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![Page 1: On the Mechanisms of the Late 20 th century sea-surface temperature trends in the Southern Ocean Sergey Kravtsov University of Wisconsin-Milwaukee Department.](https://reader035.fdocuments.us/reader035/viewer/2022062309/56649e0c5503460f94af4ef6/html5/thumbnails/1.jpg)
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/
![Page 2: On the Mechanisms of the Late 20 th century sea-surface temperature trends in the Southern Ocean Sergey Kravtsov University of Wisconsin-Milwaukee Department.](https://reader035.fdocuments.us/reader035/viewer/2022062309/56649e0c5503460f94af4ef6/html5/thumbnails/2.jpg)
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).
![Page 3: On the Mechanisms of the Late 20 th century sea-surface temperature trends in the Southern Ocean Sergey Kravtsov University of Wisconsin-Milwaukee Department.](https://reader035.fdocuments.us/reader035/viewer/2022062309/56649e0c5503460f94af4ef6/html5/thumbnails/3.jpg)
The primary cause of the general circulation
• Unequal heating of the earth’s surface
• Temperature gradients — pressure gradients
— winds
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Coriolis Force
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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.
![Page 6: On the Mechanisms of the Late 20 th century sea-surface temperature trends in the Southern Ocean Sergey Kravtsov University of Wisconsin-Milwaukee Department.](https://reader035.fdocuments.us/reader035/viewer/2022062309/56649e0c5503460f94af4ef6/html5/thumbnails/6.jpg)
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
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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.
![Page 8: On the Mechanisms of the Late 20 th century sea-surface temperature trends in the Southern Ocean Sergey Kravtsov University of Wisconsin-Milwaukee Department.](https://reader035.fdocuments.us/reader035/viewer/2022062309/56649e0c5503460f94af4ef6/html5/thumbnails/8.jpg)
Mid-latitude Jet Streams
![Page 9: On the Mechanisms of the Late 20 th century sea-surface temperature trends in the Southern Ocean Sergey Kravtsov University of Wisconsin-Milwaukee Department.](https://reader035.fdocuments.us/reader035/viewer/2022062309/56649e0c5503460f94af4ef6/html5/thumbnails/9.jpg)
Wind-driven (WDC) and thermohaline (THC) circulation
• WDC:
Surface currents
• Both types of
currents combine to
define global 3-D
circulation
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Ocean’s “weather”: mesoscale eddy field
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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
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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!
![Page 13: On the Mechanisms of the Late 20 th century sea-surface temperature trends in the Southern Ocean Sergey Kravtsov University of Wisconsin-Milwaukee Department.](https://reader035.fdocuments.us/reader035/viewer/2022062309/56649e0c5503460f94af4ef6/html5/thumbnails/13.jpg)
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
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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
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SST trends over ACC: Observations and simulations by coarse-resolution
global climate models
• SST trends match, but wind-stress trends don’t!(despite!)
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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
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“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
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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
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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
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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!)