statistical problems in climate change detection and attribution
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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. - PowerPoint PPT PresentationTRANSCRIPT
April 2002 Andreas Hense, Universität Bonn 1
Statistical problems in climate change detection and attribution
Andreas Hense,
Meteorologisches Institut
Universität Bonn
April 2002 Andreas Hense, Universität Bonn 2
Overview
• Introduction• The detection problem• The attribution problem• The Bayesian view • Summary and Conclusion
April 2002 Andreas Hense, Universität Bonn 3
Yes or No ?
Detection
Random Variations?
April 2002 Andreas Hense, Universität Bonn 4
Yes or No ?
Attribution
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The detection problem
Null Hypothesis H0 : Random Natural Variability
Alternative Hypothesis HA : No natural Variability
... and a testvariable to measure the climate change
April 2002 Andreas Hense, Universität Bonn 6
Probability for testvariable in case ofH0 < 0.05 ... 0.01
Rejection of H0
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The testvariable
• Collect the information from field data• Collect natural variability information
– „multivariate statistics“– data vector d– covariance matrix
• optimize change analysis– „optimal fingerprint“– fingerprint vector g
April 2002 Andreas Hense, Universität Bonn 8
The testvariable
• Data and fingerprint are Gaussian variables• data = fingerprint if distance | d - g | small• Mahalanobis distance D² natural measure
April 2002 Andreas Hense, Universität Bonn 9
Amplitude of modeled change
Amplitude of observed change
Hasselmann‘s optimal fingerprint: similarity measure
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April 2002 Andreas Hense, Universität Bonn 11
A detection experiment (Paeth and Hense, 2001)
Simulation time
Obs
erva
tion
tim
e
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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
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The attribution problem
Random climate variations : Control run
Climate Change: Greenhouse gase scenario
Null Hypothesis ensemble
Alternative Hypothesis ensemble
HA
H0
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The misclassification
RealityD
ecis
ion
OK
OK
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The attribution problem
• Optimal classification• Minimize the cost of misclassification• Bayes-Decision• Classical discrimination analysis
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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)
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The attribution problem
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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
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The Bayesian view
More weight Less weight
The Climate Sceptics
Equal weight Equal weight
The Uninformed
More weightLess weight
The Environmentalist
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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
April 2002 Andreas Hense, Universität Bonn 21
A Bayesian Attribution experiment
The Uninformed
April 2002 Andreas Hense, Universität Bonn 22
A Bayesian attribution experiment
The Environmentalist
The Climate Sceptics
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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
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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?