An Accelerated Discrete Ordinate Method (ADOM) Developed for Scalar Radiative Transfer by Merging Adjacent Clear‐Sky Atmospheric Layers: Forward and Jacobians Derivation

Abstract In this study, an Accelerated Discrete Ordinate Method (ADOM) is proposed to enhance the computational efficiency of multi‐layer radiative transfer (RT) simulations while maintaining a high accuracy. ADOM applies the Discrete Ordinate Method (DOM) only in scattering layers, while the radiances for the adjacent clear‐sky layers are merged and computed by non‐scattering RT theory. The merging process significantly reduces the number of layers involved, enhancing computational efficiency while the vertical structure of both the Planck function and the Rayleigh scattering single‐scattering albedo are fully accounted. This hybrid RT approach enables ADOM to be applicable across the visible to microwave spectrum. For satellite radiance assimilation, tangent linear and adjoint modules of ADOM are also developed to compute the Jacobians of all relevant parameters. Although ADOM merges adjacent clear‐sky atmospheric layers during RT calculations, the Jacobians of properties in each merged clear‐sky layer can still be accurately computed by constructing an adjoint module of the merging process. The accuracy of both the forward and adjoint modules of ADOM is evaluated against 128‐stream DOM and the finite difference results based on DOM. Notably, the computational efficiency gain of ADOM is influenced by the ratio of clear‐sky layers to cloud layers. As the number of cloud layers decreases, the efficiency of ADOM increases. In fully cloudy conditions, the runtime of ADOM converges to that of DOM.