modes of annular variability in the atmosphere and eddy-zonal flow interactions sarah sparrow 1,2,...
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Modes of Annular Variability in the Atmosphere and Eddy-Zonal Flow Interactions
Sarah Sparrow1,2, Mike Blackburn2 and Joanna Haigh1
1. Imperial College London, UK2. National Centre for Atmospheric Science, University of Reading, UK
MOCA-09 M06 Theoretical Advances in Dynamics 20 July 2009
v.6
Summary
• Motivation
• Annular variability – high and low frequencies
• Dynamics at different timescales
MotivationEquilibrium response to stratospheric heating distributions in an idealised model (Haigh et al, 2005)
Ensemble spin-up response to stratospheric heating (Simpson et al, 2009):
proposed wave refraction and low-level baroclinicity feedbacks important for tropospheric response
Stratospheric heating
Zonal wind (control)
Zonal wind response
Equatorial (E5) Uniform (U5) Polar (P10)
Motivation
• Relevant to various stratospheric forcings: (enhanced greenhouse gases; polar ozone depletion & recovery; solar variability)
• Relationship to annular variability?
• Aim here: analyse annular variability in the control integration of Haigh et al, Simpson et al.Held-Suarez dynamical core: Newtonian forcing, Rayleigh drag.
baroclinicity; wave propagation; refraction; critical line absorption…
- variability timescale related to magnitude of response (Fluctuation-Dissipation Theorem)
- Similar eddy feedback mechanism(s) suggested by previous studies of annular variability:
Leading Modes of Variability
EOF 1 (51.25%) EOF 2 (18.62%)
• EOF1 represents a latitudinal shift of the mean jet.• EOF2 represents a strengthening (weakening) and
narrowing (broadening) of the jet.• Both of these patterns are needed to describe a smooth
latitudinal migration of the jet.
Control Run
Latitude (equator to pole) →
Hei
ght
→
Phase Space Trajectories
• At low frequencies circulation is anticlockwise with a timescale of 82 ± 27 days.
• At high frequencies circulation is clockwise with a timescale of 8.0 ± 0.3 days.
Unfiltered
Periods Longer than 30 Days
Low Pass Filter
Periods Shorter than 30 Days
High Pass Filter
PC1 →P
C2
→
Phase Space View of Momentum Budget
• Eddies change behaviour at high and low frequencies and jet migration changes direction.
• At low frequencies it is unclear what drives the poleward migration.
0
1 sp
ZONAL EDDY Su dp C Cg t
PC1 →
PC
2 →
PC1 →
PC
2 →
Low Pass High Pass
Empirical Mode Decomposition (EMD): Spectra
• EMD is a technique for analysing different timescales in non-linear and non-stationary data.
• Resulting time-series are similar to band-pass filtered data.
• For a given mode a similar frequency band is sampled for both PC1 and PC2.
Period (Days) →A
mpl
itude
(m
s-1)
→
Zonal Wind PC1
Zonal Wind PC2
Empirical Mode Decomposition: Phase SpaceMode 1 Mode 2
Mode 4
Mode 3
Mode 6Mode 5
Tc = 4.96 ± 0.05 days Tc = 8.0 ± 0.3 days Tc = 20.3 ± 0.8 days
Tc = 39 ± 2 days Tc = 78 ± 5 days Tc = 198 ± 19 days
Transformed Eulerian Mean Momentum Budget
High Frequencies: • Eddies drive equatorward
migration.• Eddies out of phase with
winds near the surface.
Intermediate Frequencies:• Eddies drive poleward
migration.• Residual circulation drives
jet migration at lower levels.
• Eddies in phase with the winds near the surface.
