1. Dynamics of Indian-Ocean shallow overturning circulations
A short course on:
Modeling IO processes and phenomena
INCOIS
Hyderabad, India
November 16−27, 2015

2. References
Miyama, T., J. P. McCreary, T.G. Jensen, S. Godfrey, and A. Ishida, 2003: Structure and dynamics of the Indian-Ocean Cross-Equatorial Cell. Deep-Sea Res., 50, 2023–2048.
(MKM93) McCreary, J.P., P.K. Kundu, and R. Molinari, 1993: A numerical investigation of dynamics, thermodynamics and mixed- layer processes in the Indian Ocean. Prog. Oceanogr., 31, 181–244.
(SM04) Schott, F., J.P. McCreary, and G.C. Johnson, 2004: Shallow overturning circulations of the tropical-subtropical oceans. In: Earth Climate: The Ocean-Atmosphere Interaction, C. Wang, S.-P. Xie and J.A. Carton (eds.), AGU Geophys. Monograph Ser., 147, 261–304.

3. Questions
What are shallow overturning circulations in the world ocean? What is their role in the general ocean circulation?
What are the structures of the prominent cells in the Indian Ocean, the Subtropical Cell and the Cross- equatorial Cell?
What are their fundamental dynamics?
What is their impact on the Indian-Ocean heat budget?

4. Atlantic meridional overturning circulation
[1/2] The AMOC is a key player in the climate system. It plays an important role in: i) the meridional redistribution of heat; ii) connecting the deep ocean with the upper ocean; and iii) importing/exporting substances (e.g., CO2, nutrients).
The North Atlantic AMOC circulation is structurally complex, involving sinking at a number of locations in the North Atlantic (GIN and Labrador Seas). The figure shows places where water flows horizontally in the upper and deep ocean, but it does not depict where water actually descends.
In our model, we simplify the northern region to a single boundary constraint, in order to isolate the most fundamental processes.
The AMOC downwelling branch is very complex, involving sinking at a number of locations in the North Atlantic (GIN and Labrador Seas). The AMOC is believed to be closed by upwelling in the Southern Ocean and to interior diffusion.

5. 2d structure in an idealized GCM solution
SPC
Bryan (1991)
STC
AMOC
This study, published in 1991, used an OGCM in an idealized box domain to study the Atlantic meridional overturning circulation (AMOC).
The figure plots the meridional streamfunction of the solution, obtained by averaging the velocity field zonally.
The paper was focused on the deep thermohaline cell, and barely mentioned the shallow overturning cells at all. There was only one small paragraph devoted to the STC.
Note that there is also an SPC.
What are the 3-d structures of these cells? How do they vary on climatic time scales?

6. Subtropical Cells (STCs) in the Pacific Ocean
Schematic figure of the Pacific North and South Subtropical Cells.
There is almost 30 Sv of overturning carried into the tropics by the two cells, where it upwells in the eastern, equatorial ocean.
Lu et al. (1998)
Subtropics
Tropics
Subtropics
The STCs carry cool subtropical thermocline water into the tropics. The two cells account for almost 30 Sv of overturning.

7. 3d structure in a GCM solution
surface
upwelling
thermocline
subduction
Comment that some of the water that subducts flows across the basin where it bifurcates at the western boundary, with some flowing back to midlatitudes and the rest flowing to the equator via LLWBCs. Perhaps comment on interior vs. western-boundary pathways.
Then, note how upwelled water returns to midlatitudes.
subduction
Rothstein et al. (1998)

8. Questions
What are shallow overturning circulations in the world ocean? What is their role in the general ocean circulation?
What are the structures of the prominent cells in the Indian Ocean, the Subtropical Cell and the Cross- equatorial Cell?
What are their fundamental dynamics?
What is their impact on the Indian-Ocean heat budget?

9. Wind forcing for CEC and STC
Reversing cross-equatorial winds
Relatively steady Southeast tradewinds
Upwelling-favorable annual-mean winds (dominated by July)
The strucure of the cells is determined by the wind forcing.
Upwelling occurs in regions of coastal or open-ocean Ekman suction.
Subduction (detrainment) occurs in regions of open-ocean Ekman downwelling.
There is also some overturning associated with the inter-ocean circulatoin: the deeper portion of the ITF (200–300 m) upwells in the northern IO, and leaves the basin via the Agulhas Current.
As a result, the IO winds circulate clockwise (anticlockwise) about the equator during the summer (winter). The annual-mean winds have the summer pattern.

