1. Introduction
The Agulhas Current is the strongest western boundary current in the Southern Hemisphere. As it overshoots the African continent, part of the current leaks into the South Atlantic in the form of eddies and filaments (Gordon 1986; Gordon et al. 1992; Lutjeharms 2006; Biastoch et al. 2009). These Agulhas leakage waters are anomalously warm and salty and may affect the convective stability of the Atlantic meridional overturning circulation (AMOC) with potential impacts on global climate at a wide range of time scales (Weijer et al. 2002; Peeters et al. 2004; Beal et al. 2011; Rühs et al. 2013; Weijer and van Sebille 2014; Biastoch et al. 2015).
Recent studies suggest increasing Agulhas leakage due to climate change may stabilize the AMOC (Biastoch et al. 2009; Rouault et al. 2009; Biastoch and Böning 2013) at a time when ice sheet melting is predicted to weaken it (Gregory et al. 2005; Cheng et al. 2013). While the majority of climate models predict a weakening of the AMOC under global warming, their inability to resolve mesoscale features, such as Agulhas retroflection and leakage, may lead to erroneous projections of the climate system. The current generation of climate models overestimates average leakage strength by more than 200% (Weijer et al. 2012; Weijer and van Sebille 2014).
Whether in models or the real ocean, quantifying Agulhas leakage is difficult. An Eulerian approach, integrating the velocity field as a function of depth, is challenging (van Sebille et al. 2010; Putrasahan et al. 2015). The strong mixing and stirring, owing to the opposing major currents and the energetic eddy field, complicate the identification of water masses originating from the Indian Ocean in the South Atlantic (Boebel et al. 2003). Other classical approaches involving Agulhas ring identification and counting are incomplete because they fail to consider leakage water outside of Agulhas rings, which may account for more than 50% of the leakage transport (Loveday et al. 2015).
As a result of these challenges, a Lagrangian particle-tracking approach has been widely implemented to quantify Agulhas leakage in ocean models (Doglioli et al. 2006; Speich et al. 2006; Biastoch et al. 2008, 2009; Durgadoo et al. 2013; Weijer and van Sebille 2014). In a Lagrangian framework, particles can be tracked from the Agulhas Current into the Atlantic Ocean regardless of their pathways. However, because of limited storage space, climate model outputs are typically archived monthly, which is less than ideal for Lagrangian particle tracking because eddy time scales are far shorter. Qin et al. (2014) found that, using up to 9-day-averaged velocity fields, Lagrangian experiments show no significant changes in volume transport and particle transit times over various current systems.
Here we develop a strategy, using a Lagrangian particle-tracking model, the connectivity modeling system (CMS; Paris et al. 2013), to quantify Agulhas leakage in a new ocean-eddy-resolving (1/10°) climate model [Community Climate System Model, version 3.5 (CCSM3.5)]. As a coupled model, CCSM includes air–sea coupling effects that are important on interannual-to-decadal time scales (Putrasahan et al. 2016) but not considered in previous studies using stand-alone ocean circulation models with prescribed wind forcing (Biastoch et al. 2009; Biastoch and Böning 2013). From a climate perspective, the long-term trend of Agulhas leakage has been the focus of most early studies. Identifying interannual-to-decadal leakage variability allows us to separate long-term trends from natural variability. Moreover, leakage variability may affect regional climate through air–sea interactions, which are absent in ocean-only simulations. In this study, we demonstrate that monthly mean outputs from the climate model are sufficient for quantifying Agulhas leakage transport variability on longer-than-seasonal time scales.
2. Methods
a. CCSM and validation
We use the NCAR CCSM3.5 for this study. CCSM3.5 [the forerunner of the NCAR Community Earth System Model (CESM)] is a general circulation model coupling various components, including the Community Atmosphere Model, version 4.0 (CAM4.0); Community Land Model, version 4 (CLM4); Parallel Ocean Program, version 2 (POP2); and Community Ice Code, version 4 (CICE4).
Our simulations follow many pioneering studies exploring the effects of improving the resolution of both atmosphere and ocean components (Gent et al. 2010; Bryan et al. 2010; McClean et al. 2011; Kirtman et al. 2012). CAM4.0 is configured identically to the high-resolution run from Gent et al. (2010), with approximately 0.5° horizontal resolution and 26 vertical layers and with which CLM4 shares the same resolution. They are coupled to POP2, which has 42 vertical levels, with 10-m layer thickness in the top 100 m and gradually increasing to 250 m at 6000-m depth. The ocean component has a 0.1° horizontal resolution, with a maximum grid spacing of 11 km near the equator, decreasing to 2.5 km at high latitudes. More detailed configurations are documented by McClean et al. (2011). This work marks one of the earliest attempts of simulating global climate system with resolved mesoscale features in the ocean, such as the Agulhas retroflection and Agulhas rings (Kirtman et al. 2012; Putrasahan et al. 2015).
The outputs we analyze in this study are from an ongoing twentieth-century climate change simulation. The system is initialized from a 150-yr high-resolution simulation with fixed 1990 CO2 forcing (Kirtman et al. 2012). It is integrated for 10 years with fixed 1940 CO2 concentrations before corresponding twentieth-century CO2 levels are applied, so as to minimize the initialization shock. Further details about spinup process and model configurations can be found in Kirtman et al. (2012).
