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NASA NTRS1993

Two-dimensional radiative transfer in cloudy atmospheres - The spherical harmonic spatial grid method

A new two-dimensional monochromatic method that computes the transfer of solar or thermal radiation through atmospheres with arbitrary optical properties is described. The model discretizes the radiative transfer equation by expanding the angular part of the radiance field in a spherical harmonic series and representing the spatial part with a discrete grid. The resulting sparse coupled system of equations is solved iteratively with the conjugate gradient method. A Monte Carlo model is used for extensive verification of outgoing flux and radiance values from both smooth and highly variable (multifractal) media. The spherical harmonic expansion naturally allows for different levels of approximation, but tests show that the 2D equivalent of the two-stream approximation is poor at approximating variations in the outgoing flux. The model developed here is shown to be highly efficient so that media with tens of thousands of grid points can be computed in minutes. The large improvement in efficiency will permit quick, accurate radiative transfer calculations of realistic cloud fields and improve our understanding of the effect of inhomogeneity on radiative transfer in cloudy atmospheres.

Evans, K. F.↗

NASA NTRS1986

Field experiment for measurement of the radiative characteristics of a hazy atmosphere

Theoretical two-dimensional and three-dimensional solutions to the radiative-transfer equation have been applied to the earth-atmosphere system. A field experiment was conducted to test this theory. In the experiment the upward radiance was measured above and below a haze layer during simultaneous measurements of the haze characteristics. The measurements were conducted at a narrow near-IR channel (773 + or - 22 nm) which represents the visible and near-IR spectral region. The aerosol vertical optical thickness at eight wavelengths, as well as the vertical and horizontal profiles of the scattering coefficient, the temperature, and dew point were measured at several locations. These measurements quantified the vertical and spatial structure of the atmospheric haze and the atmospheric radiation. The result was a well-defined radiative-transfer experiment. The experimental data set is used to quantify the haze effect on upward radiance, including the adjacency effect (the effect of a bright area on the upward radiance measured above a dark adjacent area), and to test radiative-transfer models for a plane-parallel atmosphere above a nonuniform surface. A comparison is given between the theoretical prediction of upward radiance above the haze and the measurement. Agreement between theory and the experiment is discussed.

Kaufman, Y. J.↗

NASA NTRS1978

Radiative cooling in shock-heated hydrogen-helium plasmas

Axial and off-axis radiative cooling of cylindrical shock-heated hydrogen-helium plasmas is investigated theoretically and experimentally. The coupled fluid dynamic-radiative transfer equations are solved by a combination of approximation techniques aimed at simplifying the computation of the flux divergence term, namely, the quasi-isothermal approximation and the exponential approximation developed for the solid angle integration. The accuracy of the approximation schemes has been assessed and found acceptable for applying the methods to the rapid computation of the radiatively coupled flow problem. Radiative cooling experiments were conducted in a 6-inch annular arc accelerator shock tube (ANAA) for an initial pressure of 1 torr and shock speeds from 35 to 45 Km/sec. The results indicate that the lateral cooling is small compared with the axial cooling, and that better agreement is achieved between the data and the theoretical results by inclusion of the lateral temperature gradient.

Poon, P. T. Y.↗

NASA NTRS1979

Nonequilibrium radiative heating of a Jovian entry body

The influence of nonlocal thermodynamic equilibrium (NLTE) radiative transfer on radiative and convective heating of a Jovian entry body is investigated. The flow in the shock layer is assumed to be axisymmetric, viscous, and in chemical equilibrium. The chemical species considered for the collisional deactivation processes are H2, H, H+. The NLTE radiative transfer equations are derived for multilevel energy transitions. The rotational and vibrational energy modes are assumed to be in local thermodynamic equilibrium. The results indicate that higher-level energy transitions have little influence on the overall NLTE results. The NLTE results, however, are found to be greatly influenced by the temperature distributions in the shock layer. The convective and radiative heating to the entry body are reduced significantly because of the NLTE conditions; the reduction in convective heating, however, is relatively small. The influence of NLTE is found to be greater at higher entry altitudes.

