Adaption of Paleoclimate Reconstructions for

Interdisciplinary Research

Oliver Timm

International Pacific Research Center, SOEST, University of Hawai'i at Manoa

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

Indirect evidence (proxies) for climatic conditions

Chained reasoning: A non-climatic textbook example

Burglary

Alarm

Earthquake

Radio News

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 homeyou listen to radio:an earthquake hit your home area.

Chained reasoning: Analog paleoclimate example

El Nino

Historical record:

famine in Mexico

Country in turmoil

Historical archives

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

Further research in archivesreveals evidence for turmoil

Coral proxyrecord

Search for independent evidence of El Nino: coral proxy data

El Nino -Southern Oscillation:Impact on paleoclimate proxies

Sea Surface Temperatures (SST) in colors [blue=negative, red=positive anomalies]

Precipitation anomalies:dashed=negative, solid=positive

Palmyra

Reasoning in Paleoclimate Reconstruction

ENSO

temperature

rainfall

Proxy 2

Proxy 1

Proxy 3

Global/large-scale climate

regional/local scale

geobiochemical/physical/documentary information

El Nino-La Nina

Paleoclimate Reconstruction:A Simple Bayesian Network

ENSO

Proxy 1

Proxy 2

Proxy m

Conditionally independent proxy information !

Causal relation Reasoning direction

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

Multiple Linear Regressionvs Bayesian method

y(t)= a0+a

1x

1(t)+a

2x

2(t)+ ... + a

m(t) x

m(t)+e(t)

y(t) : climate signal, the ENSO index, time dependent (t)

x1(t),x

2(t) ... x

m(t): proxy indices, time dependent (t)

e(t): noise (climate variability not explained by the model)

estimate the model a0 ... a

m parameters such that the

estimated climate signal is 'closest'* to the true signal

represented:

ŷ(t)= â0+â

1x

1(t)+â

2x

2(t)+ ... + â

m(t) x

m(t)

*E{[ŷ(t)-y(t)]2} is minimized

Linear regression / Bayesian Method

Probability of x1 given y: P(x1|y)

Probability of x2 given y: P(x2|y)

...

Probability of xm given y: P(xm|y)

y(t) : climate signal, the ENSO index, time dependent (t)

x1(t),x

2(t) ... x

m(t): proxy indices, time dependent (t) 

P(y|x1,x

2,x

m)y(t)= a

0+a

1x

1(t)+a

2x

2(t)+ ... + a

m(t) x

m(t)+e(t)

x1(t) = c

1+ b

1y(t) + n

1(t)

x2(t) = c

2+ b

2y(t) + n

2(t)

...

xm(t) = c

m+ b

my(t) + n

m(t)

Example NINO3 index & Palmyra Proxy

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

Bayes fundamental rule:

P(X,Y)=P(X|Y)*P(Y)

Probability of event X given an event Yis equal to the joint probability of eventX and Y times the probability of event Y

Bayes fundamental rule:

P(X,Y)=P(X|Y)*P(Y)

Probability of event X given an event Yis equal to the joint probability of eventX and Y times the probability of event Y

Scatterplot

P(X,Y)

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)

Example NINO3 index & Palmyra Proxy

Bayes fundamental rule:

P(X|Y)=P(X,Y)/P(Y)

P(NINO3|Palmyra)=

P(NINO3,Palmyra)/P(Palmyra)

Bayes fundamental rule:

P(X|Y)=P(X,Y)/P(Y)

P(NINO3|Palmyra)=

P(NINO3,Palmyra)/P(Palmyra)

Scatterplot

P(NINO3|Palmyra)

Reconstruction using linear regression line

Bayesian method: Estimates the probability of NINO3 states

Example NINO3 index & Palmyra Proxy

High probability

Low probability

NINO3 indexMaximum likelihood reconstructionLinear Regression

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.

0-1-2 1 2

0

-1

-2

1

2

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

0

1

-1

-2

2

Training and Validation“Training” period 1930-1979 Validation period 1887-1929

Categorized ENSO reconstruction

Training period 1930-1979

time

Validation Period

NINO3 indexReconstructed Category

time

Categorized ENSO reconstruction

time

Reconstructed Category

time

Spliced Palmyra data* (Cobb et al., 2003)

* normalized and each segment detrended

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.