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A spectral acceleration approach for the spherical harmonics discrete ordinate method (SHDOM) is designed. This approach combines the correlated <i>k</i>-distribution method and some dimensionality reduction techniques applied on the optical parameters of an atmospheric system. The dimensionality reduction techniques used in this study are the linear embedding methods: principal component analysis, locality pursuit embedding, locality preserving projection, and locally embedded analysis. Through a numerical analysis, it is shown that relative to the correlated <i>k</i>-distribution method, PCA in conjunction with a second-order of scattering approximation yields an acceleration factor of 12. This implies that SHDOM equipped with this acceleration approach is efficient enough to perform spectral integration of radiance fields in inhomogeneous multi-dimensional media.