][][
][cos][cos
][][ *
**
Fp
uwu
a
vvf
Fcos
1][
adt
ud––+ ω
TEM Momentum Budget at 240 hPaM
ode 2M
ode 4La
titud
e →
Phase Angle →
][][
][cos][cos
][][ *
**
Fp
uwu
a
vvf
Fcos
1][
adt
ud––+ ω
Phase angle lagged correlation
Phase Space Angle Lag →
Mode 2
Mode 4
240 hPa 967 hPa
Cor
rela
tion
→ ][
][][cos][
cos
][][ *
**
Fp
uwu
a
vvf
Fcos
1][
adt
ud––+ ω
• Consideration of the phase lag between the zonal wind anomalies and .F at low levels, together with each mode’s circulation timescale, shows that the EP-flux source responds to low level baroclinicity with a lag of 2-4 days for all modes.
• Low frequencies: almost in phase, small .F lag.
• High frequencies: almost out of phase.
|][|
][~2
cu
qn y
Eddy propagation responds to current zonal wind anomalies.
Resulting upper level EP-flux divergence forces further zonal wind changes.
Refractive index anomalies determined by wind anomalies
Larger effect near critical lines phase offset
Refractive Index and EP-flux (single composite)
High Frequency Low Frequency
Eddies propagate towards high refractive index
Eddy feedback processes
Refractive Index determined by wind anomalies
|][|
][~2
cu
qn y
Eddies propagate towards high refractive index
Resulting EP-flux divergence drives zonal wind changes (phase offset)
Eddy source lags baroclinicity (zonal wind anomalies) by 2-4 days
Latitude Latitude Latitude Latitude
Hei
ght
Hei
ght
Hei
ght
Hei
ght
Latitude
Hei
ght
Latitude
Hei
ght
Latitude
Hei
ght
LatitudeH
eigh
t
Hig
h F
requ
ency
Low
Fre
quen
cy
Conclusions
• Annular variability at different timescales in a Newtonian forced AGCM:
– Equatorward migration of anomalies at high frequencies
– Poleward migration at low frequencies
• For all timescales the jet migration is driven by the eddies at upper levels and conveyed to lower levels by the residual circulation.
• Evidence for two feedback processes:
• Eddy source responds to low-level baroclinicity, with lag 2-4 days:
– High frequency flow is so strongly eddy driven that wind anomalies almost out of phase with wave source.
– Low frequency wind anomalies and eddy source are almost in phase.
• Wind anomalies dominate refractive index, leading to positive eddy feedback via EP-flux divergence.
• Direction of propagation from relative phases of wave source/sink and wave refraction.
MotivationEnsemble spin-up response to stratospheric heating distributions in an idealised model (Simpson et al, 2009)
Tropopause [qy] trigger
|][|
][~2
cu
qn y
Refraction feedback amplifies tropospheric anomalies
Baroclinicity feedback moves wave source
t
uF
.
E-P Flux, days 0 to 9 E-P Flux, days 20 to 29 E-P Flux, days 40 to 49
u, days 20 to 29 u, days 40 to 49Heating: δT_ref
zFz
u
Motivation
• Existing studies: mechanisms of annular variability
• Important for understanding response to forcing
- mean flow – eddy feedbacks:
- baroclinicity; wave propagation; refraction; critical line absorption…
- variability timescale related to magnitude of response? (Fluctuation-Dissipation Theorem)
- relevant to jet and storm-track response to stratospheric forcing (enhanced greenhouse gases; polar ozone depletion & recovery; solar variability)
Previously…EP Flux Anomalies: High and Low Frequency
• Low frequency: quasi-equilibrium of EP flux and wind anomalies.
• High frequency: flow is strongly evolving where eddy anomalies reflect past baroclinicity and feedback understood in terms of LC1/LC2 behaviour.
Low Frequency Composite High Frequency Composite
Reconstructed low-frequency sector composite winds at 240 hPa
Phase Space: Radial and Tangential Motion
Equatorward anomaly migration
(Higher frequencies)
Poleward anomaly migration
(Lower frequencies)
PC1
PC2
Current anomalies damped
Current anomalies reinforced