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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

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

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]

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
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