## Slide #1.

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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## Slide #2.

Some Evidence
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## Slide #3.

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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## Slide #4.

Prediction Methods  Extrapolation methods     Linear methods     Simple extrapolation Moving average Trends Simple regression Autoregression All poles method Nonlinear methods   Method of analogs Artificial neural network
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## Slide #5.

Simple Extrapolation 3 2 1 Order = 0 Fit the last few points to a polynomial
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## Slide #6.

Moving Average 1 2 3 Lags = 0 Average some number of previous points
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## Slide #7.

Trends 1 2 Lags = 0 Follow the trend of some number of previous points
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## Slide #8.

Linear Regression 2 3 Order = 0 1 Fit a polynomial to the entire data set
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## Slide #9.

Autoregression 2 4 Order = 0 xt = a0 + a1xt-1 + a2xt-2 + …
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## Slide #10.

All Poles Method Poles = 0 2 4 1 Assume a sum of poles in the complex plane
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## Slide #11.

Method of Analogs Lags = 0 2 1 Find the closest similar previous sequence
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## Slide #12.

Artificial Neural Network D aij N bi 6 neurons Lags = 3 tanh x x xt = xt-1 + bitanh[ai0 + ai1xt-1 + ai2xt-2 + ai3xt-3]
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## Slide #13.

Artificial Neural Network 6 neurons Lags = 3 xt = xt-1 + bitanh[ai0 + ai1xt-1 + ai2xt-2 + ai3xt-3]
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## Slide #14.

Artificial Neural Network 6 neurons Lags = 4 xt = xt-1 + bitanh[ai0 + ai1xt-1 + … + ai4xt-4]
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## Slide #15.

Artificial Neural Network 6 neurons Lags = 9 This year: 26 days xt = xt-1 + bitanh[ai0 + ai1xt-1 + … + ai9xt-9]
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## Slide #16.

Artificial Neural Network 6 neurons Lags = 9 Chaotic? 450-year prediction ~30-70 days frozen xt = xt-1 + bitanh[ai0 + ai1xt-1 + … + ai9xt-9]
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## Slide #17.

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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## Slide #18.

Median of 80 Predictions Prediction for this season: 91 days (March 19th thaw)
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## Slide #19.

Ice Core Data Neural Network Predictor 6 neurons Lags = 9 782,000 years xt = xt-1 + bitanh[ai0 + ai1xt-1 + … + ai9xt-9]
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## Slide #20.

Ice Core Data Average of 80 Predictions 782,000 years
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## Slide #21.

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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## Slide #22.

References  http://sprott.physics.wisc.edu/ lectures/warming.ppt (this talk)  [email protected] (contact me)
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