Search NASA⌕ Search

SEARCH · Search NASA

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

On the temperature and velocity through the photosphere of a sunspot penumbra

We investigate the structure in depth of a sunspot penumbra by means of the inversion code of the radiative transfer equation proposed by Ruiz Cobo & del Toro Iniesta (1992), applied to a set of filtergrams of a sunspot, scanning the Fe I line at 5576.1 A, with a sampling interval of 30 mA, from -120 to 120 mA from line center (data previously analyzed by Title et al. 1993). The temperature structure of this penumbra is obtained for each of the 801 pixels selected (0.32 sec x 0.32 sec). On the average, the temperatures seem to decrease as we move inward, but the differences are of the order of the rms values (approximately equal 100-200 K) at a given distance to sunspot center. The outer parts of the penumbra have also a bigger curvature in the T versus log tau(sub 5) relation than the inner parts. We realize, however, that these differences might be influenced by possible stray light effects. Compared to the quiet Sun, penumbral temperatures are cooler at deep layers and hotter at high layers. A mean penumbral model atmosphere is presented. The asymmetries observed in the intensity profile (the line is magnetically insensitive) are deduced to be produced by strong gradients of the line-of-sight velocity that sharply vary spatially along slices of almost constant distance to sunspot center. These variations suggest that such gradients are not only needed to explain the broadband circular polarization observed in sunspots (see Sanchez Almeida & Lites 1992) but are a main characteristic of the fine-scale penumbra. The results are compatible with an Evershed flow present everywhere, but its gradient with depth turns out to vary so that the flow seems to be mainly concentrated in some penumbral fibrils when studied through Dopplergrams. Finally, as by-products of this study, we put constraints to the practical usefulness of the Eddington-Barbier relation, and we explain the values of the Fourier Dopplergrams to be carrying information of layers around the centroid of the generalized response function of Dopplergrams to velocity fluctuations.

Del Toro Iniesta, J. C.↗
NASA NTRS1995

An analytic radiative transfer model for a coupled atmosphere and leaf canopy

A new analytical radiative transfer model of a leaf canopy is developed that approximates multiple-scattering radiance by a four-stream formulation. The canopy model is coupled to a homogeneous atmospheric model as well as a non-Lambertian lower boundary soil surface. The same four-stream formulation is also used for the calculation of multiple scattering in the atmosphere. Comparisons of radiance derived from the four-stream model with those calculated by an iterative numerical solution of the radiative transfer equation show that the analytic model has a very high accuracy, even with a turbid atmosphere and a very dense canopy in which multiple scattering dominates. Because the coupling of canopy and atmospheric models fully accommodates anisotropic surface reflectance and atmospheric scattering and its effect on directional radiance, the model is especially useful for application to directional radiance and measurements obtained by remote sensing. Retrieval of biophysical parameters using this model is under investigation.

Liang, Shunlin↗
NASA NTRS1994

Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres

Although neglecting polarization and replacing the rigorous vector radiative transfer equation by its approximate scalar counterpart has no physical background, it is a widely used simplification when the incident light is unpolarized and only the intensity of the reflected light is to be computed. We employ accurate vector and scalar multiple-scattering calculations to perform a systematic study of the errors induced by the neglect of polarization in radiance calculations for a homogeneous, plane-parallel Rayleigh-scattering atmosphere (with and without depolarization) above a Lambertian surface. Specifically, we calculate percent errors in the reflected intensity for various directions of light incidence and reflection, optical thicknesses of the atmosphere, single-scattering albedos, depolarization factors, and surface albedos. The numerical data displayed can be used to decide whether or not the scalar approximation may be employed depending on the parameters of the problem. We show that the errors decrease with increasing depolarization factor and/or increasing surface albedo. For conservative or nearly conservative scattering and small surface albedos, the errors are maximum at optical thicknesses of about 1. The calculated errors may be too large for some practical applications, and, therefore, rigorous vector calculations should be employed whenever possible. However, if approximate scalar calculations are used, we recommend to avoid geometries involving phase angles equal or close to 0 deg and 90 deg, where the errors are especially significant. We propose a theoretical explanation of the large vector/scalar differences in the case of Rayleigh scattering. According to this explanation, the differences are caused by the particular structure of the Rayleigh scattering matrix and come from lower-order (except first-order) light scattering paths involving right scattering angles and right-angle rotations of the scattering plane.

