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

2. Some Evidence

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

4. Prediction Methods n Extrapolation methods u Simple extrapolation u Moving average u Trends n Linear methods u Simple regression u Autoregression u All poles method n Nonlinear methods u Method of analogs u Artificial neural network

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

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

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

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

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

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

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

12. Artificial Neural Network Lags = 3 x t = x t-1 +  b i tanh[a i0 + a i1 x t-1 + a i2 x t-2 + a i3 x t-3 ] tanh x x D a ij N b i 6 neurons

13. Artificial Neural Network Lags = 3 x t = x t-1 +  b i tanh[a i0 + a i1 x t-1 + a i2 x t-2 + a i3 x t-3 ] 6 neurons

14. Artificial Neural Network Lags = 4 x t = x t-1 +  b i tanh[a i0 + a i1 x t-1 + … + a i4 x t-4 ] 6 neurons

15. Artificial Neural Network Lags = 9 x t = x t-1 +  b i tanh[a i0 + a i1 x t-1 + … + a i9 x t-9 ] 6 neurons This year: 26 days

16. Artificial Neural Network Lags = 9 x t = x t-1 +  b i tanh[a i0 + a i1 x t-1 + … + a i9 x t-9 ] 6 neurons 450-year prediction ~30-70 days frozen Chaotic?

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

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

19. Ice Core Data Neural Network Predictor Lags = 9 x t = x t-1 +  b i tanh[a i0 + a i1 x t-1 + … + a i9 x t-9 ] 6 neurons 782,000 years

20. Ice Core Data Average of 80 Predictions 782,000 years

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

22. References n http://sprott.physics.wisc.edu/ lectures/warming.ppt (this talk) http://sprott.physics.wisc.edu/ lectures/warming.ppt n sprott@physics.wisc.edu (contact me) sprott@physics.wisc.edu