Functional Fits to Some Observed Drop Size Distributions and Parameterization of Rain

Abstract

A data sample of optical spectrometer measurements that were obtained in two tropical cyclones is analyzed. The resultant drop size distributions are normalized and their shape is found to exhibit some curvature-departure from exponentiality. When the sample, ordered by rainfall rate, is divided in half, the shape (curvature) of the low-rainfall-rate half is found to be nearly identical to that of the high-rainfall-rate half. Five functional fits to the data are explored in detail; three are exponential fits-Marshall-Palmer, least-squares and ?analytical"-and two are gamma distribution function fits-an analytical and a curvilinear least-squares. The goodness-of-fit is evaluated based on error squared, and on coalescence growth error and drop evaporation error. The coalescence growth and drop evaporation are computed using simple microphysical models. The fits that are based on minimizing squared error do not characterize coalescence growth and evaporation well. An analytical gamma distribution function fit to the measured distributions provided the most reasonable compromise between satisfactory squared-error fit and realistic characterization of coalescence growth and drop evaporation. With this analytical gamma distribution function fit in mind, modifications to the widely used Marshall-Palmer-based microphysics parameterizations are proposed. These proposed simple modifications should provide a more realistic characterization of coalescence growth and drop evaporation in numerical simulations. Relations between several bulk parameters of the measured distributions and several parameters of the functional fits are derived. These relations are compared with those found by other investigators.