We validate CCSM3.5 using satellite and available in situ data. CCSM3.5 clearly captures the Agulhas retroflection and meandering front that supports the Agulhas Return Current (Fig. 1b), as seen in AVISO altimetry data (Fig. 1a). The SSH standard deviation map of CCSM3.5 (Fig. 1d) resembles that from AVISO (Fig. 1c) but has a broader and more energetic region of variability in the retroflection area. Also, the simulated eddy path into the South Atlantic is too regular (Figs. 1d,e), covering only the northern and central pathways from the three observed routes reported by Dencausse et al. (2010a). These discrepancies have been noted by previous studies using ocean models or coupled simulations of similar horizontal resolution (Maltrud and McClean 2005; McClean et al. 2011; Le Bars et al. 2013). Tracking the westernmost point of an SSH contour that represents the Agulhas Current and Agulhas Return Current cores at each time step, we find a 4° eastward bias of the mean retroflection position (22.1°E), compared to the 18°E seen in satellite observations (Dencausse et al. 2010b). The early retroflection leads to a more concentrated formation of eddies near the tip of the continental shelf. Since eddy pathways are highly sensitive to their formation sites (Dencausse et al. 2010a), the early retroflection may partially explain the regular eddy pathways shown in the modeled SSH variability map. The two-way coupling in the coupled model likely reduces the SSH variability and hence produces more realistic eddy pathways and dissipation (McClean et al. 2011).
(a) Mean absolute dynamic topography (ADT) from AVISO altimetry data, 1993–2013; (b) mean SSH from CCSM, 1941–50; (c) std dev of absolute dynamic topography from AVISO; (d) std dev of SSH from CCSM; and (e) average leakage particle transport map in 0.1° × 0.1° grid box for the first 10 years of the p2d case. White triangles mark the ACT array and the black line is the prescribed model GoodHope line.
Citation: Journal of Climate 29, 19; 10.1175/JCLI-D-15-0568.1
The Agulhas Current was measured continuously for 3 years during the Agulhas Current Time Series Experiment (ACT) from 2010 to 2013. Comparison of the observed cross-track velocity structure of the Agulhas Current from ACT at 34°S with that from CCSM3.5 shows fair agreement (Fig. 2). The observed Agulhas Current is faster and narrower than in the model and exhibits a weak undercurrent that is absent in the model mean, although it does appear intermittently. The pattern of variability of cross-track variability across the Agulhas Current is the same in the observations and the coupled simulation (Figs. 2c,d). The observed and model mean transports of the Agulhas Current at the ACT array differ by 18 Sv (1 Sv ≡ 106 m3 s−1), and this discrepancy is examined in the following section. CCSM3.5 simulates a mean Mozambique Channel transport of 18.8 Sv across the 17°S section over a 4-yr period from 1952 to 1955, comparable to the observed mean value of 16.7 Sv from 2003 to 2008 (Ridderinkhof et al. 2010). The simulated East Madagascar Current (EMC) and East Madagascar Undercurrent (EMUC) transports near 25°S of 33.4 and 3.0 Sv (averaged over 1952–55) are also in good agreement with observations. Based on several hydrographic sections measured in 2001, Nauw et al. (2008) reported a mean EMC transport of 37 Sv and a mean EMUC transport of 2.8 Sv.
(a) Observed time-mean cross-track velocity structure of the Agulhas Current at the ACT array, 2010–13. Negative, southwestward flow is shaded from red through yellow, while positive northeastward flow is shaded in blue; (b) time-mean cross-track velocity structure at the ACT array from CCSM, 1941–70; (c) observed std dev of cross-track velocity at the ACT array; and (d) std dev of cross-track velocity at the ACT array from CCSM.
Citation: Journal of Climate 29, 19; 10.1175/JCLI-D-15-0568.1
For this study, we use 30 years (1941–70) of the twentieth-century CCSM3.5 simulation, archiving monthly mean fields as well as daily means every 5 days (hereafter pentads) to run the Lagrangian particle-tracking experiments. Pentad files are created using 1-day branch runs from the restart files of the main simulation available every 5 days. Conventional models accumulate fields as they integrate and output the temporally averaged fields at a prescribed frequency. We exploit the intermediate restart files to conduct the branch runs to circumvent the model limitation that outputs are only archived at one frequency and to avoid excessive computing costs of running two parallel simulations.
b. CMS configuration
Many early Agulhas leakage studies use the Ariane toolbox (Blanke and Raynaud 1997) to track Agulhas water by constructing a closed box and recording the moment that each particle exits the box at one of its control boundaries (Doglioli et al. 2006; Biastoch et al. 2008; van Sebille et al. 2009b; Durgadoo et al. 2013). However, because of CCSM’s grid setting, our tool of choice for the Lagrangian experiment is the connectivity modeling system (Paris et al. 2013). Weijer et al. (2012) were the first to apply CMS to study Agulhas leakage in a coarse-resolution CCSM simulation.
We conducted several sensitivity tests to find the optimal configurations for quantification of Agulhas leakage, including adjusting the release section, integration length, recirculation, and turbulence module. These test runs span 10 years, from 1941 to 1950. Statistics are calculated excluding the first 2 years to rule out the ramp-up effects because of particle travel time.
In previous Agulhas leakage studies that employ a Lagrangian approach, particles were released at 32°S (Biastoch et al. 2008; van Sebille et al. 2010; Weijer et al. 2012; Biastoch and Böning 2013; Durgadoo et al. 2013; Loveday et al. 2014; Weijer and van Sebille 2014), corresponding to the site of a yearlong measurement during the WOCE in 1995 (Bryden et al. 2005). Here we seed particles into the Agulhas Current at about 34°S, following the location of the ACT array (Fig. 1, white triangles; Beal et al. 2015). Agulhas Current transport has been measured at the ACT array for 3 years, from April 2010 to February 2013, and a new long-term measurement program, the Agulhas system climate array, began along the same line in April 2015.