Mishchenko, M. I.↗
NASA NTRS1995

Radiative transfer in a semiinfinite medium with a specularly reflecting boundary

A consistent solution of the radiative transfer equation characterizing photon transport in a semi-infinite medium of refractive index greater than or equal to one is obtained following the method of Sobolev. Fresnel specular reflection, Snell's law and isotropic scattering are assumed. An algorithm is developed and its accuracy is demonstrated. A numerical Laplace transform inversion leads to an efficient evaluation for the interior flux and source function distributions.

Ganapol, B. D.↗
NASA NTRS1995

Gamma-ray transfer and energy deposition in supernovae

Solutions to the energy-independent (gray) radiative transfer equations are compared to results of Monte Carlo simulations of the Ni-56 and Co-56 decay gamma-ray energy deposition in supernovae. The comparison shows that an effective, purely absorptive, gray opacity, kappa(sub gamma) approximately (0. 06 +/- 0.01)Y(sub e) sq cm/g, where Y is the total number of electrons per baryon, accurately describes the interaction of gamma-rays with the cool supernova gas and the local gamma-ray energy deposition within the gas. The nature of the gamma-ray interaction process (dominated by Compton scattering in the relativistic regime) creates a weak dependence of kappa(sub gamma) on the optical thickness of the (spherically symmetric) supernova atmosphere: The maximum value of kappa(sub gamma) applies during optically thick conditions when individual gamma-rays undergo multiple scattering encounters and the lower bound is reached at the phase characterized by a total Thomson optical depth to the center of the atmosphere tau(sub e) approximately less than 1. Gamma-ray deposition for Type Ia supernova models to within 10% for the epoch from maximum light to t = 1200 days. Our results quantitatively confirm that the quick and efficient solution to the gray transfer problem provides an accurate representation of gamma-ray energy deposition for a broad range of supernova conditions.

Swartz, Douglas A.↗
NASA NTRS1996

A technique for determining cloud free vs cloud contaminated pixels in satellite imagery

Since the first earth orbiting satellite sent pictures of the earth back to them, atmospheric scientists have been focused on the possibilities of using that information as both a forecasting tool and as a meteorological research tool. With the latest generation of Geostationary Operational Environmental Satellites (GOES) now entering service, that view of the earth yields views at a frequency and resolution never before available. These satellites have imagers with a five band multi-spectral capability with high spatial resolution. In addition, the sounder has eighteen thermal infrared (IR) channels plus one low-resolution visible band. With a resolution as small as one kilometer, GOES provides scientists with a powerful eye on the atmosphere. Menzel and Purdom (1994) detail both the imager and sounder capability as well as other systems on the GOES satellites. Immediately apparent in the visible channel are the patterns of clouds swirling over both oceans and continents. These clouds range in size from huge planetary systems covering thousands of kilometers to puffy fair weather cumulus clouds on the order of half a kilometer in size. With the IR sensors temperature patterns are observed. High clouds appear very cold, while low stratus field show temperatures near that of the surface. The surface, in turn, generally appears warmer than the clouds. It would seem then a simple manner to determine cloud and surface temperature from the imagery, but such is not the case. While most of the atmospheric constituents are well mixed and homogeneous, water vapor is not. The water molecule, because of its unique structure and vibration modes, affects the transmittance of the atmosphere most notably in the infrared regions. There are regions of the IR spectrum where water vapor acts as a strong absorber, and at others it is nearly transparent. The transparent wavelengths are called windows, and one such window occurs at 11.2 microns. Adjacent to this window at 12.7 microns which is strongly absorbed by water vapor. These two wavelengths form what is known as a split window, the utility of which was used. Using the linearized form of the radiative transfer equation, they were able to use the split window to determine the amount of water vapor present in the atmosphere. Jedlovec developed the physical split-window (PSW) technique which determines the integrated water content (IWC). The PSW method using Visible Infrared Spin Scan Radiometer (VISSR) Atmospheric Sounder (VAS) found on the older versions of the GOES satellites was used. Recently, Jedlovec and colleagues have been attempting to apply the PSW method using full disk IR imagery obtained by the new generation of GOES satellites. IWC is essential for improved analysis and prediction of convective storms which have been observed to develop in regions of both strong and rapidly evolving moisture gradients. It has also been used in the prediction of clouds and precipitation.

