Adaption of Paleoclimate Reconstructions for Interdisciplinary Research Oliver

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

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.

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

El Nino -Southern Oscillation: Impact on paleoclimate proxies Palmyra Sea Surface Temperatures (SST) in colors [blue=negative, red=positive anomalies] Precipitation anomalies: dashed=negative, solid=positive

Reasoning in Paleoclimate Reconstruction El Nino-La Nina ENSO rainfal l Proxy 1 Global/large-scale climate temper ature Proxy 2 regional/local scale Proxy 3 geobiochemical/physical/documentary information

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

Short Review of standard reconstruction methods Linear methods Non-linear methods Multiple linear regression Non-linear regression models Principal Component Regression Neural Networks Examples: Global (mean) temperature reconstructions (Mann et al. , 1998, 1999) Stahle et al. ENSO index reconstruction

Multiple Linear Regression vs Bayesian method y(t)= a 0+a 1 x 1(t)+a 2 x 2(t)+. . . + am(t) xm(t)+e(t) y(t) : climate signal, the ENSO index, time dependent (t) x 1(t), x 2(t). . . xm(t): proxy indices, time dependent (t) e(t): noise (climate variability not explained by the model) estimate the model a 0. . . am 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)+. . . + âm(t) xm(t) *E{[ŷ(t)-y(t)]2} is minimized

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

Example NINO 3 index & Palmyra Proxy NINO 3 index Palmyra coral record 18 O (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 Y is equal to the joint probability of event X and Y times the probability of event Y Scatterplot P(X, Y)

Example NINO 3 index & Palmyra Proxy NINO 3 index Palmyra coral record 18 O (oxygen isotope concentration) Time: 1882 -1991 Nov-Mar seasonal averages P(Y) Scatterplot P(X, Y)

Example NINO 3 index & Palmyra Proxy Scatterplot P(NINO 3|Palmyra) Bayes fundamental rule: P(X|Y)=P(X, Y)/P(Y) P(NINO 3|Palmyra)= P(NINO 3, Palmyra)/P(Palmyra)

Example NINO 3 index & Palmyra Proxy High probability Low probability NINO 3 index Maximum likelihood reconstruction Linear Regression

Categorized index reconstruction 105 years with pairs of NINO 3 index and Palmyra proxy index Question how to estimate the joint probability at 40 x 40 grid points. Few categories: 2 D histogram on 3 x 3 or 5 x 5 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 2 1 0 -1 -2

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

Categorized ENSO reconstruction Validation Period Training period 1930 -1979 NINO 3 index Reconstructed Category time

Categorized ENSO reconstruction 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.