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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
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NASA NTRS1988

A new approach to resonance line scattering in planetary atmospheres

The invariant imbedding technique is applied to the problem of resonance line scattering with frequency redistribution. By applying the principles of invariance to the resonance line scattering problem a set of non-linear, integrodifferential equations for the scattering and transmission functions are derived. Thus, an alternate approach to the resonance line scattering problem is presented. Rather than solving for the specific intensity directly the invariant imbedding equations may be solved for the scattering and transmission functions from which the specific intensity may be calculated. The technique is very general and in principle, can accommodate scattering in inhomogeneous atmospheres with arbitrary frequency redistribution and scattering phase functions. Solutions to the invariant imbedding equations in some simple cases are presented. If the scattering is isotropic and completely noncoherent and the atmosphere may be modeled as homogeneous, the scattering and transmission functions may be expressed in terms of generalized H, X and Y functions. This technique is extended to the problems of coupled spectral lines and scattering of radiation from internal sources.

Yelle, Roger V.↗
NASA NTRS2001

Calculation of the Scattering Amplitude Without Partial Wave Expansion

Two developments in the direct calculation of the angular differential scattering amplitude have been implemented: (a) The integral expansion of the scattering amplitude is simplified by analytically integration over the azimuthal angle. (b) The resulting integral as a function of scattering angle is calculated by using the numerically generated wave function from a finite element method calculation. Results for electron-hydrogen scattering in the static approximation will be shown to be as accurate as a partial wave expansion with as many l's as is necessary for convergence at the incident energy being calculated.

Shertzer, J.↗
NASA NTRS1986

Variational divergence in wave scattering theory with Kirchhoffean trial functions

In a recent study of variational improvement of the Kirchhoff approximation for electromagnetic scattering by rough surfaces, a key ingredient in the variational principle was found to diverge for important configurations (e.g., backscatter) if the polarization had any vertical component. The cause and a cure of this divergence are discussed here. The divergence is demonstrated to occur for arbitrary perfectly conducting scatterers and its universal characterstics are determined, by means of a general divergence criterion that is derived. A variational cure for the divergence is prescribed, and it is tested successfully on a standard scattering model.

Bird, J. F.↗
NASA NTRS1982

Photometry and polarimetry of Titan - Pioneer 11 observations and their implications for aerosol properties

Pioneer 11 measurements of Titan's limb darkening and polarization at red and blue wavelengths are refined, and the integrated disk brightness measurements at phase angles from 22 to 96 deg, over which Titan's phase coefficient averages about 0.014 magnitudes/deg in both colors, are reduced. Comparisons of the data with vertically homogeneous multiple scattering models indicate that the single-scattering phase functions of the aerosols in both colors are flat at scattering angles between 80 and 150 deg, with a small peak at larger scattering angles. Although a vertically homogeneous model in which particles are assumed to scatter as spheres cannot simultaneously match the polarization observations of both colors for any refractive index, observed polarizations are most sensitive to the particle properties near optical depth 1/2 in each color. Models based on single scattering by spheres can therefore be successful over a range of refractive indices, if the size of the particles increases with depth and if the cross section of the particles increases sufficiently rapidly with decreasing wavelength.

Tomasko, M. G.↗
NASA NTRS1988

Properties of interstellar dust in reflection nebulae

Observations of interstellar dust in reflection nebulae are the closest analog in the interstellar medium to studies of cometary dust in our solar system. The presence of a bright star near the reflection nebula dust provides the opportunity to study both the reflection and emission characteristics of interstellar dust. At 0.1 to 1 micrometer, the reflection nebula emission is due to starlight scattered by dust. The albedo and scattering phase function of the dust is determined from observations of the scattered light. At 50 to 200 micrometers, thermal emission from the dust in equilibrium with the stellar radiation field is observed. The derived dust temperature determines the relative values of the absorption coefficient of the dust at wavelengths where the stellar energy is absorbed and at far infrared wavelengths where the absorbed energy is reradiated. These emission mechanisms directly relate to those seen in the near and mid infrared spectra of comets. In a reflection nebula the dust is observed at much larger distances from the star than in our solar system, so that the equilibrium dust temperature is 50 K rather than 300 K. Thus, in reflection nebulae, thermal emission from dust is emitted at 50 to 200 micrometer.