Wohlman, Richard A.↗
NASA NTRS1996

Internal Radiation Effects in Zirconia Thermal Barrier Coatings

Using thermal barrier coatings on combustor liners, turbine vanes, and rotating blades is important for reducing metal temperatures in current and advanced aircraft engines. Zirconia is a common coating material, and it is partially transparent to thermal radiation. Radiation becomes more significant as temperatures are raised for higher efficiency in advanced engines. Calculations are often made with radiation effects neglected inside the coating. The effect of radiation is illustrated here, where an analytical procedure is provided by using the two-flux method for the radiative contribution. A detailed study was made of ceramic thermal barrier coatings for diesel engines, and a two-flux analysis was developed for radiation in semitransparent multilayer composites. These efforts provide the basis for the present analysis where illustrative solutions are obtained for typical conditions in an aircraft engine. The formulation and solution of the exact spectral radiative transfer equations including large scattering, as is characteristic of zirconia, are rather complicated. The two-flux method is used here to provide a simplified method.

Siegel, Robert↗
NASA NTRS1979

Modeling of Radiative Heating in Base Region of Jovian Entry Probe

A theoretical model is derived to determine the average thermodynamic properties in the expanding region, recirculating region, recompression region, and neck region through application of one-dimensional conservation equations. Radiative transfer is calculated using spectrally detailed computer codes accounting for nonequilibrium. The results show that the most severe heating occurs immediately behind the frustum, and that the recompression and neck regions are the major sources of radiation that heats the base stagnation point, The radiation flux to the base point is slightly stronger with ablation than without. Its value is 0.11(43 P(sub b)/P(sub s))(sup 2) times that to the front stagnation point where the base pressure P(sub b) is defined as the average pressure in the recirculating region and P(sub s) is the front stagnation-point pressure. The time-integrated heat load to the base point is 18(43 P(sub b)/P(sub s))(sup 2) kJ/sq cm.

Park, Chul↗
NASA NTRS1997

Improved Passive Microwave Algorithms for North America and Eurasia

Microwave algorithms simplify complex physical processes in order to estimate geophysical parameters such as snow cover and snow depth. The microwave radiances received at the satellite sensor and expressed as brightness temperatures are a composite of contributions from the Earth's surface, the Earth's atmosphere and from space. Owing to the coarse resolution inherent to passive microwave sensors, each pixel value represents a mixture of contributions from different surface types including deep snow, shallow snow, forests and open areas. Algorithms are generated in order to resolve these mixtures. The accuracy of the retrieved information is affected by uncertainties in the assumptions used in the radiative transfer equation (Steffen et al., 1992). One such uncertainty in the Chang et al., (1987) snow algorithm is that the snow grain radius is 0.3 mm for all layers of the snowpack and for all physiographic regions. However, this is not usually the case. The influence of larger grain sizes appears to be of more importance for deeper snowpacks in the interior of Eurasia. Based on this consideration and the effects of forests, a revised SMMR snow algorithm produces more realistic snow mass values. The purpose of this study is to present results of the revised algorithm (referred to for the remainder of this paper as the GSFC 94 snow algorithm) which incorporates differences in both fractional forest cover and snow grain size. Results from the GSFC 94 algorithm will be compared to the original Chang et al. (1987) algorithm and to climatological snow depth data as well.

Foster, James↗
NASA NTRS1997

Atmospheric Correction of Satellite Imagery Using Modtran 3.5 Code

When performing satellite remote sensing of the earth in the solar spectrum, atmospheric scattering and absorption effects provide the sensors corrupted information about the target's radiance characteristics. We are faced with the problem of reconstructing the signal that was reflected from the target, from the data sensed by the remote sensing instrument. This article presents a method for simulating radiance characteristic curves of satellite images using a MODTRAN 3.5 band model (BM) code to solve the radiative transfer equation (RTE), and proposes a method for the implementation of an adaptive system for automated atmospheric corrections. The simulation procedure is carried out as follows: (1) for each satellite digital image a radiance characteristic curve is obtained by performing a digital number (DN) to radiance conversion, (2) using MODTRAN 3.5 a simulation of the images characteristic curves is generated, (3) the output of the code is processed to generate radiance characteristic curves for the simulated cases. The simulation algorithm was used to simulate Landsat Thematic Mapper (TM) images for two types of locations: the ocean surface, and a forest surface. The simulation procedure was validated by computing the error between the empirical and simulated radiance curves. While results in the visible region of the spectrum where not very accurate, those for the infrared region of the spectrum were encouraging. This information can be used for correction of the atmospheric effects. For the simulation over ocean, the lowest error produced in this region was of the order of 105 and up to 14 times smaller than errors in the visible region. For the same spectral region on the forest case, the lowest error produced was of the order of 10-4, and up to 41 times smaller than errors in the visible region,

