1. Dynamics of Annular Modes
Dennis L. Hartmann
Department of Atmospheric Sciences
University of Washington
Seattle, Washington USA
AGU San Francisco
13:30, December 10, 2002
A22D-01

2. Lorenz & Hartmann (2001)

4. Observational Facts
In Southern Hemisphere, Annular variability is maintained by interaction between zonal flow and transient synoptic-scale waves (Hartmann and Lo 1998), and quite easy to simulate (Yu and Hartmann 1993).

5. Dominant EOF is shift in latitude of eddy-driven jet and is
easy to model
and understand.
Dipole Pattern
Yu & Hartmann (1993)
Very
Red
Spectrum

6. Power spectrum
of PC-1
Hartmann & Lo (1998)

7. Eddy Structure
changes with
zonal index.

8. Does Eddy, Zonal-Flow Interaction contribute
to the persistence of annular modes?
• Feldstein and Lee (1998) showed that the eddy momentum fluxes
associated with high frequency (synoptic) eddies are persistent
and feed back positively on the zonal flow anomalies. Net transient
eddy feedback is smaller than high-frequency feedback effect.
• Lorenz and Hartmann (2001SH, 2002NH) used a simple linear
model to estimate quantitatively how much the covariation of
the zonal flow and the synoptic eddy forcing contributed to the
redness of the spectrum of the annular mode.

9. Northern Hemisphere
DJFM Zonal Wind
Vertically Integrated
Eddy Momentum
Forcing

10. EOF-1
EOFs of Zonal Wind
in Northern Hemisphere
EOF-2

11. Zonal Index Tendency = Eddy forcing - Drag

13. Divide eddy forcing, m, into
Stationary (t > 40 days)
Synoptic (t < 15 days)
Residual
By filtering u and v.
Calculate cross-covariance
with Zonal index (PC-1)

14. Northern Hemisphere Annular Mode High-frequency (t < 15 days)
eddies are more important
for persistence
than stationary eddies.
Even after residual eddies are
added, transient eddies are
more important for persistence
for lags larger than two weeks.
Lorenz and Hartmann (2002)

15. Lagged Regression of
u’v’ and EP Flux onto
EOF-1 averaged over
lags 8-30 days, with
eddy forcing lagging
zonal wind anomaly.

16. Co-Spectrum between Z and M suggests,
Positive lagged correlation of M following Z suggests,
Where bj is a feedback parameter
Without this feedback,
Lorenz and Hartmann (2002) N.Hemisphere case

17. First EOF of zonal wind has strong coupling
to eddy forcing at very low frequencies.

18. Conclusions
• Synoptic baroclinic eddies increase persistence of first EOF of
zonal wind. Jet is source for eddies, eddies transport momentum
into source region as they propagate away.
• Intermediate frequency eddies damp zonal flow anomalies.
These are quasi-barotropic eddies, perhaps resulting from
end of baroclinic eddy life cycle, which are refracted back into
the jet.
• Stationary eddies also feed back positively on zonal wind
anomalies. Could be similar mechanism as for synoptic eddies.
Westerlies give wave source, as waves propagate away they flux
momentum into jet.
• Positive feedback increases low-frequency (t > 2 weeks)
variance of EOF-1 by factor of two. No feedback for EOF-2.
David Lorenz will explain why no feedback for EOF-2 in later talk.

19. Questions:
How do transient and eddy feedbacks response to forcing?
Do they give a coherent feedback to forced changes?
ENSO
Stratospheric Warmings
Stratospheric Ozone Depletion
Greenhouse gas changes - global warming