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