Gonzales, Fabian O.↗
NASA NTRS2001

Inherent and Apparent Scattering Properties of Coated or Uncoated Spheres Embedded in an Absorbing Host Medium

The conventional Lorenz-Mie formalism is extended to the scattering process associated with a coated sphere embedded in an absorbing medium. It is shown that apparent and inherent scattering cross sections of a scattering particle, which are identical in the case of transparent host medium, are different if the host medium is absorptive. Here the inherent single-scattering properties are derived from the near-field information whereas the corresponding apparent counterparts are derived from the far-field asymptotic form of the scattered wave with scaling of host absorption that is assumed to be in an exponential form. The formality extinction and scattering efficiencies defined in the same manner as in the conventional sense can be unbounded. For a nonabsorptive particle embedded in an absorbing medium, the effect of host absorption on the phase matrix elements associated with polarization is significant. This effect, however, is largely reduced for strongly absorptive particles such as soot. For soot particles coated with water, the impurity can substantially reduce the single-scattering albedo of the particle if the size parameter is small. For water-coating soot and hollow ice spheres, it is shown that the phase matrix elements -P(sub 12)/P(sub 11) and P(sub 33)/P(sub 11) are unique if the shell is thin, as compared with the case for thick shell. Furthermore, the radiative transfer equation regarding a multidisperse particle system in an absorbing medium is discussed. It is illustrated that the conventional computation algorithms can be applied to solve the multiple scattering process if the scaled apparent single-scattering properties are applied.

Yang, P.↗
NASA NTRS2001

Remote-Sensing Reflectance and Inherent Optical Properties for Optically Deep Waters: A Revisit

Remote-sensing reflectance (r(rs)) is defined as the ratio of upwelling radiance to downwelling irradiance. Relationships between remote-sensing reflectance and inherent optical properties serve as the basis for ocean-color modeling, as well as for spectral deduction of oceanic constituents through analytical/semi-analytical models of ocean color. A decade ago, a simple and concise formula based on Monte Carlo simulations was developed by relating rrs to a property u, the ratio of backscattering (b(b)) to the sum of absorption (a) and backscattering (u = b(b)/(a+b(b))). This relationship generally ignored the shape differences in phase functions between molecular scattering and particle scattering. In this study, the relationship is updated with separate parameters for molecular and particle scattering, based on the Radiative Transfer Equation through use of Hydrolight numerical solutions. The new approach fits r(rs) better than an earlier traditional formula, for both clear and turbid waters.

Lee, Zhong-Ping↗
NASA NTRS2001

A Multi-Band Analytical Algorithm for Deriving Absorption and Backscattering Coefficients from Remote-Sensing Reflectance of Optically Deep Waters

A multi-band analytical (MBA) algorithm is developed to retrieve absorption and backscattering coefficients for optically deep waters, which can be applied to data from past and current satellite sensors, as well as data from hyperspectral sensors. This MBA algorithm applies a remote-sensing reflectance model derived from the Radiative Transfer Equation, and values of absorption and backscattering coefficients are analytically calculated from values of remote-sensing reflectance. There are only limited empirical relationships involved in the algorithm, which implies that this MBA algorithm could be applied to a wide dynamic range of waters. Applying the algorithm to a simulated non-"Case 1" data set, which has no relation to the development of the algorithm, the percentage error for the total absorption coefficient at 440 nm a (sub 440) is approximately 12% for a range of 0.012 - 2.1 per meter (approximately 6% for a (sub 440) less than approximately 0.3 per meter), while a traditional band-ratio approach returns a percentage error of approximately 30%. Applying it to a field data set ranging from 0.025 to 2.0 per meter, the result for a (sub 440) is very close to that using a full spectrum optimization technique (9.6% difference). Compared to the optimization approach, the MBA algorithm cuts the computation time dramatically with only a small sacrifice in accuracy, making it suitable for processing large data sets such as satellite images. Significant improvements over empirical algorithms have also been achieved in retrieving the optical properties of optically deep waters.

