Edge effect causes apparent fractal correlation dimension of uniform spatial raindrop distribution - Archive ouverte HAL Access content directly
Journal Articles Nonlinear Processes in Geophysics Year : 2009

Edge effect causes apparent fractal correlation dimension of uniform spatial raindrop distribution

(1) , (2) , (3) , (4)
1
2
3
4

Abstract

Lovejoy and Schertzer (1990a) presented a statistical analysis of blotting paper observations of the (twodimensional) spatial distribution of raindrop stains. They found empirical evidence for the fractal scaling behavior of raindrops in space, with potentially far-reaching implications for rainfall microphysics and radar meteorology. In particular, the fractal correlation dimensions determined from their blotting paper observations led them to conclude that "drops are (hierarchically) clustered" and that "inhomogeneity in rain is likely to extend down to millimeter scales". Confirming previously reported Monte Carlo simulations, we demonstrate analytically that the claims based on this analysis need to be reconsidered, as fractal correlation dimensions similar to the ones reported (i.e. smaller than the value of two expected for uniformly distributed raindrops) can result from instrumental artifacts (edge effects) in otherwise homogeneous Poissonian rainfall. Hence, the results of the blotting paper experiment are not statistically significant enough to reject the Poisson homogeneity hypothesis in favor of a fractal description of the discrete nature of rainfall. Our analysis is based on an analytical expression for the expected overlap area between a circle and a square, when the circle center is randomly (uniformly) distributed inside the square. The derived expression (r2−8r3/3+r4/2, where r denotes the ratio between the circle radius and the side of the square) can be used as a reference curve against which to test the statistical significance of fractal correlation dimensions determined from spatial point patterns, such as those of raindrops and rainfall cells. Correspondence
Fichier principal
Vignette du fichier
npg-16-287-2009.pdf (215.67 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

insu-00413396 , version 1 (27-02-2012)

Identifiers

Cite

R. Uijlenhoet, J.M. Porrà, D. Sempere Torres, Jean-Dominique Creutin. Edge effect causes apparent fractal correlation dimension of uniform spatial raindrop distribution. Nonlinear Processes in Geophysics, 2009, 16 (2), pp.287-297. ⟨10.5194/npg-16-287-2009⟩. ⟨insu-00413396⟩
178 View
180 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More