For spherical particles, \(P_{22}=P_{11}\) and \(P_{44}=P_{33}\) while these terms are not equal for aggregates due to the depolarization caused by cross-polarization within aggregates  \citep{Tazaki_2016}.  The actual angular dependency of the depolarization is difficult to model empirically for aggregates outside the RDG limit. For instance, a modest fit for depolarization calculated by T-matrix data requires several polynomial terms. Instead, we use a simple empirical model for depolarization which is fairly good inside the tested range and produces valid values when extrapolating to severa thousands of monomers.