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NASA NTRS1981

Bidirectional reflectance spectroscopy. I - Theory

An approximate analytic solution is derived for the radiative transfer equation describing particulate surface light scattering, taking into account multiple scattering and mutual shadowing. Analytical expressions for the following quantities are found: bidirectional reflectance, radiance coefficient and factor, the normal, Bond, hemispherical, and physical albedos, integral phase function and phase integral, and limb-darkening profile. Scattering functions for mixtures can be calculated, as well as corrections for comparisons of experimental transmission or reflection spectra with observational planetary spectra. The theory should be useful for the interpretation of reflectance spectroscopy of laboratory surfaces and the photometry of solar system objects.

Hapke, B.↗

NASA NTRS1981

Radiative transfer theory for active remote sensing of a layer of small ellipsoidal scatterers

The radiative transfer theory is applied within the Rayleigh approximation to calculate the backscattering cross section of a layer of randomly positioned and oriented small ellipsoids. The orientation of the ellipsoids is characterized by a probability density function of the Eulerian angles of rotation. The radiative transfer equations are solved by an iterative approach to first order in albedo. In the half space limit the results are identical to those obtained via the approach of Foldy's and distorted Born approximation. Numerical results of the theory are illustrated using parameters encountered in active remote sensing of vegetation layers. A distinctive characteristic is the strong depolarization shown by vertically aligned leaves.

Tsang, L.↗

NASA NTRS1981

Radiative transfer theory for active remote sensing of a homogeneous layer containing spherical scatterers

The radiative transfer theory with a Rayleigh scattering model is used to study the effect of volume scattering for active microwave remote sensing of low-loss and scattering dominant areas by obtaining backscattering cross sections through iterative and numerical approaches. The iterative approach gives closed form solutions which are valid when the effect of scattering is small. The depolarization of the backscattered power is shown to be a second-order effect. For the general cases, a numerical approach is used to solve the radiative transfer equations. The theoretical results are compared and illustrated for the various cases.

Shin, R. T.↗

NASA NTRS1981

N-stream approximations to radiative transfer

Schuster's two-stream approximation (1905) is first derived from Chandrasekhar's radiative transfer equation (1950), and then extended to an arbitrary number of streams. The resulting technique for solving the transfer function similar to the discrete ordinate and spherical harmonic methods, is useful for modeling atmospheres with complicated phase functions and moderate optical depths. The resulting n coupled linear differential equations are simple and consume less computer time than other approximations, yet have the same required accuracy. The approximation is also flexible with respect to the choice of patch functions, and no approximations are made on the form of the phase function, other than its expansion into Legendre polynomials. A four-stream approximation is evaluated for a Henyey-Greenstein phase function with an asymmetry factor equal to 0.5.

Acquista, C.↗

NASA NTRS1982

A climate index derived from satellite measured spectral infrared radiation

The vertical infrared radiative emitting structure (VIRES) climate index, based on radiative transfer theory and derived from the spectral radiances typically used to retrieve temperature profiles, is introduced. It is assumed that clouds and climate are closely related and a change in one will result in a change in the other. The index is a function of the cloud, temperature, and moisture distributions. It is more accurately retrieved from satellite data than is cloudiness per se. The VIRES index is based upon the shape and relative magnitude of the broadband weighting function of the infrared radiative transfer equation. The broadband weighting curves are retrieved from simulated satellite infrared sounder data (spectral radiances). The retrieval procedure is described and the error error sensitivities of the method investigated. Index measuring options and possible applications of the VIRES index are proposed.

Abel, M. D.↗

NASA NTRS1981

Radiative transfer theory for passive microwave remote sensing of random media

The radiative transfer theory is applied to a random medium for the case of passive remote sensing. A general numerical solution with Gaussian quadrature method is studied. For a medium with laminar structure or a medium with cylindrical structure, closed form solutions are obtained by solving the radiative transfer equations of a two-layer random medium. Numerical results for the general case and the two limiting cases are compared.

