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Absorption line multiple scattering in thick planetary atmosphere, using successive scattering method for single-scattering phase function based on line profile and equivalent width
Single to triplet transitions of water vapor as function of scattering angle in electron impact detection
Extinction parameters of submicron carbon, tungsten and Si particles in hydrogen measured at various temperatures, discussing scattering amplitude functions and Monte Carlo calculations
A summary is presented of optical measurements performed on a variety of cesium iodide samples to characterize quantitatively the optical quality of the materials, and to define and measure parameters which determine its suitability as a detector material for high energy cosmic ray experiments on HEAO-A. The general case of light transmission through a long rectangular slab under multiple internal reflections is discussed along with transmission and scattering as a function of wavelength at normal incidence. Scattering parameters are tabulated for encapsulated single crystal CsI and polyscin.
In this paper we treat the multiple scattering theory of radiative transfer in plane-parallel inhomogeneous atmospheres. The treatment presented here may be adopted to model atmospheres characterized by an optical depth dependent coherent scattering phase function. For the purpose of illustration we consider the semi-infinite medium in which the absorption property of the atmosphere is characterized by an exponential function. The methodology employed here is the extension of the case treated previously by the author for homogeneous atmospheres.
Three methods of approximation are described and used to separate the primary twilight brightness from the observed brightness. Photoelectric observations obtained are combined with observations from a balloon and from the observatory to derive the atmospheric scattering phase functions of 0.37 micron and 0.58 micron as a function of height. Comparison of these data with data for a Rayleigh atmosphere provide information on the optical properties of dust in the upper atmosphere.
Using the precision s- and p-wave elastic-scattering wave functions obtained previously, we have calculated the annihilation rate for positrons colliding with hydrogen atoms below the positronium-formation threshold. The s-wave results agree well with those of Humberston, while the p-wave results, which are new, contribute about 20% of the total at the higher energies.
Theoretical surface brightness profiles of spherical dark nebulae of both uniform density and a density proportional to 1/r squared are being discussed. The albedo and asymmetry factor of the dust grains and the optical radius measured from the cloud center were the variable parameters in this study, which further assumed an isotropically incident radiation field. The occurrence of dark cores in the surface brightness profiles is examined, and their frequent existence in galactic dark nebulae is interpreted as resulting from a strongly forward scattering phase function and a high optical depth of the associated objects. The shape and depth of the profiles of the dark cores is closely related to the internal density distribution of the clouds, and it is suggested that detailed observations of the surface brightness profiles of dark nebulae will reveal important information on the type of their internal density distribution and, thus, their evolutionary status.
Multiple scattering contributions to lidar returns from turbid atmospheres are derived by means of an analytical theory. It is assumed that scattering takes place mainly at small angles except for one event that scatters the light backward. The phase functions are approximated by the sum of Gaussian functions of the scattering angle in both the forward and backward directions. The three-dimensional radiative transfer equation is transformed to a one-dimensional problem by means of Fourier transforms. Neumann solutions to the transformed equation of radiative transfer are then found. A number of examples are presented for cloud, fog and haze models. The results are found to be in satisfactory agreement with results obtained from the Monte Carlo analysis of Kunkel (1974) and the theory of light pulses doubly scattered by turbid atmospheres which was developed by Eloranta (1972).
High-spatial-and-spectral-resolution observations of Venus CO2 line profiles taken over a three-year interval are analyzed using inhomogeneous atmospheric models with anisotropic scattering. The data exhibit two sudden significant changes in the structure of the atmosphere, one occurring near April 1973, and the other near November 1974. Two models are developed to describe the vertical cloud structure of the atmosphere of Venus in the more quiescent periods after these changes. For each model, the CO2 specific abundance must decrease with increasing atmospheric pressure; i.e., the clouds are thinnest high in the atmosphere and become denser with depth. No evidence is found that the cloud particles must change their scattering phase function with altitude.
The shapes of Venus' CO2 profiles are found to vary with solar phase angle. High-resolution spectra of the P16 and P14 lines in the 8689- and 7820-A bands, respectively, are presented for phase angles ranging from 6 to 158 deg. The scattering mean free path at 80 mbar, approximately the effective pressure, is 1.7 km. Use of the van de Hulst (1974) similarity relations with simple parametric scattering models is inadequate to separate effects due to the scattering phase function from those due to inhomogeneities in depth when one attempts to determine the atmospheric structure by fitting a family of such models over a wide range of phase angles.
