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Results for “Radiative transfer equation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13
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NASA NTRS1979

Lightman-Eardley instabilities and accretion disk thickening

After reviewing the role of Compton scattering in accretion disks around black holes, it is discussed whether Lightman-Eardley (LE) secular instabilities can trigger and maintain Pringle-Rees (PR) thermal instabilities. The radiative-transfer-equation and equation-of-state criteria for LE stability in alpha-viscosity-law disk models and dynamic viscosity criteria for more general situations is derived. On the basis of these considerations the LE instability is insufficient for inducing PR instabilities and hot thick inner regions important in accretion-disk models of compact hard X-ray sources. The density thinning due to radial velocity gradients in the accretion flow is suggested as a more likely and satisfactory mechanism.

Stoeger, W. R.↗
NASA NTRS1980

The Eddington limit and supercritical accretion. I - Time-independent calculations

Spherically symmetric, steady state accretion of an ionized hydrogen plasma onto a neutron star is considered for accretion rates which exceed a critical rate at which the Eddington limiting luminosity is produced. The coupled hydrodynamic and frequency integrated, radiative transfer equations are solved for accretion rates up to 10 times the nominal limit. Steady state solutions are presented that imply a multiplicity of different luminosity solutions for a single accretion rate in this 'supercritical' regime.

Burger, H. L.↗
NASA NTRS1980

Outer atmospheres of cool stars. VI - Models for Epsilon Eridani based on IUE spectra of C II, Mg II, Si II, and Si III

Observations of the ultraviolet line spectrum of the active chromosphere star, Epsilon Eridani, obtained with the IUE satellite have been analyzed. The coupled statistical equilibrium and radiative transfer equations for the prominent transitions of C II, Mg II, Si II, and Si III. A satisfactory fit to all of the line strengths can be achieved with a model similar to that recently proposed to explain bright points on the quiet sun. A surface pressure at the base of the transition region of 0.5 dynes/sq cm is derived, which is a factor of 3 higher than the quiet sun value, but a factor of 3 smaller than predicted by scaling laws, assuming a conductively heated stellar transition region. It is found that the surface fluxes of the C II 1334, 1335 and Si III 1892 emission lines are good diagnostics of pressure at the base of the transition region, but line ratio techniques using the 1892 line for estimating electron densities may be valid.

Simon, T.↗
NASA NTRS1981

Albedo and flux extinction coefficient of impure snow for diffuse shortwave radiation

Impurities enter a snowpack as a result of fallout of scavenging by falling snow crystals. Albedo and flux extinction coefficient of soot contaminated snowcovers were studied using a two stream approximation of the radiative transfer equation. The effect of soot was calculated by two methods: independent scattering by ice grains and impurities and average refractive index for ice grains. Both methods predict a qualitatively similar effect of soot; the albedo is decreased and the extinction coefficient is increased compared to that for pure snow in the visible region; the infrared properties are largely unaffected. Quantitatively, however, the effect of soot is more pronounced in the average refractive index method. Soot contamination provides a qualitative explanation for several snow observations.

Choudhury, B. J.↗
NASA NTRS1981

Small-angle approximation to the transfer of narrow laser beams in anisotropic scattering media

The broadening and the signal power detected of a laser beam traversing an anisotropic scattering medium were examined using the small-angle approximation to the radiative transfer equation in which photons suffering large-angle deflections are neglected. To obtain tractable answers, simple Gaussian and non-Gaussian functions for the scattering phase functions are assumed. Two other approximate approaches employed in the field to further simplify the small-angle approximation solutions are described, and the results obtained by one of them are compared with those obtained using small-angle approximation. An exact method for obtaining the contribution of each higher order scattering to the radiance field is examined but no results are presented.

Box, M. A.↗
NASA NTRS1980

Investigation of multiple scattering effects in aerosols

The results are presented of investigations on the various aspects of multiple scattering effects on visible and infrared laser beams transversing dense fog oil aerosols contained in a chamber (4' x 4' x 9'). The report briefly describes: (1) the experimental details and measurements; (2) analytical representation of the aerosol size distribution data by two analytical models (the regularized power law distribution and the inverse modified gamma distribution); (3) retrieval of aerosol size distributions from multispectral optical depth measurements by two methods (the two and three parameter fast table search methods and the nonlinear least squares method); (4) modeling of the effects of aerosol microphysical (coagulation and evaporation) and dynamical processes (gravitational settling) on the temporal behavior of aerosol size distribution, and hence on the extinction of four laser beams with wavelengths 0.44, 0.6328, 1.15, and 3.39 micrometers; and (5) the exact and approximate formulations for four methods for computing the effects of multiple scattering on the transmittance of laser beams in dense aerosols, all of which are based on the solution of the radiative transfer equation under the small angle approximation.

