Variability of drop size distributions: Noise and noise filtering in disdrometric data

Disdrometric measurements are affected by the spurious variability due to drop sorting, small sampling volume, and instrumental noise. As a result, analysis methods that use least squares regression to derive rainfall rate-radar reflectivity (R-Z) relationships or studies of drop size distributions can lead to erroneous conclusions. This paper explores the importance of this variability and develops a new approach, referred to as the sequential intensity filtering technique (SIFT), that minimizes the effect of the spurious variability on disdrometric data. A simple correction for drop sorting in stratiform rain illustrates that it generates a significant amount of spurious variability and is prominent in small drops. SIFT filters out this spurious variability while maintaining the physical variability, as evidenced by stable R-Z relationships that are independent of averaging size and by a drastic decrease of the scatter in R-Z plots. The presence of scatter causes various regression methods to yield different best-fitted R-Z equations, depending on whether the errors on R or Z are minimized. The weighted total least squares (WTLS) solves this problem by taking into account errors in both R and Z and provides the appropriate coefficient and exponent of Z = aR^b. For example, with a simple R versus Z least squares regression, there is an average fractional difference in a and b of Z = aR^b of 17% and 14%, respectively, when compared with those derived using WTLS. With Z versus R regression, the average fractional difference in a and b is 19% and 12%, respectively. This uncertainty in the R-Z parameters may explain 40% of the "natural variability" claimed in the literature but becomes negligible after applying SIFT, regardless of the regression methods used.