Flux comparison of Eulerian and Lagrangian estimates of Agulhas leakage: A case study using a numerical model

Estimating the magnitude of Agulhas leakage, the volume flux of water from the Indian to the Atlantic Ocean, is difficult because of the presence of other circulation systems in the Agulhas region. Indian Ocean water in the Atlantic Ocean is vigorously mixed and diluted in the Cape Basin. Eulerian integration methods, where the velocity field perpendicular to a section is integrated to yield a flux, have to be calibrated so that only the flux by Agulhas leakage is sampled. Two Eulerian methods for estimating the magnitude of Agulhas leakage are tested within a high-resolution two-way nested model with the goal to devise a mooring-based measurement strategy. At the GoodHope line, a section halfway through the Cape Basin, the integrated velocity perpendicular to that line is compared to the magnitude of Agulhas leakage as determined from the transport carried by numerical Lagrangian floats. In the first method, integration is limited to the flux of water warmer and more saline than specific threshold values. These threshold values are determined by maximizing the correlation with the float-determined time series. By using the threshold values, approximately half of the leakage can directly be measured. The total amount of Agulhas leakage can be estimated using a linear regression, within a 90% confidence band of 12 Sv. In the second method, a subregion of the GoodHope line is sought so that integration over that subregion yields an Eulerian flux as close to the float-determined leakage as possible. It appears that when integration is limited within the model to the upper 300 m of the water column within 900 km of the African coast the time series have the smallest root-mean-square difference. This method yields a root-mean-square error of only 5.2 Sv but the 90% confidence band of the estimate is 20 Sv. It is concluded that the optimum thermohaline threshold method leads to more accurate estimates even though the directly measured transport is a factor of two lower than the actual magnitude of Agulhas leakage in this model.

Relating Agulhas leakage to the Agulhas Current retroflection location

The relation between the Agulhas Current retroflection location and the magnitude of Agulhas leakage, the transport of water from the Indian to the Atlantic Ocean, is investigated in a high-resolution numerical ocean model. Sudden eastward retreats of the Agulhas Current retroflection loop are linearly related to the shedding of Agulhas rings, where larger retreats generate larger rings. Using numerical Lagrangian floats a 37 year time series of the magnitude of Agulhas leakage in the model is constructed. The time series exhibits large amounts of variability, both on weekly and annual time scales. A linear relation is found between the magnitude of Agulhas leakage and the location of the Agulhas Current retroflection, both binned to three month averages. In the relation, a more westward location of the Agulhas Current retroflection corresponds to an increased transport from the Indian Ocean to the Atlantic Ocean. When this relation is used in a linear regression and applied to almost 20 years of altimetry data, it yields a best estimate of the mean magnitude of Agulhas leakage of 13.2 Sv. The early retroflection of 2000, when Agulhas leakage was probably halved, can be identified using the regression.

Tracer Leakage from Modeled Agulhas Rings

In a numerical, isopycnal, ocean model the mixing is investigated with the environment of two idealized Agulhas rings, one that splits, and one that remains coherent. The evolution of a passive tracer , initially contained within the rings, shows that tracer leakage is associated with the for mation of filaments in the early stage of ring evolution. These filaments reach down to the ther mocline. In the deepest layers leakage occurs on a larger scale. Self-advection of the rings is ver y irregular , and it is not possible to compute a Lagrangian boundar y i n order to estimate the transport of leakage from the rings. T o describe the processes that gover n tracer leakage, in a coordinate frame moving with the ring a kinematic separatrix is defined in the streamfunction field for the nondivergent flow . Initially , filaments arise because of the elongation of the ring, which is mainly gover ned by an m 5 2 instability that is collaborating with differential rotation. Because of beta, the symmetr y i s destroyed related to the separatrix associated with a stagnation point in the flow . The filament upstream of the stagnation point grows much faster and is associated with the bulk of tracer leakage. Mixing is enhanced by time dependence of the separatrix. As a result, there are no large differences between the leakage from a coherent ring, where the m 5 2 instability equilibrates, and from a splitting ring, where the m 5 2 instability keeps growing, which confir ms that the amount of leakage is mainly gover ned by the ring’ s initial defor mation combined with unsteady self-advection of the ring and not by the splitting of the ring. The decay of tracer content in the ther mocline shows that in the first months up to 40% of the ring water can be mixed with the environment. In deeper layers the decay of tracer content may reach up to 90%.