A Hybrid Algorithm of Fast Invariant Imbedding and Doubling-Adding   Methods for Efficient Multiple Scattering Calculations
  An efficient hybrid numerical method for multiple scattering calculations is proposed. We use the well established doubling--adding method to find the reflection function of the lowermost homogeneous slab comprising the atmosphere of our interest. This reflection function provides the initial value for the fast invariant imbedding method of Sato et al., (1977), with which layers are added until the final reflection function of the entire atmosphere is obtained. The execution speed of this hybrid method is no slower than one half of that of the doubling-adding method, probably the fastest algorithm available, even in the most unsuitable cases for the fast invariant imbedding method. The efficiency of the proposed method increases rapidly with the number of atmospheric slabs and the optical thickness of each slab. For some cases, its execution speed is approximately four times faster than the doubling--adding method. This work has been published in NAIS Journal (ISSN 1882-9392) Vol. 7, 5-16 (2012). 
Kiyoshi Kawabata (Dept. of Physics, Tokyo Univ. of Science)
astro-ph.IM astro-ph.EP