Area-Perimeter Relation for Rain and Cloud Areas
The area-perimeter relation is used to explore the geometry of satellite- and radar-determined cloud and rain areas between me and 1.2 x 1 square kilometer, following Mandelbrot's theory of fractals. The data fit well with a formula in which the perimeter is roughly equal to the square root of the area raised to the power D (P VKD), where D is the fractal dimension of the perimeter. Rain and cloud perimeters are found to be fractals, with no discernible horizontal length scale between 1 and 1000 kilometers.
Jeninfer Gomez
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