Analytical Infrared Delta-Four-Stream Adding Method from Invariance Principle

Abstract

Abstract The single-layer solutions using a four-stream discrete ordinates method (DOM) in infrared radiative transfer (IRT) have been obtained. Two types of thermal source assumptions—Planck function exponential and linear dependence on optical depth—are considered. To calculate the IRT in multiple layers with a vertically inhomogeneous atmosphere, an analytical adding algorithm has been developed by applying the infrared invariance principle. The derived adding algorithm of the delta-four-stream DOM (δ-4DDA) can be simplified to work for the delta-two-stream DOM (δ-2DDA). The accuracy for monochromatic emissivity is investigated for both δ-2DDA and δ-4DDA. The relative error for the downward emissivity can be as high as 15% for δ-2DDA, while the error is bounded by 2% for δ-4DDA. By incorporating δ-4DDA into a radiation model with gaseous transmission, δ-4DDA is much more accurate than δ-2DDA. Also, δ-4DDA is much more efficient, since it is an analytical method. The computing time of δ-4DDA is about one-third of the corresponding inverse matrix method.