Deepak, A.↗
NASA NTRS1981

Verification of reflectance models in turbid waters

Inherent optical parameters of very turbid waters were used to evaluate existing water reflectance models. Measured upwelling radiance spectra and Monte Carlo simulations of the radiative transfer equations were compared with results from models based upon two flow, quasi-single scattering, augmented isotropic scattering, and power series approximation. Each model was evaluated for three separate components of upwelling radiance: (1) direct sunlight; (2) diffuse skylight; and (3) internally reflected light. Limitations of existing water reflectance models as applied to turbid waters and possible applications to the extraction of water constituent information are discussed.

Tanis, F. J.↗
NASA NTRS1980

Introduction to ocean optics

The fundamental inherent and apparent optical properties of natural waves are reviewed and relationships between these properties, as related through the radiative transfer equation, are examined. Applications of ocean optics to geophysics, biological oceanography, and ocean remote sensing are discussed.

Gordon, H. R.↗
NASA NTRS1981

The albedo of snow for partially cloudy skies

The albedo of snow is defined as the ratio of reflected to incident solar energy, and it is an important parameter in the earth's radiation budget analysis and in the study of snowpack's thermal conditions. An approximate model for calculating the incident spectral flux for partially cloudy skies is presented. The input parameters for the calculation are atmospheric precipitable water, turbidity, ozone content, surface pressure, the optical thickness of clouds, and the grain size of snow crystals. The spectral snow reflectance model considers both specular surface reflection and volumetric multiple scattering. The surface reflection is calculated by using a crystal-shape-dependent bidirectional reflectance distribution function; the volumetric multiple scattering is calculated by using a crystal-size-dependent approximate solution in the radiative transfer equation. The model yields spectral and integrated solar flux and snow reflectance as a function of solar elevation and fractional cloud-cover. The illustrative insolation and albedo values were obtained from spectral reflectance and incident flux for representative parameters of Antarctic coastal regions. A simple relationship between grain size and the overcast albedo was obtained. For a set of grain size and shape, the albedo as a function of solar elevation and fractional cloud cover was tabulated.

Choudhury, B. J.↗
NASA NTRS1981

Bidirectional reflectance spectroscopy. I - Theory

An approximate analytic solution is derived for the radiative transfer equation describing particulate surface light scattering, taking into account multiple scattering and mutual shadowing. Analytical expressions for the following quantities are found: bidirectional reflectance, radiance coefficient and factor, the normal, Bond, hemispherical, and physical albedos, integral phase function and phase integral, and limb-darkening profile. Scattering functions for mixtures can be calculated, as well as corrections for comparisons of experimental transmission or reflection spectra with observational planetary spectra. The theory should be useful for the interpretation of reflectance spectroscopy of laboratory surfaces and the photometry of solar system objects.

Hapke, B.↗
NASA NTRS1981

Radiative transfer theory for active remote sensing of a layer of small ellipsoidal scatterers

The radiative transfer theory is applied within the Rayleigh approximation to calculate the backscattering cross section of a layer of randomly positioned and oriented small ellipsoids. The orientation of the ellipsoids is characterized by a probability density function of the Eulerian angles of rotation. The radiative transfer equations are solved by an iterative approach to first order in albedo. In the half space limit the results are identical to those obtained via the approach of Foldy's and distorted Born approximation. Numerical results of the theory are illustrated using parameters encountered in active remote sensing of vegetation layers. A distinctive characteristic is the strong depolarization shown by vertically aligned leaves.

Tsang, L.↗
NASA NTRS1981

Radiative transfer theory for active remote sensing of a homogeneous layer containing spherical scatterers

The radiative transfer theory with a Rayleigh scattering model is used to study the effect of volume scattering for active microwave remote sensing of low-loss and scattering dominant areas by obtaining backscattering cross sections through iterative and numerical approaches. The iterative approach gives closed form solutions which are valid when the effect of scattering is small. The depolarization of the backscattered power is shown to be a second-order effect. For the general cases, a numerical approach is used to solve the radiative transfer equations. The theoretical results are compared and illustrated for the various cases.

