Erik van Sebille

PhD dissertation, 2009, Utrecht University, 176 pages, ISBN: 978-90-39351314

PhD dissertation, 2009, Utrecht University, 176 pages, ISBN: 978-90-39351314

- Chapter 2: Lagrangian validation of numerical drifter trajectories using drifting buoys

Published in*Ocean Model.*, 2009 [ pdf @ publisher ].

- Chapter 3: On the fast decay of Agulhas rings

Published in*J. Geophys. Res.*, 2010 [ pdf @ publisher ].

- Chapter 4: Fast northward energy transfer in the Atlantic due to Agulhas rings

Published in*J. Phys. Oceanogr.*, 2007 [ pdf @ publisher ].

- Chapter 5: Relating Agulhas leakage to the Agulhas Current retroflection location

Published in*Ocean Sci.*, 2010 [ pdf @ publisher ].

- Chapter 6: A weaker Agulhas Current leads to more Agulhas leakage

Published in*Geophys. Res. Lett.*, 2009 [ pdf @ publisher ].

- Chapter 7: Flux comparison of Eulerian and Lagrangian estimates of Agulhas leakage

Published in*Deep Sea Res. I*, 2010 [ pdf @ publisher ].

Agulhas leakage, the water that flows from the Indian Ocean to the Atlantic Ocean, plays an important role in the circulation of the Atlantic Ocean. The magnitude of this flux of warm and saline Indian Ocean water into the much colder and fresher Atlantic Ocean can be related to the strength of the Atlantic meridional overturning circulation, both in numerical ocean models and in paleoceanographic records. A change in Agulhas leakage might therefore be a precursor for northern Atlantic Ocean climate change and therefore there should be a need for a sustained monitoring program measuring the volume flux from the Indian to the Atlantic Ocean.

However, estimating the magnitude of this Agulhas leakage is not easy. The Agulhas region is the locus of three circulation systems: the subtropical gyres of the South Atlantic and Indian Oceans, and the Subtropical Front of the Southern Ocean. Agulhas leakage is only a minor and intermittent flux in the region and due to the vigorous mixing in the Cape Basin the signal is quickly diluted beyond the Agulhas Current retroflection.

The method of estimating the magnitude of Agulhas leakage which is closest to the definition of Agulhas leakage employs the trajectories of floats that start in the Agulhas Current and end in the Atlantic Ocean. In this way the Indian Ocean water in the Atlantic Ocean can be labeled and tracked allowing for the determination of, among other quantities, volumetric fluxes. For a statistical analysis on interannual time scales the number of floats required is in the order of millions and one has to turn to numerical ocean models. However, even the state-of-the-art numerical ocean models have problems simulating the circulation in the Agulhas region and the results from these models are thus not very reliable.

In order to assess which is the most reliable model, a novel way to quantify the skill of numerical ocean models in simulating Lagrangian floats is introduced in chapter 2: the two-sample Kolmogorov-Smirnov test. By computing the probability that the trajectories of drifting buoys in the real ocean are statistically different from the trajectories of numerical drifters, models without any skill can be identified. Application to three different numerical ocean models in the Agulhas region leads to the conclusion that only one of them might possess skill.

The float trajectories from the only model that might possess skill in the Agulhas region are used to assess some of the characteristics of Agulhas leakage. This is done by dividing the floats into a group that ends in the Indian Ocean and a group that ends in the Atlantic Ocean (chapter 3). The distributions of these two groups are to a high extent similar within the Agulhas Current, a result which can be explained by assuming that Agulhas leakage detaches from the Agulhas Current retroflection predominantly in Agulhas rings. These coherent anticyclones, however, decay quickly. Once the floats reach the GoodHope line halfway the Cape Basin, almost 70% of the floats is within water that has almost no relative vorticity. These floats, which are outside (anti)cyclonically rotating water, cluster in large patches which are advected northward.

Nevertheless, some of the Agulhas rings stay coherent and cross the Walvis Ridge into the Atlantic Ocean. These rings do not only carry heat and salt across the Atlantic Ocean, but also energy. As the rings decay, baroclinic and barotropic energy is radiated through the Atlantic Ocean basin. The radiation of this energy is investigated within a two-layer adiabatic model in chapter 4. It appears that an Agulhas ring can radiate baroclinic energy to the northern Atlantic Ocean within four years. In the presence of a Mid-Atlantic Ridge, this transit time is reduced to several days because the ridge facilitates barotropic--baroclinic energy conversion. Once in the northern Atlantic Ocean, the baroclinic energy may enhance the meridional overturning circulation strength. This seems to occur a little over three years after the Agulhas ring is released into the Atlantic Ocean, indifferent of the presence or absence of a Mid-Atlantic Ridge. This is important information for the design of a monitoring program, as it sets the maximum amount of smoothing which is allowed.

