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NASA NTRS2003

Theoretical Model Images and Spectra for Comparison with HESSI and Microwave Observations of Solar Flares

We have computed bremsstrahlung and gyrosynchrotron images and spectra from a model flare loop. Electrons with a power-law energy distribution are continuously injected at the top of a semi-circular magnetic loop. The Fokker-Planck equation is integrated to obtain the steady-state electron distribution throughout the loop. Coulomb scattering and energy losses and magnetic mirroring are included in the model. The resulting electron distributions are used to compute the radiative emissions. Sample images and spectra are presented. We are developing these models for the interpretation of the High Energy Solar Spectroscopic Imager (HESSI) x-ray/gamma ray data and coordinated microwave observations. The Fokker-Planck and radiation codes are available on the Web at http://hesperia.gsfc.nasa.gov/hessi/modelware.htm This work is supported in part by the NASA Sun-Earth Connection Program.

Fisher, Richard R.↗

NASA NTRS1990

A GCM parameterization for the shortwave radiative properties of water clouds

A new parameterization was developed for predicting the shortwave radiative properties of water clouds, suitable for inclusion in general circulation models (GCMs). The parameterization makes use of the simple relationships found by Slingo and Schrecker, giving the three input parameters required to calculate the cloud radiative properties (the optical depth, single scatter albedo and asymmetry parameter) in terms of the liquid water path and equivalent radius of the drop size distribution. The input parameters are then used to derive the cloud radiative properties, using standard two-stream equations for a single layer. The relationships were originally derived for fairly narrow spectral bands but it was found that it is possible to average the coefficients so as to use a much smaller number of bands, without sacrificing accuracy in calculating the cloud radiative properties. This makes the parameterization fast enough to be included in GCMs. The parameterization was programmed into the radiation scheme used in the U.K. Meteorological Office GCM. This scheme and the 24 band Slingo/Schrecker scheme were compared with each other and with observations, using a variety of published datasets. There is good agreement between the two schemes for both cloud albedo and absorption, even when only four spectral bands are employed in the GCM.

Slingo, A.↗

NASA NTRS1993

A Hybrid Symmetric FEM/MOM Formulation Applied to Scattering by Inhomogeneous Bodies of Revolution

A new symmetric formulation of the Hybrid Finite Element Method (HFEM) is described which combines elements of the Electric Field Integral Equation (EFIE) and the Magnetic Field Integral Equation (MFIE) for the exterior region along with the finite element solution for the interior problem. The formulation is applied to scattering by inhomogeneous bodies of revolution. To avoid spurious modes in the interior region a combination of vector and nodal based finite elements are used. Integral equations in the exterior region are used to enforce the Sommerfield radiation condition by matching both the tangential electric and magnetic fields between interior and exterior regions.

Lee, J-F.↗

NASA NTRS1998

The Radiated Field Generated by a Monopole Source in a Short, Rigid, Rectangular Duct

This thesis develops a method to model the acoustic field generated by a monopole source placed in a moving rectangular duct. The walls of the duct are assumed to be infinitesimally thin and the source is placed at the center of the duct. The total acoustic pressure is written in terms of the free-space pressure, or incident pressure, and the scattered pressure. The scattered pressure is the augmentation to the incident pressure due to the presence of the duct. It satisfies a homogeneous wave equation and is discontinuous across the duct walls. Utilizing an integral representation of the scattered pressure, a set of singular boundary integral equations governing the unknown jump in scattered pressure is derived. This equation is solved by the method of collocation after representing the jump in pressure as a double series of shape functions. The solution obtained is then substituted back into the integral representation to determine the scattered pressure, and the total acoustic pressure at any point in the field. A few examples are included to illustrate the influence of various geometric and kinematic parameters on the radiated sound field.

Lakota, Barbara Anne↗

NASA NTRS1977

Translational anisotropy in the cosmic microwave background radiation and far-infrared emission by galactic dust clouds

The predicted emission spectrum of galactic dust at about 10 K is compared with the spectrum of 2.8-K universal blackbody radiation and with the spectrum of the anisotropy expected in the 2.8-K radiation due to motion of earth with respect to the coordinate system in which the radiation was last scattered. The extremely anisotropic galactic-dust emission spectrum may contribute a significant background to anisotropy measurements which scan through the galactic plane. The contamination would appear in an 8-mm scan around the celestial equator, for example, as a spurious 200 km/s velocity toward declination 0 deg, right ascension 19 hr, if predictions are correct. The predicted spectrum of dust emission in the galactic plane at longitudes not exceeding about 30 deg falls below the total 2.8-K cosmic background intensity at wavelengths of at least 1 mm.