At 34°S, we release particles into the Agulhas jet only, defined as the poleward transport out to the first maximum of the vertically integrated velocity beyond the half-width of the mean jet, after Beal et al. (2015). The observed mean transport of the Agulhas Current, so defined, is 84 Sv with a standard error of 2 Sv. These values are based on 3 years of 20-min measurements de-tided with a 40-h low-pass filter and resampled at 12-h time steps. In CCSM3.5, the equivalent transport is 102 ± 2.8 Sv. At 32°S, most models, including ours, agree on a mean Agulhas Current transport around 70 Sv [69.7 ± 4.3 Sv reported by Bryden et al. (2005) and 76.3 ± 1.7 Sv in CCSM3.5, both based on time series of daily values]. The observed 15-Sv difference of mean Agulhas Current transport between 32° and 34°S can be accounted for by the latitudinal increase predicted by Sverdrup dynamics (Beal et al. 2015). We find that the additional transport in CCSM3.5 is attributed to a strong local recirculation in the model that is not present in the real ocean (Figs. 1a,b). Releasing particles at each of these two sites gives 3 Sv more of mean Agulhas leakage transport for the 34°S release case, with leakage transport time series correlating very well (correlation coefficient r = 0.91; p < 0.01). All our correlations are tested by the standard Student’s t test, using effective degrees of freedom that are estimated by the e-folding time scale of each time series and found to have p values less than 0.01, which from here on are not explicitly listed.
We determine an optimal time integration length by releasing particles at 34°S continuously for 1 year (1942), tracking their trajectories for integration lengths from 2 to 7 yr and comparing the ratio of particles that have exited our control box. The box is bounded by the ACT array, the 30°E meridian, the 45°S parallel, and an approximation of the GoodHope line (Fig. 1). The ratio starts at 92% when integrating only 2 years and converges to 97% after 5 years. We therefore decide to use a 5-yr integration length. To account for the spurious recirculation near the ACT array that may lead to overseeding particles and overestimating leakage transport, we exclude leakage particles that cross the ACT array more than once. This approach and the continuous release strategy ensure that we only report the component of leakage transport unaffected by the biased recirculation. Agulhas leakage transport time series, with and without eliminating recirculation, correlate well at 0.93, though the mean transport reduces significantly by 6 Sv with the recirculation removed (Table 1).
Statistics of Agulhas leakage transport for all sensitivity tests, including release section, recirculation, and turbulence module, from 1943 to 1949. Variable Dh is the horizontal diffusivity parameter. The first column in each test case represents the choice of configuration in this study, and therefore the correlation equals unity.
The CMS has a turbulence module that introduces a random perturbation to the velocity field used to advect particles, following the random displacement method (RDM) described by Okubo (1980). If the module is off, all particles released at the same location and time stay together, insensitive to the number of released particles. Hence, we can release one particle per grid cell and tag its corresponding volume flux. With the turbulence module on, it is necessary to release multiple particles per grid cell, each of them assigned with a small volume flux (in our tests, 0.1 Sv is assigned). A major uncertainty of this approach resides in setting the turbulence module’s parameters, including diffusivity and perturbation frequency. To test the sensitivity of leakage transport to the turbulence module we use pentad velocity fields, a diffusivity coefficient of 0.1 m2 s−1 and introduce random perturbations every day. These parameters are chosen based on previous tests using models of a similar spatial resolution (Qin et al. 2014). Introducing the turbulence module results in a −2.3-Sv difference in mean leakage transport but has a very minor influence on the leakage variability (r = 0.96; Table 1). Since the sensitivity is small and diffusivity parameters are unconstrained, we set the turbulence module off and release one particle per grid cell to track particles deterministically. The deterministic approach saves considerable computational cost and has been implemented in several previous studies that apply CMS to track Lagrangian particles (van Sebille et al. 2012, 2014; Weijer et al. 2012).
c. Release strategy and experiment design
Current-generation climate models usually archive monthly mean output that may not be suitable for measuring Agulhas leakage with a Lagrangian approach. Previous particle-tracking studies have been based on daily to 5-day mean velocity outputs from ocean-only models. Van Sebille et al. (2009a) have shown that daily and 5-day mean fields yield similar mean leakage transports, particle arrival times, and spatial distribution. We conducted a similar test using 1 year of daily and pentad outputs from CCSM3.5, with particles released daily (interpolated in the pentad case) for 10 years (1 year looping 10 times) in each case. We found these leakage transport estimates to be close, with a correlation of 0.96 at longer-than-seasonal time scales. The result using pentad fields was then compared to that using 5-daily mean fields, yielding correlations of 0.89 and 0.97 before and after the 31-day running mean, with nearly the same mean and standard deviation (mean of 11.0 Sv and standard deviation of 12.0 Sv). We conclude that for longer-than-seasonal time scales the pentad fields perform almost identically to the daily fields. Hence, from here on we test monthly output against the results using pentads, taking the latter as “truth.”
We release a particle at every grid cell along the ACT array whenever the local cross-sectional velocity is southwestward. Each is tagged with a volume transport equivalent to the local velocity multiplied by the gridcell size. These particles are then integrated using local velocity fields for 5 years with an integration time step of 1.2 h. The mean volume transport for all release particles is 0.3 Sv, with a standard deviation of comparable magnitude.
We take an approximation of the GoodHope line as the control section to determine leakage particles, following previous studies (Fig. 1, black solid line; van Sebille et al. 2009a,b; Biastoch et al. 2009). The GoodHope line is a repeat hydrographic section between Cape Town and Antarctica, to the west of the Agulhas retroflection loop in the South Atlantic (Ansorge et al. 2005). A particle is considered Agulhas leakage when it crosses the GoodHope line an odd number of times, so as to account for recirculations and eddies. We create a 30-yr leakage transport time series at daily time scale by identifying the last crossing time of each leakage particle and summing their corresponding volume transports each day.