Tiwari, S. N.↗

NASA NTRS1990

Non-grey radiation in a liquid rocket combustion chamber

The effects of radiation on droplets gasification in liquid rocket combustion chambers has been studied. The modeling includes a Legendre pseudo-spectral collocation approximation to solve the Radiative Transfer Equation (RTE). The band model has been utilized to account for non-grey emitting and absorbing gases present in the comustion chamber. The GEMCHIP II code has been utilized to study the fuel and oxidizer droplets combustion and interaction. The submodels within this code are capable of accounting for group combustion and conjugate effects between many droplets. The radiative model has been coupled with the GEMCHIP II code accounting for radial effects only, to provide the tool for studying the combustion-radiation coupling effects in a bipropellant system. The results indicate that the gasification/combustion process will be enhanced upstream of the chamber causing thicker flame sheet and associated higher combustion efficiency.

Kehtarnavaz, H.↗

NASA NTRS1991

A three dimensional radiative transfer method for optical remote sensing of vegetated land surfaces

In the application of remote sensing at optical wavelengths to vegetated surfaces from satellite borne high resolution instruments, an understanding of the various physical mechanisms that contribute to the measured signal is important. A numerical method of solving the radiative transfer equation in three dimensions is reported. The reliability of coding and accuracy of the algorithm are evaluated by benchmarching. Parametrization of the methods and results of a simulation are presented. The method is tested with experimental data of canopy bidirectional reflectance factors. The effect of spatial heterogeneity on the relationship between the simple ratio and normalized vrs absorbed Photosynthetically Active Radiation (PAR) is discussed.

Asrar, Ghassem↗

NASA NTRS2016

Expansion of Tabulated Scattering Matrices in Generalized Spherical Functions

An efficient way to solve the vector radiative transfer equation for plane-parallel turbid media is to Fourier-decompose it in azimuth. This methodology is typically based on the analytical computation of the Fourier components of the phase matrix and is predicated on the knowledge of the coefficients appearing in the expansion of the normalized scattering matrix in generalized spherical functions. Quite often the expansion coefficients have to be determined from tabulated values of the scattering matrix obtained from measurements or calculated by solving the Maxwell equations. In such cases one needs an efficient and accurate computer procedure converting a tabulated scattering matrix into the corresponding set of expansion coefficients. This short communication summarizes the theoretical basis of this procedure and serves as the user guide to a simple public-domain FORTRAN program.

scattering matrix↗

NASA NTRS1994

Analysis of the early spectra and light curve of SN 1987A

Numerical modeling of supernova spectra, light curves, and hydrodynamics requires physical inputs, numerical techniques, approximations, and assumptions which must be thoroughly understood in order to study the details of supernova explosions. Here, we discuss some of these in the context of the early evolution of supernova 1987A. Gray radiation-hydrodynamics is used to calculate the bolometric light curve and the hydrodynamic evolution of the supernova. Synthetic spectra are then obtained for the resulting density and velocity structure. The spectrum calculations are performed using a special-relativistic treatment of the radiative transfer equation in the comoving frame, line blanketing by about 10(exp 5) spectral lines, and departures from local thermodynamic equilibrium (LTE) for H I, He I, Mg II, and Ca II. We find that we are able to simultaneously fit the early light curve and spectra reasonably well, using a progenitor model from Arnett (1991a), without fine-tuning the free parameters. Temperature structures and radiative equilibrium, non-LTE effects, homologous expansion, and mean opacities are discussed.

Hauschildt, Peter H.↗

NASA NTRS2017

Radiation, Smoke and Clouds Observed in the Southeastern Atlantic With the Research Scanning Polarimeter During ORACLES

