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NASA NTRS1991

Model atmospheres and X-ray spectra of bursting neutron stars

Model atmosphere equations are derived which correspond to plane-parallel nongray atmospheres of very hot neutron stars in hydrostatic and radiative equilibrium. The nonlinear transfer equation used implements an exact photon redistribution function which precisely traces even those scattering events having large photon-electron energy exchange. The numerical results thus obtained encompass tables of the surface fluxes for 20 model atmospheres whose T(eff) ranges from 6 to 30 million K. The spectra of high gravity models are virtually identical with the blackbody spectrum shifted toward higher energies, while models approaching the Eddington limit develop a large low-energy hump.

Madej, Jerzy↗

NASA NTRS1999

Bidirectional Reflectance of Flat, Optically Thick Particulate Layers: An Efficient Radiative Transfer Solution and Applications to Snow and Soil Surfaces

We describe a simple and highly efficient and accurate radiative transfer technique for computing bidirectional reflectance of a macroscopically flat scattering layer composed of nonabsorbing or weakly absorbing, arbitrarily shaped, randomly oriented and randomly distributed particles. The layer is assumed to be homogeneous and optically semi-infinite, and the bidirectional reflection function (BRF) is found by a simple iterative solution of the Ambartsumian's nonlinear integral equation. As an exact Solution of the radiative transfer equation, the reflection function thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. Since this technique bypasses the computation of the internal radiation field, it is by far the fastest numerical approach available and can be used as an ideal input for Monte Carlo procedures calculating BRFs of scattering layers with macroscopically rough surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web at http://ww,,v.giss.nasa.gov/-crmim/brf.html and can be applied to a wide range of remote sensing, engineering, and biophysical problems. We also examine the potential effect of ice crystal shape on the bidirectional reflectance of flat snow surfaces and the applicability of the Henyey-Greenstein phase function and the 6-Eddington approximation in calculations for soil surfaces.

Mishchenko, Michael I.↗

NASA NTRS1978

Radiative transfer of X-rays in the solar corona

The problem of resonance scattering of X-ray emission lines in the solar corona is investigated. For the resonance lines of some helium-like ions, significant optical depths are reached over distances small compared with the size of typical coronal features. A general integral equation for the transfer of resonance-line radiation under solar coronal conditions is derived. This expression is in a form useful for modeling the complex three-dimensional temperature and density structure of coronal active regions. The transfer equation is then cast in a form illustrating the terms which give rise to the attenuation or enhancement of the resonance-line intensity. The source function for helium-like oxygen (O VII) under coronal conditions is computed and discussed in terms of the relative importance of scattering.

Acton, L. W.↗

NASA NTRS1978

Solar heating of the Martian dusty atmosphere

This paper examines the solar heating of the Martian atmosphere during the 1971 global dust storm observed by Mariner 9. Radiative scattering as well as absorption is included by utilizing the delta-Eddington approximation to the full radiative transfer equation. The necessary optical parameters are generated by a Mie program which uses a size distribution and a complex refractive index inferred from a number of sources, particularly from recent analyses of Mariner 9 UVS and TV observations. When uniform mixing of the dust is assumed, the solar heating per unit mass during a Martian global dust storm is remarkably uniform with height for small solar zenith angles. Heating rates may reach 80 K/day for overhead sunlight. Overall, 20% of the direct insolation is absorbed by the dust-laden atmosphere. Even optically thin widespread dust hazes may produce heating rates of several degrees Kelvin per day.

Zurek, R. W.↗

NASA NTRS1979

Diffuse reflectance of the ocean - The theory of its augmentation by chlorophyll a fluorescence at 685 nm

The radiative transfer equation is modified to include the effect of fluorescent substances and solved in the quasi-single scattering approximation for a homogeneous ocean containing fluorescent particles with wavelength independent quantum efficiency and a Gaussian shaped emission line. The results are applied to the in vivo fluorescence of chlorophyll a (in phytoplankton) in the ocean to determine if the observed quantum efficiencies are large enough to explain the enhancement of the ocean's diffuse reflectance near 685 nm in chlorophyll rich waters without resorting to anomalous dispersion. The computations indicate that the required efficiencies are sufficiently low to account completely for the enhanced reflectance. The validity of the theory is further demonstrated by deriving values for the upwelling irradiance attenuation coefficient at 685 nm which are in close agreement with the observations.

