El Nio and how to get rid of it

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El Niño and how to get rid of it

• Cécile Penland

With thanks to Prashant Sardeshmukh Ludmila
Matrosova Ping Chang Moritz Flügel Brian
Ewald Roger Temam The Climate Diagnostics
Center OGP
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Review of Linear Inverse Modeling
Assume linear dynamics dx/dt Bx x Diagnose
Green function from data G(t) exp(Bt)
ltx(tt)xT(t) gtlt x(t)xT(t) gt-1 . Eigenvectors of
G(t) are the normal modes ui. Most probable
prediction x(tt) G(t) x(t) The neat thing
G(t) G(to) t/ to
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SST Data used

• COADS (1950-2000) SSTs in 30E-70W, 30N 30S
  consolidated onto a 4x10-degree grid.
• Subjected to 3-month running mean.
• Projected onto 20 EOFs (eigenvectors of ltxxTgt)
  containing 66 of the variance.
• x, then, represents the vector of SST anomalies,
  each component representing a location, or else
  it represents the vector of Principal Components.

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El Niño can be described this way.   If LIM is
successful, prediction error does not depend on
the lag at which the covariance matrices are
evaluated. This is true for El Niño it is not
true for the chaotic Lorenz system. Below,
different colors correspond to different lags
used to identify the parameters.
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The annual cycle dx/dt Bx x lt x (tt) xT
(t) gt Q(t)d(t) Given stationary B use
(time-dependent) conservation of variance to
diagnose Q(t). Result The annual cycle of Q(t)
looks nothing like the phase locking of either El
Niño or the optimal structure to the annual
cycle. But A model generated with the
stationary B and the stochastic forcing with
cyclic statistics Q(t) does reproduce the correct
phase-locking in both.
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What do models say?

• Hybrid coupled model (Chang 1994)
• Dynamical core of GFDL Ocean model, considerably
  simplified
• Statistical atmosphere based on EOFs of observed
  wind stress
• Interactive annual cycle
• Strength of coupling determines dynamical regime
  (Note an artificial parameter d)

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Optimal initial structure for growth over lead
time t Right singular vector of G(t)
(eigenvector of GTG(t)) Growth factor over lead
time t Eigenvalue of GTG(t).
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The transient growth possible in a
multidimensional linear system occurs when an El
Niño develops. LIM predicts that an optimal
pattern (a) precedes a mature El Niño pattern (b)
by about 8 months.
(a)
(b)
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Does it? Judge for yourself! (c and d)
(d)
(c)
c) d)
In (c), the red line is the time series of
pattern correlations between pattern (a) and the
sea surface temperature pattern 8 months earlier.
The blue line is a time series index of how
strong pattern (b) is at the date shown the blue
line is an index of El Niño when it is positive
and of La Niña when it is negative.   In (d) we
see a scatter plot of the El Niño index and
pattern correlations shown in (c). Pattern (a)
really does precede El Niño! Pattern (a) with
the signs reversed precedes La Niña!
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Projection of adjoints onto O.S. and modal
timescales.
Decay mode, m 31 months
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Location of indices N3.4, IND, NTA, EA, and STA.
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R 0.36
R 0.45
EA
STA
R 0.44
R 0.61

IND
NTA
Indices. Black Unfiltered data. Red El Niño
signal.
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STA leads
PC1 leads
PC1 leads
EA leads
PC1 leads
PC1 leads
IND leads
NTA leads
Lagged correlation between El Niño indices and
PC 1.
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Projection of adjoints onto O.S. and modal
timescales.
Decay mode, m 31 months
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EOF 1 of Residual
u1 of un-filtered data
The pattern correlation between the longest-lived
mode of the unfiltered data and the leading EOF
of the residual data is 0.81.
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R 0.75
R 0.77
EA SSTA (C)
STA SSTA (C)
R 0.79
R 0.62
IND SSTA (C)
NTA SSTA (C)
Indices. Black Unfiltered data. Green El Niño
signal Trend.
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All this results from SST dynamics being
essentially linear. But linear dynamics implies
symmetry between El Niño and La Niña events. SST
anomalies appear to be positively skewed. Is the
skew significant?
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Additive Noise Model dx/dt Bx x
Multiplicative Noise Model 1 dx/dt(BAx)x x
Multiplicative Noise Model 2 dx/dtB(IIx)x x
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Conclusions

• El Niño appears to be a damped system forced by
  stochastic noise.
• There is evidence that the phase locking of El
  Niño to the annual cycle is due to the
  annually-varying statistics of the stochastic
  noise.
• An optimal initial structure for growth precedes
  a mature El Niño event by 6 to 9 months.
• The nonnormal dynamics are dominated by 3
  nonorthogonal modes.
• The essential linearity of the system allows
  isolation of the El Niño signal.

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• El Niño indices in the equatorial Indian Ocean
  and the North Tropical Atlantic Ocean are very
  similar.
• El Niño and the (parabolic) trend dominate the
  SST variability in the Indian Ocean as well as in
  the Equatorial and S. Tropical Atlantic Ocean.
• The observed skew in El Niño La Niña events IS
  NOT significant compared with realistic null
  hypothses.
• The trend IS significant compared with realistic
  null hypotheses.

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