Area-Perimeter Relation for Rain and Cloud Areas
- 9 April 1982
- journal article
- other
- Published by American Association for the Advancement of Science (AAAS) in Science
- Vol. 216 (4542) , 185-187
- https://doi.org/10.1126/science.216.4542.185
Abstract
Following Mandelbrot's theory of fractals, the area-perimeter relation is used to investigate the geometry of satellite- and radar-determined cloud and rain areas between 1 and 1.2 × 10 6 square kilometers. The data are well fit by a formula in which the perimeter is given approximately by the square root of the area raised to the power D ( P ∼ √ A D ), where D is interpreted as the fractal dimension of the perimeter. It is concluded that rain and cloud perimeters are fractals—they have no characteristic horizontal length scale between 1 and 1000 kilometers.Keywords
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