The nonlinear patterns of North American winter temperature and

precipitation associated with ENSO

Aiming Wu, William W. HsiehDept. of Earth & Ocean Sciences,

University of British Columbia

and

Amir ShabbarMeteorological Services of Canada

Downsview, Ontario

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)

Question

If x is the ENSO index, how to 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

Data

ENSO 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%)

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

Give a 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 quadraticresponse

22110 iiii aaay

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

Summary and ConclusionSummary and Conclusion

• N. Amer. 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), while linear method can not.

• 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.

Thank you !