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.
