James Gay

Clouds in 1.3 DimensionsClouds in 1.3 Dimensions

Can the fractal appearance of clouds tell us more about their nature?

OverviewOverview

• From Chaos to Self Organised Criticality

• Obtaining the Fractal Dimension of a Cloud

• Changes in Fractal Dimensions

• Summary of Results

ChaosChaos

• 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?

Self Organised Criticality (SOC)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

FractalsFractals

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

http://classes.yale.edu/fractals/MandelSet/

What is a Fractal?What is a Fractal?

• Natural Examples; Coastlines, Earthquakes, Rivers, Mountains

• But are they the same? How can we compare fractals?

http://mywebpages.comcast.net/tjbdx/

• Self Similarity:

Fractal DimensionFractal Dimension

D = 1

D = 2

D = ?

Fractal DimensionFractal Dimension

• Coastlines have infinite length?

DMddN

• Mandelbrot’s interpretation:

slope

Number of steps

http://classes.yale.edu/Fractals/

Average length of each stepConstants

MLogdLogDddNLog 1perimeter step size

Computational MeasurementComputational Measurement

• Analysing simple shapes to verify process

Cloud Fractal DimensionCloud Fractal Dimension

• Do clouds have a fractal dimension?

D = 1.17

How Reliable the Dimension?How Reliable the Dimension?

• What if different thresholds were used?

Changing ThresholdChanging Threshold

• Fractal dimension says fairly constant!Single cloud (cumulus mediocris) looking up from the bottom

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

100 120 140 160 180 200 220

Threshold

Fra

ctal

Dim

ensi

on

Dimension Over TimeDimension Over Time

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

1.16

1.18

1.2

1.22

1.24

1.26

1.28

1.3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

time (s)

fracta

l d

imen

sio

n

Dimension Over TimeDimension Over Time

• What about other clouds?

• Evidence for evolution?

1.28 1.30 1.37 1.32

1.18 1.26 1.20

Dimension For Cloud TypesDimension For Cloud Types

• Dimension varies with cloud type

• Does evolution occur within clouds?

1.33 1.33 1.18 1.16 1.32 1.21

cirrocumulus undulatus cumulus mediocris altocumulus undulatus

1.311.34 1.121.18

ConclusionConclusion

• Clouds have a measurable fractal dimension

• Implication of Self Organised Criticallity

• Dimension varies with cloud type

• Dimension varies with evolution?

AcknowledgementsAcknowledgements

• 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.