Spiraling pathways of global deep waters to the surface of the Southern Ocean

Upwelling of global deep waters to the sea surface in the Southern Ocean closes the global overturning circulation and is fundamentally important for oceanic uptake of carbon and heat, nutrient resupply for sustaining oceanic biological production, and the melt rate of ice shelves. However, the exact pathways and role of topography in Southern Ocean upwelling remain largely unknown. Here we show detailed upwelling pathways in three dimensions, using hydrographic observations and particle tracking in high-resolution models. The analysis reveals that the northern-sourced deep waters enter the Antarctic Circumpolar Current via southward flow along the boundaries of the three ocean basins, before spiraling southeastward and upward through the Antarctic Circumpolar Current. Upwelling is greatly enhanced at five major topographic features, associated with vigorous mesoscale eddy activity. Deep water reaches the upper ocean predominantly south of the Antarctic Circumpolar Current, with a spatially nonuniform distribution. The timescale for half of the deep water to upwell from 30° S to the mixed layer is ~60–90 years.


Supplementary Information
Supplementary Note 1 A motivation for this study is the set of maps in the WOCE Hydrographic Programme (WHP) atlas Volume 1: Southern Ocean (Orsi & Whitworth, 2005), with properties displayed along neutral density surfaces characterizing the Indian and Pacific Deep Waters (27.84 kg m -3 ) and the North Atlantic Deep Water (28.05 kg m -3 ). These maps were constructed by gridding hydrographic data from the National Oceanographic Data Center (NODC) and the WHP data collected in the 1990s. Fig. 1 and Supplementary   Fig. 1 show properties along the latter neutral density surface, along with the four major ACC fronts from one particular source (Orsi et al., 1995), bathymetry (single contour of 3000 m is superimposed), and the latitude band of Drake Passage, across which the deep waters must move in order to upwell to the sea surface. The gridded potential temperature shown in Supplementary Fig. 1b was replotted on the gridded depth from Supplementary Fig. 1a to produce the 3-D Fig. 1a, selecting only the region where gridded potential temperature is greater than 1.6°C. From the full map, it is clear that water well above freezing reaches the Antarctic continent in the southeastern Pacific sector, as reviewed in the main text. The oxygen and nitrate maps show the inflow of low oxygen, high nutrient waters from the Pacific and Indian Oceans, and their spiral around Antarctica, rising to the sea surface as tracked using depth in Supplementary Fig.   1a.
Careful attention to the pathway of the warmest water and most extreme oxygen and nitrate in Supplementary Fig. 1 suggests that the cores of most extreme properties shift southward across the ACC fronts over or downstream of the major topographic obstacles, particularly noticeable at the Mid-Atlantic Ridge, Southwest Indian Ridge and the Pacific-Antarctic Ridge. However, there is not enough resolution in these fields to definitively show details of shifts across fronts, and upwelling of the core of properties associated with these obstacles is difficult to extract from the hydrographic observations. The numerical model analyses clearly show both of these. These maps also do not provide transports or time scales for the upwelling water, nor do they clearly show where the properties preferentially reach the sea surface. And finally they cannot show diapycnal transformation along the pathway of particles in the southeast spiral.
The numerical models are used to explore all of these important aspects of the upwelling pathways and rates.

