Multifractal large number of drops limit in rain

Rain-drop size and position data were obtained for five different storms in the HYDROP (HYdrometeor Detection and Ranging using stereO-Photography) experiment [Desaulniers-Soucy, N., 1999. Empirical test of the multifractal continuum in rain, Ph.D. thesis, McGill University, Montréal; Desaulniers-Soucy, N., Lovejoy, S., Schertzer, D., 2001. The HYDROP experiment: an empirical method for the determination of the continuum limit in rain. Atmos. Res. 59–60, 163–197]. The data from 18 scenes of an region ≈8 m3 each containing 5000–15,000 rain drops were systematically and statistically analyzed in spheres ranging from 10 cm to 2 m in diameter. In four of the five storms, we found convincing evidence for the convergence to a multifractal scaling limit as the number of drops (N) per sphere was increased; the observed scaling exponents were quite close to those reported in the rain literature at much larger scales. By randomizing the positions of the drops, we directly compared the true fluctuation statistics with those of the classical theory; the fluctuations in the latter were significantly smaller. Careful consideration of the meteorological conditions, in particular the turbulence intensity and the drop size distributions, explained the observed variations in the scale of convergence to the multifractal regime.