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NASA NTRS1992

Multiple scattering of light in a spherical cometary atmosphere with an axisymmetric dust jet

A numerical solution has been developed for the anisotropic multiple scattering of light in a spherical shell comet atmosphere. The code has been run for a spherically symmetric coma distribution, benchmarked against past studies, and then run for the conditions of an axisymmetric dust jet at the subsolar point of the comet. The radiant flux impinging on the nucleus surface and the mean intensity of light throughout the coma were investigated.

Chick, Kenneth M.↗

NASA NTRS1985

A multiple scattering theory for EM wave propagation in a dense random medium

For a dense medium of randomly distributed scatterers an integral formulation for the total coherent field has been developed. This formulation accounts for the multiple scattering of electromagnetic waves including both the twoand three-particle terms. It is shown that under the Markovian assumption the total coherent field and the effective field have the same effective wave number. As an illustration of this theory, the effective wave number and the extinction coefficient are derived in terms of the polarizability tensor and the pair distribution function for randomly distributed small spherical scatterers. It is found that the contribution of the three-particle term increases with the particle size, the volume fraction, the frequency and the permittivity of the particle. This increase is more significant with frequency and particle size than with other parameters.

Karam, M. A.↗

NASA NTRS1993

Comparative accuracy of diffuse radiative properties computed using selected multiple scattering approximations

Computational results have been obtained for the spherical albedo, global transmission, and global absorption of plane-parallel layers composed of cloud droplets. These computations, obtained using the doubling method for the entire range of single scattering albedos and for optical depths between 0.1 and 100, are compared with corresponding results obtained using selected multiple scattering approximations. The spherical albedo and global absorption computed using asymptotic theory are found to be accurate to better than 5 percent for all values of the single scattering albedo, provided the optical thickness exceeds about 2. The diffuse two-stream approximations have relative accuracies that are much worse than 5 percent for the spherical albedo over most of the parameter space, yet are accurate to within 5 percent in the global absorption when the absorption is significant. The integrated delta-Eddington scheme appears to be the most suitable model over the entire range of variables, generally producing relative errors of less than 5 percent in both the spherical albedo and global absorption.

HARSHVARDHAN↗

NASA NTRS1975

Multiple scattered radiation emerging from continental haze layers. 2: Ellipticity and direction of polarization

The ellipticity and the direction of polarization are calculated for radiation that has undergone multiple scattering from plane parallel layers. Both the radiation emerging from the top of the layer and that transmitted through the bottom are considered. Two different phase functions are used for the scattering layer: Rayleigh and haze L. The direction of polarization of the reflected radiation shows little variation as the optical depth of the layer increases, while there is a much larger variation for the transmitted radiation. When the optical thickness is small, the direction of polarization for haze L varies rapidly with zenith angle near those angles at which the single scattered polarization is zero. The ellipticity of the radiation from haze L layers increases at first in direct proportion to the optical thickness of the layer. In general the ellipticity of the transmitted radiation is considerably greater than that of the reflected because of the greater average number of photon collisions in the former case.

Plass, G. N.↗

NASA NTRS1976

Multiple scattered radiation emerging from Rayleigh and continental haze layers. II - Ellipticity and direction of polarization

The ellipticity and the direction of polarization are calculated for radiation that has undergone multiple scattering from plane-parallel layers. Both the radiation emerging from the top of the layer and that transmitted through the bottom are considered. Two different phase functions are used for the scattering layer: Rayleigh and haze L. The direction of polarization of the reflected radiation shows little variation as the optical depth of the layer increases, but there is a much larger variation for the transmitted radiation. When the optical thickness is small, the direction of polarization for haze L varies rapidly with zenith angle near those angles at which the single-scattered polarization is zero. The ellipticity of the radiation from haze L layers increases at first in direct proportion to the optical thickness of the layer. In general, the ellipticity of the transmitted radiation is considerably greater than that of the reflected due to the greater average number of photon collisions in the former case. When the ellipticity is small, it is shown that the product of the polarization and the ellipticity is closely equal to -V/2I, where I and V are the first and fourth components of the Stokes vector.

Plass, G. N.↗

NASA NTRS1979

Multiple scattering of solar resonance radiation in the nearby interstellar medium. I

The paper presents approximate solutions obtained for a radiative transfer problem that represents a highly-idealized description of the multiple scattering of solar resonance radiation in the nearby interstellar medium. The problem of a point source in the center of a spherically symmetric cavity imbedded in an infinite uniform medium is solved for a range of cavity radii. First and second-order scattering contributions are calculated, and the Eddington approximation is used to estimate the higher order components of the radiation field. It is shown that for coherent scattering at very large cavity radii, the backscattered intensity from the cavity approaches three times the value deduced from the optically thin solution, in agreement with previous work. It is concluded that an accurate analysis of sky background will require including not only the frequency redistribution, but also the correct spatial distribution of density.