The ObseRvations of Aerosols above Clouds and their interactions (ORACLES) project is making a series of field deployments to the southeastern Atlantic with NASA ER-2 and P3 aircraft to acquire both detailed remote sensing observations and in situ measurements of the aerosols and clouds in that region. This area is home to one of the largest low-level cloud decks on Earth that is seasonally affected by vast plumes of smoke from biomass burning, which in effect provides a natural experiment testing the radiative and microphysical interactions between the smoke and the clouds. The downward solar radiation at the surface, or cloud top, is always reduced by the presence of smoke. However, whether the amount of sunlight reflected back out to space is increased, or decreased by the presence of smoke is sensitively dependent on the brightness of the clouds and the fraction of light that the smoke absorbs each time light hits a smoke particle. In this study we use data from the Research Scanning Polarimeter, an along track scanning instrument, that provides measurements of the Stokes parameters I, Q and U at 410, 470, 555, 670, 865, 960, 1590, 1880 and 2260 nm at 150 viewing angles over a range of +/- 60° from nadir for each contiguous sub-aircraft pixel (~ 300 m in size). A retrieval algorithm is applied to the data acquired with a table look up technique, similar to that of the operational POLDER algorithm, to provide a first guess of the complex refractive index, optical depth and size distribution of the smoke particles together with cloud droplet size and optical depth. A subsequent iterative fitting procedure, where the fact that the doubling/adding method allows the construction of the Green's function for the radiative transfer equation, is used to obtain an efficient and statistically optimal estimate of the aerosol and cloud retrieval parameters. These retrieval parameters are evaluated against in situ observations, when available, and the optical depth and intensive lidar variables that are measured by the High Spectral Resolution Lidar 2. Finally, the aerosol and cloud retrievals are used to evaluate the variations in top of the atmosphere, surface/cloud top shortwave radiative forcing and atmospheric absorption that are caused by variations in the smoke and clouds.

Cairns, Brian↗

NASA NTRS1983

On the line profile coefficient for stimulated emission

It is pointed out that the line profile coefficients for spontaneous and stimulated emission are identical in low-intensity radiation fields. In more intense radiation fields, however, the stimulated emission profiles in the radiative transfer equation and in the rate equations for the atomic level populations may differ from each other, owing to their different physical nature. A seeming discrepancy between the stimulated emission profiles of the usual semi-classical aproach and a recent quantum mechanical approach by Cooper et al. (1982), which should also be valid for intense 'broadband' fields, is discussed and shown to have negligible consequences for low-intensity radiation fields.

Cooper, J.↗

NASA NTRS1984

Probabilistic radiative transfer

A computationally efficient method has been developed for highly nonlinear problems in which radiative transfer is an important aspect of the heating and cooling of the medium. An approximate probabilistic radiative transfer equation is derived for one-dimensional plane-parallel atmospheres of finite or semi-infinite extent, for both spectral lines and bound-free continua. Boundary conditions, accuracy, escape probabilities, and practical aspects of complete linearization, are discussed. The method is accurate to a few tens of percent of a wide variety of realistic problems in which frequency redistribution of scattered photons dominates the transfer and escape of radiation.

Canfield, R. C.↗

NASA NTRS2006

Observing Ice in Clouds from Space

There are many satellite observations of cloud top properties and the liquid and rain content of clouds, 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 in the upper troposphere 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. These properties include cloud horizontal and vertical structure, cloud water content and some measure of particle sizes and shapes. 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. One barrier to achieving accurate global ice cloud properties is the lack of adequate observations at millimeter and submillimeter wavelengths (183-874 GHz). Recent advances in instrumentation have allowed for the development and implementation of an airborne submillimeter-wave radiometer. The brightness temperatures at these 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. The next step is a satellite mission designed to acquire global Earth radiance measurements in the submillimeter-wave region, thus bridging the measurement gap between microwave sounders and shorter-wavelength infrared and visible sensors. This presentation provides scientific justification and an approach to measuring ice water path and particle size from a satellite platform that spans a range encompassing both the hydrologically active and radiatively active components of cloud systems.

Ackerman, S.↗

NASA NTRS1974

The spectrum of density perturbations in an expanding universe

The basic dynamic equations that govern the evolution of perturbations in a Friedmann-Lemaitre universe are derived. General solutions describing the evolution of adiabatic perturbations in the density of matter are obtained, and the choice of the appropriate initial conditions is examined. The various perturbation modes are compared, and the effects of decoupling on the perturbation spectrum are studied. The scheme used to follow the evolution of density perturbations through decoupling is based on an extension of the Eddington approximation to the radiative transfer equation, and is strictly valid in both optically thick and thin limits.

