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Benjamin M. Herman

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Benjamin M. Herman and Farid F. Abraham

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Benjamin M. Herman and Douglas N. Yarger

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A method of estimating the vertical distribution of ozone by inverting the equation of radiative transfer is presented. The method allows for all orders of scattering as well as polarization of the diffusely reflected sunlight. The information content of the reflected sunlight as a function of observation angle is examined for the case where perfect measurements are assumed, and also for the case where a 1% random error is introduced into the measurements. Inversion results utilizing simulated satellite measurements are presented for several different ozone soundings.

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Derek D. Feng and Benjamin M. Herman

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The Global Positioning System/Meteorology (GPS/MET) project is an active satellite-to-satellite remote sensing experiment using the radio occultation technique. Due to the atmospheric index of refraction and gradient of the index of refraction, GPS signals propagate through the earth’s atmosphere along a slightly curved path and with slightly retarded speeds. When these signals arrive at a receiver aboard a low earth orbit satellite, the receiver records an excess phase delay compared with the phase delay of a straight line propagation in a vacuum. Using the Abel integral equations, the phase delay rates with time can be converted into the atmospheric index of refraction profile; then, using the hydrostatic equation, the pressure and temperature profiles may be derived.

This paper describes the principles of the GPS/MET occultation experiment and the detailed data analysis procedure. Data smoothing technique and error analysis are also discussed. Some GPS/MET intermediate and final retrieval results, such as ray bending angle and temperature and pressure profiles, are presented for illustration. Although random noise in the GPS/MET measurements leads to an uncertainty of ∼0.1–0.3 K in the retrieved temperatures, comparisons of the GPS/MET retrieval results with radiosonde measurements, other remote sensing observations, and numerical analyses show that without the multipath corrections the GPS/MET temperature profiles accurate to within 1°–2°C can be obtained from ∼5–7 to ∼40 km above the ground. Despite the fact that a few outstanding problems in the GPS/MET data retrievals remain to be addressed, overall the GPS/MET occultation method has been demonstrated to be capable of producing accurate, all-weather, round-the-clock, global refractive index, density, pressure, and temperature profiles of the troposphere and stratosphere.

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Benjamin M. Herman and Douglas N. Yarger

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The effects of multiple scattering on the heating rates in the ozone layer are investigated. Computations are performed for two wavelengths, one rather highly absorbing, λ=3112 Å, and one rather weakly absorbing, λ=3323 Å, and for three solar elevation angles. These results are compared with heating rates computed on the basis of a Beer's law type of exponential absorption, neglecting all scattering. It is shown that, at the weakly absorbing wavelength, and for small zenith angles, the effect of scattering is such as to increase the heating rate by about 40 per cent. At the more highly absorbing wavelength, scattering effects are small and may safely be neglected.

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Benjamin M. Herman and Samuel R. Browning

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In this paper, calculations are presented of the change in reflected flux by the earth-atmosphere system in response to increases in the atmospheric aerosol loading for a range of complex indices of refraction, solar elevation angle and ground albedo. Results show that, for small values of ground albedo, the reflected solar flux may either increase or decrease with increasing aerosol loadings, depending upon the complex part of the index of refraction of the aerosols. For high ground albedos (A > 0.4), an increase in aerosol levels always results in a decrease of reflected flux (i.e., a warming of the earth-atmosphere system).

The first part of the paper concerns itself with the computational techniques employed in this study. The method employs a numerical solution to the equation of radiation transfer and is essentially a modification of an older technique used by the authors. The modifications are detailed, and comparisons with the older technique are presented.

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Benjamin M. Herman and Samuel R. Browning

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A numerical method of solving the equation of radiative transfer for a plane parallel, horizontally homogeneous medium is presented. The method is applicable for problems with nonconservative scattering as well as for conservative scattering problems. Comparison of results for the reflected and transmitted radiation from this method with existing solutions for conservative Rayleigh scattering shows that, for optical depths up to 1-0, the present scheme is accurate to within ±0.007 unit total intensity and ±1.0 per cent polarization for an incident flux of π units per unit normal area. Results are presented for the reflected and transmitted intensity and per cent polarization for optical depths 2.0 and 4.0, for a particular problem of conservative Rayleigh scattering.

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Michael D. King and Benjamin M. Herman

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A statistical technique is developed for inferring the optimum values, of the ground albedo and the effective imaginary term of the complex refractive index of atmospheric particulates. The procedure compares measurements of the ratio of the hemispheric diffuse to directly transmitted solar flux density at the earth's surface with radiative transfer computations of the same as suggested by Herman et al. (1975). A detailed study is presented which shows the extent to which the ratio of diffuse to direct solar radiation is sensitive to many of the radiative transfer parameters. Results indicate that the optical depth and size distribution of atmospheric aerosol particles are the two parameters which uniquely specify the radiation field to the point where ground albedo and index of absorption can be inferred. Varying the real part of the complex refractive index of atmospheric particulates as well as their vertical distribution is found to have a negligible effect on the diffuse-direct ratio. The statistical procedure utilizes a semi-analytic gradient search method from least-squares theory and includes a detailed error analysis.

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Benjamin M. Herman and Louis J. Battan

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Calculations of the normalized back-scattering cross-section, σb, of ice spheres surrounded by shells of liquid water have been made from an extension of the Mie theory to a two-layer model. Curves of σb as a function of the thickness of the liquid-water shell are presented for various-sized spheres for 3.21, 4.67 and 10.0 cm radiation. It is shown that, depending upon the size of the sphere and the wavelength of the incident radiation, the back-scattering may either increase or decrease as the ice acquires a liquid-water shell. For certain-sized spheres, interference phenomena, which in some instances may lower the value of σb by several orders of magnitude, are in evidence during the course of melting.Comparisons are made between the theoretical results presented here and experimental measurements of σb for melting ice spheres performed by Atlas et al (1960).

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Robert A. Rabinoff and Benjamin M. Herman

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Corrections are made to the governing equation for the integrating nephelometer as derived by Middleton. Calculations show a fortuitous partial correction of the angular truncation error for most commonly occurring distributions of atmospheric aerosols, and rather serious errors for Junge distributions with small values of v *.

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