Forman, M. A.↗

NASA NTRS1994

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Siegel, R.↗

NASA NTRS1992

A fast operator perturbation method for the solution of the special relativistic equation of radiative transfer in spherical symmetry

A fast method for the solution of the radiative transfer equation in rapidly moving spherical media, based on an approximate Lambda-operator iteration, is described. The method uses the short characteristic method and a tridiagonal approximate Lambda-operator to achieve fast convergence. The convergence properties and the CPU time requirements of the method are discussed for the test problem of a two-level atom with background continuum absorption and Thomson scattering. Details of the actual implementation for fast vector and parallel computers are given. The method is accurate and fast enough to be incorporated in radiation-hydrodynamic calculations.

Hauschildt, P. H.↗

NASA NTRS1982

A tutorial solution to scattering of radiation in a thin atmosphere bounded below by a diffusely reflecting, absorbing surface

A simple tutorial method, based on a photon tracking procedure, is described to determine the spherical albedo for a thin atmosphere overlying a reflecting surface. This procedure is used to provide a physical structure with which to interpret the more detailed but highly mathematical analyses presented. The final equations are shown to be in good numerical agreement with more exact solutions for thin atmospheres.

Buglia, J. J.↗

NASA NTRS1987

Transient radiative cooling of a droplet-filled layer

A proposed lightweight radiator system for waste heat dissipation in space would eject streams of coolant in the form of small, hot liquid droplets. The droplets would lose radiative energy by direct exposure to the very low-temperature environment of space, and would then be collected for reuse. The cooling behavior of a layer composed of many small droplets was studied by numerical solution of the radiative integral equations. Since there is mutual interference for radiative energy dissipation, an array droplet will cool more slowly than if each drop is exposed individually. Since liquid metal droplets may be used, the study includes results for conditions with high scattering. For optically thin regions, especially with high scattering, the temperature distribution is sufficiently uniform that the cooling can be computed using the approximation of a constant layer emittance. For optically thick layers starting at uniform temperature, the temperature distributions become nonuniform with time. It was found that the cooling process goes through a starting transient; a constant emittance condition is then achieved where the emittance is lower than that for a layer at uniform temperature.

Siegel, R.↗

NASA NTRS1981

Radiative transfer theory for active remote sensing of a layer of small ellipsoidal scatterers

The radiative transfer theory is applied within the Rayleigh approximation to calculate the backscattering cross section of a layer of randomly positioned and oriented small ellipsoids. The orientation of the ellipsoids is characterized by a probability density function of the Eulerian angles of rotation. The radiative transfer equations are solved by an iterative approach to first order in albedo. In the half space limit the results are identical to those obtained via the approach of Foldy's and distorted Born approximation. Numerical results of the theory are illustrated using parameters encountered in active remote sensing of vegetation layers. A distinctive characteristic is the strong depolarization shown by vertically aligned leaves.

Tsang, L.↗

NASA NTRS1982

Radiative transfer with partial frequency redistribution in inhomogeneous atmospheres - Application to the Jovian aurora

A direct finite difference numerical solution for the equation of radiative transfer by the Feautrier method is developed for use in planetary atmospheres. The procedure described here uses a plane-parallel atmosphere, and can treat partial frequency redistribution, inhomogeneity, external or internal sources, and various boundary conditions. Isotropic scattering is assumed, but in the case of no frequency redistribution, Rayleigh scattering can also be handled. A program utilizing this method is tested in a variety of situations against more powerful and elaborate methods. The case of the Lyman alpha aurora on Jupiter is then considered, where the effects of partial frequency redistribution are shown to be of great importance. New results for the detailed line profiles for Lyman alpha in the Jovian aurora are presented. The method is quite versatile, and should be especially useful in studying a wide range of problems related to auroral or dayglow emissions in planetary atmospheres.

Gladstone, G. R.↗

NASA NTRS1984

LANDSAT-D investigations in snow hydrology

Two stream methods provide rapid approximate calculations of radiative transfer in scattering and absorbing media. Although they provide information on fluxes only, and not on intensities, their speed makes them attractive to more precise methods. The methods provide a comprehensive, unified review for a homogeneous layer, and solve the equations for reflectance and transmittance for a homogeneous layer over a non reflecting surface. Any of the basic kernels for a single layer can be extended to a vertically inhomogeneous medium over a surface whose reflectance properties vary with illumination angle, as long as the medium can be subdivided into homogeneous layers.

