The General Circulation of the Atmosphere and its Variability

1
The General Circulation of the Atmosphere and its
Variability

• Dennis L. Hartmann
• Dynamics Seminar
• October 18, 2007

Thomson 1857
2
Outline of Talk

• Description of the General Circulation in
  classical terms
• Review of some of the advances in the past
  25-40 years
• Discussion of theories of Dynamical Variability
  in the Atmosphere

Thomson 1857
3
Focus of Talk

• Dry Dynamics, mostly.
• Momentum, mostly
• My favorite things.
• Some Old Chesnuts

Ferrel 1856
4
Zonal Average Views

• Zonal Average Climatology
• Zonal Average of x x
• x - x x deviation from the zonal average
• Time average of x x
• x - x x deviation from time average

Ferrel 1859
5
Zonal Average Zonal Wind
ERA-40
Ferrel 1859
6
Zonal Average Meridional Wind
ERA-40
Ferrel 1859
7
Eddy Covariances
Zonal Average of Product
Zonal Average of Eddy Product
Product of Zonal Averages
Maury 1855
8
Eddy Meridional Temp. Flux
ERA-40
9
Eddy Meridional Momentum Flux
ERA-40
10
Eddy Meridional Momentum Flux
Transient
Total
Stationary
Stationary - JJA
ERA-40
11
Eddy-Driven Jets
When you see surface westerlies with
westerlies above, as in midlatitudes, these
westerlies are driven by large-scale eddy
momentum fluxes. The observed mean meridional
circulations export mass-averaged westerly
relative angular momentum.
12
Zonal-mean Momentum
Expand total derivative and use continuity in
p-coord.
Multiply by a cos? and average over longitude.
13
Zonal-mean Momentum
Next, integrate this over the mass of the
atmosphere.
14
Zonal-mean Momentum
Lets make this part of the drag.
In steady state, this term is zero, by mass
continuity.
So in steady state,
15
Steady, Mass-integrated Zonal-mean Momentum
Equation
Meridional eddy flux of zonal momentum
Mass-integrated mean zonal wind advection
16
Steady, Mass-integrated Zonal-mean Momentum
Advection
Peaks at around 30N, so both Hadley and Ferrel
Cells export relative angular momentum
17
Steady, Mass-integrated Zonal-mean Momentum
Advection
Eddies and MMC export relative angular momentum
from the tropics and the eddies import relative
angular momentum into extratropics, and focus it
above the surface westerlies.
18
Conclusion Eddies must move momentum poleward

• If we have a climate with easterlies in the
  tropics and westerlies in midlatitudes, and
  eddies dominate the circulation in between, then
  eddies must transport westerly momentum poleward.

19
Role of Eddies in MomentumLorenz (1952)
Ferrel 1859
20
Role of Eddies in MomentumLorenz (1967)
Ferrel 1859
21
Momentum is Funny Stuff
Consider a non-divergent, barotropic fluid
Enstrophy Equation
Steady Enstrophy Equation
22
Momentum is Funny Stuff
Steady Enstrophy Equation
If source F adds enstrophy, eddy vorticity flux
must be up-gradient (normally northward) to
maintain steady state.
Zonal Wind Equation
That would tend to accelerate the flow in the
region where the source of eddy enstrophy is
located.
23
Momentum is Funny Stuff
If angular momentum is conserved, there must also
be an easterly acceleration somewhere else, to
balance out the westerly acceleration produced in
the eddy source region.
This can be achieved, if the eddies are able to
propagate out of the source region.
N.B. Wave propagation goes in the opposite
direction to the momentum flux, so if waves
propagate out of region, momentum is transported
in.
24
Barotropic Cartoon
25
Momentum is Funny Stuff

-
-


-

Where is eddy source, and sink ?
26
Momentum is Funny Stuff
In quasi-geostrophic, baroclinic case,
Eliassen-Palm Flux Vector
How did the eddy heat flux end up in the momentum
Budget?
27
How did the eddy heat flux end up in the momentum
Budget?

• The eddy heat flux represents the form drag in a
  hydrostatic and quasi-geostrophic wave that tilts
  westward with height.
• Easy to visualize by thinking in potential
  temperature coordinates.

28
How did the eddy heat flux end up in the momentum
Budget?

• Consider the following picture of the temperature
  and pressure variations on a height surface
  associated with a westward tilting wave.

L
H
L
H
W
C
W
C
29
How did the eddy heat flux end up in the momentum
Budget?

• Add potential temperature perturbation.

L
H
L
H
30
How did the eddy heat flux end up in the momentum
Budget?

