The Concept of “Normalized” Distribution to Describe Raindrop Spectra: A Tool for Cloud Physics and Cloud Remote Sensing

Abstract

The shape of the drop size distribution (DSD) reflects the physics of rain. The DSD is the result of the microphysical processes that transform the condensed water into rain. The question of the DSD is also central in radar meteorology, because it rules the relationships between the radar reflectivity and the rainfall rate R. Normalizing raindrop spectra is the only way to identify the shape of the distribution. The concept of normalization of DSD developed in this paper is founded upon two reference variables, the liquid water content LWC and the mean volume diameter D_m. It is shown mathematically that it is appropriate to normalize by with respect to particle concentration and by D_m with respect to drop diameter. Also, may be defined as the intercept parameter that would have an exponential DSD with the same LWC and D_m as the real one. The major point of the authors' approach is that it is totally free of any assumption about the shape of the DSD. This new normalization has been applied to the airborne microphysical data of the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE) collected by the National Center for Atmospheric Research Electra aircraft. The classification of the TOGA COARE raindrop spectra into four categories [one stratiform, and three convective (0–10, 10–30, and 30–100 mm h⁻¹)] allowed the following features to be identified. 1) There is a distinct behavior of between stratiform and convective rains; typical values are 2.2 × 10⁶ m⁻⁴ for stratiform and 2 × 10⁷ m⁻⁴ for convective. 2) In convective rain, there is a clear trend for D_m to increase with R, but there is no correlation between and R. 3) The “average” normalized shape of the DSD is remarkably stable among the four rain categories. This normalized shape departs from the exponential, but also from all the analytical shapes considered up to now (e.g., gamma, lognormal, modified gamma). The stability of the normalized DSD shape and the physical variability of and D_m are discussed in respect to the equilibrium theory of List et al. The stability of the shape implies that two parameters (and only two) are needed to describe the DSD. This stability supports the robustness of rain relations parameterized by . The same TOGA COARE dataset is used to check that the rain relations parameterized by are much less dispersed than the classical ones, even after rain-type classification.