Adaption of Paleoclimate Reconstructions for Interdisciplinary Research

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Adaption of Paleoclimate Reconstructions for
Interdisciplinary Research
Oliver Timm International Pacific Research
Center, SOEST, University of Hawai'i at Manoa
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Overview

• The nature of the problem
• We are confronted with chained reasoning,
  inferences and decision making in paleoclimate
  research, environmental studies
• Basic concepts of paleoclimatic methods
• Indirect evidence (proxies) for climatic
  conditions
• Numerical simulations with climate models
• Development of theoretical concepts of past
  climates
• Specific examples
• Reconstruction of El Nino- Southern Oscillation
  (ENSO)
• Bayesian approach Reconstructing the probability
  of past El Nino/ La Nina events

Indirect evidence (proxies) for climatic
conditions
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Chained reasoning A non-climatic textbook
example

• Your house has a burglary alarm system.
• You are at work.
• You receive a call from your neighbor that the
  alarm went off.
• What to do?
• Stay at work and do not worry or go home and
  check your house.

On your way home you listen to radio an
earthquake hit your home area.
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Chained reasoning Analog paleoclimate example

• You have some prior understanding for relation
  ENSO- rain in Mexico
• You find historical evidence for famine in Mexico
  
• Reasoning Could El Nino by the cause?

Further research in archives reveals evidence for
turmoil
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El Nino -Southern OscillationImpact on
paleoclimate proxies
Palmyra
Sea Surface Temperatures (SST) in colors
bluenegative, redpositive anomalies
Precipitation anomalies dashednegative,
solidpositive
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Reasoning in Paleoclimate Reconstruction
El Nino-La Nina
ENSO
Global/large-scale climate
temperature
rainfall
regional/local scale
Proxy 2
Proxy 1
Proxy 3
geobiochemical/physical/documentary information
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Paleoclimate ReconstructionA Simple Bayesian
Network
ENSO
Proxy m
Proxy 1
Proxy 2
Conditionally independent proxy information !
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Short Review of standardreconstruction methods

• Linear methods
• Multiple linear regression
• Principal Component Regression
• Examples
• Global (mean) temperature reconstructions (Mann
  et al. , 1998, 1999)
• Stahle et al. ENSO index reconstruction

• Non-linear methods
• Non-linear regression models
• Neural Networks

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Multiple Linear Regressionvs Bayesian method

• y(t) a0a1x1(t)a2x2(t) ... am(t) xm(t)e(t)
  
• y(t) climate signal, the ENSO index, time
  dependent (t)
• x1(t),x2(t) ... xm(t) proxy indices, time
  dependent (t)
• e(t) noise (climate variability not explained by
  the model)
• estimate the model a0 ... am parameters such
  that the
• estimated climate signal is 'closest' to the
  true signal
• represented
• y(t) â0â1x1(t)â2x2(t) ... âm(t) xm(t)
• Ey(t)-y(t)2 is minimized

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Problems with linear regression model
y(t) a0a1x1(t)a2x2(t) ... am(t) xm(t)e(t)

• Causality is inverted The proxies do not
  control ENSO!
• We have indeed m equations of the following
  kind
• x1(t) c1 b1y(t) n1(t)
• x2(t) c2 b2y(t) n2(t)
• ...
• xm(t) cm bmy(t) nm(t)
• The problem of 'multicollinearity'
• Principal Component Regression

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Linear regression / Bayesian Method
x1(t) c1 b1y(t) n1(t) x2(t) c2 b2y(t)
n2(t) ... xm(t) cm bmy(t) nm(t)

• Probability of x1 given y P(x1y)
• Probability of x2 given y P(x2y)
• ...
• Probability of xm given y P(xmy)

P(yx1,x2,xm)
y(t) a0a1x1(t)a2x2(t) ... am(t) xm(t)e(t)
y(t) climate signal, the ENSO index, time
dependent (t) x1(t),x2(t) ... xm(t) proxy
indices, time dependent (t) 
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Example NINO3 index Palmyra Proxy

• NINO3 index
• Palmyra coral record ?18O(oxygen isotope
  concentration)
• Time 1887-1991
• Nov-Mar seasonal averages

Scatterplot
P(X,Y)
Bayes fundamental rule
P(X,Y)P(XY)P(Y) Probability of event X given
an event Y is equal to the joint probability of
event X and Y times the probability of event Y
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Example NINO3 index Palmyra Proxy

• NINO3 index
• Palmyra coral record ?18O(oxygen isotope
  concentration)
• Time 1882-1991
• Nov-Mar seasonal averages

Scatterplot
P(X,Y)
P(Y)
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Example NINO3 index Palmyra Proxy
Scatterplot
P(NINO3Palmyra)
Bayes fundamental rule P(XY)P(X,Y)/P(Y) P(NI
NO3Palmyra) P(NINO3,Palmyra)/P(Palmyra)
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Example NINO3 index Palmyra Proxy
High probability
Low probability
NINO3 index
Maximum likelihood reconstruction
Linear Regression
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Categorized index reconstruction

• 105 years with pairs of NINO3 index and
  Palmyra proxy index
• Question how to estimate the joint
  probability at 40x40 grid points.
• Few categories 2D histogram on
• 3x3 or 5x5 grid.

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Combining three existing ENSO reconstructions
1) Stahle et al., 1998 network of
tree-ring data (Northern Mexico, the
southwestern U.S.A. , Indonesia) 2) D'Arrigo
et al., 2005 network of tree-ring
data (Northern Mexico, the southwestern U.S.A. ,
Indonesia) 3) Mann et al., 2000 global
multiproxy network
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1
0
-1
-2
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Training and Validation
Training period 1930-1979
Validation period 1887-1929
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Categorized ENSO reconstruction
Training period 1930-1979
Validation Period
NINO3 index
Reconstructed Category
time
time
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Categorized ENSO reconstruction
Reconstructed Category
time
time
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Spliced Palmyra data (Cobb et al., 2003)
normalized and each segment detrended
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Summary
1) Bayesian methods allow for the quantification
of uncertainties/likelihoods of the estimate 2)
Probablities estimates are the 'decision-makers'
- Hypothesis-Test - Cause-Effect studies 3)
Bayesian methods can provide the needed
information for hypothesis testing. 4) Bayesian
statistics can be useful to manage different
types of paleoclimate information.