Keller, H. U.↗

NASA NTRS1981

On the multiple scattering of VHF/UHF waves in the equatorial ionosphere

Using amplitude data of radio beacons at 40, 140, and 360 MHz from ATS 6 (phase II), an attempt has been made to study scattering of these waves in the equatorial ionosphere. A comparison of observed scintillation index S sub 4 with the theoretical results of the multiple scattering approach and variation of autocorrelation time with frequency indicates that this theory explains the results to a large extent. A comparison of power spectra of amplitude records with the ionograms of a nearby equatorial station has led to the following conclusions: the change from a weak scattering regime to a strong scattering regime is gradual and occurs because of the gradual decrease in the scale size of the irregularities (i.e., broadening of the spectra) and the gradual increase in the thickness of the irregular region.

Vats, H. O.↗

NASA NTRS1994

Multiple-scattering model for inclusive proton production in heavy ion collisions

A formalism is developed for evaluating the momentum distribution for proton production in nuclear abrasion during heavy ion collisions using the Glauber multiple-scattering series. Several models for the one-body density matrix of nuclei are considered for performing numerical calculations. Calculations for the momentum distribution of protons in abrasion are compared with experimental data for inclusive proton production.

Cucinotta, Francis A.↗

NASA NTRS1973

Phase matrix induced symmetrics for multiple scattering using the matrix operator method

Entirely rigorous proofs of the symmetries induced by the phase matrix into the reflection and transmission operators used in the matrix operator theory are given. Results are obtained for multiple scattering in both homogeneous and inhomogeneous atmospheres. These results will be useful to researchers using the method since large savings in computer time and storage are obtainable.

Hitzfelder, S. J.↗

NASA NTRS1972

Degree and plane of polarization of multiple scattered light. 1: Homogeneous cloud layers

The degree of polarization and the direction of the plane of polarization are calculated by a Monte Carlo method for homogeneous layers. Two solar zenith angles and a range of optical thicknesses up to 10 are considered. The results are compared with calculations for single scattered photons. For a given pair of incident and scattered directions, there are only two possible values for the direction of the plane of polarization differing by 90 deg for single scattering from spherical aerosols. The choice between these two values depends only on the sign of the element M(-) in the first row and second column of the scattering matrix in the I, Q, U, V representation. In most cases there is little change in the direction of the plane of polarization when multiple scattering is taken into account, so that this quantity can usually be predicted from a very simple trigonometric relationship to good accuracy. Measurements of the direction of the plane of polarization at appropriately chosen angles provides information about the size distribution of the scattering centers.

Kattawar, G. W.↗

NASA NTRS1974

A three parameter analytic phase function for multiple scattering calculations

A simple procedure was developed to fit the first three moments of an actual phase function with a three parameter analytic phase function. The exact Legendre Polynomial decomposition of this function is, suitable for multiple scattering calculations. The use of this function is expected to yield excellent flux values at all depths within a medium. Since it is capable of reproducing the glory, it can be used in synthetic spectra computations from planetary atmospheres. Accurate asymptotic radiance values can also be achieved as long as the single scattering albedo omega sub 0 is greater than or equal to 0.9.

Kattawar, G. W.↗

NASA NTRS1984

The effects of the diffuse radiation fields due to multiple scattering and thermal reradiation by dust on the dynamics and thermodynamics of a dusty cometary atmosphere

A self-consistent model of a dirty, clathrate cometary nucleus is extended to account for diffuse radiation fields caused by multiple scattering and thermal reradiation of the solar continuum by dust. The model is configured to fit conditions expected for the various spacecraft which will encounter Halley's comet at 0.89 AU. The atmosphere is assumed a chemically reactive dust-gas mixture in quasi-steady spherically symmetric expansion. The effect of electron-neutral ion collisions is accounted for, along with rate constants of the various species of clathrate ice particles and radiative transfer of the solar input in the UV, visible and near-IR intervals. The opacity of the circumnuclear dust is projected to be an order of magnitude greater than previous estimates, which severely impacts the potential visibility of the nucleus to the cameras of the flyby satellites.

