The influence of bottom topography on the decay of modeled Agulhas rings

The influence of a large meridional submarine ridge on the decay of Agulhas rings is investigated with a 1 and 2-layer setup of the isopycnic primitive-equation ocean model MICOM. In the single-layer case we show that the SSH decay of the ring is primarily governed by bottom friction and secondly by the radiation of Rossby waves. When a topographic ridge is present, the effect of the ridge on SSH decay and loss of tracer from the ring is negligible. However, the barotropic ring cannot pass the ridge due to energy and vorticity constraints. In the case of a two-layer ring the initial SSH decay is governed by a mixed barotropic–baroclinic instability of the ring. Again, radiation of barotropic Rossby waves is present. When the ring passes the topographic ridge, it shows a small but significant stagnation of SSH decay, agreeing with satellite altimetry observations. This is found to be due to a reduction of the growth rate of the m = 2 instability, to conversions of kinetic energy to the upper layer, and to a decrease in Rossby-wave radiation. The energy transfer is related to the fact that coherent structures in the lower layer cannot pass the steep ridge due to energy constraints. Furthermore, the loss of tracer from the ring through filamentation is less than for a ring moving over a flat bottom, related to a decrease in propagation speed of the ring. We conclude that ridges like the Walvis Ridge tend to stabilize a multi-layer ring and reduce its decay.

Fast northward energy transfer in the Atlantic due to Agulhas rings

The adiabatic transit time of wave energy radiated by an Agulhas ring released in the South Atlantic Ocean to the North Atlantic Ocean is investigated in a two-layer ocean model. Of particular interest is the arrival time of baroclinic energy in the northern part of the Atlantic, because it is related to variations in the meridional overturning circulation. The influence of the Mid-Atlantic Ridge is also studied, because it allows for the conversion from barotropic to baroclinic wave energy and the generation of topographic waves. Barotropic energy from the ring is present in the northern part of the model basin within 10 days. From that time, the barotropic energy keeps rising to attain a maximum 500 days after initiation. This is independent of the presence or absence of a ridge in the model basin. Without a ridge in the model, the travel time of the baroclinic signal is 1300 days. This time is similar to the transit time of the ring from the eastern to the western coast of the model basin. In the presence of the ridge, the baroclinic signal arrives in the northern part of the model basin after approximately 10 days, which is the same time scale as that of the barotropic signal. It is apparent that the ridge can facilitate the energy conversion from barotropic to baroclinic waves and the slow baroclinic adjustment can be bypassed. The meridional overturning circulation, parameterized in two ways as either a purely barotropic or a purely baroclinic phenomenon, also responds after 1300 days. The ring temporarily increases the overturning strength. Th presence of the ridge does not alter the time scales.

Translation, decay and splitting of Agulhas rings in the southeastern Atlantic Ocean

All Agulhas rings that were spawned at the Agulhas retrofiec- tion between 1993 and 1996 (a total of 21 rings) have been monitored using TOPEX/Poseidon satellite altimetry and followed as they moved through the southeastern Atlantic Ocean, decayed, interacted with bottom topography and each other, or dissipated completely. Rings preferentially crossed the Walvis Ridge at its deepest parts. After having crossed this ridge they have lower translational speeds, and their decay rate decreases markedly. Half the decay of long-lived rings takes place in the first 5 months of their lifetimes. In addition to the strong decay of rings in the Cape Basin, about one third of the observed rings do not seem to leave this region at all but totally disintegrate here. The interaction of rings with bottom topography, in particular with the Verna Seamount, is shown frequently to cause splitting of rings. This will enhance mixing of the rings' Indian Ocean water into that of the southern Atlantic. This localized mixing may well provide a considerable source of warm and salty Indian Ocean water into the Atlantic overturning circulation.

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.

On the fast decay of Agulhas rings

The Indian Ocean water that ends up in the Atlantic Ocean detaches from the Agulhas Current retroflection predominantly in the form of Agulhas rings and cyclones. Using numerical Lagrangian float trajectories in a high-resolution numerical ocean model, the fate of coherent structures near the Agulhas Current retroflection is investigated. It is shown that within the Agulhas Current, upstream of the retroflection, the spatial distributions of floats ending in the Atlantic Ocean and floats ending in the Indian Ocean are to a large extent similar. This indicates that Agulhas leakage occurs mostly through the detachment of Agulhas rings. After the floats detach from the Agulhas Current, the ambient water quickly looses its relative vorticity. The Agulhas rings thus seem to decay and loose much of their water in the Cape Basin. A cluster analysis reveals that most water in the Agulhas Current is within clusters of 180 km in diameter. Halfway in the Cape Basin there is an increase in the number of larger clusters with low relative vorticity, which carry the bulk of the Agulhas leakage transport through the Cape Basin. This upward cascade with respect to the length scales of the leakage, in combination with a power law decay of the magnitude of relative vorticity, might be an indication that the decay of Agulhas rings is somewhat comparable to the decay of two-dimensional turbulence.

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.

Lagrangian validation of numerical drifter trajectories using drifting buoys: Application to the Agulhas system

The skill of numerical Lagrangian drifter trajectories in three numerical models is assessed by comparing these numerically obtained paths to the trajectories of drifting buoys in the real ocean. The skill assessment is performed using the two-sample Kolmogorov–Smirnov statistical test. To demonstrate the assessment procedure, it is applied to three different models of the Agulhas region. The test can either be performed using crossing positions of one-dimensional sections in order to test model performance in specific locations, or using the total two-dimensional data set of trajectories. The test yields four quantities: a binary decision of model skill, a confidence level which can be used as a measure of goodness-of-fit of the model, a test statistic which can be used to determine the sensitivity of the confidence level, and cumulative distribution functions that aid in the qualitative analysis. The ordering of models by their confidence levels is the same as the ordering based on the qualitative analysis, which suggests that the method is suited for model validation. Only one of the three models, a 1/10° two-way nested regional ocean model, might have skill in the Agulhas region. The other two models, a 1/2° global model and a 1/8° assimilative model, might have skill only on some sections in the region

A weaker Agulhas Current leads to more Agulhas leakage

Time series of transports in the Agulhas region have been constructed by simulating Lagrangian drifter trajectories in a 1/10 degree two-way nested ocean model. Using these 34 year long time series it is shown that smaller (larger) Agulhas Current transport leads to larger (smaller) Indian-Atlantic inter-ocean exchange. When transport is low, the Agulhas Current detaches farther downstream from the African continental slope. Moreover, the lower inertia suppresses generation of anti-cyclonic vorticity. These two effects cause the Agulhas retroflection to move westward and enhance Agulhas leakage. In the model a 1 Sv decrease in Agulhas Current transport at 32°S results in a 0.7 ± 0.2 Sv increase in Agulhas leakage.

Asymptotic gravity wave drag expressions for non-hydrostatic rotating flow over a ridge

Asymptotic expressions are derived for the mountain wave drag in flow with constant wind and static stability over a ridge when both rotation and non-hydrostatic effects are important. These expressions, which are much more manageable than the corresponding exact drag expressions (when these do exist) are found to provide accurate approximations to the drag, even when non-hydrostatic and rotation effects are strong, despite having been developed for cases where these effects are weak. The derived expressions are compared with approximations to the drag found previously, and their asymptotic behaviour in various limits is studied.