Lee, Zhong-Ping↗
NASA NTRS2004

Near Real-time Derived Products from MODIS

As part of the Short-term Prediction Research Transition (SPoRT) program at NASA/MSFC, near real-time total precipitable water and land/sea surface temperature products from MODIS, on NASA's Terra and Aqua satellites, are being derived from a subset of MODIS channels with spectral characteristics similar to those planned for the GOES-R ABI. Under the SPoRT program these products are made available to several NWS Forecast Offices to assist in the preparation of short-term forecasts. This transition activity, from research to operations, serves to prepare forecasters for the next generation of satellite observing capabilities through real-time, hands-on applications to their forecast problems. The derived products are produced from a physical retrieval algorithm which can be applied to polar or geostationary measurements. The algorithm is a perturbation solution of the radiation transfer equation for a nonscattering atmosphere requiring first-guess temperature and moisture profiles. For this application first-guess information is obtained from the latest model forecasts. The utility of this retrieval approach is that it provides a near real-time high resolution update of a model's forecasted parameter allowing forecasters to validate and monitor the performance of the model's forecast. The poster will provide a description of the retrieval methodology and examples of the derived products. Case studies will also be presented comparing these products with those obtained from the Earth Observing System (EOS) MODIS science team algorithms.

Suggs, Ron↗
NASA NTRS2004

Radiative Transfer Modeling of a Large Pool Fire by Discrete Ordinates, Discrete Transfer, Ray Tracing, Monte Carlo and Moment Methods

Five computational methods for solution of the radiative transfer equation in an absorbing-emitting and non-scattering gray medium were compared on a 2 m JP-8 pool fire. The temperature and absorption coefficient fields were taken from a synthetic fire due to the lack of a complete set of experimental data for fires of this size. These quantities were generated by a code that has been shown to agree well with the limited quantity of relevant data in the literature. Reference solutions to the governing equation were determined using the Monte Carlo method and a ray tracing scheme with high angular resolution. Solutions using the discrete transfer method, the discrete ordinate method (DOM) with both S(sub 4) and LC(sub 11) quadratures, and moment model using the M(sub 1) closure were compared to the reference solutions in both isotropic and anisotropic regions of the computational domain. DOM LC(sub 11) is shown to be the more accurate than the commonly used S(sub 4) quadrature technique, especially in anisotropic regions of the fire domain. This represents the first study where the M(sub 1) method was applied to a combustion problem occurring in a complex three-dimensional geometry. The M(sub 1) results agree well with other solution techniques, which is encouraging for future applications to similar problems since it is computationally the least expensive solution technique. Moreover, M(sub 1) results are comparable to DOM S(sub 4).

Jensen, K. A.↗
NASA NTRS2004

Frequency Integrated Radiation Models for Absorbing and Scattering Media

The objective of this work is to contribute to the simplification of existing radiation models used in complex emitting, absorbing, scattering media. The application in view is the computation of flows occurring in such complex media, such as certain stellar interiors or combusting gases. In these problems, especially when scattering is present, the complexity of the radiative transfer leads to a high numerical cost, which is often avoided by simply neglecting it. The complexity lies partly in the strong dependence of the spectral coefficients on frequency. Models are then needed to capture the effects of the radiation when one cannot afford to directly solve for it. In this work, the frequency dependence will be modeled and integrated out in order retain only the average effects. A frequency-integrated radiative transfer equation (RTE) will be derived.

Ripoll, J. F.↗
NASA NTRS2007

Method and program product for determining a radiance field in an optical environment

A hybrid method is presented by which Monte Carlo techniques are combined with iterative relaxation techniques to solve the Radiative Transfer Equation in arbitrary one-, two- or three-dimensional optical environments. The optical environments are first divided into contiguous regions, or elements, with Monte Carlo techniques then being employed to determine the optical response function of each type of element. The elements are combined, and the iterative relaxation techniques are used to determine simultaneously the radiance field on the boundary and throughout the interior of the modeled environment. This hybrid model is capable of providing estimates of the under-water light field needed to expedite inspection of ship hulls and port facilities. It is also capable of providing estimates of the subaerial light field for structured, absorbing or non-absorbing environments such as shadows of mountain ranges within and without absorption spectral bands such as water vapor or CO.sub.2 bands.

Reinersman, Phillip N.↗
NASA NTRS2011

Canopy Spectral Invariants. Part 1: A New Concept in Remote Sensing of Vegetation

The concept of canopy spectral invariants expresses the observation that simple algebraic combinations of leaf and canopy spectral reflectance become wavelength independent and determine two canopy structure specific variables the recollision and escape probabilities. These variables specify an accurate relationship between the spectral response of a vegetation canopy to incident solar radiation at the leaf and the canopy scale. They are sensitive to important structural features of the canopy such as forest cover, tree density, leaf area index, crown geometry, forest type and stand age. This paper presents the mathematical basis of the concept which is linked to eigenvalues and eigenvectors of the three-dimensional radiative transfer equation.

Knyazikhin, Yuri↗