1982
DOI: 10.1126/science.216.4542.185
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Area-Perimeter Relation for Rain and Cloud Areas

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 charact… Show more

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Cited by 633 publications
(341 citation statements)
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“…The fractal dimension has been employed widely in landscape studies (Lovejoy, 1982;Olsen et al, 1993;Turner and Ruscher, 1988;Leduc et al, 1994;Fu and Chen, 2000). It can be described by the following equation.…”
Section: Discussionmentioning
confidence: 99%
“…The fractal dimension has been employed widely in landscape studies (Lovejoy, 1982;Olsen et al, 1993;Turner and Ruscher, 1988;Leduc et al, 1994;Fu and Chen, 2000). It can be described by the following equation.…”
Section: Discussionmentioning
confidence: 99%
“…Since the shell surrounds clouds along their entire perimeter -which can be substantial due to its geometrical properties (Lovejoy, 1982;Siebesma andJonker, 2000) -Jonker et al (2008) used LES to precisely quantify the total downward mass flux through the shell. To this end, they analysed the data conditioned on the distance to the (nearest) cloud edge.…”
Section: Relevance Of the Near Vicinity Of Cloudsmentioning
confidence: 99%
“…This ratio, known as the shape factor, is extensively used in quantitative metallography. However for fractal shapes such as cloud [28] mammalÕs cerebral cortex [29], human lung [30], basins of attraction [31], this ratio is not constant but depends on the observation scale. From these observations, Mandelbrot [2] derived a perimeter-area relationship which when applied to fractured surfaces is called the ''Slit Island Method''.…”
Section: The Slit Island Methodsmentioning
confidence: 99%