Area-Perimeter Relation for Rain and Cloud Areas

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Science  09 Apr 1982:
Vol. 216, Issue 4542, pp. 185-187
DOI: 10.1126/science.216.4542.185


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 x 106 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 [See equation in the PDF], 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.