• Sketch in dz necessary to get back to a constant
  potential temperature surface dz -dtheta

L
H
L
H
31
How did the eddy heat flux end up in the momentum
Budget?

• Now lets focus in on the resulting form drag.

In westward- tilting wave, atmosphere above
exerts an eastward torque on atmosphere below,
and vice-versa.
Height of theta surface, material surface.
H
L
L
H
L
H
32
Eliassen-Palm Cross Sections
Eliassen-Palm Flux Vector
Heat Flux part dominates climatology of E-P
Cross-Sections
Tanaka, et al. 2006, JMSJ
33
How did the eddy heat flux end up in the momentum
Budget?

• In middle latitudes, baroclinic eddies have
  poleward heat fluxes that are associated with
• eddy energy production,
• upward wave propagation and
• huge form drag that moves momentum from the upper
  to the lower troposphere.

34
The Residual or Lagrangian Circulation
Use momentum (ignore tendency) and continuity,
Mean sinking is the meridional gradient of the
drag integrated down to that level. Thermo not
used.
35
Zonal Mean Circulations
Residual or Lagrangian Circulation
Heat Flux part dominates climatology of E-P
Cross-Sections
Tanaka, et al. 2006, JMSJ
36
Stationary and Transient Driving of Lagrangian
Circulation
Hadley Cell
Stationary
Eddy-Driven Cell
Transient
Tanaka, et al. 2006, JMSJ
37
If the eddy heat flux and form drag are so
dominant in the momentum budget, are lateral eddy
momentum fluxes really that important? They have
to be.

• Variability of eddy-driven jets is an important
  part, perhaps the most important part, of
  extratropical variability.
• Easiest place to see this is in the Southern
  Hemisphere.

