Examining the correlations between drop size distribution parameters using data from two side-by-side 2D-video disdrometers

As part of a long-term observation campaign, over 5000 pair samples of temporally matched 1-minute averaged drop size distribution (DSD) measurements have been recorded by two side-by-side (frequently calibrated) 2D-video disdrometers. The measurement campaign was conducted in Huntsville, Alabama, over a ten-month period, and includes a variety of rain types and regimes. The datasets have been used to examine, (i) the relationship between the mass-weighted mean diameter (Dm) and the standard deviation of the mass spectrum (σM) without any assumption on the DSD form, and (ii) the relationship between the shape parameter (μ) and slope parameter (Λ) of the gamma form of the DSD. A number of methods were used to estimate μ and Λ, including: a normalizing procedure, the method of moments, the maximum likelihood method and the L-moment method. The physical validity of the σM-Dm relationship is examined by, (i) relating the estimated Dm versus the estimated σM from the same disdrometer datasets and, (ii) by 'cross-relating' Dm from one disdrometer with the corresponding σM from the second disdrometer dataset. The same procedures were repeated to examine the physical validity of the μ-Λ relation. It is shown that the transformed variable σM′ = σMDm− 1.65, which is uncorrelated with Dm, has a narrow histogram and that σM′ ≈ constant can form a constraint which may well be applicable to other rain climatologies. For the μ-Λ relationship, the variation between μ from one unit and Λ by the second unit showed, as expected, larger scatter than using estimates from the same unit but not excessively so given that the μ estimates from the two units themselves show some instrument-to-instrument variability. While we cannot ascertain that the removal of any statistical correlations necessarily implies that the μ-Λ relation is physical, we have gone on to show that instrument limitations of accurately measuring the number concentration at the small drop end (D < 0.5 mm) are likely to be more important in giving rise to spuriously large μ values and related higher μ-Λ correlation, especially in light rain, and perhaps to a lesser extent in heavier rain.