Showing papers on "Radiative transfer published in 1975"

Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean.

Abstract: Monte Carlo simulations of the transfer of radiation in the ocean are used to compute the apparent optical properties of a flat homogeneous ocean as a function of the inherent optical properties. The data are used to find general relationships between the inherent and apparent optical properties for optical depths tau

The Simplified Exchange Approximation: A New Method for Radiative Transfer Calculations

Abstract: A new scheme for the efficient calculation of longwave radiative heating rates is proposed. Its speed and accuracy make it attractive for use in large atmospheric circulation models. The approximation suggested iswhere q is the heating rate, qe an “emissivity” heating rate calculated using the strong-line approximation and neglecting variation of line intensity with temperature, qeCTS the heating rate calculated using the cool-to-space approximation and the emissivity assumption, and qCTS the heating rate calculated by the cool-to-space approximation. Tests using a variety of soundings indicate that for both clear sky and cloudy cases the new approximation is substantially more accurate than either the emissivity or the cool-to-space approximations alone. Deviations from exact calculations are generally under 0.05 K day−1. Errors in the calculated flux at the surface are also shown to be small especially with the inclusion of a “heat from ground” term in the approximation. Some alternate schemes ...

Pure-state analysis of resonant light scattering: Radiative damping, saturation, and multiphoton effects

Abstract: A fully quantum-mechanical treatment of resonant light scattering is presented. The incident field is assumed to be described by a coherent state, and is allowed to be intense enough to cause saturation. Complete solutions are obtained for the correlated atom-field pure state vector, including multiphoton contributions of arbitrary order. The frequency spectrum of the scattered field is evaluated and is found to agree exactly with the result previously obtained by means of the quantum fluctuation-regression theorem. A derivation of the fluctuation-regression theorem and of the optical Bloch equations is given which is fully quantum mechanical and which relies upon no assumption of statistical factorization of atom and field states. The accuracy of the result found for the scattered - field spectrum is thus shown to be limited only by the assumption of the smallness of the saturated linewidth compared to the (optical) atomic resonance frequency. The one-photon approximation is analyzed in some detail. The method of adding an imaginary term to the upper-atomic-state energy is clarified, and it is shown how the vacuum and one-photon amplitudes thereby obtained may be used, within a simple and plausible iteration scheme, to construct the complete multiphoton spectrum. A variety of commonly used injection schemes and methods of representing atomic relaxation are discussed, and comparisons are made with results found by other authors. The entire analysis is performed with the aid of a canonical transformation which replaces the applied field by a $c$ number. It is thus proved quite rigorously and generally that the use of a $c$-number applied field is a fully quantum-mechanical procedure, provided only that radiation-reaction terms are retained.

The two-stream approximation in radiative transfer Including the angle of the incident radiation

Abstract: The two-stream approximation has been applied to the equation of radiative transfer to obtain two–stream models for the transfer of radiation through an optically thin plane-parallel atmosphere. The models include the dependence of the reflection and the transmission of the atmosphere on the angle of the incident radiation and on the angular dependence of the scattering phase function of the medium. The two models arise from different methods for treating the incident radiation. It is shown that the models reduce to the thin-atmosphere approximation in the limit that the optical depth of the atmosphere approaches zero. In this limit the sign of the heating caused by the presence of a scattering and absorbing layer over a reflecting surface is derived. This reveals the importance of both the zenith angle and the angular dependence of the scattering phase function. The results obtained from the two-stream models are compared with those of numerical solutions to the equation of radiative transfer. I...

Comments on the classical theory of energy transfer

Abstract: Energy transfer from an emitting molecule to an absorbing half−space is considered from the viewpoint of electromagnetic theory. The lifetime of a dipole emitter in the presence of a mirror is determined through a calculation of the complex Poynting vector in the dielectric surrounding the dipole. This method has the advantage over previous approaches to this problem in that the radiative and nonradiative components of the lifetime expression may be rigorously separated. The influence on emitter lifetime of a mirror of finite thickness is also described. A simple expression is derived describing the energy transfer rate in these layered systems. It is shown that nonradiative energy transfer results from coupling of the near field of the dipole to the surface plasmon modes in the metallic absorber. The Forster energy transfer rate law is discussed in the context of the present theory.

Radiative transfer in a plane stratified dielectric

Abstract: A model is developed for calculating radiative transfer in a stratified dielectric. This model is used to show that the reflectivity of a stratified dielectric is primarily determined by gradients in the real part of the refractive index over distances on the order of 1/10 wavelength in the medium. The effective temperature of the medium is determined by the thermodynamic temperature profile over distances of the order ?T where Im (n) dx = ?/4?

