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  • Author or Editor: J. A. Weinman x
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J. A. Weinman

Abstract

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).

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J. A. Weinman
and
M-J. Kim

Abstract

Spaceborne millimeter-wave radiometric measurements offer the potential to observe snowfall at high latitudes. A spaceborne W-band cloud radar on CloudSat has been able to observe snow. There is thus a need for a relatively simple representation of millimeter-wave scattering parameters of snow that can be incorporated into algorithms to retrieve snowfall from remotely sensed millimeter-wave brightness temperature measurements and for computing the millimeter-wave backscatter phase function of randomly oriented aggregates of ice prisms or columns.

The extinction coefficients, asymmetry factors, and backscatter phase functions describing scattering by randomly oriented aggregates of elongated cylinders were computed from the discrete dipole approximation. These parameters were also computed by means of a T-matrix model applied to single blunt cylinders by employing a phase delay that only depended on the frequency and the ratio of the volume to the projected area of the cylindrical aggregates. These scattering parameters were fitted by empirical analytical functions that only depended on that phase delay. This permitted consideration of numerous aggregate shapes with far less computational effort than that required by the discrete dipole approximation.

The results of this analysis were applied to measurements of millimeter-wave extinction, radar reflectivity, and snow size distributions obtained during the SNOW-TWO field experiment conducted by the U.S. Army in 1984. Although the simultaneity of the various measurements was not well documented, the theoretical results fell within the range of measurement uncertainty. Model results of the extinction coefficient and asymmetry factor needed to compute 183-GHz brightness temperatures measured by the NOAA Advanced Microwave Sounding Unit-B (AMSU-B) radiometers are presented in the appendix.

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J. A. Weinman
and
K. Ueyoshi

Abstract

No abstracts available.

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E. P. Shettle
and
J. A. Weinman

Abstract

Eddington's approximation was employed to compute the irradiances passing through atmospheres consisting of several different, albeit internally homogeneous, layers, as a function of solar zenith angle, albedo for single scatering, the asymmetry factor of the phase function, and the albedo of the underlying surface. Results computed for a single layer atmosphere were found to agree with more exact computations within a few percent.

Irradiances within several vertically inhomogeneous three-layer model atmospheres were computed. Effects caused by the vertically inhomogeneous structure are considered. It is noted, for example, that the irradiance within an atmosphere can be greater than that incident upon the atmosphere bemuse radiation may he partially trapped within the atmosphere. The Eddington approximation affords a means to rapidly compute irradiances within realistic inhomogeneous atmospheres with an accuracy of several percent.

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J. A. Weinman
and
P. N. Swarztrauber

Abstract

The equation of radiative transfer was approximated by the method of Giovanelli to provide the albedo of an externally illuminated, plane-parallel striated medium. The medium was assumed to consist of isotropic scatterers with a scattering coefficient per unit depth of
01lx
that depended periodically on one horizontal coordinate. The dependence of the albedo on the angle of incidence of the solar radiance, the mean optical thickness, and the wavelength and amplitude of the striations is presented for media with κ1/&kappa0 = 0.1 and 0.9.
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K. E. Kunkel
and
J. A. Weinman

Abstract

Monte Carlo techniques are utilized to compute monostatic lidar returns from turbid atmospheres. Examples are evaluated for thick hazes, clouds, fogs and rain. The effects of multiple scattering are significant in the cases considered. Results are compared with those obtained by Eloranta (1972) to describe doubly scattered lidar returns and the agreement is satisfactory, provided that higher orders of multiple scattering are negligible.

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J. H. Joseph
,
W. J. Wiscombe
, and
J. A. Weinman

Abstract

This paper presents a rapid yet accurate method, the “delta-Eddington” approximation, for calculating monochromatic radiative fluxes in an absorbing-scattering atmosphere. By combining a Dirac delta function and a two-term approximation, it overcomes the poor accuracy of the Eddington approximation for highly asymmetric phase functions. The fraction of scattering into the truncated forward peak is taken proportional to the square of the phase function asymmetry factor, which distinguishes the delta-Eddington approximation from others of similar nature. Comparisons of delta-Eddington albedos, transnmissivities and absorptivities with more exact calculations reveal typical differences of 0–0.022 and maximum differences of 0.15 over wide ranges of optical depth, sun angle, surface albedo, single-scattering albedo and phase function asymmetry. Delta-Eddington fluxes are in error, on the average, by no more than 0.5%0, and at the maximum by no more than 2% of the incident flux. This computationally fast and accurate approximation is potentially of utility in applications such as general circulation and climate modelling.

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K. E. Kunkel
,
E. W. Eloranta
, and
J. A. Weinman

Abstract

Procedures are described for the analysis of lidar data to remotely measure 1) spectra of aerosol density fluctuations, 2) radial and transverse components of the mean wind and turbulent fluctuations of the transverse component of the wind velocity in the convective boundary layer, and 3) the kinetic energy dissipation rate. Results were compared with independent data obtained with a bivane anemometer installed at the 70 m level on a tower within the scanning sector of the lidar. Good agreement was obtained whenever the lidar data had adequate signal-to-noise characteristics (i.e., S/ greater than unity).

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J. A. Weinman
,
J. T. Twitty
,
S. R. Browning
, and
B. M. Herman

Abstract

The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical small-angle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosol-laden model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few percent.

The analytical solution to the problem which considers an aerosol-laden atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.

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W. J. Williams
,
J. N. Brooks
,
D. G. Murcray
,
F. H. Murcray
,
P. M. Fried
, and
J. A. Weinman

Abstract

Infrared emission spectra were measured in the stratosphere at various altitudes and from various zenith angles by means of a balloon-borne Czerny-Turner spectrometer. The equation of radiative transfer was applied to the radiances measured at 11.2μ to yield a concentration profile of HNO3 vapor. The resulting HNO3 concentration profile was characterized by a negligible concentration below 14 km, a maximum concentration of ∼(1.5±0.5)×1010 molecules cm−3 at ∼(19±5) km, and a diminishing concentration above these altitudes.

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