Measurements of the Co-Polar Correlation Coefficient in Rainfall and Retrieval of the Drop Size Distribution

The co-polar correlation coefficient (ρ_hv) has the potential to provide more accurate retrievals of raindrop size distributions from dual-polarisation radar measurements (as well as many other applications including hydrometeor classification, ground clutter identification, and ice microphysics). However, to exploit this parameter we need to know the uncertainty in a sample of ρ_hv. We show that frequency distributions of ρ_hv estimates are highly negatively skewed. A new variable: L = - log₁₀(1 - ρ_hv) is defined, which has Gaussian error statistics, with a mean corresponding to the true ρ_hv we are attempting to estimate (i.e. zero bias), and a standard deviation depending only on the number of independent pulses σ_L=0.9/√(N-3), which can easily be determined from the Doppler spectral width. This provides a simple, accurate way of determining confidence intervals for a ρ_hv measurement. The theory is verified using observations of spherical drizzle drops. We show that it is possible to use measurements of L and Z_DR to estimate the dispersion parameter μ in the gamma drop size distribution. We find that inclusion of drop oscillations as well as mean drop shapes is essential to the retrieval. Initial retrievals suggest that μ is typically 8 and varies weakly over the range Z_DR = 0.5 - 3 dB. This contrasts with recent disdrometer parameterisations, and means that assuming a simple exponential distribution may lead to an overestimate of rain rate by 50%.