Is Global Warming for Real?

J. C. SprottDepartment of PhysicsUniversity of Wisconsin - Madison

Presented at the

Chaos and Complex Systems Seminar

In Madison, Wisconsin

On January 17, 2006

Some Evidence

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

Lake Mendota Ice Cover (John Magnuson)

782,000 years

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

Order = 0

12

3

Fit the last few points to a polynomial

Moving Average

Lags = 012 3

Average some number of previous points

Trends

Lags = 0

12

Follow the trend of some number of previous points

Linear Regression

Order = 01

2

Fit a polynomial to the entire data set

3

Autoregression

Order = 0

24

xt = a0 + a1xt-1 + a2xt-2 + …

All Poles Method

Poles = 02

4

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

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

tanh x

x

D aij N bi

6 neurons

Artificial Neural Network

Lags = 3

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

6 neurons

Artificial Neural Network

Lags = 4

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

6 neurons

Artificial Neural Network

Lags = 9

xt = xt-1 + bitanh[ai0 + ai1xt-1 + … + ai9xt-9]

6 neurons

This year: 26 days

Artificial Neural Network

Lags = 9

xt = xt-1 + bitanh[ai0 + ai1xt-1 + … + ai9xt-9]

6 neurons

450-year prediction~30-70 days frozen

Chaotic?

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 DataNeural Network Predictor

Lags = 9

xt = xt-1 + bitanh[ai0 + ai1xt-1 + … + ai9xt-9]

6 neurons

782,000 years

Ice Core DataAverage 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)