The δ-six-stream spherical harmonic expansion adding method for solar radiative transfer. (March 2020) - Xue, Dan; Zhang, Feng; Shi, Yi-Ning; Iwabuchi, Hironobu; Li, Jiangnan; Hu, Shuai; Han, Wei
Highlights: Rapid solar radiative transfer. Six-stream spherical harmonic expansion adding method. Azimuthally dependent intensity. Truncated-plus-single-scattering correction. Abstract: 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.