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NASA NTRS2008

A Three-Dimensional Analytic Model for the Scattering of a Spherical Bush

Advanced climate models require a more realistic description of canopy radiation with reasonable computational efficiency. This paper develops the mathematics of scattering from a spherical object conceptualized to be a spherical bush to provide a building block that helps to address this need of climate models. It is composed of a homogeneous distribution of individual smaller objects that scatter isotropically. In the limit of small optical depth, incident radiation will scatter isotropically as the sum of that scattered by all the individual scatterers, but at large optical depth the radiation leaving the spherical bush in a given direction is reduced by mutual shadowing of the smaller objects. In the single scattering limit, the scattering phase function and so the albedo are obtained by simple but accurate analytic expressions derived from analytic integration and numerical evaluation. Except in the limit of thin canopies, the scattering and hence albedos are qualitatively and quantitatively different than those derived from 1-D modeling.

Dickinson, Robert E.↗

NASA NTRS1971

Discrete ordinate theory of radiative transfer. 2: Scattering from maritime haze

Discrete ordinate theory was used to calculate the reflected and transmitted radiance of photons which have interacted with plane parallel maritime haze layers. The results are presented for three solar zenith angles, three values of the surface albedo, and a range of optical thicknesses from very thin to very thick. The diffuse flux at the lower boundary and the cloud albedo were tabulated. The forward peak and other features in the single scattered phase function caused the radiance in many cases to be very different from that for Rayleigh scattering. The variation of the radiance with both the zenith or nadir angle and the azimuthal angle is more marked, and the relative limb darkening under very thick layers is greater, for haze than for Rayleigh scattering. The downward diffuse flux at the lower boundary for A = O is always greater and the cloud albedo is always less for haze than for Rayleigh layers.

Kattawar, G. W.↗

NASA NTRS1973

Matrix operator theory of radiative transfer. II - Scattering from maritime haze.

Matrix operator theory is used to calculate the reflected and transmitted radiance of photons that have interacted with plane-parallel maritime haze layers. The results are presented for three solar zenith angles, three values of the surface albedo, and a range of optical thicknesses from very thin to very thick. The diffuse flux at the lower boundary and the cloud albedo are tabulated. The forward peak and other features in the single-scattered phase function cause the radiance in many cases to be very different from that for Rayleigh scattering. In particular, the variation of the radiance with both the zenith or nadir angle and the azimuthal angle is more marked and the relative limb darkening under very thick layers is greater for haze M than for Rayleigh scattering. The downward diffuse flux at the lower boundary for A = 0 is always greater and the cloud albedo is always less for haze M than for Rayleigh layers.

Kattawar, G. W.↗

NASA NTRS1988

Analysis of Voyager images of Europa - Plasma bombardment

Voyager-derived data on the albedos of Europa are presently photometrically corrected and converted into average, single-scattering form, in order to analyze them as a function of angular distance from the apex of orbital motion. A hypothesized magnetospheric modification of the Europa surface is confirmed by the UV absorption found in the 0.35-micron filter data; this absorption directly correlates with the longitudinal ion implantation distribution in both terrain types. A 'red' spectrum is found in both terrain types as well, and is found to be constant across the surface. A uniform increase is noted in the 'dark' terrain absorption over that in the 'bright' terrain.

Johnson, R. E.↗

NASA NTRS1986

Estimates of the bolometric albedos and radiation balance of Uranus and Neptune

Models possessing an upper haze layer of finite optical depth and a lower cloud layer of infinite optical depth at discrete altitudes are used to bound the wavelength-averaged phase integrals and bolometric albedos of Uranus and Neptune. The models differ in the assumed value of the particles' single scattering phase function and the wavelength dependence of the haze optical depth. A range of phase functions, from the isotropic to those characterizing Titan, Jupiter, and Saturn atmosphere particles, are discussed. The results obtained imply that the meteorological regimes in the observable atmospheres of Uranus and Neptune may differ considerably; internal heat flux could play a much more important role for Neptune than for Uranus.

