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]

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

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

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

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

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

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

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

Troposphere “dynamical core” model with Held-Suarez- like forcing Mean and variability of control run mean zonal windfirst 2 EOFs of mean u

Responses to Mechanical Forcings

Hypothesis: response in each EOF U n is proportional to projection of forcing onto U n

Reference Temperature Changes Confined to Poleward of Jet

Wind Changes Resulting From Poleward Side T ref Changes 2 K Warming 6 K Warming 4 K Warming 10 K Warming

Responses to Poleward Side Thermal Forcings

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

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

Haynes et al (1991) Instantaneous (Eliassen) response with no eddy feedback Long-time (steady, “downward control”) response utut χ χu u t + A u = f { u t + A u = f Eliassen problem u t + A u = f u=A f steady problem

Thompson et al. (2006) Eliassen response to observed forcing Δ (div F) ΔQΔQ χ utut observed calculated

Effective Torques: Mechanical Forcing

Effective Torques: Thermal Forcing

Steady forced problem

Steady forced problem Unforced (stochastic) problem

POP Spatial Patterns 8 EOFs retained – 10 day lag

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

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

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

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

Streamfunction Changes Resulting From Poleward Side T ref Changes 2 K Warming 6 K Warming 4 K Warming 10 K Warming

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

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

Eigenvalues and Timescales  -1 (days)‏  -1 (days)‏ Lag (days)‏EOFs Retained Decorrelation analysis: 1 -1 =58 days; 2 -1 =48 days