A Hybrid Algorithm of Fast Invariant Imbedding and Doubling-Adding Methods for Efficient Multiple Scattering Calculations

TL;DR

This paper introduces a hybrid numerical method combining doubling-adding and fast invariant imbedding techniques to efficiently compute multiple scattering in atmospheres, significantly reducing computation time especially for complex layered structures.

Contribution

The paper presents a novel hybrid algorithm that accelerates multiple scattering calculations by integrating doubling-adding with fast invariant imbedding, outperforming traditional methods in speed.

Findings

Hybrid method is at least twice as fast as doubling-adding.

Efficiency increases with more atmospheric layers and thicker slabs.

Speed can be approximately four times faster in some cases.

Abstract

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).