Pollack, J. B.↗

NASA NTRS1986

Vertical structure of aerosols and clouds in the atmospheres of Uranus and Neptune: Implications for their heat budgets

Models possessing an upper haze layer of finite optical depth and a lower cloud layer of infinite optical depth at discrete altitudes are used to bound the wavelength-averaged phase integrals and bolometric albedos of Uranus and Neptune. The models differ in the assumed value of the particles single scattering phase function and the wavelength dependence of the haze optical depth. A range of phase functions, from the isotropic to those characterizing Titan, Jupiter, and Saturn atmosphere particles, are discussed. The results obtained imply that the meteorological regimes in the observable atmospheres of Uranus and Neptune may differ considerably; internal heat flux could play a much more important role for Neptune than for Uranus.

Pollack, James B.↗

NASA NTRS1992

Disk-resolved photometric analysis of Europan terrains

The photometric textures of Europa geologic units possessing the same small mean photometric slope angle as found by Dominique et al. (1991) are presently examined on the basis of Hapke's (1981) photometric model. With only one exception, the particles composing the surfaces of most of the units exhibit similar scattering properties. Attention is given to the single-particle scattering functions of the two bright plains regions examined; these are noted to be no less different from each other than both are from the other units. An aging process that affects the albedos and single-particle phase functions is hypothesized for Europa.

Domingue, Deborah↗

NASA NTRS1993

On the evaluation of air mass factors for atmospheric near-ultraviolet and visible absorption spectroscopy

The interpretation of UV-visible twilight absorption measurements of atmospheric chemical constituents is dependent on how well the optical path, or air mass factor, of light collected by the spectrometer is understood. A simple single scattering model and a Monte Carlo radiative transfer scheme have been developed to study the effects of multiple scattering, aerosol scattering, surface albedo and refraction on air mass factors for scattered light observations. At fairly short visible wavelengths (less than about 450 nm), stratospheric air mass factors are found to be relatively insensitive to multiple scattering, surface albedo and refraction, as well as aerosol scattering by background aerosols. Longer wavelengths display greater sensitivity to refraction and aerosol scattering. Tropospheric air mass factors are found to be highly dependent on aerosol scattering, surface albedo and, at long visible wavelengths (about 650 nm), refraction. Absorption measurements of NO2 and O4 are shown to support these conclusions.

Perliski, Lori M.↗

NASA NTRS1981

Inelastic scattering in planetary atmospheres. I - The Ring effect, without aerosols

The contribution of inelastic molecular scattering (Rayleigh-Brillouin and rotational Raman scattering) to the filling-in of Fraunhofer lines in the light of the blue sky is studied. Aerosol fluorescence is shown to be negligible, and aerosol scattering is ignored. The angular and polarization dependences of the filling-in detail for single scattering are discussed. An approximate treatment of multiple scattering, using a backward Monte Carlo technique, makes it possible to investigate the effects of the ground albedo. As the molecular scatterings alone produce more line-filling than is observed, it seems likely that aerosols dilute the effect by contributing unaltered sunlight to the observed spectra.

