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NASA NTRS1985

Coupled atmosphere/canopy model for remote sensing of plant reflectance features

Solar radiative transfer through a coupled system of atmosphere and plant canopy is modeled as a multiple-scattering problem through a layered medium of random scatterers. The radiative transfer equation is solved by the discrete-ordinates finite-element method. Analytic expressions are derived that allow the calculation of scattering and absorption cross sections for any plant canopy layer form measurable biophysical parameters such as the leaf area index, leaf angle distribution, and individual leaf reflectance and transmittance data. An expression for a canopy scattering phase function is also given. Computational results are in good agreement with spectral reflectance measurements directly above a soybean canopy, and the concept of greenness- and brightness-transforms of Landsat MSS data is reconfirmed with the computed results. A sensitivity analysis with the coupled atmosphere/canopy model quantifies how satellite-sensed spectral radiances are affected by increased atmospheric aerosols, by varying leaf area index, by anisotropic leaf scattering, and by non-Lambertian soil boundary conditions. Possible extensions to a 2-D model are also discussed.

Gerstl, S. A.↗

NASA NTRS1986

A note on Hapke's bidirectional reflectance spectroscopy. Part 3: Correction for macroscopic roughness

The multiple-scattering theory of K. Lumme and E. Bowell (1981) was criticized by B. Hapke by stating, in particular, that energy is not conserved. It is shown that Hapke's treatment is, in this respect, inferior to that of Lumme and Bowell, and itself violates the principal concepts of radiative transfer theory. Hapke's additinal claim that, in Lumme and Bowell's work, the reflectance tends to zero at the limb is also refuted. Comment is made on the deduction of surface physical properties by modeling photometric observations.

Lumme, K.↗

NASA NTRS1985

Vertical cloud structure of Jupiter's equatorial plumes

Multiple-scattering radiative transfer calculations were used to deduce the vertical cloud structure (VCS) of Jupiter's equatorial region. The VCS model of the equatorial plumes is obtained through an analysis of Voyager images of the 6190-A methane band and the 6000-A continuum, and ground-based 8900-A methane band images. The VCS of the equatorial plumes is found to be consistent with the hypothesis that the plumes are caused by upwelling at the ammonia condensation level produced by buoyancy due to latent heat release from the condensation of water clouds nearly three scale heights below the plumes.

Stoker, C. R.↗

NASA NTRS1988

Heating rates in tropical anvils

The interaction of infrared and solar radiation with tropical cirrus anvils is addressed. Optical properties of the anvils are inferred from satellite observations and from high-altitude aircraft measurements. An infrared multiple-scattering model is used to compute heating rates in tropical anvils. Layer-average heating rates in 2 km thick anvils were found to be on the order of 20 to 30 K/day. The difference between heating rates at cloud bottom and cloud top ranges from 30 to 200 K/day, leading to convective instability in the anvil. The calculations are most sensitive to the assumed ice water content, but also are affected by the vertical distribution of ice water content and by the anvil thickness. Solar heating in anvils is shown to be less important than infrared heating but not negligible. The dynamical implications of the computed heating rates are also explored and it is concluded that the heating may have important consequences for upward mass transport in the tropics. The potential impact of tropical cirrus on the tropical energy balance and cloud forcing are discussed.

Ackerman, Thomas P.↗

NASA NTRS1990

Radiative transfer modeling constraints on the size of the spoke particles in Saturn's rings

The spoke particle sizes of Saturn's outer B ring constitute an important parameter for spoke formation and evolution theories, prompting the present effort to find constraining observations. The spokes' apparent optical depths are found to increase with wavelength. A relationship is derived for the contribution of the spokes' small particle optical depth, taking multiple-scatter and flatter spoke-region large-particle phase functions into account; the spokes' optical depths still generally appear to increase or remain constant with increasing wavelength.

Doyle, Laurance R.↗

NASA NTRS1992

Quasi-elastic nuclear scattering at high energies

The quasi-elastic scattering of two nuclei is considered in the high-energy optical model. Energy loss and momentum transfer spectra for projectile ions are evaluated in terms of an inelastic multiple-scattering series corresponding to multiple knockout of target nucleons. The leading-order correction to the coherent projectile approximation is evaluated. Calculations are compared with experiments.

