Radiative exchange among non-Lambert surfaces.
Radiative exchange in enclosures, reflectance of whose surfaces can be approximated by sum of diffuse and specular component
SPECULAR REFLECTION↗
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Point spread functions in imaging a Lambert surface from zenith through a thin scattering layer
Analytical techniques for good spatial resolution in remotely sensed images of renewable resources, such as crops, are discussed for satellite multispectral radiometry. A model is developed for an optically and geometrically thin scattering layer to account for atmospheric scattering above the object pixel of fluxes reflected from adjacent areas. The cross radiance is explored as a spread function of a point source and as a spurious component of measured radiance, and an integration over large source areas is formulated. The Henyey-Greenstein (HG) phase function is defined for an integral over a sphere and point-spread functions are presented for HG scattering. Cross radiance limited spatial resolution is also determined for the HG phase function and boundaries between reflecting and black half-planes are considered in terms of the cross radiance.
Otterman, J.↗
Modeling the non-grey-body thermal emission from the full moon
The present series of thermophysical computer models for solid-surfaced planetary bodies whose surface roughness is modeled as paraboloidal craters of specified depth/diameter ratio attempts to characterize the nongrey-body brightness temperature spectra of the moon and of the Galilean satellites. This modeling, in which nondiffuse radiation properties and surface roughness are included for rigorous analysis of scattered and reemitted radiation within a crater, explains to first order the behavior of both limb-scans and disk-integrated IR brightness temperature spectra for the full moon. Only negative surface relief can explain lunar thermal emissions' deviation from smooth Lambert-surface expectations.
Vogler, Karl J.↗
Surface properties and effective resolution from ground-based observations of Mercury
A detailed study to evaluate ground-based photographs of Mercury has been carried out. Models of the surface scattering properties have been assumed and smeared with a Gaussian function for direct comparison with center-to-limb scans along Mercury's intensity equator. Data from a range of phase angles from 31 to 92 deg have been compared with smeared models assuming a Lambert surface, a surface which obeys the Lommel-Seeliger law and one which is Minnaertian, having a variable coefficient. Within the limits of the observations a lunar Minnaert surface yields the most consistent interpretation. An objective evaluation of the resolution of the photographs is obtained in terms of Gaussian half-widths.
Beebe, R. F.↗
The delta-four-stream approximation for radiative flux transfer
An approximate technique for solving the radiative transfer problem for fluxes reflected, transmitted, and absorbed by a homogeneous scattering layer is presented. The technique is a straightforward delta-function modification of a solution to the transfer equation in closed form via the discrete-ordinates method with four streams. By the use of four streams, significant improvement in accuracy is obtained for anisotropic phase functions over that obtained by similarly employed two-stream approximations with delta-functions. However, the computational effort is increased only slightly. Equations are developed for the general case of a layer underlaid by a reflecting Lambert surface. Graphical comparisons are given of fractional error resulting from the use of this method with that resulting from the use of typical four-stream and delta-two-stream techniques.
Cuzzi, J. N.↗
Azimuthal brightness variation and albedo measurements of the Uranian rings
The recent Voyager encounter with Uranus has produced new insights and observational constraints on the structure, composition, and evolution of the Uranian rings. Careful measurements have been made of the brightness variation as a function of longitude for the alpha, beta, gamma, delta, and epsilon rings. These measurements showed a substantial variation in azimuthal brightness because of the varying width of the rings. The single scattering albedo of the epsilon ring particles was found to be 3.9 + or - 0.6 percent (for the Lambert surface) or 2.3 + or - 0.4 percent assuming the 'lunar-type' phase function. The optical depth at apoapse of the epsilon ring was found to be 0.40 + or - 0.05.
Svitek, Tomas↗
Cryogenic storage on the moon.
Cryogenic fluid storage on moon surface, considering Lambert reflection law, thermal insulation performance, incident heat flux and boil-off rates
LUNAR SURFACE↗
Lunar surface roughness - Shadowing and thermal emission.
Model for lunar surface roughness effect on emission of thermal IR radiation and casting of shadows in sunlight
THERMAL EMISSION↗
Cryogenic storage on the moon.
Cryogenic fluid storage on moon surface, considering Lambert reflection law, thermal insulation performance, incident heat flux and boil-off rates
Gabron, F.↗
Investigation of the effect of atmospheric dust on the determination of total ozone from the earth's ultraviolet reflectivity measurements, 1
Two computer algorithms are described. These algorithms were used for computing the aximuth-independent component of the intensity of the monochromatic radiation emerging at the top of a pseudo-spherical atmosphere with arbitrary vertical distribution of ozone, and with any arbitrary height distribution of up to two different kinds of aerosol. This atmospheric model was assumed to rest on a surface obeying Lambert's law of reflection.