Kattawar, G. W.↗

NASA NTRS1993

Earth observing scanning polarimeter

Climate forcing by tropospheric aerosols is receiving increased attention because of the realization that the climate effects may be large, while our knowledge of global aerosol characteristics and temporal changes is very poor. Tropospheric aerosols cause a direct radiative forcing due simply to their scattering and absorption of solar radiation, as well as an indirect effect as cloud condensation nuclei which can modify the shortwave reflectivity of clouds. Sulfate aerosols tend to increase planetary albedo through both the direct and indirect effects; a cooling due to anthropogenic sulfate aerosols has been estimated of order 1 W/sq m, noting that this is similar in magnitude to the present anthropogenic greenhouse gas warming. Other aerosols, including those from biomass burning and wind-blown desert dust are also of potential climatic importance. At present, the only global monitoring of tropospheric aerosols is a NOAA operational product, aerosol optical thickness, obtained using channel-1 (0.58-0.68 mu m) radiances from the AVHRR. With this single channel radiance data, one must use an approach which is based on the inferred excess of reflected radiance owing to scattering by the aerosols over that expected from theoretical calculations. This approach is suited only for situations where the surface has a low albedo that is well known a priori. Thus, the NOAA operational product is restricted to coverage over the ocean at AVHRR scan angles well away from sun glint, and aerosol changes are subject to confusion with changes caused by either optically thin or subpixel clouds. Because optically thin aerosols have only a small effect on the radiance, accurate measurements for optical thickness less than 0.1 (which is a typical background level) are precluded. Moreover, some of the largest and most important aerosol changes are expected over land. The Earth Observing Scanning Polarimeter (EOSP) instrument, based upon design heritage and analysis techniques developed for planetary missions, will retrieve tropospheric aerosol characteristics from measurements of multispectral radiance and polarization. Moreover, the same radiance and polarization measurements will also provide very precise information on cloud properties and maps of surface characteristics for cloud-free regions. These capabilities also give EOSP the unique ability to discriminate aerosol from clouds and surface.

Travis, Larry↗

NASA NTRS1989

Photometric phase functions of common geologic minerals and applications to quantitative analysis of mineral mixture reflectance spectra

The mass fractional abundance of components in intimately mixed, particulate surfaces is calculated from laboratory reflectance spectra using Hapke's (1981) model for bidirectional reflectance. It is found that a simplified version of the model is accurate to within 7 percent for mixtures not containing low albedo components. The model is not appropriate for mixtures with very low and high albedo components. Consideration is given to the possible improvement of the method's accuracy by using an empirical single-particle phase function to describe the scattering characteristics of all minerals, or by solving for the single-particle phase function of the minerals involved exactly using extensive bidirectional reflectance measurements and Hapke's equations for bidirectional reflectance. Also, the results are used to examine the general scattering behavior of particulate mineral surfaces.

Mustard, John F.↗

NASA NTRS1981

Radiative transfer in the surfaces of atmosphereless bodies. I - Theory. II - Interpretation of phase curves

A generalized theory of radiative transfer is presented which includes single and multiple scattering of light in particulate surfaces, and is applicable to both the surfaces of atmosphereless bodies and to laboratory samples. Single scattering is described in terms of the effects of porosity and roughness, and is formulated by means of a probabilistic method. It is shown that, for low-albedo surfaces, the effects of porosity and roughness are separable, the opposition effect is caused by the former, and the slope of the linear part of the phase curve is mainly controlled by the latter. The theory, which is applicable to all albedos and phase angles, may be used in both surface brightness and integrated brightness studies. The limiting case of roughness and volume density tending to zero yields the results of classical radiative transfer theory.

Lumme, K.↗

NASA NTRS1972

Degree and direction of polarization of multiple scattered light. II - Earth's atmosphere with aerosols.

The radiance, polarization, and direction of polarization of the radiation reflected and transmitted through the atmosphere are calculated by a Monte Carlo method on the basis of a realistic model of the atmosphere. The calculated polarization is shown to depend on the aerosol amount and to have normally a value intermediate between that for pure Rayleigh and pure aerosol scattering. The polarization for multiple scattered photons is usually less than the value calculated for single scattering, but may be larger in low-polarization regions near other regions of high polarization. The direction of polarization shows little variation with either the aerosol amount or the value of the surface albedo.

Plass, G. N.↗

NASA NTRS1978

Scattering of light from particulate surfaces. I - A laboratory assessment of multiple-scattering effects

In planetary applications it is sometimes important to know the degree to which multiple scattering is influencing the photometric properties of a surface. An investigation is conducted concerning the point at which the single-scattering approximation used in the theory developed by Hapke (1963) and Irvine (1966) breaks down. It is shown that the Hapke-Irvine photometric function provides an adequate representation of the scattering properties of particulate surfaces whose geometric albedos (or normal reflectances) do not exceed 0.3. An experiment is conducted to estimate the normal reflectance below which the Hapke-Irvine equation considered provides an adequate representation of the scattering properties of a particulate surface. The investigation makes use of a set of samples which were prepared by mixing magnesium oxide and charcoal powders. The samples have a range in normal reflectance from 0.04 to 1.04.

