Approximations to microwave attenuation in precipitation

A three-term approximation and a discrete drop-size distribution have been used to obtain an analytical expression for the microwave attenuation coefficient for precipitation. Results compared to an exact calculation using the same drop size distribution showed a relative difference of 50% or less over a broad range of rainrates (5-150 mm/hr) and wavelengths (2-5 cm). Since the use of a discrete drop-size distribution is computationally complex, the exponential size distribution formulated by Marshall and Palmer (1948) was studied. This distribution resulted in an overprediction of the attenuation coefficient of as much as 100% at a 2 cm wavelength and a 150 mm/hr rainrate, although the prediction was much closer at lower rainrates and different wavelengths.