Sellgren, Kristin↗
NASA NTRS1992

The application of the principles of invariance to the radiative transfer equation in plant canopies

Solutions of the radiative transfer equation describing photon interactions with vegetation canopies are important in remote sensing since they provide the canopy reflectance distribution required in the interpretation of satellite acquired information. The general one-dimensional two-angle transport problem for a finite copy of arbitrary leaf angle distribution is considered. Analytical solutions are obtained in terms of generalized Chandrasekhar's X- and Y-functions by invoking the principles of invariance. A critical step in the formulation involves the decomposition of the integral of the scattering phase function into a product of known functions of the incident and scattered photon directions. Several simplified cases previously considered in the literature are derived from the generalized solution. Various symmetries obeyed by the scattering operator and reciprocity relations are formally proved.

Ganapol, B. D.↗
NASA NTRS1989

The 27-28 October 1986 FIRE IFO Cirrus case study: Comparison of radiative transfer theory with observations by satellite and aircraft

Observations of cirrus and altocumulus clouds during the First International Satellite Cloud Climatology Project Regional Experiment (FIRE) are compared to theoretical models of cloud radiative properties. Three tests are performed. First, LANDSAT radiances are used to compare the relationship between nadir reflectance ot 0.83 micron and beam emittance at 11.5 microns with that predicted for model calculations using spherical and nonspherical phase functions. Good agreement is found between observations and theory when water droplets dominate. Poor agreement is found when ice particles dominate, especially using scattering phase functions for spherical particles. Even when compared to a laboratory measured ice particle phase function, the observations show increased side scattered radiation relative to the theoretical calculations. Second, the anisotropy of conservatively scattered radiation is examined using simultaneous multiple angle views of the cirrus from LANDSAT and ER-2 aircraft radiometers. Observed anisotropy gives good agreement with theoretical calculations using the laboratory measured ice particle phase function and poor agreement with a spherical particle phase function. Third, Landsat radiances at 0.83, 1.65, and 2.21 microns are used to infer particle phase and particle size. For water droplets, good agreement is found with King Air FSSP particle probe measurements in the cloud. For ice particles, the LANDSAT radiance observations predict an effective radius of 60 microns versus aircraft observations of about 200 microns. It is suggested that this descrepancy may be explained by uncertainty in the imaginary index of ice and by inadequate measurements of small ice particles by microphysical probes.

Wielicki, Bruce A.↗
NASA NTRS1985

Microwave model prediction and verifications for vegetated terrain

To understand the scattering properties of a deciduous and a coniferous type vegetation scattering models were developed assuming either a disc type leaf or a needle type leaf. The major effort is to calculate the corresponding scattering phase functions and then each of the functions is used in a radiative transfer formulation to compute the scattering intensity and consequently the scattering coefficient. The radiative transfer formulation takes into account the irregular ground surface by including the rough soil surface in the boundary condition. Thus, the scattering model accounts for volume scattering inside the vegetation layer, the surface scattering from the ground and the interaction between scattering from the soil surface and the vegetation volume. The contribution to backscattering by each of the three scattering mechanisms is illustrated along with the effects of each layer or surface parameter. The major difference between the two types of vegetation is that when the incident wavelength is comparable to the size of the leaf there is a peak appearing in the mid angular region of the backscattering curve for the disc type leaf whereas it is a dip in the same region for a needle type leaf.

Fung, A. K.↗
NASA NTRS1987

Determination of the scaled optical thickness of clouds from reflected solar radiation measurements

A method for determination of scaled optical thickness from reflected solar radiation measurements is described in which measurements of the reflected function are compared with asymptotic expressions for the reflection function of optically thick layers. Analytic formulas are derived which show the dependence of the reflection and transmission functions of nonabsorbing atmospheres on cloud optical thickness, ground albedo, and the asymmetry factor. An expression is derived which shows that the ground albedo produces a constant bias in the derived optical thickness, regardless of the value of the measured reflection function. Results from an analysis of high-resolution images, obtained in Oklahoma, of the reflection function of clouds shows the impact of details of the single scattering phase function on the derived optical thickness.

