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Results for “Radiative transfer equation”

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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
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.↗
DOE OSTI2022

General Relativistic Implicit Monte Carlo Radiation-hydrodynamics

Abstract We report on a new capability added to our general relativistic radiation-magnetohydrodynamics code, Cosmos++ : an implicit Monte Carlo (IMC) treatment for radiation transport. The method is based on a Fleck-type implicit discretization of the radiation-hydrodynamics equations, but generalized for both Newtonian and relativistic regimes. A multiple reference frame approach is used to geodesically transport photon packets (and solve the hydrodynamics equations) in the coordinate frame, while radiation–matter interactions are handled either in the fluid or electron frames then communicated via Lorentz boosts and orthonormal tetrad bases attached to the fluid. We describe a method for constructing estimators of radiation moments using path-weighting that generalizes to arbitrary coordinate systems in flat or curved spacetime. Absorption, emission, scattering, and relativistic Comptonization are among the matter interactions considered in this report. We discuss our formulations and numerical methods, and validate our models against a suite of radiation and coupled radiation-hydrodynamics test problems in both flat and curved spacetimes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Nonlinear Elimination Applied to Radiation Diffusion

We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory’s deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton. In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods Eq. (4).

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Spectral broadening from turbulence in multiscale lower hybrid current drive simulations

Abstract The scattering of lower hybrid (LH) waves due to scrape-off layer filaments is investigated. It is revealed that scattering can account for the LH spectral gap without any ad hoc modification to the wave-spectrum. This is shown using a multiscale simulation approach which allows, for the first time, the inclusion of full-wave scattering physics in ray-tracing/Fokker–Planck calculations. In this approach, full-wave scattering probabilities are calculated for a wave interacting with a statistical ensemble of filaments. These probabilities are coupled to ray-tracing equations using radiative transfer theory. This allows the modeling of scattering along the entire ray-trajectory, which can be important in the multi-pass regime. Simulations are conducted for LH current drive (LHCD) in Alcator C-Mod, resulting in excellent agreement with experimental current and hard x-ray profiles. A region in filament parameter space is identified in which the impact of scattering on LHCD is saturated. Such a state coincides with experimental LHCD measurements, suggesting saturation indeed occurs in C-Mod, and therefore the exact statistical properties of the filaments are not important.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Fully Implicit Monte Carlo (FIMC) (September 2019-September 2020 Progress Report)

This research is focused on applying the NLem method to the full thermal radiative transfer (TRT) equations in the context of a Monte Carlo solution strategy. A framework has been developed for obtaining a solution to the TRT equations using the nonlinear elimination method (NLem) method. Current efforts are focused of the development and verification of the required Monte Carlo algorithm, diffusion algorithm, and material energy solver. Once all three pieces have been verified, the algorithms will then be coupled into a fully functioning method for applying NLem to the TRT equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Analytical Modeling of Exoplanet Transit Spectroscopy with Dimensional Analysis and Symbolic Regression

Abstract The physical characteristics and atmospheric chemical composition of newly discovered exoplanets are often inferred from their transit spectra, which are obtained from complex numerical models of radiative transfer. Alternatively, simple analytical expressions provide insightful physical intuition into the relevant atmospheric processes. The deep-learning revolution has opened the door for deriving such analytical results directly with a computer algorithm fitting to the data. As a proof of concept, we successfully demonstrate the use of symbolic regression on synthetic data for the transit radii of generic hot-Jupiter exoplanets to derive a corresponding analytical formula. As a preprocessing step, we use dimensional analysis to identify the relevant dimensionless combinations of variables and reduce the number of independent inputs, which improves the performance of the symbolic regression. The dimensional analysis also allowed us to mathematically derive and properly parameterize the most general family of degeneracies among the input atmospheric parameters that affect the characterization of an exoplanet atmosphere through transit spectroscopy.

79 ASTRONOMY AND ASTROPHYSICS↗
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.↗