10. Upwelling, subduction, & inflow/outflow regions Indonesian Throughflow
Indian
upwelling
Somali/Omani
upwelling
Sumatra/Java
upwelling
5−10°S upwelling
Indonesian Throughflow
The structures of the overturning cells are determined both by the locations of the upwelling regions (Arabia, India, and Sumatra/Java) and by the source regions of subsurface (thermocline) water (subduction, ITF, southern ocean).
Upwelling off Arabia is predominantly caused by alongshore winds during the SWM. Upwelling off India by wind-stress curl and winds along the east coast of India during the SWM.
Upwelling in the 5–10S band is due to open-ocean upwelling associated with wind curl at the northern edge of the Southeast Trades.
Equatorial and eastern-ocean (Sumatra/Java) upwelling, and hence the overturning cell driven by them, are typically very weak, significant only episodically during IOD events.
Subduction, the Indonesian Throughflow, and the Southern Ocean provide sources of subsurface water.
Water that enters the basins flows out of it in the Agulhas Current.
Subduction
Agulhas Current
Southern Ocean

11. Meridional streamfunction from an IO GCM
Equatorial roll
CEC
STC
The Subtropical Cell (STC) and Cross-Equatorial Cell (CEC) in a global GCM. The figure plots annual-mean streamfunction with a “correction” for the Indonesian Throughflow.
Deep cell
Garternicht and Schott (1997)

12. Models used in Miyama et al. (2003)
MKM
2½-layer model (0.5°)
2) TOMS
4½-layer model (0.33°)
3) JAMSTEC
GCM (55 levels, 0.25°)
4) SODA reanalysis
GCM + data
5) LCS model

13. Subsurface circulation of CEC
(backward tracking from upwelling regions)
TOMS
MKM
In the bottom-left panel, the pathway in the southern hemisphere continues just as in the upper two panels.
Note in the bottom-left panel how much time it takes to cross the AS and go to the equator (9 years).
TOMS similar to MKM except it directly crosses the equator. Why can it do this?!
The paths are very sharp. Why? Because of the backward tracking: In regions of subduction, the layer-2 flow diverges; as a result, when such flows are tracked in reverse there is convergence to s single streamline.
Subsurface water crosses the equator only in a western boundary, a consequence of PV conservation

14. Subsurface circulation of CEC
(backward tracking from upwelling regions)
JAMSTEC
One pathway (top) flows directly from the source region (ITF) to the upwelling region, whereas the others first subduct, thereby taking much longer.
Subsurface water crosses the equator only in a western boundary current, a consequence of PV conservation.

15. Surface circulation of CEC (forward tracking from upwelling regions)
MKM
TOMS
In contrast, surface water can cross the equator in the interior ocean because the PV of layer 1 is changed by wind curl (see below).
Surface water crosses the equator in the interior ocean, increasingly to the east for Somali, Omani, and Indian upwellings.

16. Surface circulation of CEC (forward tracking from upwelling regions)
JAMSTEC
Particles cross the equator in the eastern ocean. Why? Because of equatorial roll.
It is surprising that even these trajectories, which are NOT confined to the surface (like the surface drifters in the next plot), also travel to the eastern ocean before bending south. That must be because Toru picked SURFACE currents here, that is the shallowest part of the CEC surface branch. If he had picked a slightly deeper trajectory (but one still in the surface branch), he should have been able to find a trajectory that does not get caught up in the roll, and so moves southward in the interior ocean.
In GCMs, surface water tends to flow across the basin in the interior ocean and only crosses the equator in the eastern basin. Particle trajectories show equatorial rolls.

17. Equatorial roll in JAMSTEC model
Equatorial roll in the JAMSTEC GCM.
Note that there is a surface convergence north of the equator because of the roll, where the surface branch of the CEC dives down to cross the equator. This convergence is why SURFACE drifters don’t cross the equator in the interior ocean.
Equator

18. Surface (10 m) trajectories in JAMSTEC model
January
July
Surface trajectories cross equator in the eastern ocean because of the equatorial roll, consistent with observed drifters.

19. Annual-mean, surface (0–75 m) circulation
in SODA reanalysis
Water from the northern upwelling regions crosses the AS, primarily as Ekman drift.
It does not cross the equator until the eastern ocean
Near-surface currents cross equator in the eastern ocean because of equatorial roll, consistent with observed drifters.

