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

Some Evidence:

Some Evidence

From Recent Seminars:

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

Prediction Methods:

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

Simple Extrapolation:

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

Moving Average:

Moving Average Lags = 0 1 2 3 Average some number of previous points

Trends:

Trends Lags = 0 1 2 Follow the trend of some number of previous points

Linear Regression:

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

Autoregression:

Autoregression Order = 0 2 4 x t = a 0 + a 1 x t- 1 + a 2 x t- 2 + …

All Poles Method:

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

Method of Analogs:

Method of Analogs Lags = 0 2 Find the closest similar previous sequence 1

Artificial Neural Network:

Artificial Neural Network Lags = 3 x t = x t- 1 + S b i tanh[ a i 0 + a i 1 x t -1 + a i 2 x t -2 + a i 3 x t -3 ] tanh x x D a ij N b i 6 neurons

Artificial Neural Network:

Artificial Neural Network Lags = 3 x t = x t- 1 + S b i tanh[ a i 0 + a i 1 x t -1 + a i 2 x t -2 + a i 3 x t -3 ] 6 neurons

Artificial Neural Network:

Artificial Neural Network Lags = 4 x t = x t- 1 + S b i tanh[ a i 0 + a i 1 x t -1 + … + a i 4 x t -4 ] 6 neurons

Artificial Neural Network:

Artificial Neural Network Lags = 9 x t = x t- 1 + S b i tanh[ a i 0 + a i 1 x t -1 + … + a i 9 x t -9 ] 6 neurons This year: 26 days

Artificial Neural Network:

Artificial Neural Network Lags = 9 x t = x t- 1 + S b i tanh[ a i 0 + a i 1 x t -1 + … + a i 9 x t -9 ] 6 neurons 450-year prediction ~30-70 days frozen Chaotic?

Conclusion:

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)

Median of 80 Predictions:

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

Ice Core Data Neural Network Predictor:

Ice Core Data Neural Network Predictor Lags = 9 x t = x t- 1 + S b i tanh[ a i 0 + a i 1 x t -1 + … + a i 9 x t -9 ] 6 neurons 782,000 years

Ice Core Data Average of 80 Predictions:

Ice Core Data Average of 80 Predictions 782,000 years

Closing Thoughts:

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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