Analytic expressions of the Transmission, Reflection, and source function for the community radiative transfer model

The phase matrix in scalar radiative transfer is symmetric that grants reciprocity principle in radiative transfer. The reciprocity principle is so useful that one may compute a single transmission matrix and a single reflection matrix for a homogeneous medium regardless of in upward or downward direction. The symmetric phase matrix is also important as one only needs to solve for a real eigensolution. An eigensolution is often used in a radiative transfer solver because of its high computational efficiency. However, the phase matrix in vectorized radiative transfer is generally not symmetric which challenges the reciprocity principle and forces us to deal with a complex eigensolution that requires a major effort in computational coding tangent-linear and adjoint models. This paper introduces an approach to retain the reciprocity principle in radiative transfer and applies a Taylor expansion of analytic transmittance and reflection matrices for a base optical depth together with a doubling-adding method beyond the base in the vectorized Community Radiative Transfer Model (CRTM). The value of the base optical depth depends on the maximum absolute value of the phase matrix elements. In comparison with other forward radiative transfer models, the extended vectorized CRTM agrees well with those models. The computational efficiency among the CRTM and those models is comparable. The tangent-linear and adjoint modules of the vectorized CRTM can be used for assimilating microwave, infrared, visible and ultraviolet sensor radiances. Published by Elsevier Ltd.