Using Physical Parameters to Describe Raindrop Size Distributions

The number and size of raindrops within a sample volume (aka, the raindrop size distribution or DSD) is often modeled with three-parameter distributions, including Gamma and lognormal distributions. For a Gamma distribution, triplets of parameters often include (N_w, D_m, μ) or (N₀, Λ, μ). One problem with using these parameters is that Λ and μ are mathematical parameters and only relate to physical DSD properties when μ = 0.

This study develops a Gamma distribution model using physical parameters of mass spectrum mean diameter (D_m) and effective variance which is defined as the mass spectrum variance (σ_m²) normalized by mass spectrum mean diameter squared (σ_m²/D_m²).

There are two main benefits of this new distribution model notation. First, these physical parameters are similar to effective radius and effective variance used to describe the shape of cloud droplet and aerosol distributions, but based on the raindrop mass spectrum distribution. And second, changes in mean diameter and effective variance represent physical changes in DSD shape.