On the Mechanisms of the Late 20th century sea-surface temperature trends in the

Southern Ocean

Sergey Kravtsov

University of Wisconsin-MilwaukeeDepartment of Mathematical Sciences

Atmospheric Science Group

Collaborators:

I. Kamenkovich, University of Miami, USA; A. Hogg, Australian National University, Australia; and J. M. Peters, University of Wisconsin-Milwaukee, USA

6th International Conference on Mathematical Modeling, Yakutsk, Russia

July 3–8, 2011

http://www.uwm.edu/kravtsov/

Geophysical Fluid Dynamics• Considers the motion of thin layers of fluid—

the atmosphere and the ocean — on a rotating

spherical Earth.

• Dominant motion — solid-body rotation; winds

and currents we observe are, in general, small

deviations from this motion; this smallness is

measured by a dimensionless Rossby number Ro.

• These layers are stratified (light fluid is above

the heavy fluid) and the local motion is quasi

two-dimensional (vertical velocities are small).

The primary cause of the general circulation

• Unequal heating of the earth’s surface

• Temperature gradients — pressure gradients

— winds

Coriolis Force

Dominant balances: Hydrostatic and geostrophic approximations

€

−g=−1ρ∂P∂z

; − fv=−1ρ∂P∂x

; fu=−1ρ∂P∂y

; f ≡2Ωsinφ

• The scale at which rotational effects become as

important as buoyancy effects is called the

Rossby radius Rd; typical values for midlatitude

atmosphere — 1000km, ocean — 50km€ €

• Eliminating pressure using equation of state

results in thermal wind relation, which connects

horizontal temperature gradients with vertical

shear of horizontal wind uz, vz.

Typical map of sea-level pressure and winds (January)

• The response of the atmospheric jet over the

Southern Ocean to anthropogenic forcing

is to intensify and shift southward

• Midlatitude jets are largely eddy-driven

• Eddies are generated at the scale of Rd

Lamont's Broecker WarnsGases Could Alter Climate

Oceans' Circulation Could Collapse

BY LAURENCE LIPPSETT

Thermohaline circulation links the Earth'soceans. Cold, dense, salty water from the NorthAtlantic sinks into the deep and drives the circulationlike a giant plunger.On the eve of the international meeting on global warming thatopened Dec. 1 in Kyoto, Japan, one of the world's leading climateexperts warned of an underestimated threat posed by the buildup ofgreenhouse gases—an abrupt collapse of the oceans'prevailing circulation system that could sendtemperatures across Europe plummeting in a span of10 years.

Mid-latitude Jet Streams

Wind-driven (WDC) and thermohaline (THC) circulation

• WDC:

Surface currents

• Both types of

currents combine to

define global 3-D

circulation

Ocean’s “weather”: mesoscale eddy field

Summary thus far• Differential heating by the sun induces equator-to-

pole thermal contrasts that drive zonal atmospheric

jets with vertical shear• These jets are unstable and generate turbulent

eddies at the Rd scale (~1000km for the atmo.); the

eddies interact with the jet and produce eastward

mid-latitude jets that reach the Earth’s surface

• The mid-latitude jet over the Southern Ocean

drives the Antarctic Circumpolar Current (ACC)• The instabilities of ACC current system lead to

oceanic eddy field (50-km scale) not explicitly

resolved by global climate models

Response of the Antarctic Circumpolat Current (ACC) to

intensifying jet stream• Hogg et al. (2008)

demonstrated in an

idealized, but eddy-

resolving three-layer

model that linearly

increasing wind stress

causes no change in

the ACC transport!

Response of ACC to increasing wind-stress II: “eddy saturation”

• ACC transport does not change

• Instead, eddy field intensifies

• Enhanced eddy mixing modifies both surface

and subsurface climate-change signatures, e.g.,

temperature trends

• These conjectures based on the idealized model

simulations were confirmed using more complete

eddy-resolving models and observations

Estimates of the eddy effects on SST in Hogg et al. (2008) model

• Typical eddy-driven

SST trends forced

by wind-stress

trends similar to the

observed (10% per

decade) are 0.1–0.2

ºC per decade

SST trends over ACC: Observations and simulations by coarse-resolution

global climate models

• SST trends match, but wind-stress trends don’t!(despite!)

Hypothesis to explain discrepancies:

• Global climate models make two compensating

errors to achieve seemingly correct SST trends

over the ACC:

• The wind-stress trends are much underestimated

due, presumably, to incompleteness of

anthropogenic forcing in many of the models

comprising the present ensemble

• The models misrepresent eddies and cannot

capture trends in eddy-induced lateral mixing

“Eddies” in coarse-resolution models: GM parameterization

€

w* = −∇ • (κ∇ρ /ρ z); u* = (κ∇ρ /ρ z)z;∇ • u*+wz* = 0.

€

∂T∂t

+ (u+ u*) • ∇T + (w +w*)∂T

∂z=∇ρ • (κ∇ρT)

• z-coordinates:

• Isopycnal coordinates:

€

ht +∇ρ (uh) =∇ρ • (κ∇ρh); h = −∂z /∂ρ

Tt + (u+ u*) • ∇ρT =∇ρ • (κh∇ρT) /h

• u* and w* —

eddy-induced transports

Application of GM scheme in global climate models

• Resulted in solutions without climate drift,

in part due to improvements in the ACC region

• The GM scheme needs to be turned off in the

mixed layer, where the slopes of isopycnals are

steep. Slope-limiting and/or taper functions were

typically used• Non-constant K(x, y, z, t) have been suggested.

We argue that this is essential to model ACC

changes forced by wind-stress trends in coarse-

resolution models

SST response in a coarse-res.

ocean model• No change in wind

• Observed wind changes

• Linearly increasing K

and KH (in mixed layer)

• The “eddy-induced”

response magnitude

consistent with that

in idealized eddy-

resolving model

• The SST trends due

to various forcings

combine linearly

Conclusions

• Correct simulation of surface response in the ACC region to various forcings has numerous implications for accurate climate prediction (coupled modes, CO2 sinks etc.)

• The ACC operates in an eddy-saturated regime:

increasing wind-stress forcing does not accelerate

the time-mean current, but energizes eddy field

• The enhanced eddy mixing induces quantitatively

important SST trends in the region• This effect can be parameterized in coarse-grid climate

models via variable GM and lateral diffusion coefficients.

Such schemes are not implemented in many of these models... (or maybe it’s better to just resolve eddies!)