1. SOLCLI Meeting 22 October 2009
The tropospheric response to idealised stratospheric forcing: its dependence on basic state
Mike Blackburn(1), Joanna D. Haigh(2), Isla Simpson(2,3), Sarah Sparrow(1,2)
(1) NCAS-Climate, Department of Meteorology, University of Reading, UK
(2) Space and Atmospheric Physics, Imperial College London, UK
(3) Department of Physics, University of Toronto, Canada.
SOLCLI Meeting 22 October 2009

2. Outline
Tropospheric response to idealised stratospheric heating (review)
Dependence on tropospheric climatological basic state
 equilibrium response
 spin-up ensembles – mechanisms
Relationship to unforced annular variability

3. Solar index regressions using reanalysis data
Observed stratospheric temperature signal
solar max - solar min
ECMWF reanalyses (ERA-40)
Crooks & Gray (2005)

4. Circulation changes over the 11-year cycle
Multiple regression analysis of NCEP/NCAR reanalysis, DJF,
Weakening and poleward shift of the mid-latitude jets.
Weakening and expansion of the Hadley cells.
Poleward shift of the Ferrell cells.
Haigh and Blackburn (2006)

5. Simplified GCM - “dynamical core” model
Based on University of Reading primitive equation model: (1)
Spectral dynamics: T42 L15
No orography
Newtonian cooling – idealised equinoctial radiative- convective equilibrium temperatures TR(lat,height) (2)
Boundary layer friction (Rayleigh drag)
(1) Hoskins & Simmons (1975)
(2) Held & Suarez (1994)
Experiments / analysis:
Equilibrium response to perturbations to stratospheric TR
(Haigh et al, 2005)
Spin-up ensembles: 200 x 50-day run
(Simpson et al, 2009)
Annular variability in control run
(Sparrow et al, 2009)

6. The model: control climate
Control run zonal wind
Control run temperature
Relaxation Temperature

7. Idealised stratospheric heating
Heating perturbations can be applied to the stratosphere by changing the relaxation temperature profile
Applied 3 different
heating perturbations 5K 0K
E5 Equatorial heating (5K)
U5 Uniform heating (5K)
P10 Polar heating (10K)
10K
Haigh et al (2005)

8. Equilibrium Response
Zonal mean Temperature E5 U5
P10
Control zonal wind
E5 case gives a similar response in the troposphere to that seen over the solar cycle
Zonal mean zonal wind E5 U5
P10

9. Ensemble spin-up Experiments
Haigh et al (2005) - Equatorial heating gave a similar tropospheric response to that seen over the solar cycle
Coherent displacement of the jet and storm-track
How does this arise?
Spin-up ensemble for the equatorial heating case:
200, 50-day runs 5K 0K
4.5K
0.5K
Simpson et al (2009)

10. Eliassen-Palm flux Flux of wave activity in latitude-height plane
Conserved following eddy group velocity (assumptions)
Components proportional to eddy heat + momentum fluxes
E-P flux divergence quantifies eddy forcing of mean state

11. Eddy-feedback processes
Ensemble spin-up response to stratospheric heating distributions in an idealised model (Simpson et al, 2009)
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: δT_ref
Tropopause [qy] trigger
Refraction feedback amplifies tropospheric anomalies
Baroclinicity feedback moves wave source 11

12. Refractive Index
We can use the refractive index to see what’s causing the change in eddy propagation.
Eddies should be refracted towards regions of higher refractive index.
Meridional PV gradient - Depends on the vertical gradients in temperature and zonal wind and meridional zonal wind curvature.
Eddy phase speed
Zonal wind

13. TR1
TR2
TR3
TR4
TR5
E5 - CONTROL
There is a dependence of the magnitude of the response to stratospheric heating on the jet latitude/width
Page 13
© Imperial College London

14. E5 dependence on tropospheric basic state
Decreasing baroclinicity
Increasing baroclinicity
TR1
TR2
TR3
TR4
TR5
Change to reference temperature TR u
Climatological zonal wind
E5δu
E5 zonal wind response
NOTE: THERE IS 1 BLANK BOX HIDING TEXT ON THE RIGHT
Equilibrium experiments with modified tropospheric reference temperature
Stronger response to stratospheric forcing for lower latitude jets
Indicative of stronger eddy feedback (despite weaker eddies in control)

