The δ-six-stream spherical harmonic expansion adding method for solar radiative transfer

A δ-six-stream spherical harmonic expansion adding method (δ-6SDA) for solar radiative transfer is proposed. δ-6SDA has similar accuracy as δ-six-stream discrete ordinates method (δ-6DOM) but it is almost three orders of magnitude faster than δ-6DOM in flux calculation. In addition, δ-6SDA is extended to calculate the azimuthally dependent intensity in this study. The truncated-plus-single-scattering (TMS) correction is introduced to improve accuracy. Two single-layer cases with the Cloud C1 phase function and Henyey-Greenstein phase function are considered to investigate the accuracy of δ-6SDA for intensity calculation. The relative errors of these two cases for δ-6SDA are generally less than 2% and 5%, respectively. The root-mean-square errors for δ-6SDA are generally smaller than δ-6DOM. The computing time of δ-6SDA is 3–4 orders of magnitude less than δ-6DOM. Due to its high accuracy and efficiency, δ-6SDA can be widely used in remote sensing for simulating satellite observations.