Three Lagrangian experiments are conducted. The “p2d” case uses pentad fields from CCSM3.5 interpolated to daily fields for input to CMS. A total of 3.9 × 106 particles are released, of which 11% passed into the South Atlantic as Agulhas leakage. The “m2d” case uses monthly mean output interpolated to daily velocity fields. Of 4.5 × 106 released particles, 12% ended in the South Atlantic. Last, the “mon” case uses the same monthly mean output, but there is no interpolation of velocity fields and particles are only released monthly in CMS. Out of 1.4 × 105 released particles, 13% reached the South Atlantic. The majority of particles for the p2d case (~200 days) arrived at the GoodHope line later than those for the m2d (~120 days) and mon (~140 days) cases (Fig. 3).
Particle transit times, traveling from the ACT array to the GoodHope line, based on a 60-day bin width. Particles travel faster in both cases using monthly mean fields, m2d (blue) and mon (black), than those from the p2d (orange) case.
Citation: Journal of Climate 29, 19; 10.1175/JCLI-D-15-0568.1
For p2d and m2d, interpolations are done by a cubic spline method to obtain daily velocity fields. Interpolating the velocity fields explicitly is to avoid any discrepancy in interpolation schemes used within CMS for the velocity fields at different temporal frequencies. Specifically, CMS requires five neighboring time steps to interpolate to the target time step, while it needs only three files if the velocity fields are available at time intervals smaller than a month. A more intuitive comparison might have been between the pentads and monthly interpolated to pentad fields, yet with daily time series we have been able to process, filter, and compare results consistently across all our tests and studies, including the initial validation of the pentad fields using daily fields.
3. Results
a. Leakage particle trajectories
The average transport distribution map summarizes the trajectories of Agulhas leakage particles for the p2d case (Fig. 1e). Transport distribution is obtained by summing transports carried by leakage particles passing through each ocean grid cell (0.1° × 0.1°) at any depth over the duration of the 30-yr experiment. This sum is then divided by the total number of release days, yielding the average leakage transport through each grid cell. A higher value indicates that more leakage particles have passed through that region at any time and depth (van Sebille et al. 2012). For all three cases, about one-tenth of the released particles leak into the South Atlantic (p2d: 11%; m2d: 12%; and mon: 13%). A quick look at the Argo floats passing through the ACT section, as of April 2015, shows that 13% (10 of 80) leak into the South Atlantic. A previous numerical study with a high-resolution nested Agulhas domain suggests that 19% of all released particles cross the GoodHope line and stay in the South Atlantic after a 5-yr integration (Biastoch et al. 2008).
Most of the particles take a relatively narrow path within the Agulhas Current until about 25°E before spreading out when entering the retroflection region. Their pathways seem confined between the shelf and the northeastern tip of the Agulhas Plateau. After crossing the GoodHope line, most particles advect northwestward with the South Atlantic gyre circulation, following the well-known path of most Agulhas rings (Lutjeharms 2006), and some leakage particles flow northward toward the shelf and along the coast, which may be related to advection by the Benguela Current.
b. Pentad versus monthly fields
The mean Agulhas leakage transports for p2d and m2d cases are 11.2 and 11.9 Sv respectively, each with a standard error of 0.5 Sv (Table 2). These results are in line with previous observational and numerical estimates of 3–20 Sv (Gordon et al. 1992; de Ruijter et al. 1999; Boebel et al. 2003; Doglioli et al. 2006; Richardson 2007; Biastoch et al. 2008, 2009). The same climate model, but configured with a lower ocean resolution (1° × 1°), has a mean Agulhas leakage of 43 Sv for the twentieth century and 34 Sv for preindustrial control simulations (Weijer et al. 2012; Weijer and van Sebille 2014). By resolving smaller-scale dynamics, our CCSM3.5 run is able to form a retroflection and constrain Agulhas leakage more realistically.
Statistics of Agulhas leakage transport for all particle-tracking experiments, calculated over the period from 1945 to 1969 (9131 days), avoiding ramp-up effects in the early years and missing values introduced by filtering; p2d is the case where we use pentad output interpolated to daily fields to release and track particle trajectories, m2d is the case using monthly mean output interpolated to daily fields, and mon is the case where particles are released monthly.
Both daily Agulhas leakage time series (p2d and m2d) show considerable variability on seasonal time scales related to the passage of individual Agulhas rings (Figs. 4a and 5). For the p2d case, leakage transport is typically 5–10 Sv, with events as large as 90 Sv (Fig. 4b). The correlation between daily p2d and m2d time series is 0.67, significant at the 99% confidence level. Zooming into the period from 1945 to 1950, the similarity between the two time series is more discernible. Most peaks from both time series coincide with their counterparts, although the p2d case has higher variability (11.1 and 9.2 Sv for p2d and m2d, respectively), with more days of extreme values on both ends of the distribution (Fig. 4b).
(a) Time series of Agulhas leakage transport from 1941 to 1970, capturing the last crossing moments of leakage particles, pentad fields (p2d; red) and that from monthly fields (m2d; blue). Zooming into the period from 1945 to 1950 shows that m2d highly correlates with p2d. (b) Histograms of leakage transport, showing extrema on both ends. The x axes on the top and bottom panels of (b) have different scales to emphasize the difference near the tail of two distributions.
