Kushner: GCC Lecture Topics

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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.

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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

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Introduction A Little Philosophy

• Thanks to Isaac Held at NOAA/GFDL.
• We dont want to get hung up on generalities,
  but its good to know what were doing and why
  were doing it.
• Conceptual models/pictures are useful but they
  are often ambiguous, only vaguely understood, and
  overplayed.

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Some Common Conceptual Models

• Conveyor belt
• 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.
• 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.

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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.

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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
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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)
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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)
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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

IRI/LDEO via J. Marshall
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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.
Annual-mean Zonal Wind
IRI/LDEO via J. Marshall
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Breakdown of Energy Transports

• Meridional Flux of Sensible Heat

Sensible-heat (T) transport is representative of
the total energy transport. 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
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Laboratory Baroclinic Waves

• The rotating annulus below is heated on the
  inside ring (orange warm, blue cold)
• 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_e
xp/exp_e/doc/bc/images/bc05.gif
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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
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Midlatitude Baroclinic Waves
Meridional Velocity Correlations
These waves propagate in packets. Their group
speed (blue) is greater than their phase speed
(red). Their crescent shape implies a
meridional convergence of zonal momentum.
Their westward phase tilt with height implies a
poleward heat transport.
Chang and Yu 1999, Chang 1993
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Explanation of Phase Tilts

• Consider fluxes of momentum and of heat (for
  simplicity, flux of buoyancy).

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Midlatitude Stationary Waves

• DJF Z500, NCEP Reanalysis

Like the transient eddies, these waves are
associated with momentum flux converges and
poleward heat transports. Unlike the transient
eddies, these waves amplify into the stratosphere.
DJF Z(60N), NCEP Reanalysis
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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
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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
  flux-gradient Kyy formulations for the BDC.
• Well return to these ideas later.

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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 1940s
  until today.
• These all represent transient initial-value
  problem models where initial conditions matter.
• For climate (equilibrated) models, initial
  conditions should be forgotten.

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Initial Value Problems

• The first set of problems well look at are
  linear wave problems.
• We start with the primitive equations.
• We scale them using the assumptions of
  quasigeostrophic scaling to obtain QG equations.
• We then assume some basic flow and linearize
  about it (as Charles did).
• Fast growing (unstable) waves are taken to be the
  relevant ones.

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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

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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.
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Models of Baroclinic Eddies Eady

• The fastest growing wave 4000 km (m6)
• Growth rate corresponds to about 2-3 days
  e-folding time

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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.
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Models of Baroclinic Eddies Charney

• Growth rate as in Eady model

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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.
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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 Changs regression
maps. Notice how the unstable waves flux
momentum into the jet core
Simmons and Hoskins 1976
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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.
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Transient Eddies in Climate Models
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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

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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.