Area-Perimeter Relation for Rain and Cloud Areas

作者：S. Lovejoy · 发表于：Science · 年份：1982 · DOI：10.1126/science.216.4542.185 · 被引用次数：709 · 研究领域：Advanced Mathematical Theories and Applications、Leaf Properties and Growth Measurement、Advanced Mathematical Theories

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 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 [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.