Chuang, S. L.↗

NASA NTRS1982

Model studies of nitric oxide fluorescence in the earth's backscattered spectrum

Fluorescent emissions from nitric oxide appear imposed upon the Rayleigh backscattered spectrum of the earth's atmosphere between 250 and 300 nm in wavelength. Satellite instruments designed to monitor the global ozone distribution can routinely observe these signals although techniques for exploiting the data are not yet available. Application of a radiative transfer equation developed for an atmosphere including absorption by ozone, molecular scattering, and nitric oxide fluorescence shows the three most prominent NO emissions relative to the 250-300 nm backscattered sunlight to be the (1,4), (1,6), and (0,3) gamma bands. Analysis of the contribution function for each emission band indicates that the fluorescent signals can provide useful information on the magnitude and variability of nitric oxide between 40 and 140 km in altitude.

Frederick, J. E.↗

NASA NTRS1982

Solar reflection from a regular array of horizontally finite clouds

The reflected flux from a regular array of 2- and 3-D clouds has been computed to estimate the effect of fractional cloud cover on albedos and the solar flux available to heat the earth's surface. The broken clouds are represented by a regular array of identical cuboids for the 3-D problem and equally spaced, infinitely long, bars for the 2-D problem. A diffusion approximation to the radiative transfer equation is used to compute the fluxes leaving each face of the cloud. Interaction between clouds is simulated by assuming diffuse exitance from the cloud faces and applying angle factors to obtain modified boundary conditions on each cloud face.

Weinman, J. A.↗

NASA NTRS1982

Comparison of LANDSAT-2 and field spectrometer reflectance signatures of south Texas rangeland plant communities

The accuracy was assessed for an atmospheric correction method that depends on clear water bodies to infer solar and atmospheric parameters for radiative transfer equations by measuring the reflectance signature of four prominent south Texas rangeland plants with the LANDSAT satellite multispectral scanner (MSS) and a ground based spectroradiometer. The rangeland plant reflectances produced by the two sensors were correlated with no significant deviation of the slope from unity or of the intercept from zero. These results indicated that the atmospheric correction produced LANDSAT MSS estimates of rangeland plant reflectances that are as accurate as the ground based spectroradiometer.

Richardson, A. J.↗

NASA NTRS1982

Prospects for the future

Atmospheric and surface fields produced from the TIROS N high resolution infrared sounder/microwave sounding unit data are discussed. The data were analyzed by direct physical inversion of the multispectral radiative transfer equation. Sea ice mapping and sea surface temperature determination are addressed.

Atlas, D.↗

NASA NTRS1982

A review of crop canopy reflectance models

Various models for calculating crop canopy reflectance, in the visible and infrared wavelengths, from the optical and geometrical properties of a canopy and its constituents are reviewed. The radiative transfer equation is discussed as well as both analytical and numerical crop reflectance models which are manifestations of the solution of this equation. Recommendations are made for further work in modeling of canopy reflectance.

Goel, N. S.↗

NASA NTRS1981

Nimbus-7 scanning multichannel microwave radiometer /SMMR/ in-orbit performance appraisal

Calibration and processing techniques enacted during first year of operation of the Nimbus-7 scanning multichannel microwave radiometer (SMMR) are described. It was found that in-orbit calibration was necessary, as was fine-tuning of the geophysical parameter retrieval parameters to account for anomalies such as lower-than-expected polarization differences in ocean radiances. Phase shifts in the scan angles were corrected in order to avoid polarization mixing. Calibration constants to eliminate cross-talk and phase shift effects were established for radiation reflected from the earth, then averaged over data from 300 orbits to fit points on a sine curve to better than 0.2 K accuracy. An iterative approach was determined to be necessary due to signal anomalies caused by antenna dish oscillations. Global ocean and atmosphere parameters used to construct a radiation model of ten latitude bands are presented for use in radiation transfer equations.

Gloersen, P.↗

NASA NTRS1982

Probing the presently tenuous link between comets and the origin of life

The possibilities of using millimeter-wave technology to probe the subsurface processes of comets to investigate links between cometary materials and the origins of life are explored. It is noted that current theories hold that the necessities for life to begin comprise a fairly uniform temperature, the presence of a solvent to give materials mobility, and the presence of atoms which can form long chains of molecules. Consideration is given to two cometary nuclei models: a core with an equal amount of liquid water and lunar material, and a nucleus with equal amounts of frozen water ice and lunar material. Solutions to the radiative transfer equation for the two models are presented to characterize identifiable emissions using radiometric spectrometer instrumentation on a spacecraft. Particular species such as OH, CN, HCN, and glycine are expected to be detectable if present.

