1. Modes of Annular Variability in the Atmosphere and Eddy-Zonal Flow Interactions Sarah Sparrow 1,2, Mike Blackburn 2 and Joanna Haigh 1 1. Imperial College London, UK 2. National Centre for Atmospheric Science, University of Reading, UK MOCA-09 M06 Theoretical Advances in Dynamics 20 July 2009 v.6

2. Summary Motivation Annular variability – high and low frequencies Dynamics at different timescales

3. Motivation Equilibrium 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)

4. 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:

5. 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) Height

6. 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 PC2

7. 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. PC1 PC2 PC1 PC2 Low Pass High Pass

8. 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) Amplitude (ms -1 ) Zonal Wind PC1 Zonal Wind PC2

9. Empirical Mode Decomposition: Phase Space Mode 1Mode 2 Mode 4 Mode 3 Mode 6Mode 5 T c = 4.96 ± 0.05 days T c = 8.0 ± 0.3 daysT c = 20.3 ± 0.8 days T c = 39 ± 2 daysT c = 78 ± 5 days T c = 198 ± 19 days

10. 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. – – + ω

11. TEM Momentum Budget at 240 hPa Mode 2 Mode 4 Latitude Phase Angle – – + ω

12. Phase angle lagged correlation Phase Space Angle Lag Mode 2 Mode 4 240 hPa967 hPa Correlation – – + ω Consideration of the phase lag between the zonal wind anomalies and.F at low levels, together with each modes 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.

13. 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 FrequencyLow Frequency Eddies propagate towards high refractive index

14. Eddy feedback processes Refractive Index determined by wind anomalies 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 Height Latitude Height Latitude Height Latitude Height Latitude Height High Frequency Low Frequency

15. 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.

17. Motivation Ensemble spin-up response to stratospheric heating distributions in an idealised model (Simpson et al, 2009) Tropopause [ q y ] trigger Refraction feedback amplifies tropospheric anomalies Baroclinicity feedback moves wave source 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 49 Heating: δ T_ref

18. 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)

19. 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

21. Reconstructed low-frequency sector composite winds at 240 hPa

22. Phase Space: Radial and Tangential Motion Equatorward anomaly migration (Higher frequencies) Poleward anomaly migration (Lower frequencies) PC1 PC2 Current anomalies damped Current anomalies reinforced