Transcript Extratropical Stratosphere-Troposphere Dynamical Coupling

Kushner: GCC Lecture Topics
• 3-D Dynamical Models …
Tropospheric eddies and the general circulation.
Simple troposphere and stratosphere-troposphere
atmospheric general circulation models.
• … Climate Models (Tropospheric GCMs) …
Building them and using them.
• … and a Little Philosophy
Please indulge me.
Three-Dimensional Dynamical Models, 1
Paul J. Kushner
University of Toronto
GCC Summer School
Banff 2005
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Outline
• Introduction: A little philosophy …
• Phenomenology: Large-scale waves and the
atmospheric general circulation.
• Theory and simple models of transient eddies:
baroclinic instabilities and lifecycles
• Introducing simple atmospheric general circulation
models.
• Conclusion: Points to take hiking
Introduction: A Little Philosophy …
• Thanks to Isaac Held at NOAA/GFDL.
• We don’t want to get hung up on generalities,
but it’s good to know what we’re doing and
why we’re doing it.
• Conceptual models/pictures are useful but
they are often ambiguous, only vaguely
understood, and overplayed.
Some Common Conceptual Models
• Conveyor belt
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• IPCC Radiative
Forcing Graphic
• STE
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In Defense of Simple Systems
• In addition to conceptual pictures, we need to
understand simple physically realizable analog
systems.
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• Held (2005):
Biologists agree without apology that a relentless
focus on E. Coli, flies and mice will lead to
progress in human biology.
• We should focus on studying such analogs in climate
systems.
Today
• I will stress the importance of midlatitude
weather (baroclinic eddies) to understand the
tropospheric and stratospheric general
circulation.
• I will try (not always successfully) to build my
arguments on physically realizable systems.
Radiative Imbalance and Transport
Top-of-Atmosphere Radiation
At each latitude,
there is an
imbalance between
absorbed and
emitted radiation
This radiative
imbalance can occur
because the
atmosphere and
oceans can move
energy around.
Hartmann 1994
A Steady-State Model
Heat Sink
Imagine heating up
water in a box.
When heating and
cooling are vertically
distributed, various
details determine the
horizontal scales of
motion.
Heat Source
But with a lateral
heating distribution, the
circulation cell tends to
fill the cell.
In steady state, there is
a balance between
baroclinic generation of
circulation and friction.
(Wallace and Hobbes)
A Steady-State Model
But with a lateral
heating distribution, the
circulation cell tends to
fill the cell.
In steady state, there is
a balance between
baroclinic generation of
circulation and friction.
(Wallace and Hobbes)
An Adjustment Model
Adjustment of a baroclinic fluid
Now suppose we turned off
the heating. The fluid
spontaneously adjusts to a
stable equilibrium.
The adjustment involves a
“poleward” flux of heat and
constituents.
The distribution of potential
temperature in the
troposphere is analogous
to these models.
As of today, we still lack a
theory for the slope of the
isentropes in the
troposphere.
Gill 1992
Annual-mean Potential Temperature
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IRI/LDEO via J. Marshall
Rotation and Jets are Important
Annual-mean Potential Temperature
The fluid-cell
examples, to be
relevant, need to be
complemented by
rotation.
The reason is that
for a rapidly rotating
hydrostatic fluid,
baroclinicity also
gives rise to zonal
jets.
These jets in turn
give rise to waves
that can transport
heat poleward much
more efficiently than
zonal motions.
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Annual-mean Zonal Wind
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IRI/LDEO via J. Marshall
Breakdown of Energy Transports
Sensible-heat (T)
transport is
representative of the
total energy
transport.
Meridional Flux of Sensible Heat
Zonally symmetric
motions do most of
the transport in the
tropics.
Waves do most of
the transport in
midlatitudes.
Stationary waves
are important in NH
winter;
At other times, and
in the SH, transient
waves dominate.
Peixoto and Oort 1992
Laboratory Baroclinic Waves
• The rotating annulus below is heated on the inside
ring (orange = warm, blue = cold)
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• The flow remains annular until the rotation is
increased enough.
• Then baroclinic instability sets in (right).
http://dennou-k.gaia.h.kyoto-u.ac.jp/library/gfd_exp/exp_e/doc/bc/images/bc05.gif
Observed Wave Spectra
Aircraft measurements of spatial spectra (upper trop)
The energetic waves
have scales
between 103-104km.
The figure suggests
a self-similar
turbulent character.
But in many ways
these waves have a
linear or weakly
nonlinear character.
