A neural-network-based fast forward operator for polarized 3D radiative transfer in low-level Arctic mixed-phase clouds

Abstract. Clouds generally have a complex three-dimensional geometry. However, realistic three-dimensional radiative transfer simulations of clouds are computationally expensive, so most retrievals of cloud properties assume one-dimensional clouds, which introduces retrieval biases. In this work, a fast forward operator for polarized 3D radiative transfer in the visible wavelength range is presented. To this end, a new approximation for 3D radiative transfer, the InDEpendent column local halF-sphere ApproXimation (IDEFAX), is introduced. The basic idea behind this approximation is similar to the independent column approximation assuming plane-parallel clouds. However, every column is approximated by an independent 3D half-spherical cloud instead of a plane-parallel homogeneous cloud. The half-spherical cloud is defined by the local cloud surface orientation angles and embedded in a cloud field with a given cloud fraction. Thus, IDEFAX has only three more parameters compared to the plane-parallel approximation. To obtain a fast forward operator, artificial neural networks were trained for both, the plane-parallel and the half-spherical cloud assumptions. IDEFAX as well as the neural network forward operators were validated against polarized 3D radiative transfer simulations with MYSTIC for low-level Arctic mixed-phase clouds using a realistic cloud field simulated with the WRF model. The use of IDEFAX significantly improves the representation of 3D radiative effects in the simulated radiance fields compared to the plane-parallel independent column approximation. Due to the implementation of the forward operator with neural networks, the computation time for both approximations is comparable and about five orders of magnitude faster than real 3D radiative transfer simulations for the shown example. The introduced neural network forward operators are constructed to be used in retrievals of cloud properties with the specMACS instrument. However, the methods are also applicable to other measurements in the visible wavelength range as well as to model data.