Showing papers on "Radiative transfer published in 1988"

Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media.

Abstract: The transfer of monochromatic radiation in a scattering, absorbing, and emitting plane-parallel medium with a specified bidirectional reflectivity at the lower boundary is considered. The equations and boundary conditions are summarized. The numerical implementation of the theory is discussed with attention given to the reliable and efficient computation of eigenvalues and eigenvectors. Ways of avoiding fatal overflows and ill-conditioning in the matrix inversion needed to determine the integration constants are also presented.

The discrete-dipole approximation and its application to interstellar graphite grains

Abstract: The discrete dipole approximation (DDA), a flexible method for computing scattering of radiation by particles of arbitrary shape, is extended to incorporate the effects of radiative reaction and to allow for possible anisotropy of the dielectric tensor of the material. Formulas are given for the evaluation of extinction, absorption, scattering, and polarization cross sections. A simple numerical algorithm based on the method of conjugate gradients is found to provide an efficient and robust method for obtaining accurate solutions to the scattering problem. The method works well for absorptive, as well as dielectric, grain materials. Two validity criteria for the DDA are presented. The DDA is then used to compute extinction cross sections for spherical graphite grains and to calculate extinction cross sections for nonspherical graphite grains with three different geometries. It is concluded that the interstellar 2175 A extinction feature could be produced by small graphite grains which should have aspect ratios not far from unity. 35 references.

Dynamics of radiative supernova remnants

Abstract: A high-resolution numerical simulation is used to study the evolution of a SNR evolving in a homogeneous uniform medium. Emphasis is placed on the transition from the adiabatic stage to the radiative pressure-driven snowplow stage, along with the possible further establishment of a momentum-conserving snowplow state. In most cases the momentum-conserving snowplow is found to be delayed beyond the merger of the remnant with the interstellar medium. 39 references.

Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation

Abstract: The efficiency of numerical calculations is discussed for selected algorithms employing the discrete ordinate method and the truncation approximation for the solar radiative intensity in moderately thick, plane-parallel scattering atmospheres. It is found that truncation of the phase function causes a significant error in the computed intensity and the magnitude of this error depends significantly on how the intensity is retrieved from the truncated radiative transfer equation. A newly developed retrieval algorithm, the IMS- method, yields the intensity field with an error ⪅1% when the number of discrete path is as small as 10 in the hemisphere for aerosol-laden atmospheres with optical thickness ⪅1.

Exact Rayleigh scattering calculations for use with the Nimbus-7 Coastal Zone Color Scanner

Abstract: For improved analysis of Coastal Zone Color Scanner (CZCS) imagery, the radiance reflected from a planeparallel atmosphere and flat sea surface in the absence of aerosols (Rayleigh radiance) has been computed with an exact multiple scattering code, i.e., including polarization. The results indicate that the single scattering approximation normally used to compute this radiance can cause errors of up to 5% for small and moderate solar zenith angles. At large solar zenith angles, such as encountered in the analysis of high-latitude imagery, the errors can become much larger, e.g.,>10% in the blue band. The single scattering error also varies along individual scan lines. Comparison with multiple scattering computations using scalar transfer theory, i.e., ignoring polarization, show that scalar theory can yield errors of approximately the same magnitude as single scattering when compared with exact computations at small to moderate values of the solar zenith angle. The exact computations can be easily incorporated into CZCS processing algorithms, and, for application to future instruments with higher radiometric sensitivity, a scheme is developed with which the effect of variations in the surface pressure could be easily and accurately included in the exact computation of the Rayleigh radiance. Direct application of these computations to CZCS imagery indicates that accurate atmospheric corrections can be made with solar zenith angles at least as large as 65 degrees and probably up to at least 70 degrees with a more sensitive instrument. This suggests that the new Rayleigh radiance algorithm should produce more consistent pigment retrievals, particularly at high latitudes.

Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method

Abstract: Radiative heat transfer in a three-dimensional participating medium was predicted using the discrete-ordinates method. The discrete-ordinates equations are formulated for an absorbing, anisotropically scattering, and re-emitting medium enclosed by gray walls. The solution strategy is discussed and the conditions for computational stability are presented. Several test enclosures are modeled. Results have been obtained for the S2, S4, S6, and S8 approximation s that correspond to 8, 24, 48, and 80 fluxes, respectively, and are compared with the exact-zone solution and the P3 differential approximation. Solutions are found for conditions that simulate absorbing media and isotropically and anisotropically scattering media. Solution accuracy and convergence are discussed for the various flux approximations. The S4, S6, and S8 solutions compare favorably with the other methods and can be used to predict radiant intensity, incident energy, and surface heat flux. A an bn B C E G / L n q r S x y z a /U,,£,TJ p a a © V Nomenclature = north-south areas, m2 = coefficients of a Legendre series = coefficients of a modified Legendre series = east-west areas, m2 = front-back areas, m2 = emissive power ( = aT4), W/m2 = incident energy, /4w/d6, W/m2 = radiant intensity, W/(m2 • Sr) = enclosure dimension, m = unit normal = heat flux, W/m2 = position vector, m = source term, W/m3 = volume of pth control volume, m3 = weight function in a direction - m (fractional area of a unit sphere) = coordinate, m = coordinate, m = coordinate, m — finite-difference weighting factor = extinction coefficient, a -f K,m~l = surface emittance = absorption coefficient, m"1 = ordinates p = cos0, £ = sin0 sin , TJ = sinG cos = outgoing direction of radiation = phase function = surface reflectance = scattering coefficient, m"1 = Boltzmann's constant, 5.669 X 1(T 8 W/(m2

The Photodissociation of CO in Circumstellar Envelopes

Abstract: The CO photodissociation rate for the unshielded ISM is calculated using recent laboratory results which confirm that photodissociation occurs by way of line absorption. A value of 2.0 x 10 to the -10th/s, an order of magnitude higher than the rate used in the past, is obtained. The new rate and a treatment of the radiative transfer and shielding are used to develop a theory for the CO abundance in the circumstellar envelopes of cool, evolved stars, and results are presented on the spatial variation of CO, C, and C(+). It is shown that these distributions play important roles in determining the observational properties of circumstellar envelopes. 29 references.

Short characteristic integration of radiative transfer problems: formal solution in two-dimensional slabs.

Abstract: A short characteristic method based on parabolic approximation of the source function is developed and applied to the solution of the two-dimensional radiative transfer problem on Cartesian meshes. The method is significantly faster for the evaluation of multidimensional radiation fields than those currently in use. Convergence as a functional of the grid resolution is discussed and linear and parabolic upwind interpolation are compared.

A simple formulation of the delta-four-stream approximation for radiative transfer parameterizations

Abstract: A systematic development of the delta-four-stream approximation for calculations of radiative fluxes in planetary atmosphere is presented. It is shown that an analytic solution for this approximation can be derived explicitly, with minimum computational effort for flux calculations. Relative accuracy checks for reflection, transmission, and absorption for numerous asymmetry factors, single-scattering albedos, optical depths, and solar zenith angles have been performed with respect to the 'exact' results computed from the adding method for radiative transfer. Overall, results from the delta-four-stream approximation yield relative accuracies within about 5 percent. This approximation is well suited to radiative transfer parameterizations involving flux and heating calculations in aerosol and cloudy atmospheres.

The GISS Global Climate-Middle Atmosphere Model. Part I: Model Structure and Climatology

Abstract: The GISS global climate model (Hansen et al.) has been extended to include the middle atmosphere up to an altitude of approximately 85 km. The model has the full array of processes used for climate research, i.e., numerical solutions of the primitive equations, calculation of radiative and surface fluxes, a complete hydrologic cycle with convective and cloud cover parameterizations, etc. In addition, a parameterized gravity wave drag formulation has been incorporated, in which gravity-wave momentum fluxes due to flow over topography, wind shear and convection are calculated at each grid box, using theoretical relationships between the grid-scale variables and expected source strengths. The parameterized waves then propagate vertically upward depending on the instantaneous wind and temperature profiles, with waves breaking at levels in which their momentum flux exceed the background saturation value. Radiative damping is also calculated, and the total momentum convergence in each layer is used to ...