Gordon, H. R.↗

NASA NTRS1980

A model theory for the fibrous absorber. Part 1: Regular fibre arrangements

The axial propagation of sound waves in a model consisting of parallel fibers is calculated. The viscous forces and the thermal conduction are taken into account. This leads to viscous waves and to thermal waves besides the usual acoustic compression wave. The potential function for the total field near a fiber is treated as the superposition of the radiated field from the fiber itself and of the scattered fields from all the other fibers. The explicit field equations for a regular square fiber arrangement is derived and the influence of the order of symmetry of the arrangement is discussed. This leads to simplifications in the field equations and to field equations for the case of a homogeneous fiber distribution.

Mechel, F. P.↗

NASA NTRS1984

Line transfer in static and expanding spherical atmospheres

The integral-operator method is extended to line and continuum transfer calculations for static and expanding spherical radiating atmospheres. A relationship is defined between radiative transfer and the source function at particular optical depths. Linearized equations are developed for the mean intensity, monochromatic scattering, line transfer, and line transfer with absorption. Numerical solutions are obtained for each equation, as well as for background absorption and scattering, partial redistribution when the line source is frequency dependent, and line transfer in connection with the expansion velocity. Finally, a solution is found for spherical expansion in concert with partial redistribution and Doppler line broadening.

Avrett, E. H.↗

NASA NTRS1994

Fast two-stream method for computing diurnal-mean actinic flux in vertically inhomogeneous atmospheres

Based on a derivation of the two-stream daytime-mean equations of radiative flux transfer, a method for computing the daytime-mean actinic fluxes in the absorbing and scattering vertically inhomogeneous atmosphere is suggested. The method applies direct daytime integration of the particular solutions of the two-stream approximations or the source functions. It is valid for any duration of period of averaging. The merit of the method is that the multiple scattering computation is carried out only once for the whole averaging period. It can be implemented with a number of widely used two-stream approximations. The method agrees with the results obtained with 200-point multiple scattering calculations. The method was also tested in runs with a 1-km cloud layer with optical depth of 10, as well as with aerosol background. Comparison of the results obtained for a cloud subdivided into 20 layers with those obtained for a one-layer cloud with the same optical parameters showed that direct integration of particular solutions possesses an 'analytical' accuracy. In the case of the source function interpolation, the actinic fluxes calculated above the one-layer and 20-layer clouds agreed within 1%-1.5%, while below the cloud they may differ up to 5% (in the worst case). The ways of enhancing the accuracy (in a 'two-stream sense') and computational efficiency of the method are discussed.

Filyushkin, V. V.↗

NASA NTRS2011

A First-Order Radiative Transfer Model for Microwave Radiometry of Forest Canopies at L-Band

In this study, a first-order radiative transfer (RT) model is developed to more accurately account for vegetation canopy scattering by modifying the basic Tau-Omega model (the zero-order RT solution). In order to optimally utilize microwave radiometric data in soil moisture (SM) retrievals over vegetated landscapes, a quantitative understanding of the relationship between scattering mechanisms within vegetation canopies and the microwave brightness temperature is desirable. The first-order RT model is used to investigate this relationship and to perform a physical analysis of the scattered and emitted radiation from vegetated terrain. This model is based on an iterative solution (successive orders of scattering) of the RT equations up to the first order. This formulation adds a new scattering term to the . model. The additional term represents emission by particles (vegetation components) in the vegetation layer and emission by the ground that is scattered once by particles in the layer. The model is tested against 1.4-GHz brightness temperature measurements acquired over deciduous trees by a truck-mounted microwave instrument system called ComRAD in 2007. The model predictions are in good agreement with the data, and they give quantitative understanding for the influence of first-order scattering within the canopy on the brightness temperature. The model results show that the scattering term is significant for trees and modifications are necessary to the . model when applied to dense vegetation. Numerical simulations also indicate that the scattering term has a negligible dependence on SM and is mainly a function of the incidence angle and polarization of the microwave observation. Index Terms Emission,microwave radiometry, scattering, soil, vegetation.

