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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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NASA NTRS1988

Solution of an integral equation encountered in studies on radiative transfer in completely absorbing leaf canopies

The leaf normal distribution function is related to the extinction coefficient of direct solar radiation by a Fredholm integral equation of the first kind. The integral equation is solved by the method of constrained least squares. The solutions are stable and correct only in extreme cases and, in general, it is not possible to recover an arbitrary leaf normal distribution function.

Myneni, Ranga B.↗
NASA NTRS1998

Combining data from lidar and in situ instruments to characterize the vertical structure of aerosol optical properties

Over the last decade, the quantification of tropospheric aerosol abundance, composition and radiative impacts has become an important research endeavor. For the most part, the interest in tropospheric aerosols is derived from questions related to the global and local (instantaneous) radiative forcing of climate due to these aerosols. One approach is to study local forcing under well-defined conditions, and to extrapolate such results to global scales. To estimate local aerosol forcing, appropriate radiative transfer models can be employed (e.g., the Fu-Liou radiative transfer code, [Fu and Liou, 1993]). In general, such models require information on derived aerosol properties [Toon, 1994]; namely the aerosol optical depth, single-scattering albedo, and asymmetry factor (phase function), all of which appear in the equations of radiative transfer. In this paper, we report on a method that utilizes lidar data and in situ aerosol size distribution measurements to deduce the vertical structure of the aerosol complex index of refraction in the near IR, thus identifying the aerosol type. Together with aerosol size distributions obtained in situ, the aerosol refractive index can be used to calculate the necessary derived aerosol properties. The data analyzed here were collected during NASA's PEM West-B (Pacific Exploratory Mission) experiment, which took place in February/March 1994. The platform for the measurements was the NASA DC-8 aircraft. The primary goal of the PEM West missions [Browell et al., 1996] was the assessment of potential anthropogenic perturbations of the chemistry in the Pacific Basin troposphere. For this purpose the timing of PEM West-B corresponded to the seasonal peak in transport from the Asian continent into the Pacific basin [Merrill et al., in press]. This period normally occurs during Northern Hemisphere spring, when the Japan jet is well developed.

Redemann, J.↗
NASA NTRS1988

Cosmic-ray transport in accelerating flows

The quasi-linear transport equation of energetic charged particles is derived, including scattering by Alfven waves propagating parallel and antiparallel to a uniform magnetic field, losses by synchrotron radiation, and acceleration of the cold background fluid supporting the waves. As in the comoving frame equations of radiative transfer, scattering, and loss terms are evaluated in the frame in which the fluid is locally at rest. The diffusion approximation is applied to the resulting equation, yielding a transport equation for the isotropic part of the distribution function and a first-order approximation to the anisotropy. The conditions under which this approximation may be applied are discussed. In the nonrelativistic regime, the standard equation of the diffusion approximation is recovered. As contributions previously investigated, new effects appear from the spatial and temporal variations of the fluid velocity as well as the synchrotron radiation terms. These are discussed in detail.

Kirk, John G.↗
NASA NTRS2015

Differences Between the HUT Snow Emission Model and MEMLS and Their Effects on Brightness Temperature Simulation

Microwave emission models are a critical component of snow water equivalent retrieval algorithms applied to passive microwave measurements. Several such emission models exist, but their differences need to be systematically compared. This paper compares the basic theories of two models: the multiple-layer HUT (Helsinki University of Technology) model and MEMLS (Microwave Emission Model of Layered Snowpacks). By comparing the mathematical formulation side-by-side, three major differences were identified: (1) by assuming the scattered intensity is mostly (96) in the forward direction, the HUT model simplifies the radiative transfer (RT) equation into 1-flux; whereas MEMLS uses a 2-flux theory; (2) the HUT scattering coefficient is much larger than MEMLS; (3 ) MEMLS considers the trapped radiation inside snow due to internal reflection by a 6-flux model, which is not included in HUT. Simulation experiments indicate that, the large scattering coefficient of the HUT model compensates for its large forward scattering ratio to some extent, but the effects of 1-flux simplification and the trapped radiation still result in different T(sub B) simulations between the HUT model and MEMLS. The models were compared with observations of natural snow cover at Sodankyl, Finland; Churchill, Canada; and Colorado, USA. No optimization of the snow grain size was performed. It shows that HUT model tends to under estimate T(sub B) for deep snow. MEMLS with the physically-based improved Born approximation performed best among the models, with a bias of -1.4 K, and an RMSE of 11.0 K.

