The calculation of scattering from precipitation particles at millimetre wave frequencies

A modified version of the Fredholm integral equation method is proposed for calculating the scattering from precipitation particles at millimeter wave frequencies. The proposed method significantly reduces the number of matrix elements to be calculated, transforms the problem of solving a single large matrix equation into that of solving a number of much smaller matrix equations, and enables a convergence check to be performed without any recalculation of matrix elements. The modification retains the major features of the Fredholm method: numerical stability, ensured convergence, and ability to calculate scattering amplitudes, for any incident direction and/or polarization as well as for any scattered direction, with just one calculation of the matrix elements. This refined Fredholm integral method is expected to be capable of accurately predicting scattering from water up to frequencies slightly above 100 GHz and from ice up to much higher frequencies.