Area-Perimeter Relation for Rain and Cloud Areas

Lovejoy, S.

doi:10.1126/science.216.4542.185

Cited by 633 publications

(341 citation statements)

References 5 publications

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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%

Land-use change in a small catchment of northern Loess Plateau, China

Chen

Wang

et al. 2001

Agriculture, Ecosystems & Environment

195

122

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Section: Discussionmentioning

confidence: 99%

Land-use change in a small catchment of northern Loess Plateau, China

Chen

Wang

et al. 2001

Agriculture, Ecosystems & Environment

195

122

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“…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%

Entrainment and detrainment in cumulus convection: an overview

Rooy

Bechtold

Fröhlich

et al. 2012

Quart J Royal Meteoro Soc

298

256

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Entrainment and detrainment processes have been recognised for a long time as key processes for cumulus convection and have recently witnessed a regrowth of interest mainly due to the capability of large-eddy simulations (LES) to diagnose these processes in more detail. This article has a twofold purpose. Firstly, it provides a historical overview of the past research on these mixing processes, and secondly, it highlights more recent important developments. These include both fundamental process studies using LES aiming to improve our understanding of the mixing process, but also more practical studies targeted toward an improved parametrised representation of entrainment and detrainment in large-scale models. A highlight of the fundamental studies resolves a long-lasting controversy by showing that lateral entrainment is the dominant mixing mechanism in comparison with the cloud-top entrainment in shallow cumulus convection. The more practical studies provide a wide variety of new parametrisations with sometimes conflicting approaches to the way in which the effect of the free tropospheric humidity on the lateral mixing is taken into account. An important new insight that will be highlighted is that, despite the focus in the literature on entrainment, it appears that it is rather the detrainment process that determines the vertical structure of the convection in general and the mass flux especially. Finally, in order to speed up progress and stimulate convergence in future parametrisations, stronger and more systematic use of LES is advocated.

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“…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%

Statistical artefacts in the determination of the fractal dimension by the slit island method

Bigerelle

Iost

2004

Engineering Fracture Mechanics

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractThis paper comments upon some statistical aspects of the slit island method which is widely used to calculate the fractal dimension of fractured surfaces or of materialsÕ features like grain geometry. If a noise is introduced when measuring areas and perimeters of the islands (experimental errors), it is shown that errors are made in the calculation of the fractal dimension and more than a false analytical relation between a physical process parameter and the fractal dimension can be found. Moreover, positive or negative correlation with the same physical process parameter can be obtained whether the regression is performed by plotting the variation of the noisy area versus the noisy perimeter of the considered islands or vice versa. Monte-Carlo simulations confirm the analytical relations obtained under statistical considerations.

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Area-Perimeter Relation for Rain and Cloud Areas

Cited by 633 publications

References 5 publications

Land-use change in a small catchment of northern Loess Plateau, China

Land-use change in a small catchment of northern Loess Plateau, China

Entrainment and detrainment in cumulus convection: an overview

Statistical artefacts in the determination of the fractal dimension by the slit island method

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