Title: The nonlinear patterns of North American winter temperature and precipitation associated with ENSO
1The nonlinear patterns of North American winter
temperature and precipitation associated with ENSO
- Aiming Wu, William W. Hsieh
- Dept. of Earth Ocean Sciences,
- University of British Columbia
- and
- Amir Shabbar
- Meteorological Services of Canada
- Downsview, Ontario
2ENSO El Niño Southern Oscillation
El Niño
La Niña
3Atmos. 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)
-
A
-
- La Niña El Niño
- Sign reversed
- Shifted eastward by 30-40(asymmetric)
-
B
-
4Question
- If x is the ENSO index, how to derive the atmos.
response y ƒ(x) ? - linear regression (or projection)
- y a x
-
-
x
x
-
-
-
- Linear method cannot extract asymmetric patterns
between x and x - Need a nonlinear method
-
-
5Nonlinear 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)
6Data
- 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)
7Bootstrap
- 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
Give a x ? NN model ? y ? (combined with EOFs) ?
atmosphere anomaly pattern associated with x
8NN 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
9SAT 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
10PCA on Lin. Nonlin. Parts of NN projection
NL NN LR
Linear regression
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11- PC1 of Lin. part vs. ENSO index ? a straight
line - PC1 of Nonlin. part vs. ENSO index ? a quadratic
curve - ?
- A quadratic
- response
12A polynomial fit
?1 , ?2 are x, x2 normalized, x is the ENSO
index
SAT
13PRCP 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
14Lin. nonlin. prcp. response to ENSO
LR NL NN
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15Lin. nonlin. prcp. PC1 vs. ENSO index
16- Summary 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 1/41/3 as much as the variance of the linear
part.
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