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Three-Dimensional Dynamical Models, 2

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Title: Three-Dimensional Dynamical Models, 2


1
Three-Dimensional Dynamical Models, 2
  • Paul J. Kushner
  • University of Toronto

GCC Summer School Banff 2005
2
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

3
Terms and Concepts
  • Quasigeostrophic Scaling
  • Potential vorticity definition

4
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.
  • 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.

air
water
5
An Adjustment Problem Homework! (Sort of)
  • 2. Rotating case (f gt 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
    cant happen why? (There are a couple of
    reasons.)
  • 3. For the ambitious solve for the equilibrium
    height and estimate the cross-channel mass flux.
    Make as many simplifying assumptions as necessary.

air
water
6
Review - 1
  • Transport is needed to explain the observed
    distribution of TOA radiation and the temperature
    distribution of the atmosphere.
  • Rotation supresses zonally symmetric
    circulations, so
  • Baroclinic waves (transient and stationary)
    must do the transport.
  • Top-of-Atmosphere Radiation

Hartmann 1994
7
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
8
Review 3
  • We described a sequence of linear models of
    baroclinic waves.

Phillips (Holton)
Eady (Gill)
Charney (Gill)
Simmons and Hoskins
9
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.
10
Transient Eddies in Climate Models
  • We have seen that we need (at least) a
    three-dimensional 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

11
Baroclinic Turbulence Models T. Schneider
Lets first look at a dry GCM developed by Tapio
Schneider. 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. 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).
Equilibrium Potential Temperature (input)

Time Mean Potential Temperature (output)
Schneider 2004
12
Baroclinic Turbulence Models T. Schneider
Equilibrium Potential Temperature

Whats 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
13
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 potential-temperature/la
titude plot of mass streamfunction (bottom). This
is the Brewer-Dobson circulation of the
troposphere, with a strong midlatitude eddy
driven component. 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.
Mass Streamfunction
Schneider 2004
14
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
15
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
16
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 Schneiders 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 models diabatic
cooling).
17
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).
18
Simple Models of Stratosphere-Troposphere Coupling
Equilibrium winds and temperatures
Scinocca and Haynes showed that adding a
stratosphere layer to this type of GCM resulted
in an interesting coupling between stratosphere
and troposphere. Their model has no stationary
waves. Instead, synoptic-scale wave packets
generate low-wavenumber waves that propagate into
the stratosphere animations. 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.
Time Evolution of Spatial Spectrum
Scinocca and Haynes 1998
19
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.

20
A Spontaneous Sudden Warming
The top plot shows a time series of polar-cap
average temperature at 50 hPa from a simulation
with time-independent 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). For comparison, a similar plot is
shown from the 2002 Southern-Hemisphere major
Warming (Baldwin et al.). The transient eddy
activity from the troposphere is therefore able
to generate a
Kushner and Polvani 2005
Kushner and Polvani 2005 Baldwin et al. 2003
21
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
Trend in Antarctic Polar-Cap Average Geopotential
Height
... has cooled the lower stratosphere. But
notice the like-signed trend in the troposphere.
Thompson and Solomon 2002
22
Cooling the Polar Stratosphere
What happens in our simple model as we cool the
polar stratosphere?
23
Response to Stratospheric Cooling
As Polar Stratosphere Cools, Jet Stream Shifts
Poleward
24
The Response is Modal
  • In the troposphere, the response matches the
    models 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.

25
Response of Upwelling Wave-Activity Flux
100 mb Vertical EP Flux
g 2
g 4
Biggest reduction at synoptic scales synoptic
eddy EP flux into the lower stratosphere
decreases.
26
The Response is Robust
Latitude of Surface Wind Max vs g
colder strat
colder strat
20 levels
40 levels
80 levels
27
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
28
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.

29
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 tomorrows story.
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