Modes of Annular Variability in the Atmosphere and

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 M 06 Theoretical Advances in Dynamics 20 July 2009 v. 6

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

Motivation Equilibrium response to stratospheric heating distributions in an idealised model (Haigh et al, 2005) Equatorial (E 5) Uniform (U 5) Polar (P 10) Stratospheric heating Zonal wind (control) Zonal wind response Ensemble spin-up response to stratospheric heating (Simpson et al, 2009): Ø proposed wave refraction and low-level baroclinicity feedbacks important for tropospheric response

Motivation • Relevant to various stratospheric forcings: (enhanced greenhouse gases; polar ozone depletion & recovery; solar variability) • Relationship to annular variability? - variability timescale related to magnitude of response (Fluctuation-Dissipation Theorem) - Similar eddy feedback mechanism(s) suggested by previous studies of annular variability: baroclinicity; wave propagation; refraction; critical line absorption… • Aim here: analyse annular variability in the control integration of Haigh et al, Simpson et al. Held-Suarez dynamical core: Newtonian forcing, Rayleigh drag.

Leading Modes of Variability EOF 1 (51. 25%) EOF 2 (18. 62%) Height → Control Run Latitude (equator to pole) → • EOF 1 represents a latitudinal shift of the mean jet. • EOF 2 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.

Phase Space Trajectories Low Pass Filter PC 2 → Unfiltered High Pass Filter PC 1 → Periods Longer than 30 Days Periods Shorter than 30 Days • 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.

Phase Space View of Momentum Budget High Pass PC 2 → Low Pass PC 1 → • Eddies change behaviour at high and low frequencies and jet migration changes direction. • At low frequencies it is unclear what drives the poleward migration.

• EMD is a technique for analysing different timescales in non-linear and non-stationary data. • Resulting timeseries are similar to band-pass filtered data. • For a given mode a similar frequency band is sampled for both PC 1 and PC 2. Amplitude (ms-1) → Empirical Mode Decomposition (EMD): Spectra Zonal Wind PC 1 Period (Days) → Zonal Wind PC 2

Empirical Mode Decomposition: Phase Space Mode 1 Tc = 4. 96 ± 0. 05 days Mode 2 Tc = 8. 0 ± 0. 3 days Mode 3 Tc = 20. 3 ± 0. 8 days Mode 4 Mode 5 Mode 6 Tc = 39 ± 2 days Tc = 78 ± 5 days Tc = 198 ± 19 days

Transformed Eulerian Mean Momentum Budget + – – ω 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.

TEM Momentum Budget at 240 h. Pa – – ω Mode 2 Latitude → + Phase Angle → Mode 4

Phase angle lagged correlation + 967 h. Pa • 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 Phase → 2 -4 Space days Angle for all Lag modes. • High frequencies: almost out of phase. Mode 4 • Low frequencies: almost in phase, small . F lag. Mode 2 Correlation → 240 h. Pa – ω –

Refractive Index and EP-flux (single composite) High Frequency Low Frequency Eddy propagation responds to current zonal wind anomalies. Resulting upper level EPflux divergence forces further zonal wind changes. Eddies propagate towards high refractive index Refractive index anomalies determined by wind anomalies Larger effect near critical lines phase offset

Height Latitude High Frequency Latitude Eddies propagate Resulting EP-flux towards high divergence drives refractive index zonal wind changes (phase offset) Height Eddy source lags Refractive Index baroclinicity (zonal determined by wind anomalies) wind anomalies by 2 -4 days Latitude Height Latitude Low Frequency Latitude Height Eddy feedback processes Latitude

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.

Motivation Ensemble spin-up response to stratospheric heating distributions in an idealised model (Simpson et al, 2009) Heating: δT_ref u, days 20 to 29 u, days 40 to 49 E-P Flux, days 0 to 9 E-P Flux, days 20 to 29 E-P Flux, days 40 to 49 Tropopause [qy] trigger Refraction feedback amplifies tropospheric anomalies Baroclinicity feedback moves wave source

Motivation • Existing studies: mechanisms of annular variability - mean flow – eddy feedbacks: - baroclinicity; wave propagation; refraction; critical line absorption… • Important for understanding response to forcing - 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 Composite High Frequency Composite • 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 LC 1/LC 2 behaviour.

Reconstructed low-frequency sector composite winds at 240 h. Pa

Phase Space: Radial and Tangential Motion Current anomalies reinforced PC 2 Equatorward anomaly migration (Higher frequencies) Current anomalies damped Poleward anomaly migration (Lower frequencies) PC 1