Hobbs, R. W.↗

NASA NTRS1983

Basis for spectral curvature algorithms in remote sensing of chlorophyll

A simple, empirically derived algorithm for estimating oceanic chlorophyll concentrations from spectral radiances measured by a low-flying spectroradiometer has proved highly successful in field experiments in 1980-82. The sensor used was the Multichannel Ocean Color Sensor, and the originator of the algorithm was Grew (1981). This paper presents an explanation for the algorithm based on the optical properties of waters containing chlorophyll and other phytoplankton pigments and the radiative transfer equations governing the remotely sensed signal. The effects of varying solar zenith, atmospheric transmittance, and interfering substances in the water on the chlorophyll algorithm are characterized, and applicability of the algorithm is discussed.

Campbell, J. W.↗

NASA NTRS1983

Improved cloud motion wind vector and altitude assignment using VAS

A CO2 cloud tracking technique to determine simultaneous heights and velocities of cloud motion winds is presented. Using animated CO2 channel imagery from VAS (Visible Infrared Spin-Scan Radiometer Atmospheric Sounder), multi-level cloud situations are separated into high, middle and low level cloud motion wind vectors by the CO2 slicing method. The VAS CO2 channel radiometric values are used in the CO2 absorption method to assign quantitative heights to the cloud vectors; cloud top pressures are determined from the ratio of the deviations in cloud produced radiances and the corresponding clear air values for three CO2 channels in a radiative transfer equation formulation. Two case studies are presented that show CO2 cloud-motion wind vectors to be in good agreement with radiosonde wind observations and CO2 cloud heights to be within a 50 mb rms deviation of radiosonde, bispectral and stereo height determinations.

Menzel, W. P.↗

NASA NTRS1983

Direct determination of surface albedos from satellite imagery

An empirical method to measure the spectral surface albedo of surfaces from Landsat imagery is presented and analyzed. The empiricism in the method is due only to the fact that three parameters of the solution must be determined for each spectral photograph of an image on the basis of independently known albedos at three points. The approach is otherwise based on exact solutions of the radiative transfer equation for upwelling intensity. Application of the method allows the routine construction of spectral albedo maps from satelite imagery, without requiring detailed knowledge of the atmospheric aerosol content, as long as the optical depth is less than 0.75, and of the calibration of the satellite sensor.

Mekler, Y.↗

NASA NTRS1983

Passive and active remote sensing of atmospheric precipitation

Both passive and active remote sensing of atmospheric precipitation are studied with the vector radiative transfer equations by making use of the Mie scattering phase functions and incorporating the raindrop-size distributions. For passive remote sensing, the Gaussian quadrature method is employed to solve for the brightness temperatures. For active remote sensing, an iterative approach carrying out to the second order in albedo is used to calculate for the bistatic coefficients, the backscattering cross sections/unit volume, and the interchannel cross talks. The calculated results are plotted as a function of rainfall rates and compared to various available experimental data. The theoretical model is easily applied to the remote sensing of aerosol particles, smoke, fog, and haze at infrared and visible frequencies.

Jin, Y. Q.↗

NASA NTRS1982

Determination of the horizontal and vertical distribution of clouds from infrared satellite sounding data

A numerical algorithm, based on a physical inversion of the radiative transfer equation, is developed to retrieve the global distribution of the horizontal cloud cover, the cloud-top pressure levels and their temperature. The algorithm makes use of infrared and microwave temperature sounding data to derive the clear-column vertical temperature profiles and then uses the same infrared sounding data to obtain the corresponding cloud parameters. Experimental verification of this method is carried out using data from the High resolution Infrared Sounder (HIRS) and the Microwave Sounding Unit (MSU) operating on the NOAA weather satellite system.

Chahine, M. T.↗