Pan, Jinmei↗
NASA NTRS2015

Polarized Bidirectional Reflectance of Optically Thick Sparse Particulate Layers: an Efficient Numerically Exact Radiative-Transfer Solution

We describe a simple yet efficient numerical algorithm for computing polarized bidirectional reflectance of an optically thick (semi-infinite), macroscopically flat layer composed of statistically isotropic and mirror symmetric random particles. The spatial distribution of the particles is assumed to be sparse, random, and statistically uniform. The 44 Stokes reflection matrix is calculated by iterating the Ambartsumian's vector nonlinear integral equation. The result is a numerically exact solution of the vector radiative transfer equation and as such fully satisfies the energy conservation law and the fundamental reciprocity relation. Since this technique bypasses the computation of the internal radiation field, it is very fast and highly accurate. The FORTRAN implementation of the technique is publicly available on the World Wide Web at http://www.giss.nasa.gov/staff/ mmishchenko/brf. It can be combined with several existing computer programs providing the requisite single-scattering properties of spherical or morphologically complex particles and applied to a wide range of optical characterization problems. Benchmark results obtained with this program can be used for testing alternative solvers of the vector radiative transfer equation.

radiative transfer↗
NASA NTRS1975

Derivation and application of the reciprocity relations for radiative transfer with internal illumination

A Green's function formulation is used to derive basic reciprocity relations for planar radiative transfer in a general medium with internal illumination. Reciprocity (or functional symmetry) allows an explicit and generalized development of the equivalence between source and probability functions. Assuming similar symmetry in three-dimensional space, a general relationship is derived between planar-source intensity and point-source total directional energy. These quantities are expressed in terms of standard (universal) functions associated with the planar medium, while all results are derived from the differential equation of radiative transfer.

Cogley, A. C.↗
NASA NTRS2020

Using Two-Stream Theory to Capture Fluctuations of Satellite-Perceived TOA SW Radiances Reflected from Clouds Over Ocean

Shortwave (SW) fluxes estimated from broadband radiometry rely on empirically gathered and hemispherically resolved fields of outgoing top-of-atmosphere (TOA) radiances. This study aims to provide more accurate and precise fields of TOA SW radiances reflected from clouds over ocean by introducing a novel semiphysical model predicting radiances per narrow sun-observer geometry. This model was statistically trained using CERES-measured radiances paired with MODIS-retrieved cloud parameters as well as reanalysis-based geophysical parameters. By using radiative transfer approximations as a framework to ingest the above parameters, the new approach incorporates cloud-top effective radius and above-cloud water vapor in addition to traditionally used cloud optical depth, cloud fraction, cloud phase, and surface wind speed. A two-stream cloud albedo – serving to statistically incorporate cloud optical thickness and cloud-top effective radius – and Cox–Munk ocean reflectance were used to describe an albedo over each CERES footprint. Effective-radius-dependent asymmetry parameters were obtained empirically and separately for each viewing-illumination geometry. A simple equation of radiative transfer, with this albedo and attenuating above-cloud water vapor as inputs, was used in its log-linear form to allow for statistical optimization. We identified the two-stream functional form that minimized radiance residuals calculated against CERES observations and outperformed the state-of-the-art approach for most observer geometries outside the sun-glint and solar zenith angles between 20 and 70∘, reducing the median SD of radiance residuals per solar geometry by up to 13.2 % for liquid clouds, 1.9 % for ice clouds, and 35.8 % for footprints containing both cloud phases. Geometries affected by sun glint (constituting between 10 % and 1 % of the discretized upward hemisphere for solar zenith angles of 20 and 70∘, respectively), however, often showed weaker performance when handled with the new approach and had increased residuals by as much as 60 % compared to the state-of-the-art approach. Overall, uncertainties were reduced for liquid-phase and mixed-phase footprints by 5.76 % and 10.81 %, respectively, while uncertainties for ice-phase footprints increased by 0.34 %. Tested for a variety of scenes, we further demonstrated the plausibility of scene-wise predicted radiance fields. This new approach may prove useful when employed in angular distribution models and may result in improved flux estimates, in particular dealing with clouds characterized by small or large droplet/crystal sizes.

