The Nonlinear Patterns of North American Winter Climate associated with ENSO

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• The Nonlinear Patterns of North American Winter
  Climate associated with ENSO
• Aiming Wu, William Hsieh
• University of British Columbia
• Amir Shabbar
• Environment Canada

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ENSO El Niño Southern Oscillation
El Niño
La Niña
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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)

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A

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• La Niña El Niño
• Sign reversed
• Shifted eastward by 30-40(asymmetric)

B
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Nonlinear Temperature Response to ENSO
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Hoerling et al 1997 J. of Climate
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Winter Precipitation Variability (Nov-Mar)
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The Three Leading EOFs of SAT and Prcp
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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

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

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Nonlinear projection via Neural Networks (NN
projection)

• x, the ENSO index
• h, hidden layer
• y, output, the atmos. response

A schematic diagram
Cost function J y y is minimized to
get optimal Wx, bx, Wh and bh (y is the
observation)
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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,19502001, 1??1?
• Nov.-Mar. North America
• Anomalies (1950-01 Clim)
• Linear detrend
• PRCP standardized
• Condensed by PCA
• 10 SAT PCs (90) retained
• 12 PRCP PCs (60)

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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
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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

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SAT anomalies

• 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

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PCA on Lin. Nonlin. Parts of NN projection
NL NN LR
Linear regression
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73
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SAT and SLP Linear and Nonlinear Projections
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• 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
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PRCP anomalies

• 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

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Lin. nonlin. prcp. response to ENSO
LR NL NN
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Prcp and SLP Linear and Nonlinear Projections
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Lin. nonlin. prcp. PC1 vs. ENSO index
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(No Transcript)
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Forecast Skill in Linear and Nonlinear Models
?1 , ?2 are x, x2 normalized, x is the ENSO
index
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• 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 1/41/3 as much as the variance of the linear
  part.

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• Merci a tout !