Abstract
The adding method, which could calculate the infrared radiative transfer (IRT) in inhomogeneous atmosphere with multiple layers, has been applied to δ-four-stream discrete-ordinates method (DOM). This scheme is referred as δ-4DDA. However, there is a lack of application for adding method of δ-four-stream spherical harmonic expansion approximation (SHM) to solve infrared radiative transfer through multiple layers. In this paper, the adding method for δ-four-stream SHM (δ-4SDA) will be obtained and the accuracy of it will be evaluated as well. The result of δ-4SDA in an idealized medium with homogeneous optical property is significantly more accurate than that of the adding method for δ-two-stream DOM (δ-2DDA). The relative errors of δ-2DDA can be over 15% in thin optical depths for downward emissivity, while errors of δ-4SDA are bounded by 2%. However, the result of δ-4SDA is slightly less accurate than that of δ-4DDA. In a radiation model with realistic atmospheric profile considering gaseous transmission, the accuracy for heating rate of δ-4SDA is significantly superior than that of δ-2DDA, especially for the cloudy sky. The accuracy for heating rate of δ-4SDA is slightly less accurate than that of δ-4DDA under water cloud conditions, while it is superior than that of δ-4DDA in ice cloud cases. Beside, the computational efficiency of δ-4SDA is higher than that of δ-4DDA.
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