”Statistiske metoder i klimaforskning”24. April, 2008, HCØ.

Climate reconstructions

using Proxy DataPeter Thejll

Torben Schmith

Bo Christiansen

What are 'proxies'?• Proxies are data that tell us about

something else– tree rings

– corals

– speleothemes

– sediment layers in lakes and oceans

– ice cores

– documentary information

– local (p,T,...) observations

– proxies of forcings

Pick your proxies based on what you want to reconstruct

How do you use proxies?

• 'Cook' the proxies to extract the relevant information– 'Train' on some target series, often

instrumental present-day data

– use • averaging, weighting – OLS!

• eigenmode-extraction from fields of proxies – OLS!

– being careful with• cross-correlated proxies

• auto-correlated proxies

• local proxies that by chance correlate with training series ('stationarity of patterns')

Climate reconstructions are important because …

• They tell us about the past …– Interpreting History (”Vikings in Greenland”,

”Decline of the Pueblo”, Mayas …)– Interpreting the present climate (”Medieval Warming

was large/small”) … politics!

• If related to forcings they tell us about …– Climate Sensitivity

• Physics interest• Prediction from ’Scenarios’

– Internal or ’natural’ variability

Our own effort to understand various reconstruction techniques

• 6 or more reconstruction techniques tested on ’sandbox’ or ’surrogate data worlds’, enabling …– ’know the answer’ – testing purposes– ’same input data’ – reduce confusion

• Found …– Large variability among all methods– No ’best method’– Importrace of ”training period”

Two tries, two results

Reconstructions of one realization of the surrogate temperature fields with the six different methods. Reconstructions are based on 57 white noise proxies, and the calibration period is the last 100 years.

Training on 1900s

Training on 1500s

Challenge• Need to use ’first principles’ to design an

”optimum climate reconstruction method”• Consider climate system

• couplings– Redundant data

» Help or obstruction?

• Forcings/Internal variability– What causes climate to change?

» Better understanding of forcing mechanisms and internal variability gives better chance to understand which proxies can be used

• Can ’econometric methods’ help?• Role of trends in training periods? (nonstationarity)• Co-integration? (Proxies and climate should be

intertwined, but are they I(1)?)