The very simplest picture of El Nio

1
The very simplest picture of El Niño
Kiel, November 2005
Gerrit Burgers1,
Geert Jan van Oldenborgh1
and Fei-Fei Jin2
1Royal Netherlands Meteorological Institute
2Florida State University, Tallahassee
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El Niño




Pattern in space and in time
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Natural variables
TE 1st natural variable h
equatorial zonal mean thermocline depth 2nd
natural variable


Jin, JAS 1997 recharge oscillator
picture Kessler, GRL2002 Is ENSO a cycle or a
series of events? McPhaden, GRL2003 h and
persistence barriers Clarke and Van Gorder, GRL
2003 Improving ENSO forecasts

After Kessler GRL 2002
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ENSO Recharge oscillator



From Jin JAS 1997

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Questions

• Difference recharge ? delayed oscillator?
• SST vs. wave dynamics?
• Do observations support the recharge
  oscillator,
• and its derivation from underlying equations?
• What do we learn along the way?
• - seasonality
• - predictability
• - phase dependence

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Jin 1997 four variables

• hW equation captures shallow-water wave
  adjustment
• as Sverdrup response
• hE reacts instantaneously to hW
• timescale SST equation necessary for oscillation
• upwelling, zonal advection etc. all lumped
  into ?1

hW and hE western and eastern Pacific
thermocline depth anomaly TE eastern Pacific
temperature anomaly ? central Pacific windstress
anomaly
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Wave dynamics version

• TE reacts instanteaneously to hE
• timescale hE equation necessary for oscillation
• close to wave oscillator form of the delayed
  oscillator

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Combining the two versions
?fast
?
?
? month-1

? ?1-1 ?

• contains extra mode that decays fast
• good approx. for slow eigenvalues (4) with
• ?-1 ?1-1 ?2 -1 decay
  times add up
• on slow manifold, hE lin. comb. of hW and TE
• hE ? ? ?1-1 (hW ? ) ? ?2-1 ?h -1
  TE

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Recharge oscillator 2-variable form

• finite wave adjustment and/or SST equation
• matters only for how hE is related to h
  and TE

• NEXT QUESTION do observations support this
  framework?

• observations monthly timeseries over
  1980-2002
• of TE , ? , hE , hw , h anomalies

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Data analysis approach
step1 - fit parameters of the 4 equations
for hW, hE, TE and ?, treating the equations
one by one - reduce these parameters to the
parameters of (TE,h) oscillator) step 2 -
calculate standard linear model fit of (TE,h)
oscillator to monthly values (i.e. minimize
rms error in 1-month forecast) step 3 examine
if results agree and are reasonable



) using h ?½(hWhE), an excellent approximation
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Step 1 method
Example fitting parameters of the hE equation
- calculate from hW ,? approximations hE as
follows
at t0 Jan 1980
determine parameters ?2 and a? such that
hEhW,? is the best approximation to
hE Criterium rms difference. It was found that
this resulted in realistic cross correlations



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Step 1 results
timescales r -16.25 month, ?1-12.75 month,
?2-12 month couplings ?h 0.0766Km-1,
a?1.6s2m-1, ? a?-1 0.67, ba? 14mK -1 2?/?48
month ? -1 17 month ?-1 4.75 month
fairly long! Bjerkness factor b ?h 1.1

• note that results depend on definitions
  variables
• fairly large uncertainties
• r(sim,obs) ?0.85 for TE, hE, hW 0.73 for ?

• Reduction to (TE,h) oscillator form

t in months, TE in K, h in m
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Step 2 results
Fit of 1-month forecasts gives

2?/?37, ? -1 24 month

Observed upper ocean heat content and
thermocline from wind-forced shallow water model
or GCM give similar results


Observed TE and h (after Billy Kessler (GRL
2002)
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Step 3 comparison
fitting 4 equations
1-month forecasts T h

if TE and h normalized on 1



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Step 3 Classical (p, q) form
2?/? ? 45 month, ? -1 ? 25 month

• damping mainly on TE equation
• h governed by Sverdrup transport, very little
  damping
• like classical damped oscillator (TE, h) (p, q)

