This document summarizes a talk given on global warming predictions. It discusses evidence from ice core data in Greenland and lake ice cover in Madison, Wisconsin. It then outlines several prediction methods that could be used, including simple extrapolation, moving averages, trends, linear regression, autoregression, the all poles method, the method of analogs, and artificial neural networks. The document demonstrates an artificial neural network approach using 6 neurons and lags of up to 9 years to predict lake ice cover. It concludes that averaging or taking the median of multiple predictions from different models may provide the most accurate longer-term prediction.

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

4. 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

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

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

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

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

9. Autoregression
4
2
Order = 0
xt = a0 + a1xt-1 + a2xt-2 + …

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

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

12. Artificial Neural Network
D aij N bi
6 neurons Lags = 3
tanh x
x
xt = xt-1 + Σbitanh[ai0 + ai1xt-1 + ai2xt-2 + ai3xt-3]

13. Artificial Neural Network
6 neurons Lags = 3
xt = xt-1 + Σbitanh[ai0 + ai1xt-1 + ai2xt-2 + ai3xt-3]

14. Artificial Neural Network
6 neurons Lags = 4
xt = xt-1 + Σbitanh[ai0 + ai1xt-1 + … + ai4xt-4]

15. Artificial Neural Network
6 neurons Lags = 9
This year: 26 days
xt = xt-1 + Σbitanh[ai0 + ai1xt-1 + … + ai9xt-9]

16. Artificial Neural Network
6 neurons Lags = 9
Chaotic?
450-year prediction
~30-70 days frozen
xt = xt-1 + Σbitanh[ai0 + ai1xt-1 + … + ai9xt-9]

17. 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)

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

19. Ice Core Data
Neural Network Predictor
6 neurons Lags = 9
782,000 years
xt = xt-1 + Σbitanh[ai0 + ai1xt-1 + … + ai9xt-9]

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

21. 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

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