15. NOTE: THERE ARE 2 BLANK BOXES HIDING EP-FLUX PLOTS ON THE RIGHT (CONTROL & ANOMALY)

16. Dynamical Mechanisms Hypotheses
Sensitivity of EP-flux propagation / refraction to basic state:
- expect spin-up to vary from t=0?
Sensitivity of critical latitude wave absorption (u=c or qy=0) :
- different spectrum of eddy phase speeds (for climatology or spin-up)?
- narrower latitude band for low-latitude jets (u/y larger)
Strength of baroclinic feedback:
- is low-latitude response more baroclinic ( higher eddy growth rates)?
- simple metrics should verify/falsify this

17. Forcing / response correlation
Eddy forcing correlates more strongly with wind response for low-latitude jets
Indicative of stronger eddy feedback onto the annular dipole
Evidence of refraction or critical line mechanisms?
Correlation between uv convergence and zonal wind anomalies, for all latitudes and heights.
Page 17
© Imperial College London

18. E5 spin-up dependence on climatology
Trop.
Strat.
Vertical integrals
Correlation of eddy forcing and zonal wind response

19. NOTE: THERE IS 1 BLANK BOX HIDING PLOTS ON THE RIGHT
Relationship to unforced internal variability
Find strongest response to forcing for lower latitude jets
How is this related to the unforced internal variability?
Fluctuation-Dissipation Theorem (FDT) predicts a stronger response for longer timescales of internal variability
Due to stronger internal (eddy) feedbacks, maintaining the leading mode(s) of variability against damping
NOTE: THERE IS 1 BLANK BOX HIDING PLOTS ON THE RIGHT

20. Timescales of variability
Low latitude jets: long timescale; stationary
1-point correlation maps of zonal wind anomalies wrt peak negative response at 200hPa
Mid-latitude jets: short timescale; propagating
Page 20
© Imperial College London

21. Annular variability in TR3 control
Evidence for 2 types of natural variability:
 poleward propagating anomalies – short timescale
 persistent stationary anomalies – long timescale
Persistent behaviour dominates for lower latitude jets
Propagating behaviour dominates for higher latitude jets

22. NOTE: THERE IS 1 BLANK BOX HIDING TEXT ON THE RIGHT
Conclusions
Previously identified eddy feedbacks responsible for the tropospheric response to idealised stratospheric heating
Large variation of response magnitude to climatological basic state
Several possible dynamical mechanisms
Response variation consistent with timescale of unforced variability (FDT)
 poleward propagating anomalies – short timescale – weak response
 persistent stationary anomalies – long timescale – strong response
Future Work
Analyse dynamics of forcing response & spin-up (mechanisms)
Dynamics of unforced variability – separate & characterise 2 types
Extended stratosphere; mechanical forcing (Alice Verweyen PhD)
NOTE: THERE IS 1 BLANK BOX HIDING TEXT ON THE RIGHT

23. SOLCLI Meeting 22 October 2009
- Thank you -
SOLCLI Meeting 22 October 2009

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

27. Climate Change: annular response
Temperature change
IPCC AR4 models
minus
A2 scenario (“business as usual”)
Zonal mean zonal wind
850hPa zonal wind
Lorenz & DeWeaver (2007)

28. Idealised GCM: annular response
Zonal wind response to localised heating 150hPa deep, 20° wide latitude
Lorenz & DeWeaver (2007)

30. Sarah Sparrow1,2, Mike Blackburn2 and Joanna Haigh1
Modes of Annular Variability in the Atmosphere and Eddy-Zonal Flow Interactions
Sarah Sparrow1,2, Mike Blackburn2 and Joanna Haigh1
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

31. Leading Modes of Variability
Control Run
EOF 1 (51.25%)
EOF 2 (18.62%)
Height →
Latitude (equator to pole) →
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.

32. Phase Space Trajectories
Unfiltered
Periods Longer than 30 Days
Low Pass Filter
Periods Shorter than 30 Days
High Pass Filter
PC1 →
PC2 →
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.

33. Phase Space View of Momentum Budget
PC1 →
PC2 →
Low Pass
High Pass
Eddies change behaviour at high and low frequencies and jet migration changes direction.
At low frequencies it is unclear what drives the poleward migration.

34. 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

35. Empirical Mode Decomposition: Phase Space
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

36. 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.

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

38. Phase angle lagged correlation– + ω
Phase Space Angle Lag →
Mode 2
Mode 4
240 hPa
967 hPa
Correlation →
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.

39. Refractive Index and EP-flux (single composite)
High Frequency
Low Frequency
Eddy propagation responds to current zonal wind anomalies.
Resulting upper level EP-flux 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

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

41. 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.