Addressing the Problems of Spatial Resolution and Adequate Sampling in Clustered Clouds and Rain

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The concentrations of raindrops and cloud droplets in the atmosphere may be regarded as random variables that fluctuate with time and location. Recent work by Jameson and Kostinski has shown that these concentrations have probability distributions that deviate from the theoretical Poisson law that applies to purely random distributions. The deviations are caused by the tendency of drops to concentrate in clumps or patches. This clustering of drops complicates the problem of distinguishing between actual time and space variability of quantities such as the rainfall rate and the drop-size distribution, and the variability arising naturally from samples containing small numbers of drops. The main objective of this project is to develop new sampling criteria for counting drops and estimating their concentration that will identify real meteorological variability and avoid the artifacts arising from small samples. Another objective is to devise new data analysis techniques to sample clouds that are clumpy in structure and to characterize their structure. Attention will also be given to developing sampling criteria for the proper description of drop-size distributions. The approach is a combination of (1) analysis of data from various instruments that measure drop sizes and concentrations and (2) theoretical investigations based on Monte Carlo simulation. The work will contribute fundamentally to cloud physics by defining accurate methods for measuring and describing the spatial and temporal structure of rain and clouds.