King, Michael D.↗
NASA NTRS2000

Intercomparison of Models Representing Direct Shortwave Radiative Forcing by Sulfate Aerosols

The importance of aerosols as agents of climate change has recently been highlighted. However, the magnitude of aerosol forcing by scattering of shortwave radiation (direct forcing) is still very uncertain even for the relatively well characterized sulfate aerosol. A potential source of uncertainty is in the model representation of aerosol optical properties and aerosol influences on radiative transfer in the atmosphere. Although radiative transfer methods and codes have been compared in the past, these comparisons have not focused on aerosol forcing (change in net radiative flux at the top of the atmosphere). Here we report results of a project involving 12 groups using 15 models to examine radiative forcing by sulfate aerosol for a wide range of values of particle radius, aerosol optical depth, surface albedo, and solar zenith angle. Among the models that were employed were high and low spectral resolution models incorporating a variety of radiative transfer approximations as well as a line-by-line model. The normalized forcings (forcing per sulfate column burden) obtained with the several radiative transfer models were examined, and the discrepancies were characterized. All models simulate forcings of comparable amplitude and exhibit a similar dependence on input parameters. As expected for a non-light-absorbing aerosol, forcings were negative (cooling influence) except at high surface albedo combined with small solar zenith angle. The relative standard deviation of the zenith-angle-averaged normalized broadband forcing for 15 models-was 8% for particle radius near the maximum in this forcing (approx. 0.2 microns) and at low surface albedo. Somewhat greater model-to-model discrepancies were exhibited at specific solar zenith angles. Still greater discrepancies were exhibited at small particle radii and much greater discrepancies were exhibited at high surface albedos, at which the forcing changes sign; in these situations, however, the normalized forcing is quite small quite small. Discrepancies among the models arise from inaccuracies in Mie calculations, differing treatment of the angular scattering phase function, differing wavelength and angular resolution, and differing treatment of multiple scattering. These results imply the need for standardized radiative transfer methods tailored to the direct aerosol forcing problem. However, the relatively small spread in these results suggests that the uncertainty in forcing arising from the treatment of radiative forcing of a well-characterized aerosol at well-specified surface albedo is smaller than some of the other sources of uncertainty in estimates of direct forcing by anthropogenic sulfate aerosols and anthropogenic aerosols generally.

Boucher, O.↗
NASA NTRS2002

Cloud Algorithm Design and Performance for the 2002 Geoscience Laser Altimeter System Mission

A satellite borne lidar instrument, the Geoscience Laser Altimeter System (GLAS), is to be launched in late 2002 and will provide continuous profiling of atmospheric clouds and aerosol on a global basis. Data processing algorithms have been developed to provide operational data products in near real time. Basic data products for cloud observations are the height of the top and bottom of single to multiple cloud layers and the lidar calibrated observed backscatter cross section up to the level of signal attenuation. In addition the optical depth and vertical profile of visible extinction cross section of many transmissive cloud layers and most haze layers are to be derived. The optical thickness is derivable in some cases from the attenuation of the molecular scattering below cloud base. In other cases an assumption of the scattering phase function is required. In both cases a estimated correction for multiple scattering is required. The data processing algorithms have been tested in part from aircraft measurements used to simulated satellite data. The GLAS lidar observations will be made from an orbit that will allow inter comparison with all other existing satellite cloud measurements.

Spinhirne, J. D.↗
NASA NTRS1972

Photometric studies of Saturn's ring and eclipses of the Galilean satellites

Reliable data defining the photometric function of the Saturn ring system at visual wavelengths are interpreted in terms of a simple scattering model. To facilitate the analysis, new photographic photometry of the ring has been carried out and homogeneous measurements of the mean surface brightness are presented. The ring model adopted is a plane parallel slab of isotropically scattering particles; the single scattering albedo and the perpendicular optical thickness are both arbitrary. Results indicate that primary scattering is inadequate to describe the photometric properties of the ring: multiple scattering predominates for all angles of tilt with respect to the Sun and earth. In addition, the scattering phase function of the individual particles is significantly anisotropic: they scatter preferentially towards the sun. Photoelectric photometry of Ganymede during its eclipse by Jupiter indicate that neither a simple reflecting-layer model nor a semi-infinite homogeneous scattering model provides an adequate physical description of the Jupiter atmosphere.

