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Hitzfelder, S. J.

Publications and source records attributed to Hitzfelder, S. J..

9 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Radiation in the earth's atmosphere - Its radiance, polarization, and ellipticity

A matrix operator method for a model of the real atmosphere is used to calculate the complete radiation field of the atmosphere. The radiance, direction and amount of polarization, and ellipticity are obtained at the top and bottom of the atmosphere for three values of the surface albedo (0, 0.15, 0.90) and five solar zenith angles, taking account of molecular absorption and scattering (including by ozone) together with the variation of the density of these molecules with height.

Hitzfelder, S. J.↗
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 NTRS1976

Multiple scattered radiation emerging from Rayleigh and continental haze layers. I - Radiance, polarization, and neutral points

The matrix operator method was used to calculate the polarization of radiation scattered on layers of various optical thicknesses, with results compared for Rayleigh scattering and for scattering from a continental haze. In both cases, there are neutral points arising from the zeros of the polarization of single scattered photons at scattering angles of zero and 180 degrees. The angular position of these Rayleigh-like neutral points (RNP) in the sky shows appreciable variation with the optical thickness of the scattering layer for a Rayleigh phase matrix, but only a small variation for haze L phase matrix. Another type of neutral point exists for non-Rayleigh phase functions that is associated with the zeros of the polarization for single scattering which occurs between the end points of the curve. A comparison of radiances calculated from the complete theory of radiative transfer using Stokes vectors with those obtained from the scalar theory shows that differences of the order of 23% may be obtained for Rayleigh scattering, while the largest difference found for a haze L phase function was of the order of 0.1%.

Kattawar, G. W.↗
NASA NTRS1976

Radiance, polarization, and ellipticity of the radiation in the earth's atmosphere

The complete radiation field including polarization is calculated for a model of the real atmosphere by the matrix operator method. The radiance, direction and amount of polarization, and ellipticity are obtained at the top and bottom of the atmosphere for three values of the surface albedo (0; 0.15 0.90) and five solar zenith angles. Scattering and absorption by molecules (including ozone) and by aerosols are taken into account together with the variation of the number density of these substances with height. All results are calculated for both a normal aerosol number and a distribution which is one-third of the normal amount at all heights. The calculated values show general qualitative agreement with the available experimental measurements. The position of the neutral points of the polarization in the principal plane is a sensitive indicator of the characteristics of the aerosol particles in the atmosphere, since it depends on the sign and value of the single scattered polarization for scattering angles around 20 deg and 160 deg for transmitted and reflected photons respectively.

Hitzfelder, S. J.↗
NASA NTRS1975

Multiple scattered radiation emerging from continental haze layers. 1: Radiance, polarization, and neutral points

The complete radiation field is calculated for scattering layers of various optical thicknesses. Results obtained for Rayleigh and haze scattering are compared. Calculated radiances show differences as large as 23% compared to the approximate scalar theory of radiative transfer, while the same differences are approximately 0.1% for a continental haze phase function. The polarization of reflected and transmitted radiation is given for various optical thicknesses, solar zenith angles, and surface albedos. Two types of neutral points occur for aerosol phase functions. Rayleigh-like neutral points arise from zero polarization that occurs at scattering angles of 0 deg and 180 deg. For Rayleigh phase functions, the position of these points varies with the optical thickness of the scattering layer. Non-Rayleigh neutral points are associated with the zeros of polarization which occur between the end points of the single scattering curve, and are found over a wide range of azimuthal angles.

Kattawar, G. W.↗
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 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 NTRS1971

An explicit form of the Mie phase matrix for multiple scattering calculations in the I, Q, U, and V representation

An explicit expression is obtained for the phase matrix in the I, Q, U, and V Stokes vector representation for a system containing a polydispersion of spherical particles. All of the symmetry relations derived by Hovenier using general arguments are established explicitly. Convenient algorithms are given for the computation of the phase matrix for a spherical polydispersion. Since this theory is so vitally important in radiative transfer, many researchers will need to compute these functions for realistic aerosols distributions. Therefore, results are presented for a haze L distribution so that other researchers will have a way of checking their programs which compute these quantities.

Kattawar, G. W.↗