Dozier, J.↗

NASA NTRS2004

Investigation of Acoustical Shielding by a Wedge-Shaped Airframe

Experiments on a scale model of an advanced unconventional subsonic transport concept, the Blended Wing Body (BWB), have demonstrated significant shielding of inlet-radiated noise. A computational model of the shielding mechanism has been developed using a combination of boundary integral equation method (BIEM) and equivalent source method (ESM). The computation models the incident sound from a point source in a nacelle and determines the scattered sound field. In this way the sound fields with and without the airfoil can be estimated for comparison to experiment. An experimental test bed using a simplified wedge-shape airfoil and a broadband point noise source in a simulated nacelle has been developed for the purposes of verifying the analytical model and also to study the effect of engine nacelle placement on shielding. The experimental study is conducted in the Anechoic Noise Research Facility at NASA Langley Research Center. The analytic and experimental results are compared at 6300 and 8000 Hz. These frequencies correspond to approximately 150 Hz on the full scale aircraft. Comparison between the experimental and analytic results is quite good, not only for the noise scattering by the airframe, but also for the total sound pressure in the far field. Many of the details of the sound field that the analytic model predicts are seen or indicated in the experiment, within the spatial resolution limitations of the experiment. Changing nacelle location produces comparable changes in noise shielding contours evaluated analytically and experimentally. Future work in the project will be enhancement of the analytic model to extend the analysis to higher frequencies corresponding to the blade passage frequency of the high bypass ratio ducted fan engines that are expected to power the BWB.

Gerhold, Carl H.↗

NASA NTRS2006

Investigation of Acoustical Shielding by a Wedge-Shaped Airframe

Gerhold, Carl H.↗

NASA NTRS1985

The use of field radiometers in reflectance factor and atmospheric measurements

Multispectral radiometers have been designed especially for the measurement of the reflectance factor of ground features. Reflectance factor data obtained with the aid of these instruments are used as 'ground truth' for aircraft and satellite experiments. The data provide a basis for the verification of models which have been developed to describe the radiation environment of surfaces. The considered radiometers can also be employed for atmospheric measurements. In the present paper, equations are developed for a number of applications. Attention is given to the reflectance factor measurement in the field, an analysis of the reflectance factor error, scattered and direct irradiance measurements, and the measurement of the atmospheric extinction coefficient.

Che, N.↗

NASA NTRS2017

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

Dlugach, Janna M.↗

NASA NTRS1991

An analytic solution of the transient behavior of backscattering thermal protective coatings exposed to combined radiative and convective heating

An analytic solution of the material response to combined radiative and convective heating is presented. The solution includes the equations of radiative transfer (within the material), coupled to a transient energy equation which contains both radiative and convective terms. The analysis allows for unlimited spectral detail, but assumes that within the range of applicability, the various material properties do not vary significantly with temperature. Also, to facilitate development of the analytic solution, it is assumed that scattering within the material dominates absorption, and the material exposed surface does not ablate. The exposed surface boundary condition includes convective heating and spectral radiation, some of which is absorbed by the surface and some which penetrates the surface.

Cornelison, Charles J.↗

NASA NTRS1997

Particle Scattering in the Resonance Regime: Full-Wave Solution for Axisymmetric Particles with Large Aspect Ratios

Reliable descriptions of the optical properties of clouds and aerosols are essential for studies of radiative transfer in planetary atmospheres. The scattering algorithms provide accurate estimates of these properties for spherical particles with a wide range of sizes and refractive indices, but these methods are not valid for non-spherical particles (e.g., ice crystals, mineral dust, and smoke). Even though a host of methods exist for deriving the optical properties of nonspherical particles that are very small or very large compared with the wavelength, only a few methods are valid in the resonance regime, where the particle dimensions are comparable with the wavelength. Most such methods are not ideal for particles with sharp edges or large axial ratios. We explore the utility of an integral equation approach for deriving the single-scattering optical properties of axisymmetric particles with large axial ratios. The accuracy of this technique is shown for spheres of increasing size parameters and an ensemble of randomly oriented prolate spheroids of size parameter equal to 10.079368. In this last case our results are compared with published results obtained with the T-matrix approach. Next we derive cross sections, single-scattering albedos, and phase functions for cylinders, disks, and spheroids of ice with dimensions extending from the Rayleigh to the geometric optics regime. Compared with those for a standard surface integral equation method, the storage requirement and the computer time needed by this method are reduced, thus making it attractive for generating databases to be used in multiple-scattering calculations. Our results show that water ice disks and cylinders are more strongly absorbing than equivalent volume spheres at most infrared wavelengths. The geometry of these particles also affects the angular dependence of the scattering. Disks and columns with maximum linear dimensions larger than the wavelength scatter much more radiation in the forward and backward directions and much less radiation at intermediate phase angles than equivalent volume spheres.

Zuffada, Cinzia↗