Cucinotta, Francis A.↗

NASA NTRS1992

Multiple resonant scattering in the Compton upscatter model of gamma-ray bursts

Resonant Compton scattering, an increasingly popular mechanism for suppressing X-rays and producing gamma rays, must be treated as a multiple-scattering process for conditions thought characteristic of gamma-ray bursts. Photons that multiply scatter with a beamed power-law electron distribution in a uniform magnetic field produce a flat spectrum between the cyclotron frequency and an optical-depth-dependent critical energy; this critical energy ranges between several hundred keV and several MeV. Above this critical energy, the gamma-ray spectrum has a shape determined by the electron distribution and described by a single-scattering model. Only electron distributions that are nearly proportional to the electron momentum are able to simultaneously suppress X-rays and produce a single-scattering spectrum. As the Thomson optical depth approaches unity, photons that experience multiple scatterings often spawn additional photons at a rate that makes the model unphysical.

Brainerd, J. J.↗

NASA NTRS1992

A solar radiation model for use in climate studies

A solar radiation routine is developed for use in climate studies that includes absorption and scattering due to ozone, water vapor, oxygen, carbon dioxide, clouds, and aerosols. Rayleigh scattering is also included. Broadband parameterization is used to compute the absorption by water vapor in a clear atmosphere, and the k-distribution method is applied to compute fluxes in a scattering atmosphere. The reflectivity and transmissivity of a scattering layer are computed analytically using the delta-four-stream discrete-ordinate approximation. The two-stream adding method is then applied to compute fluxes for a composite of clear and scattering layers. Compared to the results of high spectral resolution and detailed multiple-scattering calculations, fluxes and heating rate are accurately computed to within a few percent. The high accuracy of the flux and heating-rate calculations is achieved with a reasonable amount of computing time. With the UV and visible region grouped into four bands, this solar radiation routine is useful not only for climate studies but also for studies on photolysis in the upper atmosphere and photosynthesis in the biosphere.

Chou, Ming-Dah↗

NASA NTRS1992

Ortho-para-hydrogen equilibration on Jupiter

Voyager IRIS observations reveal that the Jovian para-hydrogen fraction is not in thermodynamic equilibrium near the NH3 cloud top, implying that a vertical gradient exists between the high-temperature equilibrium value of 0.25 at depth and the cloud top values. The height-dependent para-hydrogen profile is obtained using an anisotropic multiple-scattering radiative transfer model. A vertical correlation is found to exist between the location of the para-hydrogen gradient and the NH3 cloud, strongly suggesting that paramagnetic conversion on NH3 cloud particle surfaces is the dominant equilibration mechanism. Below the NH3 cloud layer, the para fraction is constant with depth and equal to the high-temperature equilibrium value of 0.25. The degree of cloud-top equilibration appears to depend on the optical depth of the NH3 cloud layer. Belt-zone variations in the para-hydrogen profile seem to be due to differences in the strength of the vertical mixing.

Carlson, Barbara E.↗

NASA NTRS1992

A simple analytical function for bidirectional reflectance

A simple bidirectional reflectance model based on physical scattering laws is developed to calculate the bidirectional reflectance of a wide variety of surfaces. Chandrasekhar's radiative transfer solution, obtained for the anisotropically scattering semi-infinite medium, is used to compute the multiple-scattered radiances. However, since the radiative transfer solution does not take architectural effects into consideration, we adopt Hapke's (1986) approach and add an empirical term to explain the hot-spot phenomenon and use Cox and Munk's (1954) formulation to take into account the specular reflection. The physical parameters of the model are retrieved from bidirectional reflectance measurements. For each surface, only one set of model parameters is needed for application to all illumination and viewing geometries. The validity of the model is established by comparing the computed and measured reflectances for sets of viewing and illumination angles that were not included in the inversion algorithm. Good agreement is shown between the model-computed and the observed reflectances for dense prairie vegetation canopies, a sparse desert scrub community, a plowed agricultural field, and an alkali flat.

Ahmad, Suraiya P.↗

NASA NTRS1993

Automated measurement of polarized bidirectional reflectance

An Automated Bidirectional Reflection Acquisition Measurement System (ABRAMS) has been constructed to facilitate measurement of bidirectional reflectance from soil and vegetative samples in the laboratory. The system illuminates a sample with linearly-polarized laser light, lambda = 632.8 nm, and measures the like- and cross-polarized scattered intensities over half a hemisphere. System design and polarized bidirectional reflectance measurements from a soil sample and SiO2 spherical particles are discussed in this work. It is shown that polarization information in the plane of incidence is useful for identifying certain scattering mechanisms associated with soil reflectance. This is because the like-polarized intensity, Ivv, is influenced by single-scattered light and the cross-polarized intensity, IHv, is strongly influenced by multiple-scattered light. For example, comparable levels of Ivv and IHv indicated that the reflectance of soils, is dominated by significant multiple scattering because single scattering causes minimal depolarization in the plane of incidence.

