The Nonlinear Patterns of North American Winter Climate associated with ENSO Aiming Wu, William Hsieh University of British Columbia Amir Shabbar Environment 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 °(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 Study If 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 Cost function J = || y – y´ || is minimized to get optimal W x, b x, W h and b h (y is the observation) A schematic diagram

Data ENSO index (x) 1st principal component (PC) of the tropical Pacific SSTA Nov.-Mar ,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, 1 1 Nov.-Mar.; North America Anomalies ( 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 winters 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 PC 1 -PC 2 -PC 3 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-2 b (f) d-2 e Darker color above 5% significance SAT anomalies

PCA on Lin. & Nonlin. Parts of NN projection 73% 27% NL = NN – LRLinear regression

S AT and SLP Linear and Nonlinear Projections

PC 1 of Lin. part vs. ENSO index a straight line PC 1 of Nonlin. part vs. ENSO index a quadratic curve A quadratic response

A polynomial fit 1, 2 are x, x 2 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-2 b (f) d-2 e Darker color above 5% significance PRCP anomalies

Lin. & nonlin. prcp. response to ENSO 78%22% LR + NL = NN

Prcp and SLP Linear and Nonlinear Projections

Lin. & nonlin. prcp. PC 1 vs. ENSO index

Forecast Skill in Linear and Nonlinear Models 1, 2 are x, x2 normalized, x is the ENSO index

Summary 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 !