Preferred Modes of Variability and

Their Relationship with Climate Change

The Pennsylvania State University

Department of Meteorology

Seok-Woo Son and Sukyoung Lee

- Dominant internal variability of the atmosphere

Annular Mode

SH NH[u]

SLP

Thompson et al. 2000

Leading EOF of SLP

Zonally symmetric

Quasi-barotropic

Useful for understanding

internal variability

Useful for understanding

climate change (?)

SH [u] response to global warming

SH Annular Mode

latitude

pres

sure

(hP

a)

NH Annular Mode

pres

sure

(hP

a)NH [u] trend 1968-1997

Thompson et al. 2000 Kushner et al. 2001

“Spatial pattern” of annular mode ≈ recent trend in the

observed and simulated zonal-mean circulation

To what extent annular mode is capable of

predicting zonal-mean climate change?

Purpose and Approaches

Annular mode vs. Climate change

Annular mode – EOF1 of [u] (regressed against PC1 time series)

Climate change – difference of [u] between any two adjacent runs

Internal variability of [u] with a help of EOF1 and EOF2

Structure of [u] in the statistically steady state ( [u] )

Total 49 simulations by differing radiative heating in a simple GCM

Evaluate the predictability of zonal-mean climate change by

annular mode in terms of their spatial structures.

Numerical Model A dynamic core of GFDL GCM (symmetric boundary cond.)

Driven by relaxing T toward Te with timescale of 30 days

R30L10 but zonal wave number 15

Te(C,H) = Tbase + ΔTe(C,H)

C : high-latitude cooling (K/day) H : tropical heating (K/day)

Dissipated by linear friction and 8th order hyperdiffusion

Numerical Model (Cont.)

Statistics are derived from the last 4500 days of each 5000-day

integration. Data of both hemispheres are used.

Total 49 realizationsC (0.00, 0.17, 0.33, 0.50, 0.67, 0.88, 1.00) K/day

H (0.00, 0.33, 0.67, 1.00, 1.33, 1.67, 2.00) K/day

[u]

(C,H)=(0.17,0.33)

Single Jet Intermediate Jet Double Jet

(C,H)=(0.17,1.67) (C,H)=(0.83,0.33)

[u] : Structure of Westerly Jets

Strong C & weak H → Double Jet

H ≥ 1.00K/day → Single JetSJ

WJ

DJ

One-point correlation of 250-hPa [u]'

Internal variability of the jets

TransitionWJ

Poleward PropagationDJ

Zonal-index (Jet Meander)SJ

[u] & EOFs

Time series of PC1 and PC2 Correlation PC1 vs. PC2

Transition

Poleward Propagation

Zonal-index (Jet Meander)

WJ

DJ

SJ

Poleward Propagation: i. Correlation between PC1 & PC2 is very high ii. Var(EOF2) is comparable to Var(EOF1)

Shading γ ≥ 0.5 Shading χ ≥ 0.5

Collocates with intermediate- and double-jet

Annular mode & Climate change in the modeI

Annular mode : EOF1 of [u]

Climate change : Difference of [u] between two adjacent runs

• δ[u]H (0.50,1.00) = [u] (0.50,1.33) - [u] (0.50,1.00)

• δ[u]C (0.50,1.00) = [u] (0.67,1.00) - [u] (0.50,1.00)

• [u] is regressed against PC1 time series, unit of m/s.

[u] (0.50,1.00) δ[u]C (0.50,1.00)δ[u]H (0.50,1.00)

EOF1 & δ[u]C EOF1 & δ[u]H

Predictability of Climate change by Annular mode

Predictability is always poor in a poleward propagation regime.

I. Global measure : pattern correlation between EOF1 and δ[u] from 150-950 hPa and 10-80˚

Shading correlation ≥ 0.8

Annular mode in the model is associated with eddy fluxes.

• Increase of H → enhances subtropical baroclinicity and intensifies Hadley circulation

Poor predictability of δ[u]H in a zonal-index regime

δ[u]H is associated with both eddy fluxes and mean-meridional circulation.

• Increase of C → enhances extratropical baroclinicity

δ[u]C is associated with eddy fluxes.

Predictability of δ[u]C would be better than that of δ[u]H.

