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Various articles are presented on multiple scattering problems and radiative transfer in the atmosphere. Particle size distribution and molecular absorption are also discussed.
A photometric function is proposed to describe the diffuse reflection of radiation by particulate materials. Both multiple scattering and the dominant effects of particle shadowing are included and the function is verified by comparisons with the photometries of laboratory surfaces. Brightness measurements of planetary and other diffusely scattering surfaces can be used to calculate the brightness for geometries other than those used in the measurements and for which the Minnaert function does not apply. The measurements also can be directly related to such surface characteristics as particle size, single-particle albedo, and compactness.
The linear polarization of sunlight reflected by Venus is analyzed by comparing observations with extensive multiple scattering computations. The analysis establishes that Venus is veiled by a cloud or haze layer of particles which have a narrow size distribution with a mean radius of about 1 micron. The refractive index of the particles is 1.44 at 0.55 micron wavelength with a small normal dispersion, the refractive index decreasing from the ultraviolet toward the infrared. The particles exist at a high level in the atmosphere, with the optical thickness unity occurring where the pressure is about 50 mb. The particle properties deduced from the polarization eliminate all but one of the cloud compositions which have been proposed for Venus. A concentrated solution of sulfuric acid provides good agreement with the polarization data.
A theoretical model of Saturn's rings is investigated which includes the shadowing effect and realistic anisotropic phase functions for the ring particles. The effects of multiple scattering and the finite size of the sun, including the penumbra, are rigorously included. The permissible range of the relevant parameters, including optical thickness, single scattering albedo, volume density, and phase function are investigated by comparing the theoretical results to observations of the ring brightness vs phase angle, wavelength, and elevation of the sun and earth. Anisotropic scattering by the ring particles is necessary in order to match the observations. The color dependence of the opposition effect is interpreted in terms of the albedo spectrum of the ring particles.
Hypothesized fleets of supersonic aircraft, flying at stratospheric altitude, may lead to a significant increase in the aerosol population of the stratosphere. Exact multiple scattering calculations have been carried out to determine the response of the earth's albedo to an increase of the stratospheric aerosol optical depth. It is found that a tripling of the aerosol population in the stratosphere, which represents an extreme upper limit to the effects of SST's, results in a 0.6% increase of the earth's reflectivity and a decrease of the mean surface temperature on the order of 0.3 K. Such changes could be marginally significant.
Using a multiple-scatter propagation theory, the characteristics of the transionospheric satellite-earth communication links are related to the parameters of the ionosphere. General equations for the frequency correlation functions are derived. Some approximate solutions are obtained and numerical examples are given. Also discussed are the degree of coherence and potential applications of the procedure to characterize the intense fading channel.
Results are reported for accurate multiple-scattering calculations to determine the solar-energy deposition profile in the atmosphere of Venus. It is found that most of the absorbed energy is deposited in the main cloud-layer region, located at altitudes above 35 km, and that the ground receives approximately 3% of the energy absorbed in toto by Venus. Using these results, vertical temperature profiles are computed under conditions of pure radiative equilibrium and radiative-convective equilibrium. Since the latter results satisfactorily match the temperature structure determined from various spacecraft observations, it is inferred that the greenhouse effect can account for the high surface temperature. Aerosols make an important contribution to the infrared opacity in these calculations. Preliminary three-dimensional calculations of the general circulation of the atmosphere are discussed which incorporate the results of the radiative calculations.
The infrared radiometer experiment on Mariner 10 measured limb-darkening curves for Venus in two spectral intervals, one near 11 microns and the other near 45 microns. These are analyzed in terms of the vertical opacity profile at each wavelength over a limited altitude range, approximately 60 to 80 km above the surface of the planet. Accurate multiple-scattering calculations are used to show that both opacity profiles are consistent with a model containing a cloud of sulphuric acid droplets with radii of 1.1 microns and a small amount of water vapor. Profiles of particle number density and humidity vs height are presented.
The decrease in the reflectivity of Venus in the near-UV can be explained if the clouds contain particles of elemental sulfur in addition to sulfuric acid. The low-resolution McDonald-Pittsburgh spectrum can be fitted by two sulfur-containing, multiple-scattering cloud models: (1) a mixed cloud consisting of one particle of elemental sulfur of radius 10 microns for every 670 particles of sulfuric acid of radius 1 micron, and (2) a layered cloud of optical thickness tau = 1.0 consisting of one-micron particles of sulfuric acid overlying a thick cloud of elemental sulfur particles of radius 3.6 microns. Some of the sulfur is incompletely polymerized. The source of the sulfur is photo-dissociation of COS, although some may also be recycled from the lower atmosphere. The sulfur plays a crucial role in the planetary meteorology of Venus since it is responsible for the bulk of the absorption of solar energy.