Citation: Journal of Climate 29, 19; 10.1175/JCLI-D-15-0568.1
Intermittent peaks in Agulhas leakage time series related to the passage of Agulhas rings: (a) composite of SSH for high Agulhas leakage transport events, weighted by corresponding magnitudes of transport (shaded) and streamfunction derived from depth-integrated flow (contour interval is 4 Sv); (b) composite of SSH excluding high leakage events; and (c) ensemble mean of transport evolution of 98 high-leakage events identified between 1945 and 1970 (black thick line), fitted with a Gaussian function (red solid line), with the duration of a high-leakage event set to four std devs of the fitted function, or roughly 20 days.
Citation: Journal of Climate 29, 19; 10.1175/JCLI-D-15-0568.1
Pronounced leakage events can be attributed to the passage of Agulhas rings across the GoodHope line. To illustrate this, we take the composite of sea surface height for both high Agulhas leakage transport events (>26 Sv) and the days outside such events (<26 Sv; Figs. 5a,b). The threshold of 26 Sv represents the 90th percentile of the p2d time series. The composite shows the trailing edge of a ring crossing the line, as represented by a high SSH anomaly. A leakage particle caught by an eddy, with its swirling nature, may cross the GoodHope line multiple times, but only its last crossing moment is recorded. Therefore, leakage particles are counted during the latter half of a ring passage, consistent with the SSH composite.
To quantify how much leakage occurs in rings for the p2d case, we pick out 98 ring events during 1945–70 by analyzing ±30 days centered on each transport peak (i.e., the local maxima of each event at the 26-Sv threshold; Fig. 5c). The ensemble mean of all curves is then fitted with a Gaussian function, which has a standard deviation of 5 days. We define the mean length of a ring event as plus or minus two standard deviations or 20 days. The mean transport of each ring within this window is 25.8 Sv. Dividing the accumulated transport of all 98 idealized rings by that for the entire period 1945–70, we find that 47% of leakage transport is associated with ring events in the model. This ratio is somewhat larger than the 30% leakage due to trapping eddies suggested by Doglioli et al. (2006) and similar to a recent estimate for eddying versus noneddying leakage in an ocean model (Loveday et al. 2015). The number of Agulhas rings per year is about four, smaller than observed in the altimetry record by Elipot and Beal (2015), who reported six rings per year, yet typical for simulation of similar ocean resolution (Holton et al. 2016). Nevertheless, our approach may overestimate the eddying leakage since it includes the background flow during ring-passage periods and the subjectively defined four-standard-deviation event length.
The time series of leakage from the m2d case has a smaller standard deviation and narrower distribution than p2d (blue line in Fig. 4), presumably related to smoother velocity fields and more direct paths in the interpolated monthly fields. The correlation between the p2d and m2d time series shows that using monthly velocity fields can capture a large proportion of leakage transport variability. Based on these results we surmise that leakage transport variability seems largely locally controlled by the large-scale circulation driven by wind forcing, which is well captured by the monthly mean fields. The precise eddy field is less important, although the effect of mesoscale features dominates the mean state.
c. Daily versus monthly release
The current generation of climate models typically archive monthly. To investigate whether our release strategy outperforms the case where particles are released monthly, we compare monthly means of p2d and m2d leakage transport time series with that of the monthly release case, mon. Since we are also interested in the interannual variability of Agulhas leakage, we compare 730-day low-pass-filtered p2d and m2d to 24-month low-pass-filtered mon leakage time series. If the difference between these cases is small, the computing cost of our initial temporal interpolation to daily fields can be avoided.
In a systematic analysis of Lagrangian trajectory errors corresponding to different temporal averaging periods, Qin et al. (2014) suggest that temporal averaging reduces the transit time and increases connectivity transport. We too find that particles advected with monthly fields (both m2d and mon) tend to have shorter transit time to reach the GoodHope line and slightly larger mean transport than the p2d case. More particles arrive at the GoodHope line earlier, and high leakage events last longer (Fig. 3).
On longer time scales these differences become small and the mon leakage time series follows smoothed p2d and m2d time series closely. While most peaks in all three time series are aligned, both cases using monthly fields fail to distinguish all of the individual events (Fig. 6a). To test whether two correlations are significantly different, we convert the correlation coefficients into Z values through Fisher’s Z transformation. A correlation of 0.88 between the p2d and m2d cases is shown to be significantly improved from a 0.71 correlation between p2d and mon (Table 2). This indicates that our strategy to interpolate monthly velocity fields into daily fields before releasing particles provides a better estimate of Agulhas leakage variability on monthly scales. The statistically significant improvement in correlation holds true when we apply the same comparison to 24-month (730 days for daily time series) low-pass-filtered time series (Fig. 6b). Even though the correlation is reduced at interannual scales (Table 2), the difference is statistically insignificant. Our results show that monthly mean climate model output can capture up to 80% (correlation squared) of Agulhas leakage variability on longer-than-seasonal time scales when particles are released using an interpolated daily field in CMS, while monthly release can only explain about 50% of the leakage variability.
(a) Monthly mean Agulhas leakage transport time series of p2d and m2d as well as the mon case from 1945 to 1969. The correlation coefficient between p2d and m2d is 0.88, while that between p2d and mon is 0.71. (b) The 730-day (24 month) low-pass-filtered time series for all three cases during the same period. Solid lines mark the linear multidecadal trends from 1945 to 1969, while the dashed lines represent the decadal trends of the last 10 years, from 1959 to 1969. All three cases—p2d, m2d, and mon—share comparable trends.
