Area-Perimeter Relation for Rain and Cloud Areas

1982/04/09 by S. Lovejoy · 702 citations
Agricultural and Biological Sciences · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Cartography #Fractal #Fractal dimension #Geography #Geology #Geometry #Leaf Properties and Growth Measurement #Mandelbrot set #Mathematical analysis #Mathematics #Meteorology #Perimeter #Scale (ratio) #Square (algebra)

paper · doi:10.1126/science.216.4542.185

published in Science 216(4542), 185-187 (American Association for the Advancement of Science)

openalex publication_date 1982/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23

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 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.

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