Gibbs, Daniel P.↗

NASA NTRS1992

LAI inversion from optical reflectance using a neural network trained with a multiple scattering model

The inversion of the leaf area index (LAI) canopy parameter from optical spectral reflectance measurements is obtained using a backpropagation artificial neural network trained using input-output pairs generated by a multiple scattering reflectance model. The problem of LAI estimation over sparse canopies (LAI < 1.0) with varying soil reflectance backgrounds is particularly difficult. Standard multiple regression methods applied to canopies within a single homogeneous soil type yield good results but perform unacceptably when applied across soil boundaries, resulting in absolute percentage errors of >1000 percent for low LAI. Minimization methods applied to merit functions constructed from differences between measured reflectances and predicted reflectances using multiple-scattering models are unacceptably sensitive to a good initial guess for the desired parameter. In contrast, the neural network reported generally yields absolute percentage errors of <30 percent when weighting coefficients trained on one soil type were applied to predicted canopy reflectance at a different soil background.

Smith, James A.↗

NASA NTRS1994

Minimizing systematic errors from atmospheric multiple scattering and satellite viewing geometry in coastal zone color scanner level IIA imagery

Water-leaving radiances and phytoplankton pigment concentrations are calculated from coastal zone color scanner (CZCS) radiance measurements by removing atmospheric Rayleigh and aerosol radiances from the total radiance signal measured at the satellite. The single greatest source of error in CZCS atmospheric correction algorithms in the assumption that these Rayleigh and aerosol radiances are separable. Multiple-scattering interactions between Rayleigh and aerosol components cause systematic errors in calculated aerosol radiances, and the magnitude of these errors is dependent on aerosol type and optical depth and on satellite viewing geometry. A technique was developed which extends the results of previous radiative transfer modeling by Gordon and Castano to predict the magnitude of these systematic errors for simulated CZCS orbital passes in which the ocean is viewed through a modeled, physically realistic atmosphere. The simulated image mathematically duplicates the exact satellite, Sun, and pixel locations of an actual CZCS image. Errors in the aerosol radiance at 443 nm are calculated for a range of aerosol optical depths. When pixels in the simulated image exceed an error threshhold, the corresponding pixels in the actual CZCS image are flagged and excluded from further analysis or from use in image compositing or compilation of pigment concentration databases. Studies based on time series analyses or compositing of CZCS imagery which do not address Rayleigh-aerosol multiple scattering should be interpreted cautiously, since the fundamental assumption used in their atmospheric correction algorithm is flawed.

Martin, D. L.↗

NASA NTRS1994

Airborne CO2 coherent lidar measurements of cloud backscatter and opacity over the ocean surface

The use of an airborne CO2 lidar to obtain cloud backscatter and extinction data at a thermal infrared wavelength is described. The extinction in this spectral region is proportional to the cloud liquid water content. The use of coherent detection results in high sensitivity and narrow field of view, the latter property greatly reducing multiple-scattering effects. Backscatter measurements in absolute units are obtained through a hard target calibration methodology. For clouds of low to moderate optical thickness at the lidar wavelength, both geometric thickness and optical thickness can be measured. The sea surface reflectance signal is used to obtain estimates of the cloud optical thickness. The utility of this technique results from studies that indicate that the spatial scale of variability of the sea surface reflectance is generally large compared with that of cloud optical thickness. Selected results are presented from data taken during flights over the Pacific Ocean.

Menzies, Robert T.↗

NASA NTRS1994

Incorporation of multiple cloud layers for ultraviolet radiation modeling studies

Cloud data sets compiled from surface observations were used to develop an algorithm for incorporating multiple cloud layers into a multiple-scattering radiative transfer model. Aerosol extinction and ozone data sets were also incorporated to estimate the seasonally averaged ultraviolet (UV) flux reaching the surface of the Earth in the Detroit, Michigan, region for the years 1979-1991, corresponding to Total Ozone Mapping Spectrometer (TOMS) version 6 ozone observations. The calculated UV spectrum was convolved with an erythema action spectrum to estimate the effective biological exposure for erythema. Calculations show that decreasing the total column density of ozone by 1% leads to an increase in erythemal exposure by approximately 1.1-1.3%, in good agreement with previous studies. A comparison of the UV radiation budget at the surface between a single cloud layer method and a multiple cloud layer method presented here is discussed, along with limitations of each technique. With improved parameterization of cloud properties, and as knowledge of biological effects of UV exposure increase, inclusion of multiple cloud layers may be important in accurately determining the biologically effective UV budget at the surface of the Earth.

