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NASA NTRS1993

The effects of zonal atmospheric currents on the spectra of rotating early-type stars

We suggest the existence of zonal currents in the atmospheres of rapidly rotating stars analogous to those found in planetary atmospheres. The zonal flow is assumed to be characterized by 'thin' atmospheric, nearly geostrophic flow which does not change the gravity darkening and stellar shape determined by the underlying uniformly rotating model. The contribution that such flows make to the continuum spectra of such stars is investigated. The additional rotationally induced Doppler displacement resulting from such zonal wind belts can distort the rotationally broadened stellar lines leading to significant departures from the line profiles predicted by the classical model of rotating stars. Our estimates of the zonal flow velocity stem from the assumption of a relation between it and the latitudinal wavenumber of the zonal velocity field. It is thus possible to create barotropic atmosphere models which, in turn, enable the modeling of the stellar spectrum including important spectral lines. In addition, the radiative transfer equations for the Stokes parameters I and Q are solved for the locally plane-parallel atmospheres so that the polarization structure of the radiation field is determined. We find that the presence of zonal wind belts leads to significant changes in the photospheric polarization from those characteristic of a uniformly rotating model.

Cranmer, Steven R.↗

NASA NTRS1975

On the use of a finite difference method for solving anisotropic scattering problems

A new method of solving the radiative transfer equation is developed in which the scattering and absorption coefficients may have arbitrary variations with depth, and in which both internal (thermal) emission and incident radiation are allowed. Specular and diffuse reflection at both boundaries also is taken into account. The method begins by forming a paired set of coupled first-order differential equations for the symmetric and antisymmetric parts of the radiation field after writing the scattering integral as a numerical quadrature. These differential equations are broken into finite difference form, in which the symmetric and antisymmetric parts of the radiation field are found on alternate grid points. Numerical results for a number of test problems are shown, demonstrating that the method is very fast, that it returns specific intensities and fluxes that are accurate to at least a percent, and that it can be applied to optically thick problems.

Barkstrom, B. R.↗

NASA NTRS1978

Some effects of 8-12 micron radiant energy transfer on the mass and heat budgets of cloud droplets

In standard treatments of the mass and energy budget of cloud droplets, radiant energy transfer is neglected on the grounds that the temperature difference between the droplet and its surroundings is small. This paper includes the effect of radiant heating and cooling of droplets by using the Eddington approximation for the solution of the radiative transfer equation. Although the calculation assumes that the cloud is isothermal and has a constant size spectrum with altitude, the heating or cooling of droplets by radiation changes the growth rate of the droplets very significantly. At the top of a cloud with a base at 2500 m and a top at 3000 m, a droplet will grow from 9.5 to 10.5 microns in about 4 min, assuming a supersaturation ratio of 1.0013. Such a growth rate is more than 20 times the growth rate for condensation alone, and may be expected to have a significant impact on estimates of precipitation formation as well as on droplet spectrum calculations.

Barkstrom, B. R.↗

NASA NTRS2014

Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the ordinary photons, under the approximation of large angle and large optical depth. These assumptions allow the equation to be treated using a diffusion-like approximation.

acceleration of particles↗

NASA NTRS1991

A new spherical model for computing the radiation field available for photolysis and heating at twilight

Accurate computation of atmospheric photodissociation and heating rates is needed in photochemical models. These quantities are proportional to the mean intensity of the solar radiation penetrating to various levels in the atmosphere. For large solar zenith angles a solution of the radiative transfer equation valid for a spherical atmosphere is required in order to obtain accurate values of the mean intensity. Such a solution based on a perturbation technique combined with the discrete ordinate method is presented. Mean intensity calculations are carried out for various solar zenith angles. These results are compared with calculations from a plane parallel radiative transfer model in order to assess the importance of using correct geometry around sunrise and sunset. This comparison shows, in agreement with previous investigations, that for solar zenith angles less than 90 deg adequate solutions are obtained for plane parallel geometry as long as spherical geometry is used to compute the direct beam attenuation; but for solar zenith angles greater than 90 deg this pseudospherical plane parallel approximation overstimates the mean intensity.

