Errors in the estimate of the fractal correlation dimension of raindrop spatial distribution

Theories on drop formation and quantitative rain estimation would require k nowledge not only of the statistical size distribution of drops, but also o f their statistical spatial distribution, which, in turn, determines the st atistical fluctuations of the echoes detected by meteorological radar. Of p articular interest is the question of whether such a spatial distribution c an be assumed to be either statistically homogeneous or fractal. To analyze the spatial patterns of raindrops, a reasonable and immediate way of proce eding in the estimation of the fractal dimension is through the computation of the correlation integral. In any experimental observation of raindrop d istribution, only a finite number of drops in a given space-time volume can be observed. Consequently, in this situation, the estimated value D of the fractal dimension differs from the true value Dt because of systematic (s) and random (r) errors. This paper shows that these errors can be ascribed to the finite number of raindrops and to "edge effects.'' The order of magn itude of the error components that affect the estimate of D is investigated using numerical simulations for the inference of r and s, given a "referen ce'' spatial distribution with D-t = 2. It has been found that the correlat ion dimension, estimated on the basis of a previous experimental observatio n (452 raindrops collected on a square blotting paper of 1.28 m x 1.28 m du ring a 1-s exposure to rain), could be compatible with a uniform random spa tial distribution. The paper also presents the characteristics that new exp erimental setups have to possess to permit better estimates of the raindrop correlation dimension.