Two- stream theory↗
NASA NTRS1995

Radiative Instabilities in Three-Dimensional Astrophysical Masers

Inherent instabilities in the radiative transfer for astrophysical masers have been recognized and calculated in the linear maser idealization in our previous investigations. The same instabilities are now shown to occur in the more realistic, three-dimensional geometries. Fluctuations in the emergent flux result and may be related to the observed fluctuations in the radiative flux from the 1665 MHz OH masers that have been reported to occur on timescales as short as 1000 s. The time-dependent differential equations of radiative transfer are solved numerically for three-dimensional astrophysical masers. Computations are performed for spherical and elongated (rectangular parallelepiped) geometries.

Scappaticci, Gerardo A.↗
NASA NTRS1995

A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties

An expression for the ratio of the upwelling nadir radiance L(pi, z) and the downwelling scalar irradiance E(sub od)(Z) is derived from the following equation of radiative transfer. This expression is given by RSR(z) = (L(pi, z))/E(sub od) = (f(sub b)(z)b(sub b)(z))/2 pi(k(pi, z) + c(z) - F(sub L)(z)b(sub f)(z)), where b(sub b)(z) is the backscattering coefficient, k(pi, z) is the vertical attenuation coefficient of the nadir radiance, c(z) is the beam attenuation coefficient, and f(sub b)(z) and f(sub L)(z) are shape parameters that depend on the shape of the volume scattering function and the radiance distribution. Successive approximations are subsequently applied to the above exact equation. These are f(sub b)(z) = (2 pi beta(pi - theta(sub m), z)/(b(sub b)(z))), where beta(pi - theta(sub m), z) is the volume scattering function at 180 deg minus the zenith angle of the maximum radiance, and k(pi, z) = am = c(1 - 0.52 b/c - 0.44 (b/c)(exp 2)), where m is a parameter that is numerically equal to the inverse of the average cosine of the asymptotic light field for a medium with the same inherent optical properties, a is the absorption coefficient, and b/c is the single scattering albedo. Together with f(sub L)(z) = 1.05 and application of Gershun's equation, it is shown that for nearly all oceanic cases RSR(z) identical to L(pi, z)/E(sub od)(z) = (Beta(pi - theta(sub m), z))/(a(z)(1 + m(z))).

Zaneveld, J. Ronald V.↗
NASA NTRS1967

Nonstationary radiation field

Radiation diffusion without redistribution by frequencies, equations for radiative transfer, and stellar spectrum

DIFFUSION WAVE↗
NASA NTRS1971

Indirect sensing of atmospheric temperature and water vapor using microwaves.

A prototype of the Nimbus E microwave spectrometer was flown in an airplane over various atmospheric and surface conditions. Effects of clouds and the terrestrial surface on the data are discussed. Using a multiple-regression statistical method of inverting the equation of radiative transfer, estimates of temperature and integrated contents of water vapor and liquid water in the atmosphere below the aircraft were made from the microwave data obtained at high altitude. These estimates are compared with direct measurements made by other experiments on board the aircraft, in both clear atmospheres and in the presence of clouds.