Dave, J. V.↗
Atmospheric effects on radiometry from zenith of a plane with dark vertical protrusions
Effects of an optically thin plane-parallel scattering atmosphere on radiometric imaging from the zenith of a specific surface-type are analyzed. The surface model was previously developed to describe arid steppe, where the sparse vegetation forms dark vertical protrusions from the bright soil-plane. The analysis is in terms of the surface reflectivity to the zenith r sub p for the direct beam, which is formulated as r sub p = r sub i exp (-s tan theta sub 0), where v sub i is the Lambert law reflectivity of the soil, the protrusions parameters s is the projection on a vertical plane of protrusions per unit area and theta sub 0 is the zenith angle. The surface reflectivity r sub p is approximately equal to that for the global irradiance (which is directly measured in the field) only for a narrow range of the solar zenith angles. The effects of the atmosphere when imaging large uniform areas of this type are comparable to those in imaging a Lambert surface with a reflectivity r sub p. Thus, the effects can be approximated by those in the case of a dark Lambert surface (analyzed previously), inasmuch as r sub p is smaller than the soil reflectivity r sub i for any off-zenith illumination. The surface becomes effectively darker with increasing solar zenith angle. Adjacency effects of a reflection from one area and scattering in the instantaneous field of view (object pixel) are analyzed as cross radiance and cross irradiance.
Otterman, J.↗
The effect of surface anisotropy on the accuracy of total ozone estimates from satellite observations
The total amount of ozone in a vertical column of the earth's atmosphere is being derived from satellite measurements of the intensity of ultraviolet sunlight scattered by the earth-atmosphere system. The algorithm for deriving the ozone amount utilizes the assumption that the earth's surface reflects the incident light isotropically according to Lambert's law. Natural surface reflection deviates more or less from this law. Two extreme examples of anisotropic reflection from dark ocean and from bright snow are analyzed by means of models for their effects on the derived values of ozone.
Fraser, R. S.↗
Lageos orbit and the albedo problem
The objective was to obtain an analytic expression for the radiation pressure force on a satellite due to sunlight reflected from the Earth. The Lageos satellite undergoes unexplained along-track accelerations. These accelerations are believed to be due mainly to terrestrial radiation pressure. The effect of sunlight reflected off the surface of the Earth must thus be modeled to insure an accurate orbit for Lageos. An accurate orbit is necessary for carrying out Lageos' mission of measuring tectonic plate motion, polar motion, and Earth rotation. The present investigation focuses on a spherical harmonic approach to the problem. An equation for the force was obtained by assuming the Earth's surface reflects sunlight according to Lambert's law. The equation is an integral over the whole Earth's surface. Expressions occurring inside the integral are expressed in terms of spherical harmonics. The problem is thus reduced to integrating products of spherical harmonics.
Rubincam, D. P.↗
Effect of aerosols on the estimation of total ozone in an atmospheric column from the measurements of its ultraviolet radiance
The problem of estimating the total ozone amount of an atmospheric column in the presence of stratospheric and tropospheric aerosols is studied by means of simulated spectral measurements for the five-wavelength Nimbus 4 BUV configuration and the six-wavelength Nimbus G TOMS configuration, and by analyzing such measurements with appropriate total ozone estimation procedures. The simulated spectral measurements were generated for forty different atmospheric models arrived at by varying the total ozone content and various aerosol parameters. A total of ten different values of the solar zenith angle and eight different values of the Lambert reflectivity of the underlying surface were used. It was found that the values of total ozone in an atmospheric column estimated by the five-wavelength procedure can be in error by about + or -2% as a result of particulate contamination encountered in the terrestrial atmosphere under average conditions. Errors due to tropospheric particulate contamination can be reduced significantly by taking appropriate advantage of the additional spectral measurement offered by the Nimbus G TOMS instrument.
