A computationally useful initial-value theory for determining the intensity of radiation emerging normal to the surface of the atmosphere for comparison with observed profiles. In this theory the emergent intensity E is the solution of an initial-value problem in which the independent variable is the interval length, or x, the optical thickness. The solution is determined as the thickness is varied from x equals zero when E equals zero, to x equals the desired thickness value. The computational procedure is based on the ability of modern computers to effectively solve large systems of ordinary differential equations subject to a complete set of initial conditions. The differential-integral equations of the exact theory are replaced by a system of ordinary differential equations in which the definite integrals are approximated by sums according to a quadrature formula. A suitably chosen quadrature formula can yield a very good approximation. 24 pp. Refs.
This report is part of the RAND Corporation Research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.
Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit www.rand.org/about/research-integrity.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.