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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.

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Is Global Warming for Real?

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Is global warming for real

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

Some Evidence


From recent seminars

From Recent Seminars

Greenland Ice-core Data (C. S. Clay)

782,000 years

Lake Mendota Ice Cover (John Magnuson)

150 years


Prediction methods

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

Simple Extrapolation

3

2

1

Order = 0

Fit the last few points to a polynomial


Moving average

Moving Average

Lags = 0

1

2

3

Average some number of previous points


Trends

Trends

2

1

Lags = 0

Follow the trend of some number of previous points


Linear regression

Linear Regression

2

3

Order = 0

1

Fit a polynomial to the entire data set


Autoregression

Autoregression

4

2

Order = 0

xt = a0 + a1xt-1 + a2xt-2 + …


All poles method

All Poles Method

Poles = 0

2

4

1

Assume a sum of poles in the complex plane


Method of analogs

Method of Analogs

Lags = 0

2

1

Find the closest similar previous sequence


Artificial neural network

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 network1

Artificial Neural Network

6 neurons

Lags = 3

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


Artificial neural network2

Artificial Neural Network

6 neurons

Lags = 4

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


Artificial neural network3

Artificial Neural Network

6 neurons

Lags = 9

This year: 26 days

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


Artificial neural network4

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

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

Median of 80 Predictions

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


Ice core data neural network predictor

Ice Core DataNeural 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

Ice Core DataAverage of 80 Predictions

782,000 years


Closing thoughts

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)

References


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