We present a plane parallel radiative transfer model for polarized light that provides the intensity vector field as well as analytical derivatives of the four Stokes parameters at the top of the atmosphere with respect to physical properties of spherical aerosols. The linearization consists of two steps: (1) calculation of the derivatives of the four Stokes parameters at the top of the atmosphere with respect to scattering coefficient, extinction coefficient, and expansion coefficients of the scattering phase matrix. These derivatives are calculated employing the forward-adjoint perturbation theory. General expressions are presented that can be applied for the linearization of any vector radiative transfer model that calculates the internal radiation field in the model atmosphere. (2) The second step is calculation of the derivatives of the scattering coefficient, extinction coefficient, and the expansion coefficients of the scattering phase matrix, with respect to the real and imaginary part of the refractive index, and parameters describing the size distribution (e.g., effective radius, effective variance). These derivatives are analytically calculated following Mie theory. The use of the developed linearized radiative transfer model for the retrieval of aerosol properties is demonstrated using synthetic measurements of intensity and polarization of the Global Ozone Monitoring Experiment-2 (GOME-2). Here it is shown that an iterative retrieval approach based on the linearized radiative transfer model is suited to solve the nonlinear aerosol retrieval problem, and additionally allows a solid error analysis.