Shin, R. T.↗
NASA NTRS1981

N-stream approximations to radiative transfer

Schuster's two-stream approximation (1905) is first derived from Chandrasekhar's radiative transfer equation (1950), and then extended to an arbitrary number of streams. The resulting technique for solving the transfer function similar to the discrete ordinate and spherical harmonic methods, is useful for modeling atmospheres with complicated phase functions and moderate optical depths. The resulting n coupled linear differential equations are simple and consume less computer time than other approximations, yet have the same required accuracy. The approximation is also flexible with respect to the choice of patch functions, and no approximations are made on the form of the phase function, other than its expansion into Legendre polynomials. A four-stream approximation is evaluated for a Henyey-Greenstein phase function with an asymmetry factor equal to 0.5.

Acquista, C.↗
NASA NTRS1982

A climate index derived from satellite measured spectral infrared radiation

The vertical infrared radiative emitting structure (VIRES) climate index, based on radiative transfer theory and derived from the spectral radiances typically used to retrieve temperature profiles, is introduced. It is assumed that clouds and climate are closely related and a change in one will result in a change in the other. The index is a function of the cloud, temperature, and moisture distributions. It is more accurately retrieved from satellite data than is cloudiness per se. The VIRES index is based upon the shape and relative magnitude of the broadband weighting function of the infrared radiative transfer equation. The broadband weighting curves are retrieved from simulated satellite infrared sounder data (spectral radiances). The retrieval procedure is described and the error error sensitivities of the method investigated. Index measuring options and possible applications of the VIRES index are proposed.

Abel, M. D.↗
NASA NTRS1981

Radiative transfer theory for passive microwave remote sensing of random media

The radiative transfer theory is applied to a random medium for the case of passive remote sensing. A general numerical solution with Gaussian quadrature method is studied. For a medium with laminar structure or a medium with cylindrical structure, closed form solutions are obtained by solving the radiative transfer equations of a two-layer random medium. Numerical results for the general case and the two limiting cases are compared.

Chuang, S. L.↗
NASA NTRS1982

Model studies of nitric oxide fluorescence in the earth's backscattered spectrum

Fluorescent emissions from nitric oxide appear imposed upon the Rayleigh backscattered spectrum of the earth's atmosphere between 250 and 300 nm in wavelength. Satellite instruments designed to monitor the global ozone distribution can routinely observe these signals although techniques for exploiting the data are not yet available. Application of a radiative transfer equation developed for an atmosphere including absorption by ozone, molecular scattering, and nitric oxide fluorescence shows the three most prominent NO emissions relative to the 250-300 nm backscattered sunlight to be the (1,4), (1,6), and (0,3) gamma bands. Analysis of the contribution function for each emission band indicates that the fluorescent signals can provide useful information on the magnitude and variability of nitric oxide between 40 and 140 km in altitude.

Frederick, J. E.↗
NASA NTRS1982

Solar reflection from a regular array of horizontally finite clouds

The reflected flux from a regular array of 2- and 3-D clouds has been computed to estimate the effect of fractional cloud cover on albedos and the solar flux available to heat the earth's surface. The broken clouds are represented by a regular array of identical cuboids for the 3-D problem and equally spaced, infinitely long, bars for the 2-D problem. A diffusion approximation to the radiative transfer equation is used to compute the fluxes leaving each face of the cloud. Interaction between clouds is simulated by assuming diffuse exitance from the cloud faces and applying angle factors to obtain modified boundary conditions on each cloud face.

Weinman, J. A.↗
NASA NTRS1982

Comparison of LANDSAT-2 and field spectrometer reflectance signatures of south Texas rangeland plant communities

The accuracy was assessed for an atmospheric correction method that depends on clear water bodies to infer solar and atmospheric parameters for radiative transfer equations by measuring the reflectance signature of four prominent south Texas rangeland plants with the LANDSAT satellite multispectral scanner (MSS) and a ground based spectroradiometer. The rangeland plant reflectances produced by the two sensors were correlated with no significant deviation of the slope from unity or of the intercept from zero. These results indicated that the atmospheric correction produced LANDSAT MSS estimates of rangeland plant reflectances that are as accurate as the ground based spectroradiometer.

Richardson, A. J.↗