Describing the Shape of Raindrop Size Distributions Using Uncorrelated Raindrop Mass Spectrum Parameters

AbstractRainfall retrieval algorithms often assume a gamma-shaped raindrop size distribution (DSD) with three mathematical parameters Nw, Dm, and μ. If only two independent measurements are available, as with the dual-frequency precipitation radar on the Global Precipitation Measurement (GPM) mission core satellite, then retrieval algorithms are underconstrained and require assumptions about DSD parameters. To reduce the number of free parameters, algorithms can assume that μ is either a constant or a function of Dm. Previous studies have suggested μ–Λ constraints [where Λ = (4 + μ)/Dm], but controversies exist over whether μ–Λ constraints result from physical processes or mathematical artifacts due to high correlations between gamma DSD parameters. This study avoids mathematical artifacts by developing joint probability distribution functions (joint PDFs) of statistically independent DSD attributes derived from the raindrop mass spectrum. These joint PDFs are then mapped into gamma-shaped DSD parameter j...

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