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Other consistency checks (I) Stochastic
oscillator fit
Fit parameters stochastically driven linear
system minimizing rms error 1-month forecasts
1980-2002
2-D stochastic oscillator
normalized variables time step
1 month

Period and decay scale 2p/?37 months, 1/? 24
months Amplitude driving noise e10.28,
e20.29, r(e1, e2)0.24


1-D stochastic oscillator

Reduction from 2-D oscillator 2p/?37,
1/? 24, k0.84 Fit to Niño-3 timeseries
1957-2002 2p/?37, 1/? 16, k0.82
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Other consistency checks (II)forecasts skill
skill if both T and h observations are used
gt skill if only T observations
are used
gt skill persistence




NB picture shows a posteriori skill (no
jackknife used), so it is too optimistic
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Simplest description of ENSO
2?/? ? 45month, ? -1 ? 25 month

• ? represents the net SST-wind feedback
  (Bjerkness)
• ? Sverdrup response h, waveSST dynamics
  (Wyrtki)
• 0 to first order, h reacts only to tilt
  thermocline

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Now for complications

• seasonality
• phase dependence ( a special form of
  non-linearity)

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Seasonality

• Niño3 peaks
• around Christmas
• phase locking
• spring barrier in TE
• winter barrier in h
• (McPhaden, GRL 2003)

? Let us consider seasonal recharge oscillator fit
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Seasonal recharge oscillator fit
Seasonal fit on 1-month forecasts of
NB noise driven system then gives automatically
right amplitudes TE and h




seasonal cycle amplitudes
seasonal cycle matrix elements
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Seasonal cycle in ? and ?
?,?
(month-1)




seasonal cycle in frequency and decay constants
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Spring barrier in observations
Spring barrier in observed seasonal
correlation (after McPhaden, GRL2003)




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Spring barrier recharge oscillator
NB at zero lag, fit gives automatically right
correl-ation TE and h ?




Spring barrier in seasonal correlation of
seasonal recharge oscillator system
obs ?
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Spring barrier predictability
potential predictability ) seasonal recharge
oscillator ?
?
skill ECMWF operational forecast 1987-2001
?




) is NOT forecast skill, but predictability of
linear system with parameters and noise
properties from seasonal fit
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Seasonal cycle in goodness of fit
Residues for fit on 1-month forecasts
TE

• dashed lines normalized on amplitude T, h

• solid lines normalized on amplitude monthly
  change in T, h

h
In August, recharge oscillator adds very little
to persistence Skill in predicting changes in
spring



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Spectra multiple time scales (1)?
Annual mean version single peak Seasonal
version slight shoulder around 0.7 cpy




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Spectra multiple time scales (2)?

23 years
2000 years


width spectral peak increases compared to fixed
?, ? case
simulation with phase dependent ?, ?
? 0.150.04cos? , ? 0.04?0.06cos(? ??/4)
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Phase as a function of time




T ? 4 year
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Phase and season
h
T
?
IV
III
II
I
1988
1987
IV
III
1986
II
I
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Phase dependent recharge oscillator
II
I
I I I III IV N
99 65 41 71 start DJF
JFMA 2?/? 52 35 33 45 1/? 12
200 90 10 ? 0.8 0.7 0.4
0.6
III
IV
start season when phase usually starts ?
normalized error of seasonal dependent fit
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El Niño unstable, ENSO stable?

• Part of the cycle may be unstable, even if
  averaged
• over a full cycle the system is damped
• Goes hand in hand with skewness

• Example of a neutral cycle with a ?(? ) and ? (?)
  that contain terms
• cos(?) and ? cos(2?)
• picture by Debabrata Panja,
• work in progress

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Conclusions

• TE and h natural variables
• Simplest formulation of
• ENSO recharge oscillator
• Seasonal recharge oscillator describes spring
  barrier well
• Predictability estimate if ENSO would be pure
  recharge oscillator
• 12 - 18 months, depends on season
• Both variations in decay/growth ? and phase
  propagation ?
• in recharge oscillator framework
• - Phase propagation in spring, decay in
  winter
• - Growth before El Nino, phase
  propagation at El Niño