Summary

• Strong C & weak H → Double Jet

• H ≥ 1.00 K/day → Single Jet

Structure of Westerly Jet

Internal Variability• Strong C & weak H → Poleward propagation (Comparable effect of EOF2)• Weak C & strong H → Zonal index (Dictated by EOF1)• Broad transition zone

• Dependent on the dominant internal variability

• Relative good in a transition regime

Predictability of Climate change by Annular mode

Internal variability Both poleward propagation and zonal index (e.g., Feldstein 1998; Hartmann and Lo 1998) with γ ≈ 0.5 and χ ≈ 0.3 (Son and Lee 2005b).

Application to the Southern Hemisphere

[u]: structure of the jet

SH

Applied to the SH climate change at equinoctial condition Global warming at SH → ENSO-like tropical heating & enhanced extratropical baroclinicity (Son and Lee 2005a) → increase of H and C.

Structure of the jet Wide range of interannual variability from single- to double-jet states

EOF1 & δ[u]C

SH

EOF1 & δ[u]H

SH

Application to the Southern Hemisphere (Cont.)

Predictability is marginally good in the SH-like parameter regime.

Annular mode may not be useful for understanding paleoclimate change.

EOF1 & δ[u]C

SH

EOF1 & δ[u]H

SH

Slight climate drift to the poleward propagation regime → poor predictability.

Any comment and suggestion are welcome. Thank you!

Contact information

Seok-Woo Son: sus141@psu.edu

Dependency of internal variability to the mean flow

The meridional radiation of the waves is prohibited if the PV gradient of the ambient flow is sufficiently sharp (e.g., Hoskins and Ambrizzi 1993)

Poleward propagation of westerly anomalies may occur only when the PV gradient is relatively weak and broad.

The latitudinal distance over which the value of 250-hPa quasi-geostrophic PV gradient ([q]y) is greater than 60% of its maximum value. Shading for ≥ 35˚.

Prediction of Climate-change ‘Direction’ by Annular mode?

[u] (0.50,100) δ[u]C (0.50,100)δ[u]H (0.50,100)

Climate change direction (positive or negative phase of annular mode) is determined not by the annular mode but by the nature of external forcing.

Climate change associated with C increase (broadening of extratropical baroclinic zone) → positive phase of annular mode (in phase).

Climate change associated with H increase (warming at tropics) → negative phase of annular mode (out of phase).

+-

Prediction of Climate-change ‘Direction’ ? (Cont.)

SH [u] response to global warming

SH Annular Mode

Kushner et al. 2001

Climate change in SH is in phase with SH annular mode.

By the overwhelming effect of enhanced baroclinicity (C) over

tropical warming (H) ?

Climate change in SH: tropical warming & enhanced extratropical baroclinicity (Son and Lee 2005a) → increase of H and C.

A

δφC

II. Local measure : latitudinal distance between extrema of EOF1 and δ[u] at 250 hPa

• δφC : between EOF1 and δ[u]C EOF1 & δ[u]C (line A) • δφH : between EOF1 and δ[u]H

• measured at both subtropics and extratropics

Predictability of Climate change by Annular mode

δφC (low-latitude) δφC (mid-latitude)

δφH (low-latitude) δφH (mid-latitude)

Shading δφ ≤ 2˚ Weak latitudinal dependency of δ[u]C prediction by annular mode. Poor predictability of δ[u]H in a zonal-index regime is due to the mid-latitudes.

Shading γ ≥ 0.5

Predictability is generally good when γ ≤ 0.5 or Var(EOF1) ≥ 2•Var(EOF2)

A

δφC

II. Local measure : Compare amplitude of 250-hPa |EOF1| and |δ[u]| at 250 hPa

EOF1 & δ[u]C (line A)

Prediction of Climate-change ‘Amplitude’ by Annular mode?

Prediction of Climate-change ‘Amplitude’ by Annular mode?

shading: δφC ≤ 2˚ shading: δφH ≤ 2˚

ratio |δ[u]|/|EOF1|

difference (|δ[u]| - |EOF1|)

Predictable? No theories yet!

Ratios vary only by a factor of two!• Ratios of |δ[u]C| to |EOF1| are 0.3 to 0.8.

• Ratios of |δ[u]H| to |EOF1| are 1.0 to 2.5