Kurum, Mehmet↗

NASA NTRS1989

Transient radiative cooling of an absorbing and scattering cylinder

The transient cooling of an absorbing, emitting, and scattering cylinder is studied by using the forward integration of energy transfer equations. The analysis presented here provides cooling curves for a cylindrical region, initially at uniform temperature and then suddenly exposed to a much cooler environment. Results are presented for several optical radii and different values of the scattering albedo.

Siegel, R.↗

NASA NTRS1997

Temperature Distribution in a Composite of Opaque and Semitransparent Spectral Layers

The analysis of radiative transfer becomes computationally complex for a composite when there are multiple layers and multiple spectral bands. A convenient analytical method is developed for combined radiation and conduction in a composite of alternating semitransparent and opaque layers. The semi- transparent layers absorb, scatter, and emit radiation, and spectral properties with large scattering are included. The two-flux method is used, and its applicability is verified by comparison with a basic solution in the literature. The differential equation in the two-flux method Is solved by deriving a Green's function. The solution technique is applied to analyze radiation effects in a multilayer zirconia thermal barrier coating with internal radiation shields for conditions in an aircraft engine combustor. The zirconia radiative properties are modeled by two spectral bands. Thin opaque layers within the coating are used to decrease radiant transmission that can degrade the zirconia insulating ability. With radiation shields, the temperature distributions more closely approach the opaque limit that provides the lowest metal wall temperatures.

Siegel, Robert↗

NASA NTRS2003

The Role of Analytic Methods in Computational Aeroacoustics

As air traffic grows, annoyance produced by aircraft noise will grow unless new aircraft produce no objectionable noise outside airport boundaries. Such ultra-quiet aircraft must be of revolutionary design, having unconventional planforms and most likely with propulsion systems highly integrated with the airframe. Sophisticated source and propagation modeling will be required to properly account for effects of the airframe on noise generation, reflection, scattering, and radiation. It is tempting to say that since all the effects are included in the Navier-Stokes equations, time-accurate CFD can provide all the answers. Unfortunately, the computational time required to solve a full aircraft noise problem will be prohibitive for many years to come. On the other hand, closed form solutions are not available for such complicated problems. Therefore, a hybrid approach is recommended in which analysis is taken as far as possible without omitting relevant physics or geometry. Three examples are given of recently reported work in broadband noise prediction, ducted fan noise propagation and radiation, and noise prediction for complex three-dimensional jets.

Farassat, F.↗

NASA NTRS2010

A First-Order Radiative Transfer Model for Microwave Radiometry of Forest Canopies at L-Band

In this study, a new first-order radiative transfer (RT) model is developed to more accurately account for vegetation canopy scattering by modifying the basic r-co model (the zero-order RT solution). In order to optimally utilize microwave radiometric data in soil moisture (SM) retrievals over moderately to densely vegetated landscapes, a quantitative understanding of the relationship between scattering mechanisms within vegetation canopies and the microwave brightness temperature is desirable. A first-order RT model is used to investigate this relationship and to perform a physical analysis of the scattered and emitted radiation from vegetated terrain. The new model is based on an iterative solution (successive orders of scattering) of the RT equations up to the first order. This formulation adds a new scattering term to the i-w model. The additional term represents emission by particles (vegetation components) in the vegetation layer and emission by the ground that is scattered once by particles in the layer. The new model is tested against 1.4 GHz brightness temperature measurements acquired over deciduous trees by a truck-mounted microwave instrument system called ComRAD in 2007. The model predictions are in good agreement with the data and they give quantitative understanding for the influence of first-order scattering within the canopy on the brightness temperature. The model results show that the scattering term is significant for trees and modifications are necessary to the T-w model when applied to dense vegetation. Numerical simulations also indicate that the scattering term has a negligible dependence on SM and is mainly a function of the angle and polarization of the microwave observation.

