Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “radiative transfer equations”

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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Remote sounding of cloudy atmospheres. I - The single cloud layer

The relaxation method for the inverse solution of the radiative transfer equation is applied in a dual-frequency scheme for the determination of complete vertical temperature profiles in cloudy atmospheres from radiance observations alone, without any additional information related to the expected solutions. The dual-frequency principle employs to advantage a property in the Planck function of the dependence of intensity on frequency. This property leads to the formulation of a new convergence criterion for the selection of cloud-sounding frequencies to be used for reconstructing the clear column radiance from observations made in the presence of a broken cloud layer in all fields of view. The principle is applied to the case of observations in two adjacent or partially overlapping fields of view and to the case of observations in a single field of view. The solutions are illustrated by numerical examples in the dual-frequency ranges of the 4.3 and 15-micron CO2 bands of the terrestrial atmosphere.

Chahine, M. T.↗
NASA NTRS1975

A modified Henyey method for computing radiative transfer hydrodynamics

The implicit hydrodynamic code of Kutter and Sparks (1972), which is limited to optically thick regions and employs the diffusion approximation for radiative transfer, is modified to include radiative transfer effects in the optically thin regions of a model star. A modified Henyey method is used to include the solution of the radiative transfer equation in this implicit code, and the convergence properties of this method are proven. A comparison is made between two hydrodynamic models of a classical Cepheid with a 12-day period, one of which was computed with the diffusion approximation and the other with the modified Henyey method. It is found that the two models produce nearly identical light and velocity curves, but differ in the fact that the former never has temperature inversions in the atmosphere while the latter does when sufficiently strong shocks are present.

Karp, A. H.↗
NASA NTRS1975

A study of the effects of vertical resolution and measurement errors on an iteratively inverted temperature profile

A direct inversion method for inverting the temperature profile from satellite-measured radiation is discussed. The nth power of the weighting function in the integral radiative-transfer equation is used as the weight in the averaging process. The vertical resolution of the inverted temperature profile and the response of the inverted temperature profile to the measurement errors are examined in terms of n. It is found that for smaller values of n, the vertical resolution and the effect of measurement errors are reduced. When n = 0, both the vertical resolution and error effect are minimum. The temperature profile is adjusted by a constant; any structure different from the initial shape cannot be resolved. This is equivalent to the case where the entire atmosphere is treated as one layer with a fixed shape of temperature profile. When n approaches infinity, both the vertical resolution and error effect are maximum. This is equivalent to the case where the entire atmosphere is divided into m (the number of spectral channels) layers. Within each layer, the temperatures are adjusted by a constant, and any structure different from the initial shape cannot be resolved. Also, the shape of the final solution is closer to the initial profile if the value of n is smaller.

Chow, M.-D.↗
NASA NTRS1976

The proper weighting function for retrieving temperatures from satellite measured radiances

One class of methods for converting satellite measured radiances into atmospheric temperature profiles, involves a linearization of the radiative transfer equation: delta r = the sum of (W sub i) (delta T sub i) where (i=1...s) and where delta T sub i is the deviation of the temperature in layer i from that of a reference atmosphere, delta R is the difference in the radiance at satellite altitude from the corresponding radiance for the reference atmosphere, and W sub i is the discrete (or vector) form of the T-weighting (i.e., temperature weighting) function W(P), where P is pressure. The top layer of the atmosphere corresponds to i = 1, the bottom layer to i = s - 1, and i = s refers to the surface. Linearization in temperature (or some function of temperature) is at the heart of all linear or matrix methods. The weighting function that should be used is developed.

Arking, A.↗
NASA NTRS1976

A single field of view method for retrieving tropospheric temperature profiles from cloud-contaminated radiance data

An iterative method is presented to retrieve single field of view (FOV) tropospheric temperature profiles directly from cloud-contaminated radiance data. A well-defined temperature profile may be calculated from the radiative transfer equation (RTE) for a partly cloudy atmosphere when the average fractional cloud amount and cloud-top height for the FOV are known. A cloud model is formulated to calculate the fractional cloud amount from an estimated cloud-top height. The method is then examined through use of simulated radiance data calculated through vertical integration of the RTE for a partly cloudy atmosphere using known values of cloud-top height(s) and fractional cloud amount(s). Temperature profiles are retrieved from the simulated data assuming various errors in the cloud parameters. Temperature profiles are retrieved from NOAA-4 satellite-measured radiance data obtained over an area dominated by an active cold front and with considerable cloud cover and compared with radiosonde data. The effects of using various guessed profiles and the number of iterations are considered.