Dahlback, Arne↗

NASA NTRS1983

A non-spherically symmetric model for absorption regions near quasars

An approximate analytic solution of the radiative-transfer equation is used to estimate upper limits on the fraction of sky covered (Omega/4pi) by absorption regions near broad absorption-line quasars. The resonance scattering of line radiation tends to 'fill in' absorption troughs, and regions with large Omega/4pi produce troughs that are severely 'filled in'. PHL 5200 and several other broad absorption line quasars have absorption troughs that are flat-bottomed and deep. It is noted that these quasars probably have small Omega/4pi. Simple solutions are obtained for the case of large optical depth and a point central source using a two-stream model for the radiation field. It is shown that the scattered radiation can produce flat-bottomed absorption troughs if the logarithmic velocity derivative in the outflow is constant. For a large class of models, Omega/4pi is approximately less than the residual intensity (the fraction left after absorption) in a deep flat-bottomed absorption trough.

Junkkarinen, V. T.↗

NASA NTRS1993

Radiative interactions in molecular gases under local and nonlocal thermodynamic equilibrium conditions

Basic formulations, analyses, and numerical procedures are presented to investigate radiative heat interactions in diatomic and polyatomic gases under local and nonlocal thermodynamic equilibrium conditions. Essential governing equations are presented for both gray and nongray gases. Information is provided on absorption models, relaxation times, and transfer equations. Radiative flux equations are developed which are applicable under local and nonlocal thermodynamic equilibrium conditions. The problem is solved for fully developed laminar incompressible flows between two parallel plates under the boundary condition of a uniform surface heat flux. For specific applications, three diatomic and three polyatomic gases are considered. The results are obtained numerically by employing the method of variation of parameters. The results are compared under local and nonlocal thermodynamic equilibrium conditions at different temperature and pressure conditions. Both gray and nongray studies are conducted extensively for all molecular gases considered. The particular gases selected for this investigation are CO, NO, OH, CO2, H2O, and CH4. The temperature and pressure range considered are 300-2000 K and 0.1-10 atmosphere, respectively. In general, results demonstrate that the gray gas approximation overestimates the effect of radiative interaction for all conditions. The conditions of NLTE, however, result in underestimation of radiative interactions. The method developed for this study can be extended to solve complex problems of radiative heat transfer involving nonequilibrium phenomena.

Tiwari, S. N.↗

NASA NTRS1994

The effect of sea ice on the solar energy budget in the astmosphere-sea ice-ocean system: A model study

A coupled one-dimensional multilayer and multistream radiative transfer model has been developed and applied to the study of radiative interactions in the atmosphere, sea ice, and ocean system. The consistent solution of the radiative transfer equation in this coupled system automatically takes into account the refraction and reflection at the air-ice interface and allows flexibility in choice of stream numbers. The solar radiation spectrum (0.25 micron-4.0 micron) is divided into 24 spectral bands to account adequately for gaseous absorption in the atmosphere. The effects of ice property changes, including salinity and density variations, as well as of melt ponds and snow cover variations over the ice on the solar energy distribution in the entire system have been studied quantitatively. The results show that for bare ice it is the scattering, determined by air bubbles and brine pockets, in just a few centimeters of the top layer of ice that plays the most important role in the solar energy absorption and partitioning in the entire system. Ice thickness is important to the energy distribution only when the ice is thin, while the absorption in the atmosphere is not sensitive to ice thickness exceeds about 70 cm. The presence of clouds moderates all the sensitivities of the absorptive amounts in each layer to the variations in the ice properties and ice thickness. Comparisons with observational spectral albedo values for two simple ice types are also presented.

Jin, Z.↗

NASA NTRS1982

Theoretical quasar emission-line ratios. V - Balmer continuum emission

Isothermal, isobaric models of quasar emission line regions are presented which include an improved treatment of radiative transfer in the bound-free continua, based on a generalization of frequency-integrated line transfer techniques and on the use of a probabilistic radiative transfer equation which explicitly distinguishes between the flux divergence coefficient and the photon escape probability. It is found that Balmer continuum emission can be obtained without compromising observed line ratios. It is also established that optically thin or thick Balmer continuum emission models with blended Fe II line are consistent with 4000-2000 A 'blue bump' observations, and that the improved radiative transfer treatment makes order-of-magnitude corrections to level populations and local cooling rates calculated with past techniques.

