James Gay

1
Clouds in 1.3 Dimensions
Can the fractal appearance of clouds tell us more
about their nature?

• James Gay

2
Overview

• From Chaos to Self Organised Criticality
• Obtaining the Fractal Dimension of a Cloud
• Changes in Fractal Dimensions
• Summary of Results

3
Chaos

• Why should we be able to predict the weather at
  all?
• Within the disorder of chaos we find the ordered
  patterns.
• Can these patterns provide an insight into the
  nature of clouds?

4
Self Organised Criticality (SOC)

• Fluctuations around critical states

• SOC Like grains of sand dropping onto a pile
• Avalanches of any size

How Nature Works, Per Bak, 1996
5
Fractals

• One of the easiest ways of identifying SOC
  systems is simply finding a fractal structure

http//classes.yale.edu/fractals/MandelSet/
6
What is a Fractal?

• Self Similarity

http//mywebpages.comcast.net/tjbdx/

• Natural Examples Coastlines, Earthquakes,
  Rivers, Mountains
• But are they the same? How can we compare
  fractals?

7
Fractal Dimension
D 1
D ?
D 2
8
Fractal Dimension

• Coastlines have infinite length?

• Mandelbrots interpretation

http//classes.yale.edu/Fractals/
Number of steps
Average length of each step
Constants
slope
perimeter
step size
9
Computational Measurement

• Analysing simple shapes to verify process

10
Cloud Fractal Dimension

• Do clouds have a fractal dimension?

D 1.17
11
How Reliable the Dimension?

• What if different thresholds were used?

12
Changing Threshold

• Fractal dimension says fairly constant!

13
Dimension Over Time
14
Dimension Over Time

• What about other clouds?

1.18
1.26
1.20

• Evidence for evolution?

1.32
1.28
1.30
1.37
15
Dimension For Cloud Types

• Dimension varies with cloud type

1.33
1.33
1.18
1.32
1.16
1.21
cirrocumulus undulatus
cumulus mediocris
altocumulus undulatus

• Does evolution occur within clouds?

1.34
1.18
1.12
1.31
16
Conclusion

• Clouds have a measurable fractal dimension
• Implication of Self Organised Criticallity
• Dimension varies with cloud type
• Dimension varies with evolution?

17
Acknowledgements

• Iver Cairns
• Department of Meteorology, McGill University,
  Canada, A Short Course in Cloud Physics, R. R.
  Rogers, 1979.
• Copernicus, New York, How Nature Works, Per Bak,
  1996.
• Harper Collins Publishers, New York, A
  Photographic Guide to the Weather of Britain and
  Europe, David M. Ludlum, 2001.
• Harper Row, New York, Turbulent Mirror - An
  Illustrated Guide to Chaos Theory and the Science
  of Wholeness, John Briggs and F. David Peat,
  1989.
• ULC Press, London, The Essence of Chaos, Edward
  Lorenz, 1993.