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

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

Circulation changes over the 11-year cycle

• 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)

Multiple regression analysis of NCEP/NCAR reanalysis, DJF, 1979-2002

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)

Experiments / analysis:

1. Equilibrium response to perturbations to stratospheric TR(Haigh et al,

2005)

2. Spin-up ensembles: 200 x 50-day run(Simpson et al, 2009)

3. Annular variability in control run(Sparrow et al, 2009)

(1) Hoskins & Simmons (1975)

(2) Held & Suarez (1994)

The model: control climate

Control run zonal wind

Control run temperature

Relaxation Temperature

Idealised stratospheric heating

• Heating perturbations can be applied to the stratosphere by changing the relaxation temperature profile

P10 Polar heating (10K)

5K0K

5K 0K

E5 Equatorial heating (5K) U5 Uniform heating (5K)

10K

• Applied 3 different

heating perturbations

Haigh et al (2005)

Equilibrium ResponseZonal mean Temperature

Zonal mean zonal wind

Control zonal wind

E5 U5 P10

E5 U5 P10

E5 case gives a similar response in the troposphere to that seen over the solar cycle

• 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

Ensemble spin-up Experiments

5K 0K4.5K0.5K

Simpson et al (2009)

• 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

Eliassen-Palm flux

Eddy-feedback processes

Ensemble spin-up response to stratospheric heating distributions in an idealised model (Simpson et al, 2009)

Tropopause [qy] trigger

|][|

][~2

cu

qn y

Refraction feedback amplifies tropospheric anomalies

Baroclinicity feedback moves wave source

t

uF

.

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 49Heating: δT_ref

zF

z

u

E5 dependence on tropospheric basic state

• 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)

TR1 TR2 TR3 TR4

Decreasing baroclinicity Increasing baroclinicity

TR5

TR

u

E5δu

NOTE: THERE IS 1 BLANK BOX

HIDING TEXT ON THE RIGHT

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

© Imperial College LondonPage 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 uv convergence and zonal wind anomalies, for all latitudes and heights.

E5 spin-up dependence on climatology

Correlation of eddy forcing and zonal wind response

Vertical integrals

Strat.Trop.

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 dampingNOTE: THERE IS 1

BLANK BOX HIDING PLOTS ON

THE RIGHT

© Imperial College LondonPage 20

Timescales of variability

• 1-point correlation maps of zonal wind anomalies wrt peak negative response at 200hPa

• Mid-latitude jets: short timescale; propagating

• Low latitude jets: long timescale; stationary

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

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

- Thank you -

SOLCLI Meeting 22 October 2009

Reconstructed low-frequency sector composite winds at 240 hPa

Climate Change: annular response

Lorenz & DeWeaver (2007)

IPCC AR4 models

2080-2099 minus 1980-1999

A2 scenario (“business as usual”)

Zonal mean zonal wind 850hPa zonal wind

Temperature change

Idealised GCM: annular response

Lorenz & DeWeaver (2007)

Zonal wind response to localised heating 150hPa deep, 20° wide latitude

Modes of Annular Variability in the Atmosphere and Eddy-Zonal Flow Interactions

Sarah Sparrow1,2, Mike Blackburn2 and Joanna Haigh1

1. Imperial College London, UK2. National Centre for Atmospheric Science, University of Reading, UK

MOCA-09 M06 Theoretical Advances in Dynamics 20 July 2009

v.6

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) →

Hei

ght

→

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 →P

C2

→

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.

0

1 sp

ZONAL EDDY Su dp C Cg t

PC1 →

PC

2 →

PC1 →

PC

2 →

Low Pass High Pass

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) →A

mpl

itude

(m

s-1)

→

Zonal Wind PC1

Zonal Wind PC2

Empirical Mode Decomposition: Phase SpaceMode 1 Mode 2

Mode 4

Mode 3

Mode 6Mode 5

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

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.

][][

][cos][cos

][][ *

**

Fp

uwu

a

vvf

Fcos

1][

adt

ud––+ ω

TEM Momentum Budget at 240 hPaM

ode 2M

ode 4La

titud

e →

Phase Angle →

][][

][cos][cos

][][ *

**

Fp

uwu

a

vvf

Fcos

1][

adt

ud––+ ω

Phase angle lagged correlation

Phase Space Angle Lag →

Mode 2

Mode 4

240 hPa 967 hPa

Cor

rela

tion

→ ][

][][cos][

cos

][][ *

**

Fp

uwu

a

vvf

Fcos

1][

adt

ud––+ ω

• 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.

|][|

][~2

cu

qn y

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 Frequency Low Frequency

Eddies propagate towards high refractive index

Eddy feedback processes

Refractive Index determined by wind anomalies

|][|

][~2

cu

qn y

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 Latitude Latitude Latitude

Hei

ght

Hei

ght

Hei

ght

Hei

ght

Latitude

Hei

ght

Latitude

Hei

ght

Latitude

Hei

ght

LatitudeH

eigh

t

Hig

h F

requ

ency

Low

Fre

quen

cy

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.