Circular depolarisation ratio of radar returns from rain: validity of the second-order solution of RT equation

A simple method is proposed for predicting the circular depolarisation ratio (CDR) of radar returns from rain using the second-order solution of the time-dependent radiative transfer equation. The calculation is made for pulses with carrier frequencies of 16 GHz and 34.8 GHz to compare with results previously obtained by a rigorous analytical-numerical procedure for a semi-infinite region containing spherical raindrops. It is shown that the solution, including up to the second-order, is sufficient to evaluate the CDR at 16 GHz, and provides a general trend for the higher frequency of 34.8 GHz. However, the CDR at 34.8 GHz is about 4.5 dB below the rigorous results at the maximum. This implies that at the higher frequency the multiple scattering of the higher order rather than the second order contributes to a high value of the CDR