Advanced doubling-adding method for radiative transfer in planetary atmospheres

The doubling-adding method (DA) is one of the most accurate tools for detailed multiple-scattering calculations. The principle of the method goes back to the nineteenth century in a problem dealing with reflection and transmission by glass plates. Since then the doubling-adding method has been widely used as a reference tool for other radiative transfer models. The method has never been used in operational applications owing to tremendous demand on computational resources from the model. This study derives an analytical expression replacing the most complicated thermal source terms in the doubling-adding method. The new development is called the advanced doubling-adding (ADA) method. Thanks also to the efficiency of matrix and vector manipulations in FORTRAN 90/95, the advanced doubling-adding method is about 60 times faster than the doubling-adding method. The radiance (i.e., forward) computation code of ADA is easily translated into tangent linear and adjoint codes for radiance gradient calculations. The simplicity in forward and Jacobian computation codes is very useful for operational applications and for the consistency between the forward and adjoint calculations in satellite data assimilation. ADA is implemented into the Community Radiative Transfer Model (CRTM) developed at the U.S. Joint Center for Satellite Data Assimilation.