Fluctuation Properties of Precipitation. Part VI: Observations of Hyperfine Clustering and Drop Size Distribution Structures in Three-Dimensional Rain

Abstract

In past work it is argued that rain consists of patches of coherent, physical drop size distributions passing in an unpredictable fashion for an unknown duration over a sensor. This leads to the detection both of correlations among drops and of clustering. While the analyses thus far support this characterization, in this final paper in this series, techniques are developed demonstrating that clustering of drops of a specific size in rain is occurring even on scales as small as a few centimeters. Moreover, using video disdrometer data processed to achieve high temporal resolution, it is shown that drops of different sizes are also cross correlated over times from 0.01 to several seconds. It is then shown that physical patches of drop size distributions (often exponential in form) exist and can be measured even over time periods as small as 2?3 s. Such distributions may be the result of enhanced drop interactions due to clustering or perhaps simply stochastic ?accidents? brought about by some ?clustering? mechanism. Since most drop spectra are measured over considerably longer intervals, however, observed distributions are likely probability mixtures of many short duration spectra. Such mixed distributions exhibit enhanced variance and curvatures reminiscent of gamma spectra often described in the literature. Thus, as measurement intervals increase, the form of the observed drop distributions apparently changes from an exponential-like distribution, to a mixture of distributions, finally returning once again to an exponential when the averaging is over very long intervals and a wide variety of conditions. It is also shown that for these data, much of the variability in rainfall rate arises due to concentration fluctuations rather than to changes in the average drop size. For completeness, it is also shown that the dimensionality of drop counts and rainfall rate are consistent with Euclidean scaling over distances from centimeters to kilometers. Finally, a specific example of drop clustering in wide sense statistically stationary rain is also given. These observations cannot be explained in terms of a nonhomogeneous Poisson process. Consequently, it appears most appropriate to characterize clustering and the structure of rain in terms of correlations and probability ruling discussed here and in previous papers in this series. This approach can be used to simulate rain numerically in order to explore not only the statistical properties of the rain itself, but also to achieve a better understanding of the effect of raindrop clustering and rainfall variability on a variety of topics, such as signal statistics and interpretations of remote sensing measurements.