Charache, Darryl H.↗

NASA NTRS1994

Asymmetry parameters of the phase function for densely packed scattering grains

Spatial correlation among densely packed particles can substantially change their single-scattering properties, thus making questionable the applicability of the independent scattering approximation in calculations of light scattering by planetary regoliths. The same problem arises in geophysics in light scattering computations for snow, frosts, and bare soil. In this paper, we use a dense-medium light-scattering theory based on the introduction of the static structure factor to calculate asymmetry parameters of the phase function for densely packed particles with real refractive indices 1.31 and 1.66, approximating water ice and soil particles, respectively, and imaginary refractive indices 0, 0.01, and 0.3. For sparsely distributed, independently scattering grains, the calculated asymmetry parameters are always positive and always larger than those for densely packed particles. For densely packed grains, the asymmetry parameters may be negative but only for radius-to-wavelength ratios from about 0.1 to about 0.4. With decreasing particle size, the calculated asymmetry parameters tend to zero independently of the compaction state. In the geometrical optics regime, the asymmetry parameters for densely packed scatterers are positive and very close to those for independently scattering grains. These results may have important implications for remote sensing of the Earth and solid planetary surfaces. In particular, it is demonstrated that negative asymmetry parameters derived with some approximate multiple-scattering theories may be physically irrelevant and can be the result of using an inaccurate bidirectional reflection function combined with the ill-conditionally of the inverse scattering problem.

Mishchenko, Michael I.↗

NASA NTRS1995

An analytic radiative transfer model for a coupled atmosphere and leaf canopy

A new analytical radiative transfer model of a leaf canopy is developed that approximates multiple-scattering radiance by a four-stream formulation. The canopy model is coupled to a homogeneous atmospheric model as well as a non-Lambertian lower boundary soil surface. The same four-stream formulation is also used for the calculation of multiple scattering in the atmosphere. Comparisons of radiance derived from the four-stream model with those calculated by an iterative numerical solution of the radiative transfer equation show that the analytic model has a very high accuracy, even with a turbid atmosphere and a very dense canopy in which multiple scattering dominates. Because the coupling of canopy and atmospheric models fully accommodates anisotropic surface reflectance and atmospheric scattering and its effect on directional radiance, the model is especially useful for application to directional radiance and measurements obtained by remote sensing. Retrieval of biophysical parameters using this model is under investigation.

Liang, Shunlin↗

NASA NTRS1994

Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres

Although neglecting polarization and replacing the rigorous vector radiative transfer equation by its approximate scalar counterpart has no physical background, it is a widely used simplification when the incident light is unpolarized and only the intensity of the reflected light is to be computed. We employ accurate vector and scalar multiple-scattering calculations to perform a systematic study of the errors induced by the neglect of polarization in radiance calculations for a homogeneous, plane-parallel Rayleigh-scattering atmosphere (with and without depolarization) above a Lambertian surface. Specifically, we calculate percent errors in the reflected intensity for various directions of light incidence and reflection, optical thicknesses of the atmosphere, single-scattering albedos, depolarization factors, and surface albedos. The numerical data displayed can be used to decide whether or not the scalar approximation may be employed depending on the parameters of the problem. We show that the errors decrease with increasing depolarization factor and/or increasing surface albedo. For conservative or nearly conservative scattering and small surface albedos, the errors are maximum at optical thicknesses of about 1. The calculated errors may be too large for some practical applications, and, therefore, rigorous vector calculations should be employed whenever possible. However, if approximate scalar calculations are used, we recommend to avoid geometries involving phase angles equal or close to 0 deg and 90 deg, where the errors are especially significant. We propose a theoretical explanation of the large vector/scalar differences in the case of Rayleigh scattering. According to this explanation, the differences are caused by the particular structure of the Rayleigh scattering matrix and come from lower-order (except first-order) light scattering paths involving right scattering angles and right-angle rotations of the scattering plane.

Mishchenko, M. I.↗