A New Approach to the Auxiliary Equation with Application to the Greenhouse Effect

摘要

Part of the heating of the atmosphere is due to the fact that the incident solar radiation has one absorption coefficient and the escaping planetary gas another. This is referred to as the greenhouse effect. An idealized theory of the greenhouse effect for a gray planetary atmosphere of infinite depth was developed by R. Wildt of Yale University in previous work. Numerical results for the temperature profile were given. These employed accurate numerical values for the Hopf q function and the Chandrasekhar H function, which are now available. This memorandum shows how to treat the problem for the case of an atmosphere of finite depth. First an initial value problem for the basic integral equation for the source function is obtained. Then an effective numerical procedure is described, and some computational results are presented. (Author)