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Statistical problems in climate change detection and attribution. Andreas Hense, Meteorologisches Institut Universität Bonn. Overview. Introduction The detection problem The attribution problem The Bayesian view Summary and Conclusion. Yes or No ?. Random Variations?. Detection.

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statistical problems in climate change detection and attribution

Statistical problems in climate change detection and attribution

Andreas Hense,

Meteorologisches Institut

Universität Bonn

Andreas Hense, Universität Bonn

overview
Overview
  • Introduction
  • The detection problem
  • The attribution problem
  • The Bayesian view
  • Summary and Conclusion

Andreas Hense, Universität Bonn

slide3

Yes or No ?

Random Variations?

Detection

Andreas Hense, Universität Bonn

slide4

Yes or No ?

Attribution

Andreas Hense, Universität Bonn

the detection problem
The detection problem

Null Hypothesis H0 : Random Natural Variability

Alternative Hypothesis HA : No natural Variability

... and a testvariable to measure the climate change

Andreas Hense, Universität Bonn

slide6

Probability for testvariable in case of

H0 < 0.05 ... 0.01

Rejection of H0

Andreas Hense, Universität Bonn

the testvariable
The testvariable
  • Collect the information from field data
  • Collect natural variability information
    • „multivariate statistics“
    • data vector d
    • covariance matrix S
  • optimize change analysis
    • „optimal fingerprint“
    • fingerprint vector g

Andreas Hense, Universität Bonn

the testvariable8
The testvariable
  • Data and fingerprint are Gaussian variables
  • data = fingerprint if distance | d - g | small
  • Mahalanobis distance D² natural measure

Andreas Hense, Universität Bonn

slide9

Amplitude of modeled change

Amplitude of observed change

Hasselmann‘s optimal fingerprint: similarity measure

Andreas Hense, Universität Bonn

a detection experiment paeth and hense 2001
A detection experiment (Paeth and Hense, 2001)

Observation time

Simulation time

Andreas Hense, Universität Bonn

the attribution problem
The attribution problem
  • Assumption for detection
    • climate change g is constant
    • no variability in climate change scenario
  • Assume a climate change ensemble
    • defines an Alternative - Hypothesis HA
  • Only possible by climate modelling

Andreas Hense, Universität Bonn

the attribution problem13
The attribution problem

Random climate variations : Control run

Null Hypothesis ensemble

H0

Climate Change: Greenhouse gase scenario

Alternative Hypothesis ensemble

HA

Andreas Hense, Universität Bonn

the misclassification
The misclassification

Reality

OK

Decision

OK

Andreas Hense, Universität Bonn

the attribution problem15
The attribution problem
  • Optimal classification
  • Minimize the cost of misclassification
  • Bayes-Decision
  • Classical discrimination analysis

Andreas Hense, Universität Bonn

the attribution problem16
The Attribution problem
  • Bayes Decision with least costs is given if
    • observation part of Control if prob(obs | control) > prob(obs | scenario)
    • observation part of scenario if prob(obs | control) < prob(obs | scenario)

Andreas Hense, Universität Bonn

the attribution problem17
The attribution problem

Andreas Hense, Universität Bonn

the bayesian view
The Bayesian View
  • Sir Thomas Bayes 1763
    • allows you to start with what you already believe (in climate change)
    • to see how new information changes your confidence in that belief

Andreas Hense, Universität Bonn

the bayesian view19
The Bayesian view

Less weight

More weight

The Climate Sceptics

Equal weight

Equal weight

The Uninformed

Less weight

More weight

The Environmentalist

Andreas Hense, Universität Bonn

a bayesian attribution experiment
A Bayesian attribution experiment
  • ECHAM3/LSG 1880-1979 Control
  • ECHAM3/LSG in 2000 Scenario
  • NCEP Reanalysis Data 1958-1999 Observations
  • Northern hemisphere area averages
    • near surface (2m) Temperature
    • 70 hPa Temperature
  • joint work with Seung-Ki Min, Heiko Paeth and Won-Tae Kwon

Andreas Hense, Universität Bonn

a bayesian attribution experiment21
A Bayesian Attribution experiment

The Uninformed

Andreas Hense, Universität Bonn

a bayesian attribution experiment22
A Bayesian attribution experiment

The Environmentalist

The Climate Sceptics

Andreas Hense, Universität Bonn

summary and conclusion
Summary and Conclusion
  • Climate change detection and attribution are classical statistical prodecures
    • detection: Mahalanobis distance
    • attribution: discriminant analysis
  • attribution: internal variability in climate change scenario through ensemble simulations
  • Bayesian statistics unified view

Andreas Hense, Universität Bonn

summary and conclusion24
Summary and Conclusion
  • Application to ECHAM3/LSG Ensemble and NCEP Reanalysis data
  • Northern Hemisphere area averaged temperatures (2m and 70 hPa)
    • 1995-1999 increasing classification into ECHAM3/LSG in model year 2000
    • weak evidence and 10% to 15% misclassification risk
  • Missing processes in climate change simulation?

Andreas Hense, Universität Bonn