Hodges, D. B.↗
NASA NTRS1976

Thermal microwave emission from half-space random media

Brightness temperatures resulting from microwave thermal emission from a half-space random medium are calculated. The random medium has a nonuniform temperature profile and is characterized by correlation functions that possess both vertical and lateral variations. Radiative transfer equations are derived. They are solved with an iterative integral equation approach for small scattering albedo and with a numerical approach for general cases. New results are illustrated, discussed, and compared with various special cases. Phenomena caused by resonant scattering, which is absent under Rayleigh approximations, are revealed. Scattering in the lateral direction contributes to the decrease of the equivalent reflectivity and the increase of the brightness temperature.

Tsang, L.↗
NASA NTRS1976

The diffusion approximation. An application to radiative transfer in clouds

It is shown how the radiative transfer equation reduces to the diffusion equation. To keep the mathematics as simple as possible, the approximation is applied to a cylindrical cloud of radius R and height h. The diffusion equation separates in cylindrical coordinates and, in a sample calculation, the solution is evaluated for a range of cloud radii with cloud heights of 0.5 km and 1.0 km. The simplicity of the method and the speed with which solutions are obtained give it potential as a tool with which to study the effects of finite-sized clouds on the albedo of the earth-atmosphere system.

Arduini, R. F.↗
NASA NTRS1976

Remote sensing of chlorophyll concentration: State-of-the-art, 1975

Remote measurement of chlorophyll concentration of the world's oceans from satellite observations could potentially be extremely useful for assessments of productivity in large areas for which measurements by other means would be impractical. The basis of these measurements rests with the physics of the interaction of light with material dissolved and suspended in the water. It is theoretically possible to predict the nature of light upwelled from the ocean surface from a solution to the radiative transfer equation. Practically, however, this is difficult. Monte-Carlo methods presently are thought to be the most viable method to treat the general theoretical problem. With restrictive assumptions of the nature of scattering, it is possible to construct simpler models. Algorithms developed to relate chlorophyll concentration (or some other parameter, i.e., seechi depth) to the upwelled light spectrum are discussed.

Atwell, B. H.↗
NASA NTRS1977

Effect of surface roughness on the microwave brightness temperature of soils

The effect of surface roughness on the brightness temperature of a moist terrain was studied through the modification of Fresnel reflection coefficient and using the radiative transfer equation. Model calculations are in good qualitative agreement with the observed dependence of the brightness temperature on the moisture content in the surface layer.

Choudhury, B. J.↗
NASA NTRS1976

Theory of thermal microwave emission from a two-layer medium

Thermal microwave emission from a scattering layer overlying a homogeneous half space is studied with the radiative transfer approach. Scattering models of random medium and discrete spherical scatterers are used. The radiative transfer equations are solved by both the classical method and the invariant imbedding method. The brightness temperatures of the two-layer model exhibit distinguishing features important to microwave passive remote sensing.

Tsang, L.↗
NASA NTRS1977

Thermal microwave emission from a random inhomogeneous layer over a homogeneous medium using the method of invariant imbedding

The paper studies thermal microwave emission from an inhomogeneous slab of a random medium, with possible nonuniform absorption, scattering, and temperature profiles, bounded by different dielectrics on both sides. The invariant imbedding method is used to cast the boundary value problem of the radiative transfer equations into an initial value problem at zero slab thickness. As a numerical example, the angular and polarization variations of brightness temperatures for ice over water are considered.

Tsang, L.↗
NASA NTRS1977

Albedo of the ocean-atmosphere system - Influence of sea foam

The influence of the ocean's optical properties and wind induced sea surface foam (white caps) on the short-wave albedo of the ocean-atmosphere system is studied by solving the radiative transfer equation using a Monte Carlo method. It is found that for a foam free ocean, the planetary albedo of a very clear ocean is at most 10 percent greater than that for a totally absorbing ocean. However, the introduction of a relatively small amount of sea foam on the surface can produce a considerable increase in the albedo, especially if the foam is highly reflecting. For example, it is shown that for foam which is totally reflecting (the foam albedo is 1), an increase in the wind speed from 6 to 14 m/sec would double the planetary albedo for small solar zenith angles.

