Constraining the rain drop size distribution using the co-polar correlation coefficient and differential reflectivity

The rain drop size distribution (DSD) is commonly assumed to take the form of a gamma distribution, described by three parameters: the drop number concentration (N₀), median drop diameter (D₀) and the shape parameter (μ). Knowledge of drop shape as a function of drop diameter allows retrieval of N₀ and D₀ using radar reflectivity (Z) and differential reflectivity (Z_DR), leaving μ to either be assumed or constrained empirically. Dual wavelength rainfall rate retrievals, such as those from the dual wavelength Global Precipitation Mission satellite are also strongly sensitive to μ. Illingworth and Caylor (1991) first proposed the combined use of the co-polar correlation coefficient ρ_HV (which characterises the variety of drop shapes in a sample volume) and Z_DR to estimate µ. Here, we demonstrate how this can be used to derive quantitative estimates of μ. This is achieved by constructing a new variable log₁₀(1- ρ_HV) which has Gaussian error statistics. The width of the Gaussian distribution is derived as a function of the number of independent pulses, allowing us to construct a rigorous confidence interval in our estimates of ρ_HV. In addition we demonstrate how the imperfect co-location of the horizontal and vertical sample volumes may be accounted for. Preliminary retrievals of μ will be presented in stratiform and convective rainfall events. The retrieval is verified by direct comparison with the observed DSD from a co-located disdrometer.