jay mccreary dynamics of indian-ocean shallow overturning circulations a short course on: modeling...

Jay McCreary

Dynamics of Indian-Ocean shallow Dynamics of Indian-Ocean shallow overturning circulationsoverturning circulations

A short course on:

Modeling IO processes and phenomena

University of TasmaniaHobart, Tasmania

May 4–7, 2009

ReferencesReferences1) Miyama, T., J. P. McCreary, T.G. Jensen, S. Godfrey, and A.

Ishida, 2003: Structure and dynamics of the Indian-Ocean Cross-Equaotorial Cell. Deep-Sea Res., 50, 2023–2048.

2) (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.

3) (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.

QuestionsQuestions

1) What are shallow overturning circulations in the world ocean? What is their role in the general ocean circulation?

2) What are the structures of the prominent cells in the Indian Ocean, the Subtropical Cell and the Cross-equatorial Cell?

3) What are their fundamental dynamics?

4) What is their impact on the Indian-Ocean heat budget?

What are the 3-d structures of these cells? How do they vary on climatic time scales?

2d structure in an idealized GCM solution

SPC

Bryan (1991)

STC

AMOC

Tropics SubtropicsSubtropicsLu et al. (1998)

Subtropical Cells (STCs) in the Pacific Ocean

The STCs carry cool subtropical thermocline water into the tropics. The two cells account for almost 30 Sv of overturning.

Rothstein et al. (1998)

surface

thermocline

upwelling

subduction

subduction

3d structure in a GCM solution

QuestionsQuestions





Upwelling, subduction, and inflow/outflow regions in Indian Ocean

Somali/Omaniupwelling

Indianupwelling

5-10°S upwelling

Sumatra/Javaupwelling

Subduction

Indonesian Throughflow

Southern OceanAgulhas Current

C.I. = 1 Sv

Garternicht and Schott (1997)from global GCM (Semtner)

Equator

Meridional streamfunction from an IO GCM

Deep cell

Shallow cells

Equatorial roll

Models used in Miyama et al. (2002)

1) MKM 2½-layer model (0.5°)

2) TOMS 4½-layer model (0.33°)

3) JAMSTEC GCM (55 levels, 0.25°)

4) SODA reanalysisGCM + data

5) LCS model

Annual-mean, layer-2 circulation in MKM model

Subtropical Cell

Layer 1

Layer 2

MKM TOMS

Subsurface water crosses the equator in a western boundary, a consequence of PV conservation

Subsurface circulation of CEC (backward tracking from upwelling regions)

Subsurface circulation of CEC (backward tracking from upwelling regions)

JAMSTEC

Subsurface water crosses equator in a western boundary current, a consequence of PV conservation.

Surface water crosses equator in interior ocean, increasingly to the east for Somali, Omani, and Indian upwellings

MKM TOMS

Surface circulation of CEC (forward tracking from upwelling regions)

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.

Surface circulation of CEC (forward tracking from upwelling regions)

JAMSTEC

Equator

Equatorial roll in JAMSTEC model

Surface trajectories cross equator in the eastern ocean because of equatorial roll, consistent with observed drifters.

January

July

Surface (10 m) trajectories in JAMSTEC model

Annual-mean, surface (0–75 m) circulation in SODA reanalysis

Near-surface currents cross equator in the eastern ocean because of equatorial roll, consistent with observed drifters.

3d structure of CEC in JAMSTEC model

QuestionsQuestions





STC dynamics

Wind forcing for STC

Wind curl along the northern edge of Southeast Trades

Eq.

Basic processes for STC

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 water that upwells first flows northward along the western boundary and then eastward across the basin, a remotely forced response due to the radiation of Rossby waves from the upwelling region.

There is an additional recirculation, the so-called “β plume.”

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.

Basic processes for STC

Consider the response in layer 2 of a 2½-layer model forced by a mass sink (upwelling into layer 1) south of the equator.

CEC dynamics

a) Why does surface water cross the equator in the interior ocean?

b) What causes the equatorial roll?

Wind forcing for CEC

The IO winds circulate clockwise (anticlockwise) about the equator during the summer (winter). The annual-mean winds have the summer pattern.

EQ

Wind (boreal Summer, annual mean)

Ekman Transport

Ekman transport appears to be involved off the equator.But, what dynamics are involved near the equator?

EQ

Wind (boreal Winter)

Ekman Transport

Basic processes for CEC

fyy

y

L

XV

L

XyV

xx

x

1

/1

0

0

The Sverdrup transport is

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.

LyxXyYxXx /)()()( 0

Consider forcing by τx that is antisymmetric about the equator

but V can be rewritten

Analytic solution

Consider the equations for a 1½-layer model,

Then,

For a τx that is antisymmetric about the equator

and so h never changes in response to this wind! So, no geostrophic currents are ever generated, and the total flow field is entirely Ekman drift.

.0)()(

,/'

,/'

yxt

yy

xx

hvhuh

hhgfu

hhgfv

,)/(')/( 2ey

xxt wfhhgfh

,00

y

y

yLwe

Linear, continuously stratified (LCS) model

1) Model equations of motion linearized about a state of rest and Nb(z)

2) Solutions expressed as sums of 50 vertical modes

3) Horizontal resolution is 0.25°

4) Realistic Indian-Ocean coastline

5) Forced by Hellerman and Rosenstein (1983) winds

6) Spun up for 10 years

meridional velocity

Symmetric zonal wind

meridional velocity

Antisymmetric zonal wind

CEC dynamics

a) Why does surface water cross the equator in the interior ocean?

b) What causes the equatorial roll?

Section at 70 E

meridional velocity

Symmetric meridional wind

1) Total wind 2) Zonal wind 3) Meridional wind

LCS solution forced by July HR winds. Cross-equatorial flow is driven by τx (middle), and equatorial roll is driven by τy.

Roles of zonal and meridional winds

Courtesy of Toru Miyama

Meridional velocity zonally averaged between 40–100ºE. The linear model reproduces the GCM solution very well!

Comparison of LCS and GCM solutions

Courtesy of Toru Miyama

QuestionsQuestions





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.

There is a net annual-mean heat flux into the Indian Ocean, …

… 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.

Subtropical CellDriven 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 CellDriven 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 fluxThe observed annual-mean heat flux into the IO exists only because of upwelling associated with the STC and CEC.

Conclusions

Wind forcing for CEC

Upwelling-favorable annual-mean winds (dominated by July)

Reversing cross-equatorial winds

As a result, the IO winds circulate clockwise (anticlockwise) about the equator during the summer (winter). The annual-mean winds have the summer pattern.

Equations: A useful set of simpler equations is a version of the GCM equations linearized about a stably stratified background state of no motion. The resulting equations are

where Nb2 = –gbz/ is assumed to be a function only of z. Vertical mixing

is retained in the interior ocean.

To model the mixed layer, wind stress enters the ocean as body force with structure Z(z).

Linear, continuously stratified (LCS) model

Vertical modes: With the assumptions that ν = κ = A/Nb2(z), the ocean

has a flat bottom, and convenient surface and bottom boundary conditions, solutions can be represented as expansions in the normal (barotropic and baroclinic) modes, ψn(z), of the system. Expansions for the u, v, and p fields are

where the expansion coefficients are functions of only x, y, and t. The resulting equations for un, vn, and pn are

Thus, the ocean’s response can be separated into a superposition of independent responses associated with each mode.

jay mccreary dynamics of indian-ocean shallow overturning circulations a short course on: modeling...

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