Puetter, R. C.↗

NASA NTRS1981

Spectral albedos of midlatitude snowpacks

Spectral albedos of impure-nonhomogeneous snowpacks, typical of midlatitudes, from 400 to 2200 nm were modeled through a numerical solution of the radiative transfer equation in the two-stream approximation. Discrete depth-dependent values of density, grain size and impurity concentration were used to characterize the snowpacks. The model is for diffuse incident radiation, and the numerical method is based on doubling and invariant imbedding. The effect of soot impurities on snowpack albedos is illustrated when a snowpack is several centimeters deep and soot reduces the albedos at visible wavelengths, however, when a snowpack is only a few centimeters deep, soot may increase the albedos at visible wavelengths. By adjusting soot content and snow grain size, good quantitative agreement with some observations at the Cascade Mountains (Washington) and at Point Barrow (Alaska) are obtained; however, the model grain sizes are found to be fifty to four hundred percent larger than the measured values. For satellite snowcover observations, a model for effective albedo of partially snow-covered areas was developed and compared with some NOAA-2 observations of the southeastern United States.

Choudhury, B.↗

NASA NTRS1994

Basic theory for polarized, astrophysical maser radiation in a magnetic field

Fundamental alterations in the theory and resulting behavior of polarized, astrophysical maser radiation in the presence of a magnetic field have been asserted based on a calculation of instabilities in the radiative transfer. I reconsider the radiative transfer and find that the relevant instabilities do not occur. Calculational errors in the previous investigation are identified. In addition, such instabilities would have appeared -- but did not -- in the numerous numerical solutions to the same radiative transfer equations that have been presented in the literature. As a result, all modifications that have been presented in a recent series of papers (Elitzur 1991, 1993) to the theory for polarized maser radiation in the presence of a magnetic field are invalid. The basic theory is thus clarified.

Watson, William D.↗

NASA NTRS2018

Radiative Transfer Modeling of Phytoplankton Fluorescence Quenching Processes

We report the first radiative transfer model that is able to simulate phytoplankton fluorescence with both photo chemical and non-photo chemical quenching included. The fluorescence source term in the inelastic radiative transfer equation is proportional to both the quantum yield and scalar irradiance at excitation wavelengths. The photo chemical and non photo chemical quenching processes change the quantum yield based on the photosynthetic active radiation. A sensitivity study was performed to demonstrate the dependence of the fluorescence signal on chlorophyll a concentration, aerosol optical depths and solar zenith angles. This work enables us to better model the phytoplankton fluorescence, which can be used in the design of new space-based sensors that can provide sufficient sensitivity to detect the phytoplankton fluorescence signal. It could also lead to more accurate remote sensing algorithms for the study of phytoplankton physiology.

Inelastic scattering↗

NASA NTRS1984

Reflectivity of the atmosphere-inhomogeneous surfaces system Laboratory simulation

Theoretical two- and three-dimensional solutions of the radiative transfer equation have been applied to the earth-atmosphere system. Such solutions have not been verified experimentally. A laboratory experiment simulates such a system to test the theory. The atmosphere was simulated by latex spheres suspended in water and the ground by a nonuniform surface, half white and half black. A stable radiation source provided uniform illumination over the hydrosol. The upward radiance along a line orthogonal to the boundary of the two-halves field was recorded for different amounts of the hydrosol. The simulation is a well-defined radiative transfer experiment to test radiative transfer models involving nonuniform surfaces. Good agreement is obtained between the measured and theoretical results.

Mekler, Y.↗

NASA NTRS1981

Inference of dust opacities for the 1977 Martian great dust storms from Viking Lander 1 pressure data

The tidal heating components for the dusty Martian atmosphere are computed based on dust optical parameters estimated from Viking Lander imaging data, and used to compute the variation of the tidal surface pressure components at the Viking Lander sites as a function of season and the total vertical extinction optical depth of the atmosphere. An atmospheric tidal model is used which is based on the inviscid, hydrostatic primitive equations linearized about a motionless basic state the temperature of which varies only with height, and the profiles of the tidal forcing components are computed using a delta-Eddington approximation to the radiative transfer equations. Comparison of the model results with the observed variations of surface pressure and overhead dust opacity at the Viking Lander 1 site reveal that the dust opacities and optical parameters derived from imaging data are roughly representative of the global dust haze necessary to reproduce the observed surface pressure amplitudes, with the exception of the model-inferred asymmetry parameter, which is smaller during the onset of a great storm. The observed preferential enhancement of the semidiurnal tide with respect to the diurnal tide during dust storm onset is shown to be due primarily to the elevation of the tidal heating source in a very dusty atmosphere.

