the nonlinear patterns of north american winter temperature and precipitation associated with enso

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 !