Gordon, H. R.↗
NASA NTRS1978

A new inversion method for remote sounding of planetary atmospheres

An inversion method which is applicable to high resolution observations where the spectral lines are fully resolved is described. The technique is based on matching calculated slopes of the spectral line profiles with slopes of the observed lineshapes, and involves finding an inverse solution to the derivative of the radiative transfer equation with respect to frequency. The method is applied to inversion of ozone absorption lines in the earth's atmosphere and the results are compared with those obtained by a conventional method. Advantages include narrower weighting functions providing a higher vertical resolution; higher atmospheric level which may be probed, more faster and more stable convergence, and more accurate retrieved profiles.

Abbas, M. M.↗
NASA NTRS1978

Effect of surface roughness on the microwave emission from soils

The effect of surface roughness on the brightness temperature of a moist terrain was studied through the modification of Fresnel reflection coefficient and using the radiative transfer equation. The modification involves introduction of a single parameter to characterize the roughness. It is shown that this parameter depends on both the surface height variance and the horizontal scale of the roughness. Model calculations are in good quantitative agreement with the observed dependence of the brightness temperature on the moisture content in the surface layer. Data from truck mounted and airborne radiometers are presented for comparison. The results indicate that the roughness effects are greatest for wet soils where the difference between smooth and rough surfaces can be as great as 50K.

Choudhury, B. J.↗
NASA NTRS1977

Comparison of predicted and observed solar radiation in an urban area

Measurements of the downward solar radiant flux in the St. Louis area are compared with predictions from an approximate solution to the radiative transfer equation. The atmospheric aerosols were assumed to have a power size distribution and the refractive indices suggested by Fischer (1973) for an urban area. On a relatively clean day, the predictions compared well with observations. On a hazy day, the comparison was poor with the a priori choice of aerosol properties. The particles on the hazy day apparently had more submicron particles than those found in the assumed size distribution, and the particles were considerably less absorbing than those observed by Fischer. These changes could represent the effects of relative humidity and different air mass characteristics.

Bergstrom, R. W.↗
NASA NTRS1978

The D/H and C/H ratios in Jupiter from the CH3D phase

A study is made of D/H and C/H ratios in Jupiter from the CH3D phase, noting the previous investigations have yielded inconsistent results. Spectra are analyzed by a comprehensive comparison with realistically computed synthetic spectra generated by the numerical solution of the radiative transfer equation for inhomogeneous Jovian and telluric atmospheric models. Results are presented in terms of: (1) the apparent enhancement of both D and C in Jupiter, (2) the apparent deuterium overabundance, and (3) the variability of the CH3D column abundance.

Beer, R.↗
NASA NTRS1978

Remote sensing of optical properties in continuously stratified waters

The radiative transfer equation is solved by Monte Carlo methods for natural waters in which the optical properties are distributed with depth. It is demonstrated that interpreting the reflectance of a continuously stratified ocean in terms of an equivalent homogeneous ocean yields the average of a particular combination of the water's optical properties over the dimensionless penetration depth. Although in general the dimensionless penetration depth cannot be remotely measured, a method is presented for estimating the actual penetration depth from the remote observations if the medium's absorption coefficient is known, independent of depth, and sufficiently large. The application of this to the remote measurement of the vertical distribution of suspended sediments is discussed in detail.

Gordon, H. R.↗
NASA NTRS1978

Solar heating of the Martian dusty atmosphere

This paper examines the solar heating of the Martian atmosphere during the 1971 global dust storm observed by Mariner 9. Radiative scattering as well as absorption is included by utilizing the delta-Eddington approximation to the full radiative transfer equation. The necessary optical parameters are generated by a Mie program which uses a size distribution and a complex refractive index inferred from a number of sources, particularly from recent analyses of Mariner 9 UVS and TV observations. When uniform mixing of the dust is assumed, the solar heating per unit mass during a Martian global dust storm is remarkably uniform with height for small solar zenith angles. Heating rates may reach 80 K/day for overhead sunlight. Overall, 20% of the direct insolation is absorbed by the dust-laden atmosphere. Even optically thin widespread dust hazes may produce heating rates of several degrees Kelvin per day.

Zurek, R. W.↗