Transcript Extratropical Stratosphere-Troposphere Dynamical Coupling

Three-Dimensional Dynamical Models, 2
Paul J. Kushner
University of Toronto
GCC Summer School
Banff 2005
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Outline
• Review
• Using a simple dry AGCM to study
The tropospheric general circulation.
The distribution of relative humidity in the
troposphere.
The connections between the stratosphere
and the troposphere.
• Strengths and weaknesses of simple models
Terms and Concepts
• Quasigeostrophic Scaling:
• Potential vorticity definition:
An Adjustment Problem: Homework! (Sort of)
• This example illustrates the impact of rotation (and some
subtleties).
• The diagram below represents the cross section of a channel
going into the screen.
air
water
• Initially, the fluid is sloped (gently) and is at rest. (Imagine
holding it in place with a sheet of plexiglass.)
• 1. Non-rotating case (f = 0): estimate the cross channel
transport of mass and cross-channel speed you would obtain
afterwards, in terms of the slope, of g, and of the mean layer
depth.
An Adjustment Problem: Homework! (Sort of)
• 2. Rotating case (f > 0). On the f plane, you could imagine
removing the plexiglass and setting up a geostrophically
balanced flow into the screen with this original slope. In this
case, there would be no cross-channel mass flux. This can’t
happen: why? (There are a couple of reasons.)
air
water
• 3. For the ambitious: solve for the equilibrium height and
estimate the cross-channel mass flux. Make as many simplifying
assumptions as necessary.
Review - 1
• Transport is needed to
explain the observed
distribution of TOA
radiation and the
temperature distribution
of the atmosphere.
Top-of-Atmosphere Radiation
• Rotation supresses
zonally symmetric
circulations, so …
Hartmann 1994
• … Baroclinic waves
(transient and
stationary) must do the
transport.
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Review – 2
Meridional Velocity Correlations
Transient baroclinic
waves transport
much of the energy
in the extratropics.
They travel in
packets and have
characteristic phase
tilts that correspond
to systematic effects
on the mean flow.
A set of models of
increasing complexity
accounts for these
structures.
Chang and Yu 1999, Chang 1993
Review – 3
• We described a sequence of linear models of
baroclinic waves.
Phillips (Holton)
Eady (Gill)
Simmons and Hoskins
Charney (Gill)
Review – 4
Nonlinear Baroclinic Lifecycles
Nonlinear primitive equations models showed how
baroclinic eddies can be set up, grow, and saturate.
But there needs to be a way of restoring the baroclinicity
for them to be sustained.
Transient Eddies in Climate Models
• We have seen that we need (at least) a threedimensional primitive equations model to
properly capture baroclinic eddy structure.
• We began talking about a dry nonlinear
primitive equations model with the following
forcing and dissipation:
Baroclinic Turbulence Models: T. Schneider
Let’s first look at a dry GCM
developed by Tapio Schneider.
Equilibrium Potential Temperature (input)
In his model, the tropospheric
equilibrium temperature profile is
convectively unstable.
The deep tropics are constrained
to be close to an “effective” moist
adiabat with strong thermal
damping. In midlatitudes, the
damping is weaker.
Time Mean Potential Temperature (output)
Notice that the end climate is
stably stratified. The dark line in
the upper third of the figure is the
tropopause (defined in a special
way).
Schneider 2004
Baroclinic Turbulence Models: T. Schneider
Equilibrium Potential Temperature
What’s interesting here is that
there is no dry convective
adjustment in the model: the
baroclinic eddies set the
stratification of the extratropics.
In the same paper, Schneider
argues that the same dynamics
establishes the gross features of
the tropopause.
Time Mean Potential Temperature
Schneider 2004
Baroclinic Turbulence Models: T. Schneider
Time Mean Potential Temperature
His definition of the tropopause is
based on the flux of mass
between isentropic surfaces,
represented at right in a potentialtemperature/latitude plot of mass
streamfunction (bottom). This is
the Brewer-Dobson circulation of
the troposphere, with a strong
midlatitude eddy driven
component.
Mass Streamfunction
The dotted lines mark typical
surface potential temperature
values. Most of the return flow
occurs at temperatures below the
average surface temperature, in
“cold air outbreaks. “
Schneider 2004
Baroclinic Turbulence Models: T. Schneider
Based on the idea that baroclinic
eddies diffuse PV in the interior
and potential temperature at the
surface, Schneider derives the
following scaling relationship:
This implies that the lowermost
isentrope that reaches the
tropopause should originate in the
tropics.
The plot at left represents the
LHS and RHS of this estimate for
a very wide range of simulations.
The estimate is very robust.
Schneider 2004
Eddy Diffusivity
Here is some
observational support
for the idea that
baroclinic eddies are
diffusive in some way.
The contours in the plot
represent 850mb DJF
temperatures.
The red vectors
represent (the divergent
part of) the heat flux
from the NCEP
Reanalysis.
The blue vectors
represent (the divergent
part of) the
downgradient flux
using the formula at
right.