Kurum, Mehmet↗

NASA NTRS1992

Simulation of space measurements of vegetation canopy bidirectional reflectance factors

A vegetation canopy receives both monodirectional and scattered radiation which is then reflected back into the atmosphere according to its bidirectional reflectance distribution function (BRDF). Remote measurements are typically the angular and spectral distributions of radiations exiting the atmosphere. The evaluation of vegetation canopy bidirectional reflectance factors requires a numerical solution of the canopy radiative transfer equation. A horizontally homogeneous vegetation canopy, of finite physical depth, filled densely with small leaves and bounded by a flat Lambertian ground surface is considered. The canopy is illuminated spatially uniformly by monodirectional radiation. The scattered intensity distribution emerging at the top of the canopy in all directions in the upper hemisphere is evaluated. The magnitude, sign and angular distribution of atmospheric effects are wavelength specific and depend on the composition of the atmosphere. The net atmospheric effect is positive (negative) at the red (near-infrared) wavelength due to strong scattering (absorption) in the atmosphere. The angular distribution of these effects is bowl-shaped. Thus, off-nadir remote observations, especially at shorter wavelengths, are most affected by atmospheric perturbations.

Myneni, R. B.↗

NASA NTRS1993

Radiation/convection coupling in rocket motor and plume analysis

A method for describing radiation/convection coupling to a flow field analysis was developed for rocket motors and plumes. The three commonly used propellant systems (H2/O2, RP-1/O2, and solid propellants) radiate primarily as: molecular emitters, non-scattering small particles (soot), and scattering larger particles (Al2O3), respectively. For the required solution, the divergence of the radiation heat flux was included in the energy equation, and the local, volume averaged intensity was determined by a solution to the radiative transfer equation. A rigorous solution to this problem is intractable, therefore, solution methods which use the ordinary and improved differential approximation were developed. This radiation model was being incorporated into the FDNS code, a Navier-Stokes flowfield solver for multiphase, turbulent combusting flows.

Saladino, A. J.↗

NASA NTRS2006

Heat Transfer In High-Temperature Multilayer Insulation

The combined radiation/conduction heat transfer in high-temperature multilayer insulations for typical reentry of reusable launch vehicles from low Earth orbit was investigated experimentally and numerically. The high-temperature multilayer insulation investigated consisted of gold-coated reflective foils separated by alumina fibrous insulation spacers. The steady-state heat transfer through four multilayer insulation configurations was investigated experimentally over the temperature range of 300-1300 K and environmental pressure range of 1.33 10(exp -5)-101.32 kPa. It was shown that including the reflective foils reduced the effective thermal conductivity compared to fibrous insulation sample at 1.5 times the density of the multilayer sample. A finite volume numerical model was developed to solve the governing combined radiation/conduction heat transfer equations. The radiation heat transfer in the fibrous insulation spacers was modeled using the modified two-flux approximation assuming anisotropic scattering and gray medium. The numerical model was validated by comparison with steady-state experimental data. The root mean square deviation between the predicted and measured effective thermal conductivity of the samples was 9.5%.

Daryabeigi, Kamran↗

NASA NTRS1973

Unsteady, combined radiation and conduction in an absorbing, scattering, and emitting medium.

The transient cooldown of a gray, absorbing, isotropic scattering, emitting, and conducting medium bounded by gray, diffusely emitting and reflecting parallel plates is considered. Numerical solutions are obtained for the initial boundary-value problem with a discontinuous decrease in temperature at one boundary. The quasi-steady equation of radiative transfer is solved using Gaussian quadrature and a matrix eigenvector technique together with explicit numerical solution of the unsteady energy equation. Temperature and energy flux distributions are presented for variations of optical thickness, boundary emissivity, albedo, and conduction-radiation parameter.

Weston, K. C.↗

NASA NTRS1975

Remote monitoring of environmental particulate pollution - A problem in inversion of first-kind integral equations

The determination of the microstructure, chemical nature, and dynamical evolution of scattering particulates in the atmosphere is considered. A description is given of indirect sampling techniques which can circumvent most of the difficulties associated with direct sampling techniques, taking into account methods based on scattering, extinction, and diffraction of an incident light beam. Approaches for reconstructing the particulate size distribution from the direct and the scattered radiation are discussed. A new method is proposed for determining the chemical composition of the particulates and attention is given to the relevance of methods of solution involving first kind Fredholm integral equations.

Fymat, A. L.↗