Silk, J.↗

NASA NTRS2013

Radiative Transfer Theory Verified by Controlled Laboratory Experiments

We report the results of high-accuracy controlled laboratory measurements of the Stokes reflection matrix for suspensions of submicrometer-sized latex particles in water and compare them with the results of a numerically exact computer solution of the vector radiative transfer equation (VRTE). The quantitative performance of the VRTE is monitored by increasing the volume packing density of the latex particles from 2 to 10. Our results indicate that the VRTE can be applied safely to random particulate media with packing densities up to 2. VRTE results for packing densities of the order of 5 should be taken with caution, whereas the polarized bidirectional reflectivity of suspensions with larger packing densities cannot be accurately predicted. We demonstrate that a simple modification of the phase matrix entering the VRTE based on the so-called static structure factor can be a promising remedy that deserves further examination.

Radiative transfer↗

NASA NTRS1978

The solar reflectance of a snow field

The radiative transfer equation was solved using a modified Schuster-Schwartzschild approximation to obtain an expression for the solar reflectance of a snow field. The parameters in the reflectance formula are the single scattering albedo and the fraction of energy scattered in the backward direction. The single scattering albedo is calculated from the crystal size using a geometrical optics formula and the fraction of energy scattered in the backward direction is calculated from the Mie scattering theory. Numerical results for reflectance are obtained for visible and near infrared radiation for different snow conditions. Good agreement was found with the whole spectral range. The calculation also shows the observed effect of aging on the snow reflectance.

Choudhury, B. J.↗

NASA NTRS1998

Emittance Theory for Cylindrical Fiber Selective Emitter

A fibrous rare earth selective emitter is approximated as an infinitely long cylinder. The spectral emittance, epsilon(lambda), is obtained by solving the radiative transfer equations with appropriate boundary conditions and uniform temperature. For optical depths, Kappa(R) = alpha(lambda)R, where alpha(lambda) is the extinction coefficient and R is the cylinder radius, greater than 1 the spectral emittance is nearly at its maximum value. There is an optimum cylinder radius, R(opt), for maximum emitter efficiency, eta(E). Values for R(opt) are strongly dependent on the number of emission bands of the material. The optimum radius decreases slowly with increasing emitter temperature, while the maximum efficiency and useful radiated power increase rapidly with increasing temperature.

Chubb, Donald L.↗

NASA NTRS1993

A Fourier-Riccati approach to radiative transfer. I - Foundations

The three-dimensional equation of radiative transfer is formally solved using a Fourier-Riccati approach while calculations are performed on cloudy media embedded in a two-dimensional space. An extension to Stephens' work this study addresses the coupling between space and angle asserted by the equation of transfer. In particular, the accuracy of the computed radiation field as it is influenced by the angular resolution of the phase function and spatial discretization of the cloudy medium is discussed. The necessity of using a large number of quadrature points to calculate fluxes even when the phase function is isotropic for media exhibiting vertical and horizontal inhomogeneities is demonstrated. Effects of incorrect spatial sampling on both radiance and flux fields are also quantified by example. Radiance and flux comparisons obtained by the Fourier-Riccati model and the independent pixel approximation for inhomogeneous cloudy media illustrate the inadequacy of the latter even for tenuous clouds.

Gabriel, P. M.↗

NASA NTRS1988

Radiative aspects of Antarctic ozone hole in 1985

In order to investigate the radiative heating effects of aerosols during September - October, 1985, at Antarctica, researchers solved the radiative transfer equation using a one-dimensional model, which includes the absorption of solar energy by water vapor, carbon dioxide, ozone and aerosols, the thermal emission and absorption by the above species and in addition, Rayleigh and Mie scattering, and the surface scattering effects. In this calculation, they used data of ozone density, water vapor density and aerosol extinction at 0.385, 0.453, 0.525 and 1.02 mu m in the stratosphere obtained by SAGE II satellite and meteorological data from NOAA. Results show that the Antarctic stratosphere is nearly in radiative equilibrium during that period, if the effects of aerosols are excluded. It is also shown that the heating effects of aerosols are too small to cause effective upward motions, in spite of some ambiguous parameters such as aerosol composition. The parameter dependences of results are also discussed.

Akiyoshi, H.↗