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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 235 records · Page 13
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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.↗
NASA NTRS1978

Microwave brightness of polar firn as measured by Nimbus 5 and 6 ESMR

The microwave emission from a half-space medium characterized by coordinate dependent scattering and absorbing centers was calculated by numerically solving the radiative transfer equation by the method of invariant imbedding. A Mie scattering phase function and surface polarization was included in the calculation. Also included are the physical temperature profile and the temperature variation of the index of refraction for ice. Using published values of grain size and temperature profile data of polar firn, the brightness temperature was calculated for the 1.55 cm and 0.8 cm wavelengths. For selected regions in Greenland and Antarctica, the results are in reasonable agreement with the observed Nimbus-5 and Nimbus-6 ESMR data.

Chang, A. T. C.↗
NASA NTRS1978

Two-stream theory of spectral reflectance of snow

Spectral reflectance of snow under diffuse illumination is studied using the two-stream approximation of the radiative transfer equation. The scattering and absorption within the snowcover due to the randomly distributed ice grains are characterized by the single scattering albedo and anisotropic phase function. Geometric optics calculations are used to relate the scattering and absorption parameters to grain size and density of snow. Analytical expressions for the intensity within the snowpack and the asymptotic flux extinction coefficient are also obtained. Good agreement is shown between the theory and available experimental data on visible and near-infrared reflectance and asymptotic flux extinction coefficient. The theory also may be used to explain the observed effect of aging on the snow reflectance.

Choudhury, B. J.↗
NASA NTRS1979

Estimating tropical cyclone outer surface winds from satellite microwave data

Warm temperature anomalies over tropical cyclones are sensed by the 55.45 GHz channel of the Nimbus 6 Scanning Microwave Spectrometer. Radial brightness temperature gradients are related to radial surface pressure gradients through the hydrostatic and radiative transfer equations. Surface wind speeds outside of the radius of maximum wind are calculated from the pressure gradients and compared with observations.

Kidder, S. Q.↗
NASA NTRS1979

Determination of tropical cyclone surface pressure and winds from satellite microwave data

An approach to the problem of deducing wind speed and pressure around tropical cyclones is presented. The technique, called the Surface Wind Inference from Microwave data (SWIM technique, uses satellites microwave sounder data to measure upper tropospheric temperature anomalies which may then be related to surface pressure anomalies through the hydrostatic and radiative transfer equations. Surface pressure gradients outside of the radius of maximum wind are estimated for the first time. Future instruments may be able to estimate central pressure with + or - 0/1 kPa accuracy.

Kidder, S. Q.↗