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

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

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

Simple Extrapolation Order = Fit the last few points to a polynomial

Moving Average Lags = Average some number of previous points

Trends Lags = Follow the trend of some number of previous points

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

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

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

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

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

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

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

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

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?

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)

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

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

Ice Core Data Average of 80 Predictions 782,000 years

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

References n lectures/warming.ppt (this talk) lectures/warming.ppt n (contact me)