Annular Modes

1. Annular Modes • Leading patterns of variability in extratropics of each hemisphere • Strongest in winter but visible year-round in troposphere; present in “active seasons” in stratosphere [Thompson and Wallace, 2000]

2. Climate forcings and annular modes Tropospheric response to ozone depletion [Thompson & Solomon, 2002] GCM response to global warming [Kushner et al., 2001]

3. Response to altered stratospheric radaiative state[Kushner & Polvani 2004]

4. The fluctuation – dissipation theorem[Leith and others] response projection of variance of autocorrelation time forcing unforced mode of unforced mode

5. Response to altered stratospheric radaiative state[Kushner & Polvani 2004]

6. Haynes et al (1991) Instantaneous (Eliassen) response Long-time (steady, “downward control”) response ut χ χ u

7. Haynes et al (1991) Instantaneous (Eliassen) response Long-time (steady, “downward control”) response ut χ χ u How to do this problem in the presence of eddies?

8. Model Setup • GFDL dry dynamical core • T30 resolution • Linear radiation and friction schemes • Held-Suarez-like reference temperature profile but modified for perpetual solstitial conditions • Friction twice the value used by Held and Suarez (1994) to reduce decorrelation times

9. Troposphere “dynamical core” model with Held-Suarez-like forcingMean and variability of control run mean zonal wind first 2 EOFs of mean u

10. Responses to Mechanical Forcings

11. Hypothesis: response in each EOF Un is proportional to projection of forcing onto Un

12. Reference Temperature Changes Confined to Poleward of Jet

13. Wind Changes Resulting From Poleward Side Tref Changes 2 K Warming 4 K Warming 6 K Warming 10 K Warming

14. Responses to Poleward Side Thermal Forcings

15. L Governing eqs of system Assume anomalous eddy fluxes depend linearly on anomalous u (and neglect time lags) + stochastic term: Linearize about unforced time-mean state [U,V,Ω,Θ](φ,p) Anomalies [u,v,ω,T, Fu,FT](φ,p,t)

16. L Governing eqs of system Nonlinear balance: Linearize about unforced time-mean state [U,V,Ω,Θ](φ,p) Anomalies [u,v,ω,T, Fu,FT](φ,p,t) Neglect advection of static stability anomalies where = Eliassen response

17. Haynes et al (1991) Instantaneous (Eliassen) response with no eddy feedback Long-time (steady, “downward control”) response ut χ u χ ut + Au = f Eliassen problem { ut + Au = f -1 ut + Au = f u=A f steady problem

18. Eliassen response to observed forcing Thompson et al. (2006) Δ(divF) ΔQ χ observed calculated ut

19. Effective Torques: Mechanical Forcing

20. Effective Torques: Thermal Forcing

21. Steady forced problem

22. Steady forced problem Unforced (stochastic) problem

23. POP Spatial Patterns 8 EOFs retained – 10 day lag

24. POP Projections: Response Versus Effective Torques circles indicate mechanically forced trials; squares thermally forced trials

25. Implications • Response depends on projected effective forcing and on autocorrelation time τ • Model simulations need to have good EOFs (or POPs) and their autocorrelation times • Simplified GCMs tend to have good modal structures but exaggerated τ, which is sensitive to model parameters (Gerber) • Kushner-Polvani case has very long τ (>200 d) and is thus highly sensitive • Response to tropical forcing does not fit the pattern – strong Hadley circulation response

27. Changes in Temperature -5 K / Equator +5 K / Equator - 5 K / Pole + 5 K / Pole

28. Changes in E-P Flux Divergence -5 K / Equator +5 K / Equator - 5 K / Pole + 5 K / Pole

29. Streamfunction Changes Resulting From Poleward Side Tref Changes 2 K Warming 4 K Warming 6 K Warming 10 K Warming

30. Direct Response to Forcing 4 K Warming 4 K Warming 4 K Cooling 4 K Cooling

31. Response to Forcing Including Eddy Flux Changes 4 K Warming 4 K Warming 4 K Cooling 4 K Cooling

32. EOFs Retained Lag (days)‏ -1 (days)‏ -1 (days)‏ 4 10 58 41 4 40 66 51 8 10 60 41 8 40 65 51 Eigenvalues and Timescales Decorrelation analysis: 1-1=58 days; 2-1=48 days