Kushner and Held 1998
A Simple Model of Tropospheric Humdity
RH in Held-Suarez Dry GCM. Galewsky et al. 2005.
It has recently been realized that the humidity distribution can be reconstructed by
advecting a water-like tracer by the large scale flow. This figure shows how the
“Held-Suarez” dry AGCM represents this. Like Schneider’s model, only baroclinic
eddies are active in midlatitudes.
A non-interactive water tracer flux is set at the surface. The tracer is advected until
saturation is reached, at which point it is removed.
Notice the dry subtropics. Subtropical dryness is often ascribed to the descending
branch of the Hadley Cell (here driven by the model’s diabatic cooling).
A Simple Model of Tropospheric Humdity
Tracers of Last Saturation. (Galewsky et al. 2005)
The darkest red colors indicate the point of origin of saturated parcels.
Lighter shading indicates the probability that the air at a particular latitude and height
was last saturated at the point of origin.
This plot suggests that the lower-tropospheric subtropics are dry because baroclinic
eddies transport air from the subtropics, along isentropes, to the cold extratropical
upper troposphere, and back again. The lower-tropospheric RH minimum thus has
relatively little to do with the Hadley Cell.
A similar analysis works for the observations (NCEP Reanalysis + MATCH).
Simple Models of Stratosphere-Troposphere Coupling
Scinocca and Haynes showed that
adding a stratosphere layer to this
type of GCM resulted in an
interesting coupling between
stratosphere and troposphere.
Equilibrium winds and temperatures
Their model has no stationary
waves.
Instead, synoptic-scale wave
packets generate low-wavenumber
waves that propagate into the
stratosphere … animations.
Time Evolution of Spatial Spectrum
Lorenzo Polvani and I used this kind
of model to study the problem of the
coupling between the stratosphere
and troposphere. We focused on
the importance of these transient
eddies.
Scinocca and Haynes 1998
Polvani and Kushner 2002
Teq( g = 3 )
• Stratosphere: blend polar night
and summer profiles.
• Strength of polar vortex tuned by
g.
•
Troposphere: baroclinically unstable
profile.
•
Flat lower boundary, so no stationary
waves (Southern Hemisphere
conditions) … animations.
A Spontaneous Sudden Warming
The top plot shows a time series of
polar-cap average temperature at 50
hPa from a simulation with timeindependent forcing.
At Day 7121, there is a seven
standard deviation peak in
temperature.
This corresponds to a split-vortex
major warming event in the model
(bottom left, in 750K PV).
Kushner and Polvani 2005
For comparison, a similar plot is
shown from the 2002 SouthernHemisphere major Warming
(Baldwin et al.).
The transient eddy activity from the
troposphere is therefore able to
generate a
Kushner and Polvani 2005; Baldwin et al. 2003
Stratosphere-Troposphere Coupling
• The problem we are interested in: influence of
springtime ozone loss on the tropospheric circulation.
Springtime ozone
loss in the Southern
Hemisphere ...
Trend in
Antarctic Ozone
Gillett and Thompson 2004
... has cooled the
lower stratosphere.
Trend in Antarctic
Polar-Cap Average
Geopotential Height
But notice the likesigned trend in the
troposphere.
Thompson and Solomon 2002
Cooling the Polar Stratosphere
g=2
g=3
g=4
What happens in our simple model as we cool the polar
stratosphere?
Response to Stratospheric Cooling
As Polar
Stratosphere
Cools, Jet
Stream Shifts
Poleward
The Response is “Modal”
Annular Mode
Response
Residual
•In the troposphere, the response matches the model’s “annular mode.”
•The residual is concentrated in the stratosphere.
•In the response, the baroclinic eddy activity shifts poleward.
•The coupling between the troposphere and the stratosphere is very tight.
The Response is Robust
Latitude of Surface Wind Max vs g
colder strat 
colder strat 
20 levels
40 levels
80 levels
The World of General Circulation Models
• In a comprehensive GCM, we see the same
tropospheric response to ozone depletion (Gillett and
Thompson 2004):
The tropospheric
response accounts for
the observed DJF
trends.
Although our simple
model showed this
general behaviour,
Gillett and Thompson
demonstrated
quantitative agreement
with the obs.
Simulated response
to ozone depletion
(UKMO model)
Trend in Antarctic
Polar-Cap Average
Geopotential Height
Strengths of these Simple Models
• We have seen several examples of how baroclinic
eddies and their associated circulations influence the
climate system.
The residual circulation seems to set or at least
influence tropopause structure.
The eddies seem to dry out the extratropical
troposphere.
The eddies drive planetary waves and are
implicated strat-trop coupling.
• We use the model to get a handle on the
mechanisms.
• But we must bear in mind their limitations.
Weaknesses of these Simple Models
• These models are highly tunable and so can be
“forced” to agree with observations.
• They are thus difficult to compare directly with
observations, which is the main theme of this
workshop.
• Even though they are simple, they are not simple to
understand.
• We will have to move into the world of GCMs – this
will be tomorrow’s story.