Nonlinear AO signature in Northern Hemisphere winter climate and its

changes under global warming

Aiming Wu and William W. Hsieh

Dept. of Earth and Ocean SciencesUniversity of British Columbia

Co-workers: A. Shabbar, G. J. Boer, and F. W. Zwiers

Outline

• Methodology and Data

• Nonlinear association between AO and N. Hemis. winter climate

(a) observation (1948-2002) (b) CCCma CGCM2

• Changes of AO behavior under global warming (a) observation (1901-1950 vs. 1951-2000) (b) CCCma CGCM2 201-yr (“IS92a” forcing scenario)

• Conclusions

Background

(a) Composites of atmos. anomalies during high and low AO index months show asymmetric spatial patterns nonlinear association between AO and climate fields

(b) Linear regression only gives strictly symmetric patterns for opposite phases of AO

We come to a nonlinear regression or projection ……

Nonlinear projection via NNh = tanh (Wx • x + bx)

y = Wh • h + bh

y = f (x)

As x varies, both amplitude and spatial

pattern of y change

LP: amplitude changes, spatial pattern fixed

Output layer

AO index

Hidden neurons

Observational Data• Sea level pressure (SLP, 5º 5º, NCAR, 20ºN~90ºN) AO index The standardized leading principal

component (PC) of winter (NDJFM) SLP anomalies

• 500mb geo-potential height (Z500, 2.5º 2.5º, NCEP reanalysis, 20ºN~90ºN)

• Land surface air temperature (SAT) and precipitation (PRCP), from CRU-UEA (UK), 0.5º 0.5º

• Monthly, 1948-2002, winter season (NDJFM)

• Data compressed by PCA, with 10 SLP, 10 Z500, 12 SAT and 12 PRCP PCs retained (to train NN model)

Model DataCCCma CGCM2 201-yr simulation (1900-2100)• with “IS92a” forcing scenario • 3 ensemble members • anomalies based on 30-year running

climatology (to remove the long-term trend)• 4 periods (each 50 5 3 = 750 winter

months)

P1: 1901-1950 P2: 1951-2000

P3: 2001-2050 P4: 2051-2100 • NN projection of model AO index onto model

SLP, Z500, etc, and for each period, separately

Observational results

(based on 1948-2002)

NLP = Linear part + Nonlinear part

Linear regression

PCA

(Over 99% variance by mode 1)

y = -0.743 -0.172x + 0.763x2 + 0.018x3 – 0.007x4 –

0.001x5

PC1 of nonlinear component & AO index

LinNL

LinNLδ

(a) (b) (c)

CCCma CGCM2 results

(P2: 1951-2000)

Model P2

OBS 1948-02 SLP

H

H

H

H

HL

L L

L

L

H

H

H

L

L

Model P2

OBS 1948-02 Z500

H

H

L

L

H

H

H

H

H

H

H

L

L

LL

L

L

Changes under global warming

(compare P1, P2, P3, P4)

SLP

CGCM2

L L

H H

HH

L L

H

HH

H

Linear

Z500

CGCM2

H

H

H

H

L L

L L

H H

H H

Linear

CGCM2

SLP

L

L

L

L

L

L

L

L

H

H

H

H

H

H H

Nonlin.

Z500

CGCM2

LL L

L

L

L

LL

H H

H

H

H

H

Nonlin.

1901-1950 1951-2000

OBS. SLP

(Nonlinear)

L

L

L

LH

H

H

L

(a) (b)

(c) (d)

CGCM2

SLP

H

L

H

H H

L

L

L

L

L

L

H

(a)

(d)(c)

(b)CGCM2

Z500

H H

H H

LL

L

L

L

L

H

H

H

H

cbxaxy 2

With a small change in mean state,

xx̂

then 2)2(ˆ bxxbay

Feedback of the nonlinear component to the linear component ?

As

We assume

cxbxay 2ˆˆˆ

Conclusions1. NLP extracts nonlinear (mainly quadratic)

association btw. AO and N. H. winter climate, which is dominant over the Pacific- N. Amer. West Coast (while linear component is dominant over Euro-Atlantic)

2. The observed nonlinear AO behavior and its changes under global warming are well simulated by CCCma CGCM2

3. The shift of the nonlinear AO teleconnection towards the Pacific seems to be linked to global warming

4. Under global warming, nonlinear component may affect linear component