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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

Some Evidence

From Recent Seminars
Greenland Ice-core Data (C. S. Clay)

782,000 years
Lake Mendota Ice Cover (John Magnuson)

150 years

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
3 2 1 Order = 0

Fit the last few points to a polynomial

Moving Average

1 2 3

Lags = 0

Average some number of previous points

Trends
2
1

Lags = 0

Follow the trend of some number of previous points

Linear Regression
2
3

Order = 0 1

Fit a polynomial to the entire data set

Autoregression

2

4

Order = 0

xt = a0 + a1xt-1 + a2xt-2 + …

All Poles Method

Poles = 0 2
4 1

Assume a sum of poles in the complex plane

Method of Analogs

Lags = 0 2

1

Find the closest similar previous sequence

Artificial Neural Network
D aij N bi 6 neurons Lags = 3

tanh x

x

xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + ai2xt-2 + ai3xt-3]

Artificial Neural Network
6 neurons Lags = 3

xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + ai2xt-2 + ai3xt-3]

Artificial Neural Network
6 neurons Lags = 4

xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + … + ai4xt-4]

Artificial Neural Network
6 neurons Lags = 9

This year: 26 days xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + … + ai9xt-9]

Artificial Neural Network
6 neurons Lags = 9 Chaotic?

450-year prediction ~30-70 days frozen xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + … + ai9xt-9]

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

Prediction for this season: 91 days (March 19th thaw)

Ice Core Data Neural Network Predictor
6 neurons Lags = 9

782,000 years xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + … + ai9xt-9]

Ice Core Data Average of 80 Predictions

782,000 years

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



References


http://sprott.physics.wisc.edu/ lectures/warming.ppt (this talk)



sprott@physics.wisc.edu

(contact me)


				
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