This possible influence of Agulhas leakage on the strength of the Atlantic meridional overturning circulation is one of the reasons why a monitoring program of the magnitude of Agulhas leakage is required. It is unfeasible to base such a program on float trajectories in the real ocean as the amount of floats required is orders of magnitude larger than what is currently used. For that reason possible monitoring strategies have to be developed: Relations between the Agulhas leakage transport determined by (numerical) Lagrangian floats and easier-to-measure quantities. Three of such strategies have been assessed within the high-resolution numerical ocean model with the goal to yield a workable proxy or index.

The first strategy for monitoring the magnitude of Agulhas leakage, which is discussed in chapter 5, is based on the location of the Agulhas Current retroflection. There appears to be a significant correlation between the westward extent of the retroflection and the amount of Agulhas leakage over the GoodHope line halfway the Cape Basin on a three month time scale. In this relation, a more westward retroflection leads to a larger Agulhas leakage transport. However, the wide confidence band in the best linear fit of this relation makes the monitoring strategy of limited use for estimating the magnitude of Agulhas leakage in the real ocean. When the estimate is applied to satellite altimetry data, the confidence band is too wide for any variability of Agulhas leakage transport to be significant, except for when the Agulhas system is in an early retroflection and the Agulhas Current retroflection is so far east that Agulhas leakage is almost stopped.

The second strategy introduced for monitoring the magnitude of Agulhas leakage in the real ocean is based on the strength of the Agulhas Current upstream of the retroflection (chapter 6). This monitoring strategy is based on the correlation between Agulhas Current strength and the location where the Agulhas Current outcrops and separates from the African continental slope. When the Agulhas Current is stronger, the increased inertia causes an enhanced outcropping of the isotherms, which leads to an earlier detachment from the continent. Due to the shape of the continent, a more upstream detachment yield a less westward oriented Agulhas Current. This leads to an eastward migration of the Agulhas Current retroflection, and consequently a reduced Agulhas leakage transport. Therefore, a stronger Agulhas Current leads to less Agulhas leakage, but this anticorrelation is only significant when the Agulhas Current strength time series is smoothed to biennial averages.

The third monitoring strategy discussed which might be used for monitoring the magnitude of Agulhas leakage is based on Eulerian fluxes at the GoodHope line (chapter 7). By comparing the Eulerian (three-dimensional velocity-based) flux time series to the float-determined Agulhas leakage transport time series, an optimum thermohaline threshold domain is determined. The two time series have the highest correlation when the domain is defined such that only the water warmer than 14.6°C and more saline than 35.33 psu is used in the Eulerian velocity integration. With these threshold values only the thermocline part of the water can directly be measured. However, an estimate of the total Agulhas leakage flux can be obtained by doubling the flux of warm and saline water. It seems to be possible to also directly integrate over all Agulhas leakage but in that case the uncertainty level in the estimate is much higher.

All in all, it appears to be possible to design an Agulhas leakage transport monitoring system. Using the relation between Agulhas Current retroflection location and the magnitude of Agulhas leakage, the basis for such a system should be satellite altimetry. To enhance the accuracy of the estimates, this altimetry system could be augmented with mooring arrays either in the Agulhas Current at 32°S or at the GoodHope line halfway the Cape Basin.

However, estimating the magnitude of this Agulhas leakage is not easy. The Agulhas region is the locus of three circulation systems: the subtropical gyres of the South Atlantic and Indian Oceans, and the Subtropical Front of the Southern Ocean. Agulhas leakage is only a minor and intermittent flux in the region and due to the vigorous mixing in the Cape Basin the signal is quickly diluted beyond the Agulhas Current retroflection.

The method of estimating the magnitude of Agulhas leakage which is closest to the definition of Agulhas leakage employs the trajectories of floats that start in the Agulhas Current and end in the Atlantic Ocean. In this way the Indian Ocean water in the Atlantic Ocean can be labeled and tracked allowing for the determination of, among other quantities, volumetric fluxes. For a statistical analysis on interannual time scales the number of floats required is in the order of millions and one has to turn to numerical ocean models. However, even the state-of-the-art numerical ocean models have problems simulating the circulation in the Agulhas region and the results from these models are thus not very reliable.

In order to assess which is the most reliable model, a novel way to quantify the skill of numerical ocean models in simulating Lagrangian floats is introduced in chapter 2: the two-sample Kolmogorov-Smirnov test. By computing the probability that the trajectories of drifting buoys in the real ocean are statistically different from the trajectories of numerical drifters, models without any skill can be identified. Application to three different numerical ocean models in the Agulhas region leads to the conclusion that only one of them might possess skill.