Thermal Radiation in Packed and Fluidized Beds

Abstract: Etude du transfert radiatif dans les lits fluidises ou a garnissage. Presentation des techniques experimentales existantes pour la determination des proprietes radiatives. Analyse de l'interaction du rayonnement avec d'autres modes de transfert de chaleur

Three-dimensional radiation in absorbing-emitting-scattering media using the discrete-ordinates approximation

Abstract: The discrete-ordinates S 4 approximation is used to study radiative transfer in three-dimensional rectangular enclosures containing an absorbing-emitting-scattering medium. The S 4 approximation is evaluated by comparison with the zone method and the spherical-harmonics P 3 approximation.

Radiative transfer in vegetation canopies with anisotropic scattering

Abstract: The governing equation and various leaf models for photon transport in vegetation canopies that scatter anisotropically are presented. For idealized leaf-angle distributions and for simple canopy scattering models, the general transport equation and its azimuthal average are shown to reduce to standard forms encountered in radiative transfer and particle transport problems. In general, however, standard transport descriptions are not directly applicable to canopy problems. A realistic anisotropic and non-rotationally invariant scattering transfer function is examined and exact scattering models are derived. A variant of the discrete- ordinates method is then proposed for solving the canopy transport equation numerically. Finally, numerical results for a variety of agricultural canopies are compared with various theoretical and measured results.

Predicting Radiative Transfer in Axisymmetric Cylindrical Enclosures Using the Discrete Ordinates Method

Abstract: Radiation codes have been developed based on the S 2 and S 4 discrete ordinates approximations which involve solving the radiation transport equation in 4 and 12 directions, respectively. Evaluation of the codes against exact numerical solutions and experimental data show that both these approximations predict radiative fluxes with acceptable accuracy. The models are also evaluated treating them as part of an overall predictive scheme for pulverized coal combustion. The comparative importance of the various input parameters on the model predictions is evaluated via a detailed sensitivity study based on Fourier analysis technique. This analysis shows that the predictions arc most sensitive to the particle number densities and temperatures, while little sensitivity to the absorption and scattering efficiencies is detected.

Parametric Hurricane Wave Prediction Model

Abstract: A spectral wave model based on a numerical solution of the radiative transfer equation is used to create a synthetic data base on wave conditions within hurricanes. The results indicate that both the velocity of forward movement and maximum wind velocity within the storm play an important role in determining both the magnitude of the waves generated and the spatial distribution of these waves. An equivalent fetch for hurricane wave generation that is a function of these two parameters is proposed. This concept, combined with the standard JONSWAP fetch-limited growth relationships, provides a simple means for estimating wave conditions within hurricanes.

Predicting Radiative Transfer in Rectangular Enclosures Using the Discrete Ordinates Method

Abstract: Discrete ordinates solutions of the radiative transfer equation in two-and three-dimensional rectangular enclosures containing absorbing-emitting-scattering media have been obtained using S2, Se, Sg and Sg, approximations. Evaluation against exact analytical and numerical solutions show that while all of these approximations provide acceptable predictions of the radiation fluxes in twodimensional enclosures, use of the higher order (higher than S1,) approximations is not justified due to substantial increase in computational time and negligible improvement in the accuracy of the predictions. However, for three-dimensional enclosures, the 52 approximation is grossly in error. S1 S1) and S5, approximations predict wall heat fluxes and the temperatures of the medium accurately in these enclosures, but, once again, S4, approximation is shown to be adequate. A study of the sensitivity of the predicted net heat absorption by the walls to the dimensions of the system, and radiative properties of the medium and t...

Improved Methods for the Measurement and Analysis of Stellar Magnetic Fields

Abstract: The paper presents several improved methods for the measurement of magnetic fields on cool stars which take into account simple radiative transfer effects and the exact Zeeman patterns. Using these methods, high-resolution, low-noise data can be fitted with theoretical line profiles to determine the mean magnetic field strength in stellar active regions and a model-dependent fraction of the stellar surface (filling factor) covered by these regions. Random errors in the derived field strength and filling factor are parameterized in terms of signal-to-noise ratio, wavelength, spectral resolution, stellar rotation rate, and the magnetic parameters themselves. Weak line blends, if left uncorrected, can have significant systematic effects on the derived magnetic parameters, and thus several methods are developed to compensate partially for them. The magnetic parameters determined by previous methods likely have systematic errors because of such line blends and because of line saturation effects. Other sources of systematic error are explored in detail. These sources of error currently make it difficult to determine the magnetic parameters of individual stars to better than about + or - 20 percent.