The film formation effects are examined of self-induced clouds and condensed films of volatile condensible materials (VCMs) which outgas from such sources as paints, coatings, adhesives, and other nonmetallic surfaces of satellites. A semi-empirical theory for the multiple scattering of free neutral molecules from dielectric surfaces which includes the effects of condensation and evaporation is defined and a mathematical model of the process is developed. The formation rate of thin surface films is considered to be the net accumulation of two simultaneous molecular processes; emission (evaporation) and adsorption (condensation). The net formation rate is considered to be dependent upon the temperature of the surface nodes, the mass and temperatures of the gas molecules, and the total pressure of the incident molecular flux. Apparatus and procedures for measuring these parameters are presented.
The paper summarizes recent cometary UV observations, most of which were made in Ly-alpha light with instruments aboard earth-orbiting satellites. These include OAO-2 observations of comets Bennett and Tago-Sato-Kosaka, OGO-5 observations of comets Bennett and Encke, and numerous observations of comet Kohoutek. Models for the production of cometary hydrogen atoms are described, including the fountain, syndyname, and parent-daughter models. Calculations of emission line profiles and multiple-scattering effects are also discussed. Results of observations and interpretations are reviewed for each cited comet, far-UV observations in other emission lines are noted, and the use of comets as solar-wind probes is considered. It is concluded that the results of the present cometary Ly-alpha observations strongly support the concept of an icy conglomerate solid cometary nucleus and suggest water to be one of the most abundant molecules in comets.
The current status of predictions by one dimensional models is reported. The following items are discussed: (1) model mechanics; (2) the parametric simulation of vertical transport, the effects of diurnally varying reactants; and (3) molecular multiple scattering. Possible sinks for chlorofluoromethanes is discussed as well as the uncertanties involved on making predictions of stratospheric ozone change.
Self-consistent Hartree-Fock-Slater molecular cluster models for the chemisorption of carbon monoxide on a (100) transition metal surface are presented. Energy levels and charge distribution for the CO:Ni5 cluster in C sub 4v symmetry are obtained, and the variation of binding energies with height of the CO molecule above the surface of nickel is studied in detail. Comparison is made with experimental binding energy spectra and with the multiple-scattering results of Batra and Bagus. The redistribution in energy of free-atom valence levels is studied by means of local-densities-of-states diagrams.
Multiple scattering problems in a plane layer often permit the convenient use of different methods joined together. Sample numerical results to illustrate this point refer to X- and Y-functions, asymptotic fitting, the small-loss approximations, polarization in high orders, and photon path distribution.
The two remote sensing problems of temperature profiling and aerosol characterization (complex refractive index, size distribution) are considered. These problems differ only in the explicit form of the source function which, for aerosols, includes contributions from both single and multiple scattering processes. When the observables are the spectral extinction or the single scattering of the source radiation, the associated problem is completely analogous to the linearized temperature inversion problem. Methods for obtaining the solution of the linear problem are classified following three main categories: (1) derivation of properties that all solutions satisfy, which must then be properties of the actual solution; (2) regularization of the ill-posed problem; and (3) data changes within their domain of uncertainty in order to avoid the basic instability. A number of unexplored methods are indicated.
A balloon-borne magnetic core digitized spark chamber with two assemblies of spark-chambers above and below the scintillation counters was used to measure the medium energy gamma ray flux from the galactic center region. Gamma ray calculations are based on the multiple scattering of the pair electrons in 15 aluminum plates interleaved in the spark chamber modules. Counting rates determined during ascent and at ceiling indicate the presence of diffuse component in this energy range. Preliminary results give an integral flux between 15 and 70 MeV compared to the differential points in other results.
Three types of aerosol were detected from observations of the Martian sky, Phobos, and the sun with the Viking imaging cameras. Atmospheric optical depths were derived from observations of the objects' brightness. Data on the absorption coefficient, mean size, and shape of aerosols were obtained from studies of the sky brightness, using a multiple-scattering computer code. The aerosol types were water ice ground fog, a higher-level ice cloud (polar hood), and soil particles suspended at heights up to 30 km. The properties of each type of aerosol are discussed. The data are subjected to thorough analysis, and the results are summarized.
The formation of X-ray spectral features due to iron in a relatively cool cloud of gas with a Thomson depth greater than 1 surrounding a compact source of continuum X-rays is described. Coupled equations are solved for the ionization structure of the cloud and for the radiative transfer of the X-rays. Photoionization suppresses the strength of emission lines and absorption edges. Comptonization of the radiation broadens emission lines, fills in absorption edges, and produces a high-energy cutoff. In order to describe multiple scattering, a Fokker-Planck equation is derived which includes an important modification of the Kompaneets equation. Narrow resonance lines are treated with an escape probability formalism.