A tutorial solution to scattering of radiation in a thin atmosphere bounded below by a diffusely reflecting, absorbing surface

A simple tutorial method, based on a photon tracking procedure, is described to determine the spherical albedo for a thin atmosphere overlying a reflecting surface. This procedure is used to provide a physical structure with which to interpret the more detailed but highly mathematical analyses presented. The final equations are shown to be in good numerical agreement with more exact solutions for thin atmospheres

The effect of remote zones on the accuracy of evaluating the Molodensky

An analytical method is presented for determining the error in computing the gravity anomaly from the Molodensky integral if geoidal undulation data in remote zones are neglected. The error is given in terms of the usual degree variance and a set of parameters which are functions only of the size of the area in which undulation data are taken. A numerical calculation using Kaula's degree variances indicates that it is necessary to integrate the Molodensky integral over approximately a hemisphere in order to reduce the effect of neglected data to the order of 1 milligal in the computation of gravity anomaly

Direct computation of orbital sunrise or sunset event parameters

An analytical method is developed for determining the geometrical parameters which are needed to describe the viewing angles of the Sun relative to an orbiting spacecraft when the Sun rises or sets with respect to the spacecraft. These equations are rigorous and are frequently used for parametric studies relative to mission planning and for determining instrument parameters. The text is wholly self-contained in that no external reference to ephemerides or other astronomical tables is needed. Equations are presented which allow the computation of Greenwich sidereal time and right ascension and declination of the Sun generally to within a few seconds of arc, or a few tenths of a second in time

Effect of ephemeris errors on the accuracy of the computation of the tangent point altitude of a solar scanning ray as measured by the SAGE 1 and 2 instruments

An analysis was made of the error in the minimum altitude of a geometric ray from an orbiting spacecraft to the Sun. The sunrise and sunset errors are highly correlated and are opposite in sign. With the ephemeris generated for the SAGE 1 instrument data reduction, these errors can be as large as 200 to 350 meters (1 sigma) after 7 days of orbit propagation. The bulk of this error results from errors in the position of the orbiting spacecraft rather than errors in computing the position of the Sun. These errors, in turn, result from the discontinuities in the ephemeris tapes resulting from the orbital determination process. Data taken from the end of the definitive ephemeris tape are used to generate the predict data for the time interval covered by the next arc of the orbit determination process. The predicted data are then updated by using the tracking data. The growth of these errors is very nearly linear, with a slight nonlinearity caused by the beta angle. An approximate analytic method is given, which predicts the magnitude of the errors and their growth in time with reasonable fidelity

An asymptotic expansion approach to the inverse radiative transfer problem

An iterative technique which recovers density profiles in a nonhomogeneous absorbing atmosphere is derived. The technique is based on the concept of factoring a function of the density profile into the product of a known term and a term which is not known, but whose power series expansion can be found. This series converges rapidly under a wide range of conditions. A demonstration example of simulated data from a high resolution infrared heterodyne instrument is inverted. For the examples studied, the technique is shown to be capable of extracting features of ozone profiles in the troposphere and to be particularly stable

Introduction to the Theory of Atmospheric Radiative Transfer

The fundamental physical and mathematical principles governing the transmission of radiation through the atmosphere are presented, with emphasis on the scattering of visible and near-IR radiation. The classical two-stream, thin-atmosphere, and Eddington approximations, along with some of their offspring, are developed in detail, along with the discrete ordinates method of Chandrasekhar. The adding and doubling methods are discussed from basic principles, and references for further reading are suggested

Heat Transfer and Boundary-Layer Transition on a Highly Polished Hemisphere-Cone in Free Flight at Mach Numbers Up to 3.14 and Reynolds Numbers Up to 24 x 10(exp 6)

A highly polished hemisphere-cone having a ratio of nose radius to base radius of 0.74 and a half-angle of 14.5 was flight tested at Mach numbers up to 4.70. Temperature and pressure data were obtained at Mach numbers up to 3.14 and a free-stream Reynolds number of 24 x 10(exp 6) based on body diameter. The nose of the model had a surface roughness of 2 to 5 microinches as measured with an interferometer. The measured Stanton numbers were in good agreement with theory. Transition Reynolds numbers based on the laminar boundary-layer momentum thickness at transition ranged from 2,190 to 794. Comparison with results from previous tests of blunt shapes having a surface roughness of 20 to 40 microinches showed that the high degree of polish was instrumental in delaying the transition from laminar to turbulent flow