Citation: Journal of Climate 29, 19; 10.1175/JCLI-D-15-0568.1
Considering the climatic relevance of long-term Agulhas leakage changes, we include a comparison of linear trends of Agulhas leakage using different integrating fields. We calculate linear trends of various period lengths with shifted starting years to test if trends are sensitive to the chosen periods (Fig. 6). All three cases capture significant decreasing trends within the 25-yr period from 1945 to 1969 (−1.2, −1.1, and −1.3 Sv decade−1 for p2d, m2d, and mon, respectively; p < 0.01). The difference between each 25-yr trend is not statistically significant. During the last 10 years (1959–69), all three cases agree on a significant increasing trend of about 1.1 Sv decade−1, consistent with the values suggested by a recent study reporting an increasing trend since the late 1960s (Biastoch et al. 2015).
4. Conclusions
We quantify Agulhas leakage volume transport in the global ocean-eddy-resolving climate model CCSM3.5, using the CMS Lagrangian particle-tracking model. Ours is one of the earliest attempts to quantify Agulhas leakage in an ocean-eddy-resolving global climate model. Climate model outputs are typically archived monthly owing to limited storage, which has been considered less than ideal for particle tracking. In a twentieth-century simulation, we compare Agulhas leakage time series from monthly mean and daily mean fields available every 5 days (pentad). In two particle-tracking experiments, m2d and p2d, these monthly and pentad velocity fields are interpolated such that particles are released daily in CMS. In addition, leakage transport from both experiments are compared to that of a monthly release case, mon.
Using pentad velocity fields, we find a mean Agulhas leakage transport of 11.2 Sv, less than one-third of previous estimates from CCSM4 with a 1.0° ocean (Weijer et al. 2012). The daily leakage transport time series is highly variable, with transport events up to 90 Sv. These intermittent events are associated with the passage of Agulhas rings. Overall, 47% of leakage transport can be attributed to rings, with the remaining occurring as background flow. This result is consistent with previous studies (Doglioli et al. 2006; Loveday et al. 2015), which estimate as little as one-third of Agulhas leakage may be trapped in rings.
We find a correlation of 0.88 between m2d and p2d leakage time series over a seasonal time scale and 0.83 on an interannual time scale. The correlations are statistically significant improvements from using monthly release particles. Hence, by using interpolated monthly-to-daily fields, we can use mean monthly climate model outputs to produce Agulhas leakage estimates that capture up to 80% of the variability at longer-than-seasonal time scales. Although using monthly outputs produces a larger mean leakage transport, our results imply that leakage variability may be largely controlled by large-scale forcings with longer temporal scales than mesoscale eddies (Durgadoo et al. 2013; Loveday et al. 2015) because variability is well retained by the monthly mean outputs.
Our simulation and earlier studies show that resolving mesoscale features in the Agulhas Current system is necessary to form a retroflection and constrain Agulhas leakage realistically (e.g., Biastoch et al. 2008). Yet once the horizontal resolution is sufficiently high, our experience demonstrates that one can use monthly mean outputs to estimate Agulhas leakage variability using a Lagrangian approach, as long as the focus is on variability at longer-than-seasonal time scales. By interpolating the monthly fields to daily fields before releasing particles, skill in capturing leakage variability is further improved at longer-than-seasonal time scales. If short-term (shorter than seasonal) leakage variability is of interest, higher-temporal-resolution velocity fields are recommended.
We are eager to know if Agulhas leakage response to changing westerlies and to upstream conditions in the Agulhas Current are consistent with previous ocean model studies, which suggest an increasing leakage since the 1960s (Biastoch et al. 2009). With the 30-yr output, we find oscillating signals at interannual time scale. While the mean leakage transport decreases in the 1950s, it increases again in the late 1960s, which appears in line with early studies. These decadal changes can be fully assessed when the climate change simulation is complete.
Acknowledgments
This research was supported by the NSF (Award OCE1154986). CCSM output data are on the University of Miami Center for Computational Science machine named VISX. Data will be made available from the corresponding author upon request. BPK acknowledges support from the NSF (Awards OCE1419569 and OCI0749165). We thank three anonymous reviewers for their insightful comments.
REFERENCES
Ansorge, I. J., S. Speich, J. R. E. Lutjeharms, G. J. Göni, C. W. Rautenbach, P. W. Froneman, M. Rouault, and S. Garzoli, 2005: Monitoring the oceanic flow between Africa and Antarctica: Report of the first GoodHope cruise. S. Afr. J. Sci., 101, 29–35.
Beal, L. M., and Coauthors, 2011: On the role of the Agulhas system in ocean circulation and climate. Nature, 472, 429–436, doi:10.1038/nature09983.
Beal, L. M., S. Elipot, A. Houk, and G. M. Leber, 2015: Capturing the transport variability of a western boundary jet: Results from the Agulhas Current Time-Series Experiment (ACT). J. Phys. Oceanogr., 45, 1302–1324, doi:10.1175/JPO-D-14-0119.1.
Biastoch, A., and C. W. Böning, 2013: Anthropogenic impact on Agulhas leakage. Geophys. Res. Lett., 40, 1138–1143, doi:10.1002/grl.50243.
Biastoch, A., J. R. E. Lutjeharms, C. W. Böning, and M. Scheinert, 2008: Mesoscale perturbations control inter-ocean exchange south of Africa. Geophys. Res. Lett., 35, L20602, doi:10.1029/2008GL035132.
Biastoch, A., C. W. Böning, F. U. Schwarzkopf, and J. R. E. Lutjeharms, 2009: Increase in Agulhas leakage due to poleward shift of Southern Hemisphere westerlies. Nature, 462, 495–498, doi:10.1038/nature08519.
Biastoch, A., J. V. Durgadoo, A. K. Morrison, E. van Sebille, W. Weijer, and S. M. Griffies, 2015: Atlantic multi-decadal oscillation covaries with Agulhas leakage. Nat. Commun., 6, 10082, doi:10.1038/ncomms10082.
