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)