Is Global Warming for Real?

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Is Global Warming for Real?

• J. C. Sprott
• Department of Physics
• University of Wisconsin - Madison
• Presented at the
• Chaos and Complex Systems Seminar
• In Madison, Wisconsin
• On January 17, 2006

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Some Evidence
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From Recent Seminars
Greenland Ice-core Data (C. S. Clay)
782,000 years
Lake Mendota Ice Cover (John Magnuson)
150 years
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Prediction Methods

• Extrapolation methods
• Simple extrapolation
• Moving average
• Trends
• Linear methods
• Simple regression
• Autoregression
• All poles method
• Nonlinear methods
• Method of analogs
• Artificial neural network

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Simple Extrapolation
3
2
1
Order 0
Fit the last few points to a polynomial
6
Moving Average
Lags 0
1
2
3
Average some number of previous points
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Trends
2
1
Lags 0
Follow the trend of some number of previous points
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Linear Regression
2
3
Order 0
1
Fit a polynomial to the entire data set
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Autoregression
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2
Order 0
xt a0 a1xt-1 a2xt-2
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All Poles Method
Poles 0
2
4
1
Assume a sum of poles in the complex plane
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Method of Analogs
Lags 0
2
1
Find the closest similar previous sequence
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Artificial Neural Network
D aij N bi
Lags 3
6 neurons
tanh x
x
xt xt-1 Sbitanhai0 ai1xt-1 ai2xt-2
ai3xt-3
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Artificial Neural Network
Lags 3
6 neurons
xt xt-1 Sbitanhai0 ai1xt-1 ai2xt-2
ai3xt-3
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Artificial Neural Network
Lags 4
6 neurons
xt xt-1 Sbitanhai0 ai1xt-1 ai4xt-4
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Artificial Neural Network
Lags 9
6 neurons
This year 26 days
xt xt-1 Sbitanhai0 ai1xt-1 ai9xt-9
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Artificial Neural Network
Lags 9
6 neurons
Chaotic?
450-year prediction 30-70 days frozen
xt xt-1 Sbitanhai0 ai1xt-1 ai9xt-9
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Conclusion

• Eight predictors with ten or more values for the
  parameter give 80 very different predictions
• We could take an average of all the predictions
• Better yet, take the median of the predictions
  (half higher, half lower)

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Median of 80 Predictions
Prediction for this season 91 days (March 19th
thaw)
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Ice Core DataNeural Network Predictor
Lags 9
6 neurons
782,000 years
xt xt-1 Sbitanhai0 ai1xt-1 ai9xt-9
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Ice Core DataAverage of 80 Predictions
782,000 years
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Closing Thoughts

• The Earth is getting warmer
• Human activity may not be the main cause
• Global warming may not be a bad thing
• Technological solutions may be available and
  relatively simple

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References

• http//sprott.physics.wisc.edu/
  lectures/warming.ppt (this talk)
• sprott_at_physics.wisc.edu (contact me)