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| Titel |
Edge effect causes apparent fractal correlation dimension of uniform spatial raindrop distribution |
| VerfasserIn |
R. Uijlenhoet, J. M. Porrà, D. Sempere Torres, J.-D. Creutin |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 16, no. 2 ; Nr. 16, no. 2 (2009-04-09), S.287-297 |
| Datensatznummer |
250013139
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| Publikation (Nr.) |
 copernicus.org/npg-16-287-2009.pdf |
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| Zusammenfassung |
| Lovejoy and Schertzer (1990a) presented a statistical analysis of
blotting paper observations of the (two-dimensional) 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 (πr2−8r3/3+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. |
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