Rosenkranz, P. W.↗
NASA NTRS1972

Penetration of solar irradiances through the atmosphere and plant canopies.

The equation of radiative transfer is applied to an analysis of solar irradiances penetrating into a plant canopy covered by a turbid atmosphere. The method of discrete coordinates is applied to vertically inhomogeneous atmospheres and plant canopies. It is shown that four-point quadrature yields results with an accuracy that is consistent with irradiance measurements. It is believed that the presented computational scheme may have considerable agricultural applications.

Weinman, J. A.↗
NASA NTRS1972

Statistical versus nonstatistical temperature inversion methods

Vertical temperature profiles are derived from radiation measurements by inverting the integral equation of radiative transfer. Because of the nonuniqueness of the solution, the particular temperature profile obtained depends on the numerical inversion technique used and the type of auxiliary information incorporated in the solution. The choice of an inversion algorithm depends on many factors; including the speed and size of computer, the availability of representative statistics, and the accuracy of initial data. Results are presented for a numerical study comparing two contrasting inversion methods: the statistical-matrix inversion method and the nonstatistical-iterative method. These were found to be the most applicable to the problem of determining atmospheric temperature profiles. Tradeoffs between the two methods are discussed.

Smith, W. L.↗
NASA NTRS1973

A non-LTE study of silicon line formation in early-type main-sequence atmospheres.

We have computed populations of 16 levels of Si III-V and radiation fields in all connecting transitions; in particular the first six Si III triplet levels, including the 4553 line, and the first six Si IV levels including 4089. The computations were done for four non-LTE H-He model atmospheres, provided by Auer and Mihalas. Estimates of corresponding MK types are B1.5 V, B0.5 V, O9 V, and O6. Solutions were obtained by iterating the linearized equations of radiative transfer and statistical equilibrium, except that for less important lines an approximate equivalent two-level atom treatment was used. Continuous opacities of C, N, O, and Ne were included. All abundances were solar values.

Kamp, L. W.↗
NASA NTRS1974

Model calculations for diffuse molecular clouds

A steady state isobaric cloud model is developed. The pressure, thermal, electrical, and chemical balance equations are solved simultaneously with a simple one dimensional approximation to the equation of radiative transfer appropriate to diffuse clouds. Cooling is mainly by CII fine structure transitions, and a variety of heating mechanisms are considered. Particular attention is given to the abundance variation of H2. Inhomogeneous density distributions are obtained because of the attenuation of the interstellar UV field and the conversion from atomic to molecular hyrodgen. The effects of changing the model parameters are described and the applicability of the model to OAO-3 observations is discussed. Good qualitative agreement with the fractional H2 abundance determinations has been obtained. The observed kinetic temperatures near 80 K can also be achieved by grain photoelectron heating. The problem of the electron density is solved taking special account of the various hydrogen ions as well as heavier ones.

Glassgold, A. E.↗
NASA NTRS1974

Viscous, radiating hypersonic flow about a blunt body

The viscous, radiating hypersonic flow past an axisymmetric blunt body is analyzed based on the Navier-Stokes equations, plus a radiative equation of transfer derived from the Milne-Eddington differential approximation. The fluid is assumed to be a perfect gas with constant specific heats, a constant Prandtl number of order unity, a viscosity coefficient varying as a power of the temperature, and an absorption coefficient varying as the first power of the density and as a power of the temperature. The gray gas assumption is invoked, thereby making the absorption coefficient independent of the spectral frequency. Limiting forms of the solutions are studied as the freestream Mach number freestream Reynolds number and the temperature ratio across the shock wave, go to infinity, and as the Bouguer number and the density ratio across the shock wave go to zero. The method of matched asymptotic expansions is used in the analysis, and it is shown that there is a far-field precursor, composed of two regions, in which the fluid mechanics can be neglected for all practical purposes but included for completeness.

Passamaneck, R. S.↗