An empirical formula for the prediction of rain attenuation in frequency range 0.6 - 100 GHz

An empirical formula for calculating the extinction cross section (ECS) by raindrops over a broad frequency range is first derived based on extensive calculations made on a widely varying in mean radius of modified Pruppacher and Pitter (MPP) raindrop models ranging from 0.25 to 3.5 mm. The expansion coefficients in the empirical formula are determined by least-squares curve fitting of numerical data obtained by the volume integral equation formulation (VIEF). The formula satisfies the frequency and raindrop size dependence. Numerical results obtained from the empirical formula for calculating the ECS are generally in good agreement with those calculated by the VIEF for raindrops with mean radius varying from 0.25 to 3.5 mm in the frequency range from 0.6 to 100 GHz. The average error in the ECS is less than 10%. The formula thus provides a simple and inexpensive method for calculating the ECS of raindrops, which otherwise requires complicated and expensive methods of calculation. By implementing this empirical formula of ECS into the rain attenuation equation, a new numerically empirical formula for calculating the specific rain attenuation is also proposed. The validity of the empirical formula for calculating the specific rain attenuation is also checked by comparing the obtained results of specific rain attenuation with those obtained from Li et al.'s (1995) solution, Yeo et al.'s (1993) measurement, and Olsen et al.'s (1978) power-law equation.