Veverka, J.↗

NASA NTRS2021

An Efficient and Accurate Algorithm for Computing Grid-Averaged Solar Fluxes for Horizontally Inhomogeneous Clouds

A computationally efficient method is presented to account for the horizontal cloud inhomogeneity by using a radiatively equivalent plane parallel homogeneous (PPH) cloud. The algorithm can accurately match the calculations of the reference (rPPH) independent column approximation (ICA) results, but use only the same computational time required for a single plane parallel computation. The effective optical depth of this synthetic sPPH cloud is derived by exactly matching the direct transmission to that of the inhomogeneous ICA cloud. The ffective9 scattering asymmetry factor is found from a pre-calculated albedo inverse look-up-table that is allowed to vary over the range from -1.0 to 1.0. In the special cases of conservative scattering and total absorption, the synthetic method is exactly equivalent to the ICA, with only a small bias (about 0.2% in flux) relative to ICA due to imperfect interpolation in using the look-up tables. In principle, the ICA albedo can be approximated accurately regardless of cloud inhomogeneity. For a more complete comparison, the broadband shortwave albedo and transmission calculated from the synthetic sPPH cloud and averaged over all incident directions, have the RMS biases of 0.26% and 0.76%, respectively, for inhomogeneous clouds over a wide variation of particle size. The advantages of the synthetic PPH method are that (1) it is not required that all the cloud subcolumns have uniform microphysical characteristic, (2) it is applicable to any 1D radiative transfer scheme, and (3) it can handle arbitrary cloud optical depth distributions and an arbitrary number of cloud subcolumns with uniform computational efficiency.

cloud inhomogeneity↗

NASA NTRS1975

A photometric function for diffuse reflection by particulate materials

A photometric function is proposed to describe the diffuse reflection of radiation by particulate materials. Both multiple scattering and the dominant effects of particle shadowing are included and the function is verified by comparisons with the photometries of laboratory surfaces. Brightness measurements of planetary and other diffusely scattering surfaces can be used to calculate the brightness for geometries other than those used in the measurements and for which the Minnaert function does not apply. The measurements also can be directly related to such surface characteristics as particle size, single-particle albedo, and compactness.

Meador, W. E.↗

NASA NTRS1984

Satellite observation of SO2 from El Chichon - Identification and measurement

Absorption bands between 300 nm and 315 nm were observed in spectral scans of the atmospheric albedo made by the solar backscattered ultraviolet instrument (SBUV) on Nimbus 7 following the eruption of El Chichon. It is shown that these bands coincide with peaks in the absorption coefficient spectrum of SO2 and use the magnitude of the absorption to estimate the column content of SO2 present. A maximum concentration of 15 matm-cm of SO2 was observed west of Hawaii on April 15; the minimum detectable amount of SO2 in a single scan is about 1 matm-cm. The disappearance of the band structure at wavelengths below 300 nm indicates that the SO2 was between 20 km and 30 km altitude. An excess albedo was also observed near 300 nm which was attributed to increased scattering from volcanic aerosols; the wavelength of the scattering feature indicates that the aerosols also were near 25 km altitude.

Mcpeters, R. D.↗

NASA NTRS1987

Determination of the scaled optical thickness of clouds from reflected solar radiation measurements

A method for determination of scaled optical thickness from reflected solar radiation measurements is described in which measurements of the reflected function are compared with asymptotic expressions for the reflection function of optically thick layers. Analytic formulas are derived which show the dependence of the reflection and transmission functions of nonabsorbing atmospheres on cloud optical thickness, ground albedo, and the asymmetry factor. An expression is derived which shows that the ground albedo produces a constant bias in the derived optical thickness, regardless of the value of the measured reflection function. Results from an analysis of high-resolution images, obtained in Oklahoma, of the reflection function of clouds shows the impact of details of the single scattering phase function on the derived optical thickness.

King, Michael D.↗