transport and satellite along-track sea surface gradients. Applying
constant linear models and assuming a constant vertical current structure,
the transport proxies were extended using 22 years of along-track
satellite data to produce two 22-year time series of Agulhas Current
transports . The Agulhas Current transport proxies
in this study replicates the methods used by but
applies these using a regional HYCOM simulation of the Agulhas Current
.
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 .
On average, 1.6 mesoscale meanders pass through the ACT array at 34∘ S
per year . In HYCOM, an average of
5 anticyclonic eddies passed over the array per year. The poorer performance
of the Tjet proxy in HYCOM (26 %)
compared to the in situ Tjet
proxy (55 %) of is due to various model discrepancies
including the consistent merging of the anticyclonic eddies with the
Agulhas Current in the northern region , which
is due to poorly resolved eddy interactions and dissipation processes
, a limitation of many numerical ocean models in
this region .
Furthermore, although the resolution of HYCOM is able to capture the
mesoscale dynamics of eddies , it fails to
resolve the near-coastal features, such as the inshore surface-intensified
cyclonic motion in this simulation. This would require a finer resolution
at the coast in order to reveal smaller offshore displacements, ∼50 km, associated with these meander events . The
poorer performance of the Tjet
proxy in HYCOM and possibly in the in situ study, may also
be because it only represents the southwestward component of the flow,
whereas the input sea surface slope reflects the net flow along the
array. Therefore, based on these findings further analysis focused
on the Tbox proxy only.
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 . The transport
proxy only included the transport of the portion of the eddy that
was reflected in the SSH signal across the array, whether it was the
southwestward or northeastward portion of the eddy or both. Although
the transport proxy may capture the SSH signal of the eddies along
the array, the correlation of the regression models decreases offshore.
Therefore transport estimates inshore would be more accurate than
the transport estimates offshore when the current is in a meandering
state.
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. improved the representation of
the southern Agulhas Current by applying a higher-order momentum advection
scheme, resulting in a well-defined meandering current rather than
a continuous stream of eddies. found that the
use of relative wind forcing significantly decreased eddy intensities
and a study by focused on the current stress feedback between the ocean and atmosphere and
demonstrated a reduction of mesoscale variability by coupling the
ocean model with an atmospheric model. Improving the mesoscale variability
in HYCOM could therefore yield better results for the transport proxy,
specifically for the offshore regression models, in the future. In
order to effectively mirror the performance of the in situ
transport proxy , a numerical model that accurately
simulates Agulhas meanders and the vertical variability, including
an accurate representation of the Agulhas Undercurrent is required
and this has not yet been achieved in existing regional configurations.
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 . Using the numerical model,
it was concluded that the correlation between the Agulhas Current
transport and gradient in sea surface height was greater than r=0.78
for any 3-year measuring period, and is therefore an adequate
timescale to build an accurate transport proxy .
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, >3 years, would increase the skill of the
transport proxy, since the linear relationship would include more
current variability over longer periods of time. The results showed
that calculating the transport proxy over longer or shorter time periods
did not necessarily improve the performance of the proxy, thereby
suggesting that the current dynamics for any 3-year period in the
model could be very similar, in agreement with the results obtained
in , suggesting that the results were consistent
despite the model biases. This suggests that 3 years is an appropriate
time-period to develop the transport proxy of the Agulhas Current
in HYCOM.
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 availability
Data sets are available upon request by contacting the corresponding author.
Author contributions
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.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
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.
Review statement
This paper was edited by Matthew Hecht and reviewed by three
anonymous referees.
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