The effect of stratospheric aerosols on the earth's monthly zonal radiation balance is investigated using a model layer consisting of 75% H2SO4, which is the primary constituent of the background aerosol layer. The reduction in solar energy absorbed by the earth-atmosphere system is determined through the albedo sensitivity, defined here as the change in albedo per unit mid-visible optical depth of the aerosol layer. The optically thin approximation is used in conjunction with the Henyey-Greenstein phase function for scattering to simplify computations. Satellite derived planetary albedos are used as the frame of reference about which the change in albedo is computed. An infrared radiative transfer model is used to estimate the increased greenhouse effect attributed to the aerosol layer. The infrared heating tends to compensate for the albedo effect in altering the radiation balance. The results indicate that the dominant influence of the thin model stratospheric aerosol layer is an increased reflection of solar energy all over the globe except for the polar-winter region, but the change in the radiation balance is seen to be uniform and small equatorwards of 50%.
Jupiter was observed in six continuum wavelength channels in the region 4100-8300 A, using a silicon vidicon imaging photometer. Spectral reflectivities and high spatial resolution limb-darkening curves for several belts and zones have been extracted from the data. Simple model fits to the data yield information regarding spectral and spatial variations in single-scattering albedos and shape of particle single-scattering phase functions. Belts appear to be more backscattering than zones, particularly in the blue. The data are in moderate agreement with limb-darkening predicted by models derived from the center-to-limb variation in equivalent width of the H2 4-0 S(1) quadrupole line (Cochran, 1976) in the South Tropical Zone, but strongly disagree with the results of such models for the North Equatorial Belt.
Observational data are compared on the distribution of very small micrometeoroids (1 billionth to 1 hundred-millionth g), the scattering source function of the zodiacal light, the distribution of larger micrometeoroids (at least 1 hundred-thousandth g) as observed from Helios A and Pioneer 10, and the distribution of meteoroids from the sample seen from earth. The experiments, analyses, and simulations involved in obtaining these data are described in detail. It is shown that the various groups of data can be reconciled only by small albedos that decrease outward from 0.1 to at least about 3.3 AU for the particles which produce both the zodiacal light and the observed meteors. The results also indicate that there must be a maximum in the distribution of the larger particles somewhere between the orbits of earth and Jupiter. It is suggested that a search for fireballs in Jupiter's atmosphere by the television cameras of the MJS 77 mission should aid in locating this maximum.
The paper analyzes the effects of atmospheric and sea surface scattering on the determination of ocean color from satellite imagery and proposes an algorithm for removing a large portion of these effects. The algorithm is based on the observations that (1) the upward radiance from the unwanted photons can be divided into effects resulting from Rayleigh scattering alone and those resulting from aerosol scattering alone, (2) the aerosol scattering phase function should be nearly independent of wavelength, and (3) the Rayleigh component can be computed without a knowledge of the sea surface roughness. The ratio of the aerosol optical thickness at the wavelength of interest to the aerosol optical thickness at 750 nm is used in the algorithm since it is assumed that the ocean is totally absorbing in a band of wavelengths around 750 nm. The calculation of this ratio from satellite measurements alone and the accuracy of the procedure are considered.
The microwave emission from a half-space medium characterized by coordinate dependent scattering and absorbing centers was calculated by numerically solving the radiative transfer equation by the method of invariant imbedding. A Mie scattering phase function and surface polarization was included in the calculation. Also included are the physical temperature profile and the temperature variation of the index of refraction for ice. Using published values of grain size and temperature profile data of polar firn, the brightness temperature was calculated for the 1.55 cm and 0.8 cm wavelengths. For selected regions in Greenland and Antarctica, the results are in reasonable agreement with the observed Nimbus-5 and Nimbus-6 ESMR data.
Mie theory, which is generally used to describe the scattering behavior of particles at a certain wavelength, is only rigorously correct for spherical particles. Particles found as atmospheric constituents, with the exception of cloud droplets, are, however, decidedly nonspherical. An investigation is, therefore, conducted regarding the significant ways in which the scattering behavior of irregularly shaped particles differs from that of spheres. A systematic method is formulated for treating the real scalar scattering behavior. A description is presented of a new semiempirical theory based on simple physical principles and data obtained in laboratory measurements, which successfully reproduces the single scattering phase function for a wide range of particle shapes, sizes, and refractive indices.
The author has developed a technique for testing various charge-transfer approximation schemes for consistency with the requirements of the Kohn variational principle for the amplitude to guarantee that the amplitude is correct to second order in the scattering wave functions. Applied to Born-type approximations for charge transfer it allows the selection of particular groups of first-, second-, and higher-Born-type terms that obey the consistency requirement, and hence yield more reliable approximation to the amplitude.