A three parameter analytic phase function for multiple scattering calculations

Abstract: A simple procedure was developed to fit the first three moments of an actual phase function with a three parameter analytic phase function. The exact Legendre Polynomial decomposition of this function is, suitable for multiple scattering calculations. The use of this function is expected to yield excellent flux values at all depths within a medium. Since it is capable of reproducing the glory, it can be used in synthetic spectra computations from planetary atmospheres. Accurate asymptotic radiance values can also be achieved as long as the single scattering albedo omega sub 0 is greater than or equal to 0.9.

Direct measurement of the radiative lifetimes of the A2Σ+ (V′ = 0) states of OH and OD

Abstract: The fluorescent decay of the A 2Σ+ (V′ = 0) state of OH and OD has been measured for N′ ? 8 for OH and N′ ? 9 for OD using pulsed dye laser excitation and at total gas pressures ? 1 mtorr. For the rotationless molecule, a radiative lifetime of 0.688 ± 0.021 μsec for OH and 0.692 ±0.021 μsec for OD was obtained, where the error bars are three standard deviations. In addition, OH exhibited a 8 ± 2% lengthening of the radiative lifetime between N′ = 1 and N′ = 8.

Solution of the comoving-frame equation of transfer in spherically symmetric flows. I. Computational method for equivalent-two-level-atom source functions.

Abstract: The equation of radiative transfer in the comoving frame makes possible an economical solution of the line formation problem in spherical atmospheres expanding with arbitrarily large velocities A stable differencing scheme and a frequency-by-frequency elimination procedure have been developed to solve the partial differential equations that describe the radiation field in the comoving frame Numerical results were obtained for a large number of illustrative models involving line formation by two-level atoms, electron scattering, and continuous absorption Selected results that simulate situations in the stellar winds of hot stars and similar objects are discussed In addition to P Cygni and other very broad profiles, extreme center-to-limb variations are obtained that show both limb darkening and limb brightening For very high velocity flows with very weak or nonexistent continuum and electron-scattering opacities, the flux profiles are very nearly symmetric about the laboratory wavelength and have shapes reminiscent of those observed in the nuclei of Seyfert galaxies Comparisons are presented between the results of Sobolev-type escape probability calculations and those obtained here The force of radiation on the gas is examined in a number of situations; the mechanism mentioned by Noerdlinger and Rybicki for the disruption of radiatively driven envelopes in planar geometriesmore » is shown to become inoperative for even slightly extended spherical systems« less

Fluorescence and energy transfer near interfaces: The complete and quantitative description of the Eu+3/mirror systems

Abstract: The classical electromagnetic description of fluorescent emission and energy transfer in the Eu+3/mirror systems is shown to be in quantitative agreement with the results of eight experimental systems studied by the fatty acid monolayer assembly technique. The emitter lifetime measured as a function of distance from the mirror(s) is found to be consistent with an isotropic spatial orientation for the emitter in all cases; furthermore, it is shown to be exclusively so in most of these cases. Both the quantum yield and the radiative lifetime of the luminescent state of the Eu+3 ion are determined by theoretical fits to the data. Whereas the quantum yield spans a range of 0.69–0.86, the radiative lifetime of the electric dipole transition at 612 nm is nearly constant, as required, with a value of 803±29 μsec. Both the quantitative agreement between theory and experiment and the consistency among the eight experimental systems in predicting the radiative lifetime provide a clear demonstration of the utility of the fatty acid monlayer assembly technique as a method of measurement of emission properties of lunimescent systems and of dielectric properties of surfaces.

Radiative and nonradiative transitions in the first excited singlet state of symmetrical methyl-substituted acetones

Abstract: Radiative and nonradiative rates of symmetrically substituted, methylated acetones have been measured in the gas phase. Observed radiative lifetimes are compared to calculated radiative lifetimes obtained from the Strickler−Berg (SB) expression. The calculated values are greater by a factor of 8−9, and an empirical procedure by which the true radiative lifetime can be estimated from the SB expression and the geometry−sensitive correction parameter is given. The rates of nonradiative transitions are reduced appreciably by the α, α′ substitution of methyl groups to the C−C−CO−C−C skeleton. The steric crowding introduced by methyl group substitution is considered to be responsible for suppressing the vibrational motion of the promoting modes. In most cases, the S1 → T1 intersystem crossing predominates over the other nonradiative transitions.

