The phase matrix truncation impact on polarized radiance

While several papers deal with effects of truncation techniques on the total radiance there is a lack of such studies concerning polarized radiance. We present our first results obtained in studying the impact of phase matrix truncation on the accuracy of polarized radiance. Like for the total radiance, the single scattering (TMS) correction is crucial and efficient in case of the polarized radiance. We show that there is a systematic error on polarized radiance that increases with truncation factor and optical depth. This error is not induced by the restitution of the phase matrix angular dependency as a function of the number of terms in the Legendre polynomials expansion. Given a truncation factor, this error reaches a maximum asymptotic value for optical depth corresponding to the saturation of polarization. For the cloud droplet that we use in our study, the maximum error is 4.5% at λ=412nm. It raises the question of whether the condition for scale invariance of the scalar radiative transfer equation...