Rainfall microphysics and radar properties: Analysis methods for drop size spectra

Analyses are performed of experimental drop size spectra to explore the relationships among integral parameters for rain. The data used in this work were acquired with an airborne optical 2D precipitation probe in TOGA COARE during a 4-month period in 1992-93. It is assumed that the experimental size spectra can be described by a gamma drop size distribution (DSD) of the form N(D) = N0Dmu exp(-Lambda D) involving three parameters (N-0, mu, Lambda), which are determined using a new method of truncated moments. The method allows for truncation of the DSD at the large-diameter end of the spectrum due in part to instrumental effects and also in part to the trajectory of the aircraft through a rain streamer that has been sorted by wind shear. An effect analogous to truncation can occur at the small-diameter end of the size spectrum due to evaporation. However, truncation of the spectrum at the small-diameter end is not considered in this work. It is found that spectra with small space and timescales display considerable fluctuations in all three of the DSD parameters. It is also shown that the method of truncated moments yields distributions of the DSD parameters that have smaller average and modal values than when using untruncated moments. The data are stratified separately into classes according to each of the two DSD parameters D-m (mass-weighted mean diameter) and mu. The latter parameter describes the shape of the distribution. Empirical analyses between the reflectivity factor Z and rainfall rate R are performed for the data in each of these classes, and it is found that the results are consistent with that predicted by theory. A synthesis of the results of these empirical analyses is presented in the form of a new rain parameter diagram, which allows for changes in DSD shape.