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

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Overview

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

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Yes or No ?
Random Variations?
Detection
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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
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Probability for testvariable in case of H0 lt
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 S
• optimize change analysis
• optimal fingerprint
• fingerprint vector g

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The testvariable

• Data and fingerprint are Gaussian variables
• data fingerprint if distance d - g small
• Mahalanobis distance D² natural measure

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Amplitude of modeled change
Amplitude of observed change
Hasselmanns optimal fingerprint similarity
measure
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A detection experiment (Paeth and Hense, 2001)
Observation time
Simulation time
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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
Null Hypothesis ensemble
H0
Climate Change Greenhouse gase scenario
Alternative Hypothesis ensemble
HA
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The misclassification
Reality
OK
Decision
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) gt prob(obs
  scenario)
• observation part of scenario
  if prob(obs control) lt 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
Less weight
More weight
The Climate Sceptics
Equal weight
Equal weight
The Uninformed
Less weight
More 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

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A Bayesian Attribution experiment
The Uninformed
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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?