Blanke, B., and S. Raynaud, 1997: Kinematics of the Pacific equatorial undercurrent: An Eulerian and Lagrangian approach from GCM results. J. Phys. Oceanogr., 27, 1038–1053, doi:10.1175/1520-0485(1997)027<1038:KOTPEU>2.0.CO;2.
Boebel, O., J. Lutjeharms, C. Schmid, W. Zenk, T. Rossby, and C. Barron, 2003: The Cape Cauldron: A regime of turbulent inter-ocean exchange. Deep-Sea Res. II, 50, 57–86, doi:10.1016/S0967-0645(02)00379-X.
Bryan, F. O., R. Tomas, J. M. Dennis, D. B. Chelton, N. G. Loeb, and J. L. McClean, 2010: Frontal scale air–sea interaction in high-resolution coupled climate models. J. Climate, 23, 6277–6291, doi:10.1175/2010JCLI3665.1.
Bryden, H. L., L. M. Beal, and L. M. Duncan, 2005: Structure and transport of the Agulhas Current and its temporal variability. J. Oceanogr., 61, 479–492, doi:10.1007/s10872-005-0057-8.
Cheng, W., J. C. H. Chiang, and D. Zhang, 2013: Atlantic meridional overturning circulation (AMOC) in CMIP5 models: RCP and historical simulations. J. Climate, 26, 7187–7197, doi:10.1175/JCLI-D-12-00496.1.
Dencausse, G., M. Arhan, and S. Speich, 2010a: Routes of Agulhas rings in the southeastern Cape basin. Deep-Sea Res. I, 57, 1406–1421, doi:10.1016/j.dsr.2010.07.008.
Dencausse, G., M. Arhan, and S. Speich, 2010b: Spatio-temporal characteristics of the Agulhas Current retroflection. Deep-Sea Res. I, 57, 1392–1405, doi:10.1016/j.dsr.2010.07.004.
de Ruijter, W. P. M., A. Biastoch, S. S. Drijfhout, J. R. E. Lutjeharms, R. P. Matano, T. Pichevin, P. J. van Leeuwen, and W. Weijer, 1999: Indian–Atlantic interocean exchange: Dynamics, estimation and impact. J. Geophys. Res., 104, 20 885–20 910, doi:10.1029/1998JC900099.
Doglioli, A. M., M. Veneziani, B. Blanke, S. Speich, and A. Griffa, 2006: A Lagrangian analysis of the Indian–Atlantic interocean exchange in a regional model. Geophys. Res. Lett., 33, L14611, doi:10.1029/2006GL026498.
Durgadoo, J. V., B. R. Loveday, C. J. C. Reason, P. Penven, and A. Biastoch, 2013: Agulhas leakage predominantly responds to the Southern Hemisphere westerlies. J. Phys. Oceanogr., 43, 2113–2131, doi:10.1175/JPO-D-13-047.1.
Elipot, S., and L. M. Beal, 2015: Characteristics, energetics, and origins of Agulhas Current meanders and their limited influence on ring shedding. J. Phys. Oceanogr., 45, 2294–2314, doi:10.1175/JPO-D-14-0254.1.
Gent, P. R., S. G. Yeager, R. B. Neale, S. Levis, and D. A. Bailey, 2010: Improvements in a half degree atmosphere/land version of the CCSM. Climate Dyn., 34, 819–833, doi:10.1007/s00382-009-0614-8.
Gordon, A. L., 1986: Interocean exchange of thermocline water. J. Geophys. Res., 91, 5037–5046, doi:10.1029/JC091iC04p05037.
Gordon, A. L., R. F. Weiss, W. M. Smethie, and M. J. Warner, 1992: Thermocline and intermediate water communication between the South Atlantic and Indian Oceans. J. Geophys. Res., 97, 7223–7240, doi:10.1029/92JC00485.
Gregory, J. M., and Coauthors, 2005: A model intercomparison of changes in the Atlantic thermohaline circulation in response to increasing atmospheric CO2 concentration. Geophys. Res. Lett., 32, L12703, doi:10.1029/2005GL023209.
Holton, L., J. Deshayes, B. C. Backeberg, B. R. Loveday, J. C. Hermes, and C. J. C. Reason, 2016: Spatio-temporal characteristics of Agulhas leakage: A model inter-comparison study. Climate Dyn., doi:10.1007/s00382-016-3193-5, in press.
Kirtman, B. P., and Coauthors, 2012: Impact of ocean model resolution on CCSM climate simulations. Climate Dyn., 39, 1303–1328, doi:10.1007/s00382-012-1500-3.
Le Bars, D., H. A. Dijkstra, and W. P. M. de Ruijter, 2013: Impact of the Indonesian Throughflow on Agulhas leakage. Ocean Sci., 9, 773–785, doi:10.5194/os-9-773-2013.
Loveday, B. R., J. V. Durgadoo, C. J. C. Reason, A. Biastoch, and P. Penven, 2014: Decoupling of the Agulhas leakage from the Agulhas Current. J. Phys. Oceanogr., 44, 1776–1797, doi:10.1175/JPO-D-13-093.1.
Loveday, B. R., P. Penven, and C. J. C. Reason, 2015: Southern annular mode and westerly-wind-driven changes in Indian–Atlantic exchange mechanisms. Geophys. Res. Lett., 42, 4912–4921, doi:10.1002/2015GL064256.
Lutjeharms, J. R. E., 2006: The Agulhas Current. Springer, 329 pp.
Maltrud, M. E., and J. L. McClean, 2005: An eddy resolving global 1/10° ocean simulation. Ocean Modell., 8, 31–54, doi:10.1016/j.ocemod.2003.12.001.
