Satellite data assimilation requires a fast and accurate radiative transfer model. In general, the radiative transfer vector is solved from a differential and integral equation that includes absorption, scattering and polarization. In the past, we developed a multi-layer discrete-ordinate method (Weng, 1992; Schulz et al., 1999) to discretize the vector radiative equation to formulate a set of the ordinary differential equations so that the radiance can be solved using an eigenvalue procedure. The merit of the discrete-ordinate method was seemly demonstrated because the solution is in a mathematically elegant form. In this study, we further prove that the radiance gradient (or Jacobian) used for the adjoint computation can be also best derived analytically, not resorting to a lengthy parameterization scheme as used in today's data assimilation system. However, it is found that in a vertically stratified scattering and emission atmosphere, the procedure for determining the coefficients in the general solutions is not optimized and as a result a large amount of computer resource (e.g. high memory and long computational time) is required. This deficiency may impair the use of the discrete-ordinate method for satellite data assimilation conditions where atmospheric stratification is finely required. This study will improve the aspect of VDISORT for more general applications.

Weng, F., 1992: A multi-layer discrete-ordinate method for vector radiative transfer in vertically-inhomogeneous; emitting and scattering atmosphere, Part I: Theory, J. Quant. Spectrosc. Radiat. Trans., 47, 19-33.

Schulz, F. M., K. Stamnes and F. Weng, 1999: An improved and generalized discrete ordinate radiative transfer model for polarized (vector) radiative transfer computations, Quant. Spectrosc. Radiat. Trans,, 61, 105-122.