The float trajectories from the only model that might possess skill in the Agulhas region are used to assess some of the characteristics of Agulhas leakage. This is done by dividing the floats into a group that ends in the Indian Ocean and a group that ends in the Atlantic Ocean (chapter 3). The distributions of these two groups are to a high extent similar within the Agulhas Current, a result which can be explained by assuming that Agulhas leakage detaches from the Agulhas Current retroflection predominantly in Agulhas rings. These coherent anticyclones, however, decay quickly. Once the floats reach the GoodHope line halfway the Cape Basin, almost 70% of the floats is within water that has almost no relative vorticity. These floats, which are outside (anti)cyclonically rotating water, cluster in large patches which are advected northward.

Nevertheless, some of the Agulhas rings stay coherent and cross the Walvis Ridge into the Atlantic Ocean. These rings do not only carry heat and salt across the Atlantic Ocean, but also energy. As the rings decay, baroclinic and barotropic energy is radiated through the Atlantic Ocean basin. The radiation of this energy is investigated within a two-layer adiabatic model in chapter 4. It appears that an Agulhas ring can radiate baroclinic energy to the northern Atlantic Ocean within four years. In the presence of a Mid-Atlantic Ridge, this transit time is reduced to several days because the ridge facilitates barotropic--baroclinic energy conversion. Once in the northern Atlantic Ocean, the baroclinic energy may enhance the meridional overturning circulation strength. This seems to occur a little over three years after the Agulhas ring is released into the Atlantic Ocean, indifferent of the presence or absence of a Mid-Atlantic Ridge. This is important information for the design of a monitoring program, as it sets the maximum amount of smoothing which is allowed.

This possible influence of Agulhas leakage on the strength of the Atlantic meridional overturning circulation is one of the reasons why a monitoring program of the magnitude of Agulhas leakage is required. It is unfeasible to base such a program on float trajectories in the real ocean as the amount of floats required is orders of magnitude larger than what is currently used. For that reason possible monitoring strategies have to be developed: Relations between the Agulhas leakage transport determined by (numerical) Lagrangian floats and easier-to-measure quantities. Three of such strategies have been assessed within the high-resolution numerical ocean model with the goal to yield a workable proxy or index.

The first strategy for monitoring the magnitude of Agulhas leakage, which is discussed in chapter 5, is based on the location of the Agulhas Current retroflection. There appears to be a significant correlation between the westward extent of the retroflection and the amount of Agulhas leakage over the GoodHope line halfway the Cape Basin on a three month time scale. In this relation, a more westward retroflection leads to a larger Agulhas leakage transport. However, the wide confidence band in the best linear fit of this relation makes the monitoring strategy of limited use for estimating the magnitude of Agulhas leakage in the real ocean. When the estimate is applied to satellite altimetry data, the confidence band is too wide for any variability of Agulhas leakage transport to be significant, except for when the Agulhas system is in an early retroflection and the Agulhas Current retroflection is so far east that Agulhas leakage is almost stopped.

The second strategy introduced for monitoring the magnitude of Agulhas leakage in the real ocean is based on the strength of the Agulhas Current upstream of the retroflection (chapter 6). This monitoring strategy is based on the correlation between Agulhas Current strength and the location where the Agulhas Current outcrops and separates from the African continental slope. When the Agulhas Current is stronger, the increased inertia causes an enhanced outcropping of the isotherms, which leads to an earlier detachment from the continent. Due to the shape of the continent, a more upstream detachment yield a less westward oriented Agulhas Current. This leads to an eastward migration of the Agulhas Current retroflection, and consequently a reduced Agulhas leakage transport. Therefore, a stronger Agulhas Current leads to less Agulhas leakage, but this anticorrelation is only significant when the Agulhas Current strength time series is smoothed to biennial averages.

The third monitoring strategy discussed which might be used for monitoring the magnitude of Agulhas leakage is based on Eulerian fluxes at the GoodHope line (chapter 7). By comparing the Eulerian (three-dimensional velocity-based) flux time series to the float-determined Agulhas leakage transport time series, an optimum thermohaline threshold domain is determined. The two time series have the highest correlation when the domain is defined such that only the water warmer than 14.6°C and more saline than 35.33 psu is used in the Eulerian velocity integration. With these threshold values only the thermocline part of the water can directly be measured. However, an estimate of the total Agulhas leakage flux can be obtained by doubling the flux of warm and saline water. It seems to be possible to also directly integrate over all Agulhas leakage but in that case the uncertainty level in the estimate is much higher.

All in all, it appears to be possible to design an Agulhas leakage transport monitoring system. Using the relation between Agulhas Current retroflection location and the magnitude of Agulhas leakage, the basis for such a system should be satellite altimetry. To enhance the accuracy of the estimates, this altimetry system could be augmented with mooring arrays either in the Agulhas Current at 32°S or at the GoodHope line halfway the Cape Basin.