Laser induced fluorescence from NH2(2A1). State selected radiative lifetimes and collisional de‐excitation rates

Abstract: Time resolved fluorescence from the first excited (2A1) state of NH2 has been observed following excitation of the radical in its ground state by means of a pulsed tunable dye laser. Specific rotational levels within a number of vibronic states were populated, decay rates measured as a function of total pressure for a variety of added gases, and zero pressure lifetimes and collisional de‐excitation rates evaluated. Measured zero pressure lifetimes are good approximations to the vibrational state radiative lifetimes, typically 10 μsec for the (0, 9, 0) state. Collisional de‐excitation rate constants were measured as 1.0×10−9 cm3 molecule−1⋅sec−1 for NH3, independent of vibronic state, and for the Σ (0, 9, 0) level were found for other gases in the ratio NH3:CO:H2:N2:CH4:Ar:He=1.0:0.47:0.46:0. 40:0.30:0.152:0.145. Using excitation by a tunable cw dye laser, steady state spectra of NH2 have been obtained and collisional energy transfer observed within the (2A1) excited electronic state of NH2. Transfer was o...

Thermal microwave emission from a scattering layer

Abstract: The microwave radiometric temperature of heterogeneous materials is altered by internal scattering. Radiative transfer theory and a Rayleigh scattering model are used to obtain the microwave temperature and its polarization as a function of view angle for emission from a nonuniformly thick layer containing scatterers. The scatter-induced change in brightness temperature is generally negative and may be many tens of degrees. There are situations, however, such as the emission from ice over freshwater, where the scatterers may increase the brightness temperature by as much as 30°C. Lunar microwave temperatures may be decreased from a few degrees to more than 50°C depending upon wavelength and upon the specific lunar target; the brightness temperature as a function of wavelength of a lava flow may be decreased from 1°C to more than 30°C by near-surface vesicles; snow may appear from a few degrees to more than 60°C darker as it ages; and air bubbles in ice over freshwater may increase the brightness temperature by as much as 30°C or decrease it by as much as 50°C depending upon the thickness of the ice and the size and concentration of the bubbles.

A two‐dimensional mean circulation model for the atmosphere below 80km

Abstract: The paper sets out the detailed formulation of a numerical model whose purpose is the study of the interactions of dynamics, photochemistry and radiation in the stratosphere and mesosphere. Two integrations of the model for 900 days are described in which many features of the atmosphere are reproduced but with important differences of detail. The dependent variables are zonal means of the relevant meteorological quantities, held as functions of time, latitude and height (log pressure) with a resolution of μ/19 in latitude and 0.5 in pressure scale height. Eddy fluxes of heat and matter are treated by large-scale diffusion coefficients. This treatment is not applicable to momentum fluxes: these are currently specified from observations made mainly from the selective chopper radiometer on the Nimbus V spacecraft. Radiative coolings due to CO2 and O3 emission are computed from simplified expressions which are essentially cooling-to-space approximations with emissivities obtained by curve-fitting against the results of more elaborate treatments. Absorption of solar radiation by ozone is obtained from tabulations of absorption against ozone amount traversed. Radiation and latent heat release in the troposphere are specified climatologically. The photochemistry in the integrations described here is the classical ozone scheme but, with a view to investigating possible stratospheric pollution problems, integrations have been performed with the inclusion of reactions involving nitrogen and hydrogen compounds. These will be described in a later paper.

Evolution of rotating interstellar clouds. I - Numerical techniques

Abstract: A method is described for the numerical calculation of the hydrodynamic evolution of a self-gravitating configuration in two space dimensions with assumed axial symmetry. The calculation is formulated in cylindrical coordinates with respect to a moving Eulerian grid and is solved using explicit hydrodynamics combined with implicit radiative transfer. The physics included is appropriate for calculation of the collapse of a rotating protostellar cloud. The gravitational field is obtained by means of an alternating-direction iterative technique. Numerical tests to demonstrate the correctness of the method are presented for special cases.

Radiation reaction and vacuum fluctuations in spontaneous emission

Abstract: A Heisenberg-picture treatment of spontaneous emission is given, and the origin of radiative line shifts and widths is discussed. It is shown that radiation reaction and vacuum fluctuations provide complementary conceptual bases for the interpretation of these radiative corrections. Alternative approaches are discussed, including the use of a random classical field to simulate the effects of the quantum-electrodynamical radiation field.

Formation of Molecular Lines in Stellar Atmospheres

Abstract: Statistical equilibrium of electronic states of diatomic molecules in stellar atmospheres is examined. Atmospheres discussed are representative of the sun, Arcturus (K-giant) and Betelgeuse (M-supergiant). A comparison of the relative collisional and radiative contributions to the equilibrium of the ground electronic state shows that this state is collisionally controlled and that the line source function for vibration-rotation transitions within this state is equivalent to the Planck function. Examination of the equilibrium for excited electronic states demonstrates that the exchange between these states and the ground electronic state is most probably determined by radiative excitation. This result implies that scattering rather than pure absorption is the appropriate mechanism for the formation of lines belonging to these electronic transitions. The scattering hypothesis is given a preliminary check against solar observations. Areas for future investigations are outlined.