We will focus on the
transient waves but
show stationary
waves for
comparison …
animations
Gage and Nastrom 1985
Midlatitude Baroclinic Waves
Meridional Velocity Correlations
These waves
propagate in
packets.
Their group
speed (blue) is
greater than their
phase speed
(red).
Their westward
phase tilt with
height implies a
poleward heat
transport.
Their “crescent”
shape implies a
meridional
convergence of
zonal momentum.
Chang and Yu 1999, Chang 1993
Explanation of Phase Tilts
• Consider fluxes of momentum and of heat
(for simplicity, flux of buoyancy).
–
Midlatitude Stationary Waves
DJF Z*500, NCEP Reanalysis
Like the
transient
eddies, these
waves are
associated with
momentum flux
converges and
poleward heat
transports.
DJF Z*(60N), NCEP Reanalysis
Unlike the
transient
eddies, these
waves amplify
into the
stratosphere.
Transient and Stationary Eddies
We see that both transient
and stationary eddies play a
large role in stratospheric
variability and transports of
heat and momentum.
Randel 1992
On Eddy Fluxes of Heat and Momentum
• The stationary and transient eddies share
some common features and their flux
contributions rarely seem to cancel.
• We expect this reinforcement because of the
robust tendency for atmospheric waves to flux
potential vorticity downgradient.
• Dylan discussed this in the context of fluxgradient Kyy formulations for the BDC.
• We’ll return to these ideas later.
Transient and Stationary Wave Models
• We will now run through a set of models that
capture the main features of transient eddies,
representing work that extends from the
1940’s until today.
• These all represent transient “initial-value
problem” models where initial conditions
matter.
For climate (equilibrated) models, initial
conditions should be forgotten.
Initial Value Problems
•
The first set of problems we’ll look at are
linear wave problems.
1. We start with the primitive equations.
2. We scale them using the assumptions of
quasigeostrophic scaling to obtain QG
equations.
3. We then assume some basic flow and
linearize about it (as Charles did).
4. Fast growing (unstable) waves are taken to
be the relevant ones.
Models of Baroclinic Eddies: Phillips
• We linearize the equations about this basic state
using QG scaling.
• When we add waves to this basic state, we find:
Holton: A Growing Baroclinic Wave
This model has some of the
basic elements we are
looking for, in particular the
westward phase tilt with
height and the right kind of
growth rates.
Notice the x-z plane
circulation accompanying
the growing wave: all these
agree qualitatively with
observed waves.
Models of Baroclinic Eddies: Eady
• The fastest growing wave: 4000 km (m=6)
• Growth rate corresponds to about 2-3 days efolding time:
Gill: A Growing Eady Wave
This model has the
appropriate phase tilt with
height.
It suggests that a strong
interaction between the
surface and tropopause can
help baroclinic waves grow.
Models of Baroclinic Eddies: Charney
• Growth rate as in Eady model:
Gill: A Growing Charney Wave
In this model, the vertical
phase tilt and heat fluxes
are more surface trapped.
The vertical scale of the
wave is a strong function of
beta and u.
Linear Baroclinic Eddies: Simmons and Hoskins
Basic State Wind, Temperature,
and Growing Wave
Modern computers made it
possible to avoid QG
scaling, include spherical
effects and a realistic basic
state.
The resulting waves looked
more and more like Chang’s
regression maps.
Notice how the unstable
waves flux momentum into
the jet core
Simmons and Hoskins 1976
Nonlinear Baroclinic Eddies
Polvani et al. 2004
Simmons and Hoskins 1978
Nonlinear simulations allowed the baroclinic waves to
run through life cycles of growth, saturation and decay.
Notice how the waves sharpen the jet.
The Polvani et al. calculations showed the packet
structure clearly.
Transient Eddies in Climate Models
Transient Eddies in Climate Models
• We now look for the simplest models that can
maintain a general circulation similar to nature.
• We think of a dry atmosphere in which the
temperature is relaxed back to a baroclinically
unstable profile of temperature.
• The PBL and sponge (!) are damped with Rayleigh
friction.
• This system is not fully realizable (Rayleigh drag).
• Animations …
Points to Take Hiking
• Baroclinic eddies play a central part in the general
circulation, so we should get to know them.
• Baroclinic eddies can be captured by a sequence of
more and more sophisticated models.
• By putting them in a climate setting (the simple
AGCM), we will now be able to see how baroclinic
eddies:
Set the stratification of the troposphere.
Influence the connection of the stratosphere to the
troposphere.