McClean, J. L., and Coauthors, 2011: A prototype two-decade fully-coupled fine-resolution CCSM simulation. Ocean Modell., 39, 10–30, doi:10.1016/j.ocemod.2011.02.011.
Nauw, J. J., H. M. van Aken, A. Webb, J. R. E. Lutjeharms, and W. P. M. de Ruijter, 2008: Observations of the southern East Madagascar Current and undercurrent and countercurrent system. J. Geophys. Res., 113, C08006, doi:10.1029/2007JC004639.
Okubo, A., 1980: Diffusion and Ecological Problems: Mathematical Models. Springer, 254 pp.
Paris, C. B., J. Helgers, E. van Sebille, and A. Srinivasan, 2013: Connectivity modeling system: A probabilistic modeling tool for the multi-scale tracking of biotic and abiotic variability in the ocean. Environ. Modell. Software, 42, 47–54, doi:10.1016/j.envsoft.2012.12.006.
Peeters, F. J. C., R. Acheson, G.-J. A. Brummer, W. P. M. de Ruijter, R. R. Schneider, G. M. Ganssen, E. Ufkes, and D. Kroon, 2004: Vigorous exchange between the Indian and Atlantic Oceans at the end of the past five glacial periods. Nature, 430, 661–665, doi:10.1038/nature02785.
Putrasahan, D. A., L. M. Beal, B. P. Kirtman, and Y. Cheng, 2015: A new Eulerian method to estimate “spicy” Agulhas leakage in climate models. Geophys. Res. Lett., 42, 4532–4539, doi:10.1002/2015GL064482.
Putrasahan, D. A., B. P. Kirtman, and L. M. Beal, 2016: Modulation of SST interannual variability in Agulhas leakage region associated with ENSO. J. Climate, doi:10.1175/JCLI-D-15-0172.1, in press.
Qin, X., E. van Sebille, and A. Sen Gupta, 2014: Quantification of errors induced by temporal resolution on Lagrangian particles in an eddy-resolving model. Ocean Modell., 76, 20–30, doi:10.1016/j.ocemod.2014.02.002.
Richardson, P. L., 2007: Agulhas leakage into the Atlantic estimated with subsurface floats and surface drifters. Deep-Sea Res. I, 54, 1361–1389, doi:10.1016/j.dsr.2007.04.010.
Ridderinkhof, H., P. M. van der Werf, J. E. Ullgren, H. M. van Aken, P. J. van Leeuwen, and W. P. M. de Ruijter, 2010: Seasonal and interannual variability in the Mozambique Channel from moored current observations. J. Geophys. Res., 115, C06010, doi:10.1029/2009JC005619.
Rouault, M., P. Penven, and B. Pohl, 2009: Warming in the Agulhas Current system since the 1980’s. Geophys. Res. Lett., 36, L12602, doi:10.1029/2009GL037987.
Rühs, S., J. V. Durgadoo, E. Behrens, and A. Biastoch, 2013: Advective timescales and pathways of Agulhas leakage. Geophys. Res. Lett., 40, 3997–4000, doi:10.1002/grl.50782.
Speich, S., J. R. E. Lutjeharms, P. Penven, and B. Blanke, 2006: Role of bathymetry in Agulhas Current configuration and behaviour. Geophys. Res. Lett., 33, L23611, doi:10.1029/2006GL027157.
van Sebille, E., C. N. Barron, A. Biastoch, P. J. van Leeuwen, F. C. Vossepoel, and W. P. M. de Ruijter, 2009a: Relating Agulhas leakage to the Agulhas Current retroflection location. Ocean Sci., 5, 511–521, doi:10.5194/os-5-511-2009.
van Sebille, E., A. Biastoch, P. J. van Leeuwen, and W. P. M. de Ruijter, 2009b: A weaker Agulhas Current leads to more Agulhas leakage. Geophys. Res. Lett., 36, L03601, doi:10.1029/2008GL036614.
van Sebille, E., P. J. van Leeuwen, A. Biastoch, and W. P. M. de Ruijter, 2010: Flux comparison of Eulerian and Lagrangian estimates of Agulhas leakage: A case study using a numerical model. Deep-Sea Res. I, 57, 319–327, doi:10.1016/j.dsr.2009.12.006.
van Sebille, E., M. H. England, J. D. Zika, and B. M. Sloyan, 2012: Tasman leakage in a fine-resolution ocean model. Geophys. Res. Lett., 39, L06601, doi:10.1029/2012GL051004.
van Sebille, E., J. Sprintall, F. U. Schwarzkopf, A. Sen Gupta, A. Santoso, M. H. England, A. Biastoch, and C. W. Böning, 2014: Pacific-to-Indian Ocean connectivity: Tasman leakage, Indonesian Throughflow, and the role of ENSO. J. Geophys. Res. Oceans, 119, 1365–1382, doi:10.1002/2013JC009525.
Weijer, W., and E. van Sebille, 2014: Impact of Agulhas leakage on the Atlantic overturning circulation in the CCSM4. J. Climate, 27, 101–110, doi:10.1175/JCLI-D-12-00714.1.
Weijer, W., W. P. M. de Ruijter, A. Sterl, and S. S. Drijfhout, 2002: Response of the Atlantic overturning circulation to South Atlantic sources of buoyancy. Global Planet. Change, 34, 293–311, doi:10.1016/S0921-8181(02)00121-2.
Weijer, W., and Coauthors, 2012: The Southern Ocean and its climate in CCSM4. J. Climate, 25, 2652–2675, doi:10.1175/JCLI-D-11-00302.1.