Brunk, W. E.↗
NASA NTRS1977

Complex refractive index of Martian dust - Wavelength dependence and composition

The size distribution and complex refractive index of Martian dust-cloud particles observed in 1971 with the Mariner 9 UV spectrometer are determined by matching the observed single-scattering albedo and phase function with Mie-scattering calculations for size distributions of spheres. Values of phase function times single-scattering albedo are presented for 12 wavelength intervals in the range from 190 to 350 nm, and best-fit values are obtained for the absorption index. It is found that the absorption index of the dust particles increases with decreasing wavelength from 350 to about 210 nm and then drops off shortward of 210 nm, with a structural shoulder occurring in the absorption spectrum between 240 and 250 nm. A search for a candidate material that can explain the strong UV absorption yields TiO2, whose anatase polymorph has an absorption spectrum matching that of the Martian dust. The TiO2 content of the dust particles is estimated to be a few percent or less.

Pang, K.↗
NASA NTRS1992

Scattering properties of Venus' surface

Radar backscatter functions Sigma-(carat)(sub 0)(phi) for incidence angles between 0 less than or equal to phi less than or equal to 4-10 deg were derived from Magellan altimetry radar echoes. The procedure includes constrained solution of a system of simultaneous equations for which the echo-spectrum and echo time profile are inputs. A practical and workable set of constraints was applied; optimization and improved results are expected as the analysis matures. The scattering functions yield information on small-scale surface structures (tens of centimeters to tens of meters) but averaged over hundreds of sq km. RMS surface slopes derived from fits of analytic functions to the Sigma-(carat)(sub 0)(phi) results were converted to map form and show patterns similar to those reported using other techniques. While all three forms are found on Venus, fit residuals imply that an exponential scattering function matches data better than either the Hagfors or Gaussian form in most areas, although the Hagfors function may be a better descriptor at some sites. Limited study of image data indicates that average backscatter cross section, and possibly its slope, can be derived at oblique angles (17 deg less than or equal to phi less than or equal to 45 deg). Offsets of the echo peak in altimetry spectra are surprisingly common and are loosely correlated with Venus topography, but no cause for this phenomenon was identified.

Tyler, G. L.↗
NASA NTRS1975

Prolongation structures of nonlinear evolution equations

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Wahlquist, H. D.↗
NASA NTRS1994

Dynamics of hard sphere colloidal dispersions

Our objective is to perform on homogeneous, fully equilibrated dispersions the full set of experiments characterizing the transition from fluid to solid and the properties of the crystalline and glassy solid. These include measurements quantifying the nucleation and growth of crystallites, the structure of the initial fluid and the fully crystalline solid, and Brownian motion of particles within the crystal, and the elasticity of the crystal and the glass. Experiments are being built and tested for ideal microgravity environment. Here we describe the ground based effort, which exploits a fluidized bed to create a homogeneous, steady dispersion for the studies. The differences between the microgravity environment and the fluidized bed is gauged by the Peclet number Pe, which measures the rate of convection/sedimentation relative to Brownian motion. We have designed our experiment to accomplish three types of measurements on hard sphere suspensions in a fluidized bed: the static scattering intensity as a function of angle to determine the structure factor, the temporal autocorrelation function at all scattering angles to probe the dynamics, and the amplitude of the response to an oscillatory forcing to deduce the low frequency viscoelasticity. Thus the scattering instrument and the colloidal dispersion were chosen such as that the important features of each physical property lie within the detectable range for each measurement.

Zhu, J. X.↗
NASA NTRS1978

Radiative transfer calculated from a Markov chain formalism

The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.

Esposito, L. W.↗