The Nonlinear Patterns of North American Winter Climate associated

with ENSO

Aiming Wu, William HsiehUniversity of British Columbia

Amir ShabbarEnvironment Canada

ENSO = El Niño + Southern Oscillation

El Niño La Niña

Atmos. Response to ENSO is nonlinear

+-

+ +-+

-

Composite of Z500 and tropical precipitation during El Niño (A) and La Niña (B)

(from Hoerling et al 1997 J. of Climate)

B

A

La Niña El Niño

• Sign reversed

• Shifted eastward by 30-40°(asymmetric)

Nonlinear Temperature Response to ENSO

Hoerling et al 1997 J. of Climate

+-

+

Winter Precipitation Variability (Nov-Mar)

The Three Leading EOFs of SAT and Prcp

Objective of the StudyIf x is the ENSO index, how do we derive the

atmos. response y = ƒ(x) ?

• linear regression (or projection) y = a • x

+ + -- + -•Linear method cannot extract asymmetric patterns between –x and +x•Need a nonlinear method

–x +x

Nonlinear projection via Neural Networks

(NN projection)

• x, the ENSO index

• h, hidden layer

• y´, output, the atmos. response

hh bhWy'

bWh

)tanh( xx x

Cost function J = || y – y´ || is minimized to get optimal Wx, bx, Wh and bh (y is the observation)

A schematic diagram

DataENSO index (x)

•1st principal component (PC) of the tropical Pacific SSTA

•Nov.-Mar.

•1950-2001,monthly

•SST data from ERSST-v2 (NOAA)

•Linear detrend

•standardized

Atmos. Fields (y)

•surface air temp. (SAT) and precip.(PRCP)

•From CRU-UEA (UK)

•Monthly,1950–2001, 11•Nov.-Mar.; North America

•Anomalies (1950-01 Clim)

• Linear detrend

•PRCP standardized

•Condensed by PCA

10 SAT PCs (~90%) retained

12 PRCP PCs (~60%)

Significance by Bootstrap

• A single NN model may not be stable (or robust)

• Bootstrap: randomly select one winter’s data 52 times from the 52-yr data (with replacement) one bootstrap sample

• Repeat 400 times train 400 NN models average of the 400 models as the final solution

400 NN models

Given an x NN model y (combined with EOFs) atmosphere anomaly pattern associated with x

NN projecton in the SAT PC1-PC2-PC3

space•Green: 3-D

•Blue: projected on 2-D PC plane

• “C” extreme cold state; “W” extreme warm state

•Straight line: linear proj.

•Dots: data points

•as ENSO index takes on its

(a) min. (d) max. (b) 1/2 min. (e) 1/2 max. (c) a-2b (f) d-2e

•Darker color above 5% significance

SAT anomalies

PCA on Lin. & Nonlin. Parts of NN projection

73% 27%

NL = NN – LRLinear regression

•PC1 of Lin. part vs. ENSO index a straight line

•PC1 of Nonlin. part vs. ENSO index a quadratic curve

A quadratic response

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A polynomial fit

1 , 2 are x, x2 normalized, x is the ENSO index

SAT

•as ENSO index takes on its

(a) min. (d) max. (b) 1/2 min. (e) 1/2 max. (c) a-2b (f) d-2e

•Darker color above 5% significance

PRCP anomalies

Lin. & nonlin. prcp. response to ENSO

78% 22%

LR + NL = NN

Lin. & nonlin. prcp. PC1 vs. ENSO

index

Forecast Skill in Linear and Nonlinear Models

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1 , 2 are x, x2 normalized,

x is the ENSO index

Summary and ConclusionSummary and Conclusion

•N. American winter climate responds to ENSO in a nonlinear fashion (exhibited by asymmetric SAT and PRCP patterns during extreme El Niño and La Niña events).

• The nonlinear response can be successfully extracted by the nonlinear projection via neural networks (NN).

•NN projection consists of a linear part and a nonlinear part. The nonlinear part is mainly a quadratic response to the ENSO SSTA, accounting for 1/4~1/3 as much as the variance of the linear part.

Merci a tout !