20. 3d structure of CEC in JAMSTEC model
As shown in the earlier drifter JAMSTEC tracks, some trajectories get caught up in the equatorial roll. For such trajectories, the arrow near the equator would move north of the equator (and so disappear) as it extends eastward.
One near-surface flow trajectory begins in the Somali upwelling region, flows across the equator below the surface in the equatorial roll, and eventually flows southward into the SIO in the eastern ocean.
CEC water flows into the NIO below the surface along the western boundary.
As shown in other drifter JAMSTEC tracks, some trajectories get caught up in the equatorial roll. For such trajectories, the arrow just south of the equator first shifts north of the equator (and so disappears) as it extends eastward.

21. Questions
What are shallow overturning circulations in the world ocean? What is their role in the general ocean circulation?
What are the structures of the prominent cells in the Indian Ocean, the Subtropical Cell and the Cross- equatorial Cell?
What are their fundamental dynamics?
What is their impact on the Indian-Ocean heat budget?

22. STC dynamics

23. Wind forcing for the STC
Wind curl along the northern edge of Southeast Trades
There is wind curl along the northern edge of the Southeast Trades, which causes Ekman suction and a thermocline ridge.
Furthermore, there is upwelling along the ridge.

24. Basic STC processes
Consider the response in layer 2 of a 2½-layer model forced by a mass sink (upwelling into layer 1) south of the equator.
Eq.
Finally, the subsurface flow also includes the circulation of the Subtropical Gyre. As a result of all of these contributions, layer-2 STC water enters the upwelling region from the north.
There is an additional recirculation, the so-called “β plume.”
The upwelled water is supplied by eastward currents that extend to the western boundary, a remote response due to the radiation of Rossby waves from the upwelling region.
Ekman suction causes entrainment from layer 2 to layer 1.
There is a general westward flow from the western boundary to feed this upwelling.
But the entrainment also induces a clockwise circulation in layer 2 (the “β-plume”), which ensures that flow enters the upwelling region on the northern side of the upwelling region.

25. Basic STC processes
Consider the response in layer 2 of a 2½-layer model forced by a mass sink (upwelling into layer 1) south of the equator.
The source of water for the STC is from the southeastern ocean, either via a subsurface flow through the southern boundary or by subduction.
As in the theoretical schematic, the subsurface water circulates around the STG, bends eastward about 5ºS, and flows eastward to the upwelling region.
In the STC trajectory shown, subsurface (layer 2) water flows into the SIO across the southern boundary. It first circulates around the upwelling region before entering it on its northern flank.

26. CEC dynamics
Why does surface water cross the equator in the interior ocean?
What causes the equatorial roll?

27. Wind forcing for the CEC
The IO winds circulate clockwise (anticlockwise) about the equator during the summer (winter). The annual-mean winds have the summer pattern.
The IO winds circulate clockwise (anticlockwise) about the equator during the SWM (NEM).
The annual-mean winds are dominated by the summer winds, and have the summer pattern.

28. Basic CEC processes Ekman transport EQ Wind (boreal Winter)
Ekman drift is the driving force of the CEC. Applying Ekman theory to the equatorial region, however, is not usually possible since f → 0 there.
Wind (boreal Summer, annual mean)
Ekman transport appears to be involved off the equator. But, what dynamics are involved near the equator, where f → 0 and Ekman drift is not (usually) defined?

29. Analytic solution
Consider forcing by τx that is antisymmetric about the equator
The steady-state Sverdrup transport forced by this wind is
and V can be rewritten
Remarkably, the Sverdrup flow is equal to the Ekman drift for this special wind field, and the Ekman drift is still well defined even at the equator!
Thus, for this special wind the Sverdrup and Ekman transports are equal. It follows that the concept of Ekman flow can be extended to the equator, since τx tends to zero as f does.

30. Analytic solution Consider the equations for a 1½-layer model,
Solving for a single h equation gives
Furthermore, there is no Ekman pumping associated with this wind forcing, so h never changes.
So, the total flow field is entirely Ekman drift.
For a τx that is antisymmetric about the equator
Since we = 0, h never changes in response to this wind! Therefore, no geostrophic currents are ever generated, and the total flow field is entirely ageostrophic Ekman drift. 30

31. Solutions to the LCS model
The LCS equations of motion are linearized about a state of rest and Nb(z)
Solutions are expressed as sums of 50 vertical modes
Horizontal resolution is ∆x = ∆y = 0.25°
Realistic Indian-Ocean coastline
Forced by Hellerman and Rosenstein (1983) winds
Spun up for 10 years

32. Symmetric zonal wind meridional velocity
There is no cross-equatorial flow forced by an eastward, zonal wind stress. There is downwelling at equator.
meridional velocity