38
Southern Hemisphere Eddy-Driven Jet.
Lots of Ocean, not much topography, fairly
zonally symmetric, most of form drag from high
wavenumbers. Clear, almost seasonally
invariant eddy-driven jet.
39
Southern Hemisphere Eddy-Driven Jet.
Form Drag by Zonal Wavenumber
N H
1-3
S H
gt8
4-7
Total
1-3
Tanaka, et al. 2006
40
Southern Hemisphere Eddy-Driven Jet.
Lots of Ocean, not much topography, fairly
zonally symmetric, most of form drag from high
wavenumbers. Clear, almost seasonally
invariant eddy-driven jet.
Eddy-Driven Jet
Subtropical Jet
41
Southern Hemisphere Eddy-Driven Jet.
Eddy-Driven Jet
Subtropical Jet
Lorenz Hartmann, 2001
42
Southern Hemisphere Eddy-Driven Jet.
Lots of Ocean, not much topography, fairly
zonally symmetric, most of form drag from high
wavenumbers. Clear, almost seasonally
invariant eddy-driven jet. Primary mode of
low-frequency variability is North-South movement
of the Eddy-Driven Jet.
43
Southern Hemisphere Eddy-Driven Jet.
Hartmann and Lo, 1998
44
Southern Hemisphere Eddy-Driven Jet.
First EOF of zonal wind almost independent of
season.
Amplitude of EOF 1 is slowly varying, with most
variance gt 20 days
Hartmann and Lo, 1998
45
Southern Hemisphere Eddy-Driven Jet.
First EOF represents N-S shift of eddy driven jet.
1.5 standard deviation of PC-1 corresponds to
10 latitude shift of surface westerlies.
Hartmann and Lo, 1998
46
Southern Hemisphere Eddy-Driven Jet.
Momentum Budget of Meridional Eddy-Jet Meandering
Residual Circ.
Barotropic
Baroclinic aka Form Drag
Drag determined as residual
Hartmann and Lo, 1998
47
Momentum Budget of Meridional Eddy-Jet Meandering
Barotropic
Baroclinic aka Form Drag
Total Eddy Forcing
Residual Circ.
Drag determined as residual
Hartmann and Lo, 1998
48
Southern Hemisphere Eddy-Driven Jet.
Lots of Ocean, not much topography, fairly
zonally symmetric, most of form drag from high
wavenumbers. Clear, almost seasonally
invariant eddy-driven jet. Primary mode of
low-frequency variability is North-South movement
of the Eddy-Driven Jet. Eddy fluxes and residual
circulation adjust to new position of jet, so
that net tendency is small and jet is stable in
new position. Despite being relatively small in
climatology, meridional momentum flux convergence
seems to play a central role in N-S movement of
eddy-driven jet.
49
Southern Hemisphere Eddy-Driven Jet.
Lots of Ocean, not much topography, fairly
zonally symmetric, most of form drag from high
wavenumbers. Clear, almost seasonally
invariant eddy-driven jet. Primary mode of
low-frequency variability is North-South movement
of the Eddy-Driven Jet. Eddy fluxes and residual
circulation adjust to new position of jet, so
that net tendency is small and jet is stable in
new position. But, are the eddies passive or
active, and do eddies add a positive feedback
that adds persistence to departures of the
eddy-driven jet position?
50
Positive Eddy Feedback
Focus on vertical average momentum balance and
meridional wave propagation.
Lorenz Hartmann, 2001
51
Positive Eddy Feedback
Zu
M-d/dy(uv)
Vertical mean zonal wind and eddy momentum
forcing of first EOF (N-S shift) are coherent
across a broad range of frequencies and forcing
leads wind, except for very long periods where
they come into phase.
Lorenz Hartmann, 2001
52
Positive Eddy Feedback
Zu is red
M-d/dy(uv) is whiter
Lorenz Hartmann, 2001
53
Positive Eddy Feedback
Zu
M-d/dy(uv)
synoptic 2-7 days
b
Clues
a
a. M remembers Z
b. High-frequency eddies produce low-frequency
forcing.
Lorenz Hartmann, 2001
54
Simple Model ofPositive Eddy Feedback
M-d/dy(uv)
Linear System
Assume part of momentum forcing depends on zonal
wind.
Choose b to explain long-term memory, then z
without feedback can be computed.
b. High-frequency eddies produce low-frequency
forcing, because they respond to zonal flow.
Lorenz Hartmann, 2001
55
Why is Transient Eddy Feedback Positive?Are
Eddy-Driven Jets Self-Sustaining?
Wave source is baroclinic instability, which
produces wave energy near the surface where the
meridional temperature gradient is large.
Waves propagate upward in westerly winds
Form drag produces a huge downward zonal
momentum flux
A thermally direct overturning
circulation develops to balance the
momentum budget.
Diabatic heating must balance heating by
overturning cell.
If waves can propagate out of baroclinic zone
they can bring in angular momentum.
Yu Hartmann 1993
56
Why is Transient Eddy Feedback Positive?Are
Eddy-Driven Jets Self-Sustaining?
Yu Hartmann 1993
57
Why is Transient Eddy Feedback Positive?Are
Eddy-Driven Jets Self-Sustaining?
Yu Hartmann 1993
58
Why is Transient Eddy Feedback Positive?Are
Eddy-Driven Jets Self-Sustaining?
So the eddy source and eddy momentum flux
convergence can just follow the jet. The
meridional cell forced by the form drag of the
growing eddies also follows the eddy source,
which is the jet.
Remaining problem is to bring along the
diabatic heating that sustains the meridional
cell associated with the form drag. If the
heating is driven by the departure from
equilibrium forced by the meridional
circulation, this is not a problem, the heating
couplet follows the circulation.
59
Are Meridional Displacements of Eddy-Driven Jets
Self-Sustaining?
Use momentum (ignore tendency) and continuity,
To sustain jet in new location, need to move
diabatic heating with wave driving.
60
Are Meridional Displacements of Eddy-Driven Jets
Self-Sustaining?
To sustain jet in new location, need to move
diabatic heating with wave driving.
Works fine in simple models with Newtonian
heating, if baroclinic zone is broad
Eddy momentum driving can define shape of heating.
61
Southern Hemisphere Eddy-Driven Jet.
Eddy-Driven Jet
Subtropical Jet
Lorenz Hartmann, 2001
62
SAM Precip
30
45
60
Sen Gupta England, 2006
63
Why is Transient Eddy Feedback Positive?Are
Eddy-Driven Jets Self-Sustaining?
Yu Hartmann 1993
64
Momentum Budget of Meridional Eddy-Jet Meandering
Barotropic
Baroclinic aka Form Drag
Total Eddy Forcing
Residual Circ.
Drag determined as residual
Hartmann and Lo, 1998
65
SAM Precip
30
45
60
Sen Gupta England, 2006
66
Parameterizing EddiesLorenz (1967)
Ferrel 1859
67
Conclusion

• We can explain in simple terms that eddy
  momentum fluxes are associated with the
• growth, propagation and absorption of waves.
• It is hard to imagine a climate of Earth, in
  which eddies do not move momentum poleward.
• The interaction of eddies with jets and
  diabatic heating produces interesting
  variability, about which we are still learning.

Thomson 1857