Supplementary Note 3
Unresolved sub-grid scale physics and dynamics and temporal averaging of the model velocities have an impact on particle trajectories. Thus we performed multiple sensitivity analyses using SOSE to assess the impact of varying model averaging timescales and Lagrangian methods on our results. First, the impact of adjusting the temporal averaging of model velocity data is compared for daily averaged, 5-day averaged and 30-day averaged velocities (Supplementary Fig. 5). SOSE velocities were saved as daily averaged output, but due to limited computer resources CM2.6 velocity output is only available as 5-day averages and CESM output is only available as 30-day averages. The maximum storage interval for accurate Lagrangian particle tracking depends on several factors related to dominant scales of length, velocity, model grid size and time.
Experiments in the global 1/10°OFES model (the same resolution as CM2.6 and CESM used here) showed that connectivity transports and transit times (bulk measure of the flow) were relatively insensitive to time averaging on timescales of 3-days to 30-days (Qin et al., 2014). Here we compare the impact of timeaveraging velocities on our particular results, and we use SOSE because it has sufficiently high temporal resolution output available to test this ( Supplementary Fig. 3), while CESM has only 30 day averaged output. We find that pathways are insensitive to averaging velocities on 5-day timescales compared to daily timescales north and within the ACC, but south of the ACC particle-transport is slightly higher in the 5-day averaged experiment than the daily averaged experiment ( Supplementary Fig. 3b,d). The 30-day averaged experiment is also qualitatively similar to the daily and 5-day averaged experiment, but with somewhat less particle-transport in the ACC and more particle-transport south of the ACC than the experiment using daily averages ( Supplementary Fig. 3c,e). It is important to note that only single-particle statistics are used in this analysis, which are expected to be mainly affected by the most energetic parts of the flow and thus are less sensitive to sampling frequency than other Lagrangian statistics. This could explain why the CESM results are similar to CM2.6 and SOSE even though the mesoscale is not well sampled in CESM.
Further work is needed to fully interpret the differences in the experiments with different timescale averages, but the qualitative agreement of the upwelling pathways in SOSE with velocity averaging timescales up to 30-days suggest that our analysis of 30-day averaged velocities in CESM is justified.
Second, for some applications it is useful to add stochastic noise to trajectories with the aim of parameterizing diffusion by unresolved eddy motions that are absent in the explicitly resolved eddy field. Because the models used here are eddy-resolving or eddy-permitting, we have chosen not to include stochastic noise in the trajectory motions. To test whether the inclusion of stochastic noise significantly impacts our results, we repeated the experiment in SOSE with the addition of a random walk scheme. An additional displacement is added to particles at each time step by implementing the random number generator algorithm described in Kinderman & Monahan (1977) with zero mean and unit variance and a horizontal diffusivity of 25 m 2 s -1 and a vertical diffusivity of 1x10 -5 m 2 s -1 . We show in Supplementary Figure 4 that the resulting pathways do not change significantly with the inclusion of diffusion. With diffusion, there is slightly less particle-transport that travels close to the Antarctic continent and slightly less particle-transport following the Agulhas Current southward from 30°S, and a very slight increase in particle-transport within the ACC.
There are several limitations to this comparison that are important to note. First, the stochastic noise we added to the trajectories is unbiased (positive and negative displacements are equally probable), which we know is not true in reality. Secondly, there are important sub-mesoscale advection and mixing processes not resolved in the models that are not parameterized. We acknowledge these limitations, and while the comparison in Supplementary Figure 4 is a first step toward determining the impact of mixing on particle trajectories, further work is needed to represent mixing processes more realistically.
Finally, sufficiently large numbers of particle trajectories are important to accurately represent the volume transport and provide robust statistics. We test the sensitivity of the particle pathways to the number of particles released by halving the number of particle trajectories used in the pathway analysis in SOSE ( Supplementary Fig. 5). The comparison shows that the upwelling pathways are insensitive to halving the number of particles, indicating that we have released sufficient numbers of particles to capture the spatial structure of the upwelling pathways.

Supplementary Note 4
Upwelling across the 1000 m depth surface in CESM and SOSE is similar to that in CM2.6 (Supplementary Figs. 6a and 7a). Note that because CESM output is 30-day averages, the eddy kinetic energy (contoured in blue in Fig. S6a) does not include transient mesoscale variability on timescales less than 30-days. However, the spatial patterns of high EKE in CESM are very similar to those in CM2.6, which includes variability between 5-days and 30-days.  Total  70  79  41  Atlantic  61  72  48  Indian  68  78  50  Pacific  58  68  41  CM2.6  Total  62  72  28  Atlantic  49  61  28  Indian  68  78  48  Pacific  47  60  22  SOSE  Total  92  96  81  Atlantic  89  96  82  Indian  76  82  29  Pacific  109  111  93 Supplementary Table 1: Timescales of upwelling in each model and each ocean basin. The mode is determined by first smoothing the transit time distribution, then finding the maximum value in the distribution.
Supplementary Figure 1: Properties of the neutral density surface 28.05 kg m -3 , from the WOCE Hydrographic Programme Atlas Volume 1: Southern Ocean (Orsi & Whitworth, 2005):(a) Depth (m), (b) potential temperature (°C), (c) oxygen (umol/kg), (d) nitrate (umol/kg). Superimposed on the WHP maps are the 3000 m bathymetric contour (gray), ACC fronts (Orsi et al., 1995) (blue), and the latitude range of Drake Passage (green). CM2.6 Indian particle pathways with >3.5% particle-transport CM2.6 Pacific particle pathways with >3.5% particle-transport Supplementary Figure 5: Sensitivity of pathways in SOSE to halving the number of particles included in the pathway calculation. Percent of particle-transport visiting each 1°latitude x 1°longitude grid column from release at 30°S and before reaching the surface mixed layer for (a) all of the upwelled particle trajectories, (b) half of the total upwelled particle trajectories, and (c) all particle trajectories minus half of the particle trajectories (a-b). Supplementary