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

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

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?

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

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

What is a Fractal? Natural Examples; Coastlines, Earthquakes, Rivers, Mountains But are they the same? How can we compare fractals? Self Similarity:

Fractal Dimension D = 1 D = 2 D = ?

Fractal Dimension Coastlines have infinite length? Mandelbrot’s interpretation: slope Number of steps Average length of each step Constants perimeterstep size

Computational Measurement Analysing simple shapes to verify process

Cloud Fractal Dimension Do clouds have a fractal dimension? D = 1.17

How Reliable the Dimension? What if different thresholds were used?

Changing Threshold Fractal dimension says fairly constant!

Dimension Over Time

What about other clouds? Evidence for evolution?

Dimension For Cloud Types Dimension varies with cloud type Does evolution occur within clouds? cirrocumulus undulatus cumulus mediocrisaltocumulus undulatus

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

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