Zurek, R. W.↗

NASA NTRS1986

The temperature structure in accretion flows onto massive protostars

Radiation transfer problems involved in the infall of dust and gas during star formation are studied. Dust properties are discussed, and modifications of spherical radiative transfer equations are presented that permit forward scattering by dust to be treated for the small size of the star relative to the inner radius of the shell. A procedure for deriving the stellar radiation field incident on the inner edge of the shell is developed. The temperature correction procedure of Cassinelli and Hartmann (1975) for extended stellar atmospheres is modified so that the multitemperature nature of the grains in the cloud may be derived. Temperature distributions for three schematic models in which the density is prespecified are discussed. Radiative acceleration of grains is addressed, showing that the proper mean opacity differs by a large factor from the Rosseland mean opacity that is commonly used. Emergent fluxes for the models are given.

Wolfire, Mark G.↗

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 NTRS2006

A Mission to Observe Ice in Clouds from Space

To date there have been multiple satellite missions to observe and retrieve cloud top properties and the liquid in, and precipitation from, clouds. There are currently a few missions that attempt to measure cloud ice properties as a byproduct of other observations. However, we do not yet quantitatively understand the processes that control the water budget of the upper troposphere where ice is the predominant phase, and how these processes are linked to precipitation processes and the radiative energy budget. The ice in clouds either melts into rain or is detrained, and persists, as cirrus clouds affecting the hydrological and energy cycle, respectively. Fully modeling the Earth's climate and improving weather and climate forecasts requires accurate satellite measurements of various cloud properties at the temporal and spatial scales of cloud processes. The uncertainty in knowledge of these ice characteristics is reflected in the large discrepancies in model simulations of the upper tropospheric water budget. Model simulations are sensitive to the partition of ice between precipitation and outflow processes, i.e., to the parameterization of ice clouds and ice processes. This presentation will describe the Submillimeter-wave InfraRed Ice Cloud Experiment (SIRICE) concept, a satellite mission designed to acquire global Earth radiance measurements in the infrared and submillimeter-wave region (183-874 GHz). If successful, this mission will bridge the measurement gap between microwave sounders and shorter-wavelength infrared and visible sensors. The brightness temperatures at submillimeter-wave frequencies are especially sensitive to cirrus ice particle sizes (because they are comparable to the wavelength). This allows for more accurate ice water path estimates when multiple channels are used to probe into the cloud layers. Further, submillimeter wavelengths offer simplicity in the retrieval algorithms because they do not probe into the liquid and near surface portions of clouds, thus requiring only one term of the radiative transfer equation (ice scattering) to relate brightness temperatures to ice. Scientific justification and the SIRICE approach to measuring ice water path and particle size that span a range encompassing both the hydrologically active and radiatively active components of cloud systems will be presented.

Ackerman, S.↗

NASA NTRS1992

Polarimetric signatures of a coniferous forest canopy based on vector radiative transfer theory

Complete polarization signatures of a coniferous forest canopy are studied by the iterative solution of the vector radiative transfer equations up to the second order. The forest canopy constituents (leaves, branches, stems, and trunk) are embedded in a multi-layered medium over a rough interface. The branches, stems and trunk scatterers are modeled as finite randomly oriented cylinders. The leaves are modeled as randomly oriented needles. For a plane wave exciting the canopy, the average Mueller matrix is formulated in terms of the iterative solution of the radiative transfer solution and used to determine the linearly polarized backscattering coefficients, the co-polarized and cross-polarized power returns, and the phase difference statistics. Numerical results are presented to investigate the effect of transmitting and receiving antenna configurations on the polarimetric signature of a pine forest. Comparison is made with measurements.

Karam, M. A.↗