資料紹介
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
Entire presentation available on WWW
Some Evidence
From Recent Seminars
Greenland 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
1
2
3
Fit the last few points to a polynomial
Moving Average
Lags = 0
1
2
3
Average some number of previous points
Trends
Lags = 0
1
2
Follow the trend of some number of previous points
Linear Regression
Order = 0
1
2
Fit a polynomial to the entire data set
3
Autoregression
Order = 0
2
4
xt = a0 + a1xt-1 + a2xt-2 + …
All Poles Method
Poles = 0
2
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 + Sbitanh[ai0 + ai1xt-1 + ai2xt-2 + ai3xt-3]
tanh x
x
D aij N bi
6 neurons
Artificial Neural Network
Lags = 3
xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + ai2xt-2 + ai3xt-3]
6 neurons
Artificial Neural Network
Lags = 4
xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + … + ai4xt-4]
6 neurons
Artificial Neural Network
Lags = 9
xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + … + ai9xt-9]
6 neurons
This year: 26 days
資料の原本内容
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
Entire presentation available on WWW
Some Evidence
From Recent Seminars
Greenland 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
1
2
3
Fit the last few points to a polynomial
Moving Average
Lags = 0
1
2
3
Average some number of previous points
Trends
Lags = 0
1
2
Follow the trend of some number of previous points
Linear Regression
Order = 0
1
2
Fit a polynomial to the entire data set
3
Autoregression
Order = 0
2
4
xt = a0 + a1xt-1 + a2xt-2 + …
All Poles Method
Poles = 0
2
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 + Sbitanh[ai0 + ai1xt-1 + ai2xt-2 + ai3xt-3]
tanh x
x
D aij N bi
6 neurons
Artificial Neural Network
Lags = 3
xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + ai2xt-2 + ai3xt-3]
6 neurons
Artificial Neural Network
Lags = 4
xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + … + ai4xt-4]
6 neurons
Artificial Neural Network
Lags = 9
xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + … + ai9xt-9]
6 neurons
This year: 26 days
Artificial Neural Network
Lags = 9
xt = xt-1 + Sbitanh[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 Data Neural Network Predictor
Lags = 9
xt = xt-1 + Sbitanh[ai0 + ai1xt-1 + … + ai9xt-9]
6 neurons
782,000 years
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)