Spontaneous and stimulated emission from quasifree electrons

Abstract: This article presents a unified formulation and review of an extensive class of radiation effects and devices based on free or quasifree electrons. The effects and devices reviewed include slow-wave radiators [such as \ifmmode \check{C}\else \v{C}\fi{}erenkov, Smith-Purcell, and TWT (traveling-wave tube) effects and devices], periodic bremsstrahlung radiators [such as undulator radiation, magnetic bremsstrahlung FEL's (free-electron lasers), and coherent bremsstrahlung in the crystal lattice], and transverse-binding radiators [such as the CRM (cyclotron resonance maser) and channeling radiation]. Starting from a general quantum-electrodynamic model, both quantum and classical effects and operating regimes of these radiation devices are described. The article provides a unified physical description of the interaction kinematics, and presents equations for the characterization of spontaneous and stimulated radiative emission in these various effects and devices. Universal relations between the spontaneous and stimulated emission parameters are revealed and shown to be related (in the quantum limit) to Einstein relations for atomic radiators and (in the classical limit) to the relations derived by Madey for magnetic bremsstrahlung FEL for on-axis radiative emission. Examples for the application of the formulation are given, estimating the feasibility of channeling radiation x-ray laser and optical regime Smith-Purcell FEL, and deriving the gain equations of magnetic bremsstrahlung FEL and CRM for arbitrary electron propagation direction, structure (wiggler) axis, and radiative emission angle.

Accurate calculated tabulations of IR and Raman CO 2 line broadening by CO 2 , H 2 O, N 2 , O 2 in the 300–2400-K temperature range

Abstract: Pressure-broadening coefficients for 12C16O2 lines have been calculated with a recent model derived from the Robert and Bonamy approach which leads to more accurate results than the previouslyused Anderson-Tsao-Curnutte model. Systematic calculations of CO2–CO2, CO2–H2O, CO2–N2, and CO2–O2 broadening coefficients in the 300–2400-K temperature range are presented. The results are suitable for both IR and Raman lines and should be useful for spectra calculations. Tabulations of the broadening coefficients are given together with simple analytical expressions for their rotational quantum number and temperature dependences.

Energy branching in the Io plasma torus: The failure of neutral cloud theory

Abstract: Model calculations are used to explore the energy source characteristics of the energy branching of the hot Io plasma torus. It is assumed that the energy is derived from the kinetic energy acquired by ions created in the rotating planetary magnetic field, and that Coulomb collisions with the electron gas control the flow of energy to the ionizing and radiative processes. The results show that neutral cloud theory is qualitatively inadequate. It is shown that neutral cloud theory can only support a dominantly singly ionized system (at the measured electron densities in the plasma torus) and that it fails to predict observed plasma properties relative to variations in number density.

Interference coefficients for overlapping oxygen lines in air

Abstract: Interference coefficients describe the non-Lorentzian effect that arises as pressure broadening causes lines to overlap. These coefficients, one for each line, are at moderate pressures related linearly to absorption and dispersion. They are determined here for the 5-mm wavelength oxygen lines broadened by air. The method includes four a priori constraints on off-diagonal elements of the relaxation matrix, which produce the interference effect: (1) detailed balance; (2) intra-branch submatrices are assumed to be identical; (3) coupling between the + and - branches is ignored; (4) coupling between the (positive-frequency) resonances and the nonresonant and negative-resonant branches is represented by a small bias term in the interference coefficients. The linear equations relating measured dispersion to the interference coefficients are solved by the Twomey-Tikhonov method, which minimizes a cost function, subject to the condition of constant measurement-error variance. The cost function is chosen to minimize the variation of elements along diagonals of the intra-branch relaxation submatrix. Implications for atmospheric radiative transfer are briefly discussed.