Marconi, M. L.↗

NASA NTRS1993

Multiple scattering effects on the Linear Depolarization Ratio (LDR) measured during CaPE by a Ka-band air-borne radar

Air-borne radar measurements of thunderstorms were made as part of the CaPE (Convection and Precipitation/Electrification) experiment in Florida in July 1991. The radar has two channels, X-band (10 GHz) and Ka-band (34.5 GHz), and is capable of measuring cross-polarized returns as well as co-polarized returns. In stratiform rain, the cross-polarized components can be observed only at the bright band region and from the surface reflection. The linear depolarization ratios (LDR's) measured at X-band and Ka-band at the bright band are nearly equal. In convective rain, however, the LDR in Ka-band often exceeds the X-band LDR by several dB, and sometimes by more than 10 dB, reaching LDR values of up to -5 dB over heavy convective rain. For randomly oriented hydrometeors, such high LDR values cannot be explained by single scattering from non-spherical scattering particles alone. Because the LDR by single backscatter depends weakly on the wavelength, the difference between the Ka-band and X-band LDR's suggests that multiple scattering effects prevail in the Ka-band LDR. In order to test this inference, the magnitude of the cross-polarized component created by double scattering was calculated using the parameters of the airborne radar, which for both frequencies has beamwidths of 5.1 degrees and pulse widths of 0.5 microsecond. Uniform rain beyond the range of 3 km is assumed.

Iguchi, Toshio↗

NASA NTRS1975

A three-parameter analytic phase function for multiple scattering calculations

A very simple procedure has been developed to fit the first three moments of an actual phase function with a three-parameter analytic phase function. The exact Legendre polynomial decomposition of this function is known which makes it quite suitable for multiple scattering calculations. The use of this function can be expected to yield excellent flux values at all depths within a medium. Since it is capable of reproducing the glory, it can be used in synthetic spectra computations from planetary atmospheres. Accurate asymptotic radiance values can also be achieved as long as the single scattering albedo is not less than 0.9.

Kattawar, G. W.↗

NASA NTRS1987

Hydrogen Balmer alpha intensity distributions and line profiles from multiple scattering theory using realistic geocoronal models

The H Balmer alpha nightglow is investigated by using Monte Carlo models of asymmetric geocoronal atomic hydrogen distributions as input to a radiative transfer model of solar Lyman-beta radiation in the thermosphere and atmosphere. It is shown that it is essential to include multiple scattering of Lyman-beta radiation in the interpretation of Balmer alpha airglow data. Observations of diurnal variation in the Balmer alpha airglow showing slightly greater intensities in the morning relative to evening are consistent with theory. No evidence is found for anything other than a single sinusoidal diurnal variation of exobase density. Dramatic changes in effective temperature derived from the observed Balmer alpha line profiles are expected on the basis of changing illumination conditions in the thermosphere and exosphere as different regions of the sky are scanned.

Anderson, D. E., Jr.↗

NASA NTRS1977

Multiple scattering in reflection nebulae. I - A Monte Carlo approach. II - Uniform plane-parallel nebulae with foreground stars. III - Nebulae with embedded illuminating stars

A method for calculating the surface brightness distribution on a plane-parallel reflection nebula of uniform density illuminated by a star located either in front of, behind, or arbitrarily inside the scattering medium is proposed. The Monte Carlo technique is used to find solutions to the radiative transfer problem. The scattering properties of the nebular particles are parameterized by the albedo for single scattering and a three-parameter analytic phase function. Calculations are then presented for the surface brightness distribution across the face of such nebulae with (1) a foreground star and (2) immersed stars. The calculations include the full effects of multiple scattering, are independent of a particular assumed grain material or size distribution, and are applicable to any wavelength region for which observations can be obtained.

Witt, A. N.↗

NASA NTRS1982

The effects of isotropic multiple scattering and surface albedo on the photochemistry of the troposphere

The present study is believed to be the first investigation which combines a detailed tropospheric photochemical model with a radiative code that realistically considers the important physical processes in the cloudless troposphere which control the transfer of incoming solar radiation. It is found in most cases that the inclusion of the multiple scattering code significantly alters the photolytic reaction frequencies. This in turn alters the vertical distribution of some key tropospheric species. In the case of ozone a decrease was found, while O(1D) and OH showed increased concentrations. The increases are especially evident for the species which are highly dependent on photolysis processes that occur shortward of about 320 nm. The photolysis frequencies for ozone photolysis calculated with the Anderson-Meier model are in general in excellent agreement with recent measurements

Augustsson, T. R.↗

NASA NTRS1992

Adaptation of the University of Wisconsin High Spectral Resolution Lidar for Polarization and Multiple Scattering Measurements

A new implementation of the High Spectral Resolution Lidar (HSRL) in an instrument van which allows measurements during field experiments is described. The instrument was modified to provide measurements of depolarization. In addition, both the signal amplitude and depolarization variations with receiver field of view are simultaneously measured. These modifications allow discrimination of ice clouds from water clouds and observation of multiple scattering contributions to the lidar return.

Eloranta, E. W.↗