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

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 home you 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 Mexico You find historical evidence for famine in Mexico Reasoning: Could El Nino by the cause? Further research in archives reveals evidence for turmoil Coral proxy record 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 temper ature rainfal l Proxy 2Proxy 1Proxy 3 Global/large-scale climate regional/local scale geobiochemical/physical/documentary information El Nino-La Nina

Paleoclimate Reconstruction: A Simple Bayesian Network ENSO Proxy 1Proxy 2 Proxy m Conditionally independent proxy information ! Causal relation Reasoning direction

Short Review of standard reconstruction 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 Regression vs Bayesian method y(t)= a 0 +a 1 x 1 (t)+a 2 x 2 (t) a m (t) x m (t)+e(t) y(t) : climate signal, the ENSO index, time dependent (t) x 1 (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 a 0... a m parameters such that the estimated climate signal is 'closest'* to the true signal represented: ŷ(t)= â 0 +â 1 x 1 (t)+â 2 x 2 (t) â m (t) x m (t) *E{[ŷ(t)-y(t)] 2 } is minimized

Problems with linear regression model Causality is inverted: The proxies do not control ENSO! We have indeed m equations of the following kind x 1 (t) = c 1 + b 1 y(t) + n 1 (t) x 2 (t) = c 2 + b 2 y(t) + n 2 (t)... x m (t) = c m + b m y(t) + n m (t) The problem of 'multicollinearity'  Principal Component Regression y(t)= a 0 +a 1 x 1 (t)+a 2 x 2 (t) a m (t) x m (t)+e(t)

Linear regression / Bayesian Method Probability of x 1 given y: P(x 1 |y) Probability of x 2 given y: P(x 2 |y)... Probability of x m given y: P(x m |y) y(t) : climate signal, the ENSO index, time dependent (t) x 1 (t),x 2 (t)... x m (t): proxy indices, time dependent (t) P(y|x 1,x 2,x m ) y(t)= a 0 +a 1 x 1 (t)+a 2 x 2 (t) a m (t) x m (t)+e(t) x 1 (t) = c 1 + b 1 y(t) + n 1 (t) x 2 (t) = c 2 + b 2 y(t) + n 2 (t)... x m (t) = c m + b m y(t) + n m (t)

Example NINO3 index & Palmyra Proxy NINO3 index Palmyra coral record  18 O (oxygen isotope concentration) Time: Nov-Mar seasonal averages Bayes fundamental rule: P(X,Y)=P(X|Y)*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 Bayes fundamental rule: P(X,Y)=P(X|Y)*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 Scatterplot P(X,Y)

Example NINO3 index & Palmyra Proxy NINO3 index Palmyra coral record  18 O (oxygen isotope concentration) Time: 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 index Maximum likelihood reconstruction Linear 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

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

Training and Validation “Training” period Validation period

Categorized ENSO reconstruction Training period time Validation Period NINO3 index Reconstructed 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.