On the simplified expression of realistic raindrop shapes

Abstract

The Pruppacher-and-Pitter (PP) raindrop model has been well accepted as a realistically distorted raindrop model. To employ this model for the investigation of radio wave attenuation by rain requires tedious numerical calculations. In this Letter a simple mathematical formula is used to simplify and improve the expression of the nonaxisymmetric distorted raindrop shapes, enabling the scattered field by rain to be derived analytically. The coefficients in the formula are determined for different raindrop sizes by translating the polar coordinates vertically and fitting the shapes of the Pruppacher-and-Pitter-form raindrops to the shapes discussed in this Letter. Using the least-squares method, a general expression for the coefficients in terms of the raindrop sizes is obtained. A comparison of the raindrop shapes obtained from the Pruppacher and Pitter expression and the expression in this Letter demonstrates the validity of the simplified formula for realistically distorted raindrops.