Dave, J. V.↗
Voyager disk resolved photometry of the Saturnian satellites
The scattering properties of the icy satellites of Saturn are studied. Scans of intensity along the photometric equator near opposition are analyzed, and disk-resolved measurements of intensity are fitted to simple photometric functions. Histograms of the albedo distribution across the satellite disks are constructed, and the geometric albedos are determined as a function of wavelength. It is found that, at low phase angles, Rhea and Dione closely follow lunar behavior with almost no limb darkening. Mimas, Tethys, and especially Enceladus show significant limb darkening at low phase angles, which suggest multiple scattering is important for their surfaces. No satellite's surface can be described by Lambert's law. The darker satellites are redder, and the darker areas of each satellite are redder. A longitudinal dark stripe which represents a 15 percent decrease in albedo is situated near the center of the trailing side of Tethys. Mimas and Enceladus both have remarkably flat spectral reflectances into the ultraviolet.
Buratti, B. J.↗
UV 380 nm Reflectivity of the Earth's Surface
The 380 nm radiance measurements of TOMS (Total Ozone Mapping Spectrometer) have been converted into a global data set of daily (1979 to 1992) Lambert equivalent reflectivities R of the Earth's surface and boundary layer (clouds, aerosols, surface haze, and snow/ice). Since UV surface reflectivity is between 2 and 8% for both land and water during all seasons of the year (except for ice and snow cover), reflectivities larger than the surface value indicates the presence of clouds, haze, or aerosols in the satellite field of view. Statistical analysis of 14 years of daily data show that most snow/ice-free regions of the Earth have their largest fraction of days each year when the reflectivity is low (R less than 10%). The 380 nm reflectivity data shows that the true surface reflectivity is 2 to 3% lower than the most frequently occurring reflectivity value for each TOMS scene. The most likely cause of this could be a combination of frequently occurring boundary-layer water or aerosol haze. For most regions, the observation of extremely clear conditions needed to estimate the surface reflectivity from space is a comparatively rare occurrence. Certain areas (e.g., Australia, southern Africa, portions of northern Africa) are cloud-free more than 80% of the year, which exposes these regions to larger amounts of UV radiation than at comparable latitudes in the Northern Hemisphere. Regions over rain-forests, jungle areas, Europe and Russia, the bands surrounding the Arctic and Antarctic regions, and many ocean areas have significant cloud cover (R greater than 15%) more than half of each year. In the low to middle latitudes, the areas with the heaviest cloud cover (highest reflectivity for most of the year) are the forest areas of northern South America, southern Central America, the jungle areas of equatorial Africa, and high mountain regions such as the Himalayas or the Andes. The TOMS reflectivity data show the presence of large nearly clear ocean areas and the effects of the major ocean currents on cloud production.
Herman, J. R.↗
Time variability of Martian bolometric albedo
A time series of calibrated bolometric albedo maps of Mars is presented which establish accurate values of surface bolometric albedo and demonstrate changes in the bolometric appearance of specific regions with time of year and atmospheric conditions. The maps were constructed from Viking infrared thermal mapping data and provide global coverage at latitudes between -60 and +60 deg at 1 x 1 deg spatial resolution for a period spanning a Martian year and including the global dust storms of 1977. During dust-free periods, the bolometric albedo maps are found to be similar to classical earth-based visual albedo maps. A distinctly bimodal distribution of bolometric surface albedos is obtained even during the dust storms, with typical Lambert albedos of 0.27 and 0.16 for the bright and dark Martian surfaces, respectively. Atmospheric effects including dust storms are found to influence strongly apparent surface albedos, especially for dark areas, while neither bright nor dark regions show measurable long-term variations of bolometric albedo during clear periods.
Pleskot, L. K.↗
The C-12/C-13 ratio in stellar atmospheres. VI - Five luminous cool stars
A simple curve-of-growth technique is described for extracting the C-12/C-13 ratio for M stars from high-resolution spectra of CO infrared vibration-rotation lines. The technique is applied to the CO lines at 1.6 and 2.3 microns in spectra of two M supergiants (Alpha Ori and Alpha Sco), two M giants (Alpha Her and Beta Peg), and a Mira-type variable (Chi Cyg). As a check on the CO analysis, the C-12/C-13 ratio is derived from the red CN system at 8000 A for Alpha Sco, Alpha Ori, and Beta Peg. The CO analysis is also applied to the K giant Alpha Boo as a check. The CN and CO results are found to be in general agreement, and the C-12/C-13 ratio in all the examined stars is shown to be considerably lower than the solar-system value. It is suggested that these stars were formed from clouds with a C-12/C-13 ratio of 40 to 89 and that their atmospheres now exhibit an enhancement of C-13 abundance due to internal production and mixing to the surface.
Hinkle, K. H.↗