33. Antisymmetric zonal wind
Case of an idealized, anti-symmetric, zonal wind stress. As discussed above the response is a southward Ekman drift, even on the equator.
meridional velocity

34. CEC dynamics
Why does surface water cross the equator in the interior ocean?
What causes the equatorial roll?

35. Symmetric meridional wind
Section at 70 E
Simple wind case. Meridional wind stress produces a meridional cell.
meridional velocity

36. Roles of zonal and meridional winds
1) Total wind
2) Zonal wind
3) Meridional wind
Three solutions of the LCS model: with both zonal and meridional wind stress, with only zonal wind, and with only meridional wind.
The equatorial roll does not exist with only zonal winds.
With only meridional winds, only the equatorial roll is generated, and not any flows farther from the equator.
The downwelling during spring and fall exists even in 2), and so is caused by the zonal wind stress.
Courtesy of Toru Miyama
LCS solution forced by July HR winds. Cross-equatorial flow is driven by τx (middle), and equatorial roll is driven by τy.

37. Comparison of LCS and GCM solutions
1) The two solutions are very similar, showing that the flows are predominantly linear phenomena.
Courtesy of Toru Miyama
Meridional velocity zonally averaged from 40–100ºE. The linear model reproduces the GCM solution very well!

38. Questions
What are shallow overturning circulations in the world ocean? What is their role in the general ocean circulation?
What are the structures of the prominent cells in the Indian Ocean, the Subtropical Cell and the Cross- equatorial Cell?
What are their fundamental dynamics?
What is their impact on the Indian-Ocean heat budget?

39. Impact of STC and CEC during the SWM
So, the heat flux into the ocean is caused by oceanic upwelling. Advection then spreads cool SSTs away from the upwelling region, causing heating over a larger area.
Upwelling regions are places where ocean dynamics affects Q. This process is an essential element of the ocean-to-atmosphere feedback that generates climate modes (e.g., ENSO, IOD).
During the SWM, there are several major upwelling areas driven by alongshore winds, positive wind curl off India, and negative wind curl in the 5–10S band (which has positive Ekman pumping since f < 0. These regions dominate in the annual mean.
The h1 field shallows in these regions due to upwelling, eventually entraining cool subsurface water.
The upwelling cools SST and is altered by advection.
There is a net heat flux into the ocean in the upwelling regions, because the saturation humidity goes down, so that there is less evaporation and latent heat loss, and hence there is a net Q into the ocean.
Note that the property that ocean dynamics impacts Q is an essential element of ENSO theories.
MKM (1993)

40. Annual-mean Q There is an annual-mean heat flux Q into the IO, …
… that vanishes when cooling due to upwelling is dropped from the model. In this model, then, the annual-mean heating happens entirely because of upwelling.
How model dependent is this result? Perhaps in this model it is overemphasized because heating in the 5–10°S band is too strong.
The pattern of the net annual-mean heat flux into the IO is very similar to that during the SWM.
There is a heat loss without the cooling due to upwelling, so that the net heat flux into the IO is CAUSED BY the upwelling.

41. Comparison to the Pacific Ocean
1) The tropical Pacific is also heated on the annual mean due to equatorial upwelling.
Similarities: There is a net heat flux into the Pacific because of upwelling in the cold tongue. There are two meridional overturning cells.
Lu and McCreary (1996)
Differences: The Pacific upwelling is on the equator. The cell strength is 35−40 Sv, much stronger than in the IO: In the MKM93 solution, the overturning strength is only 11.5 Sv (5 Sv for the CEC, and 6.5 Sv for the STC).

42. Conclusions Subtropical Cell Cross-equatorial Cell Heat flux
The STC is driven by upwelling caused by Ekman pumping at the northern edge of the Southeast Trades (5–10ºS). Subsurface water for the upwelling comes from the north, due to the formation of a “β-plume.”
Cross-equatorial Cell
The CEC is driven by upwelling in the northern ocean. Its source waters are all from the southern hemisphere, requiring cross-equatorial flow.
Subsurface flow crosses the equator only near the western boundary due to PV conservation.
Near-surface water crosses the equator in the interior ocean. It is driven by the antisymmetric component of the zonal wind, which drives a southward, annual-mean, cross-equatorial Ekman drift.
Because of the equatorial roll, the CEC surface branch dives below the surface as it crosses the equator. Moreover, flow right at the surface (e.g., as measured by surface drifters) can cross only near the eastern boundary.
Heat flux
The observed annual-mean heat flux into the IO exists only because of upwelling associated with the STC and CEC.