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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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
AVIRIS data represent a new and important approach for the retrieval of atmospheric and surface parameters from optical remote sensing data. Not only as a test for future space systems, but also as an operational airborne remote sensing system, the development of algorithms to retrieve information from AVIRIS data is an important step to these new approaches and capabilities. Many things have been learned since AVIRIS became operational, and the successive technical improvements in the hardware and the more sophisticated calibration techniques employed have increased the quality of the data to the point of almost meeting optimum user requirements. However, the potential capabilities of imaging spectrometry over the standard multispectral techniques have still not been fully demonstrated. Reasons for this are the technical difficulties in handling the data, the critical aspect of calibration for advanced retrieval methods, and the lack of proper models with which to invert the measured AVIRIS radiances in all the spectral channels. To achieve the potential of imaging spectrometry, these issues must be addressed. In this paper, an algorithm to retrieve information about both atmospheric and surface parameters from AVIRIS data, by using model inversion techniques, is described. Emphasis is put on the derivation of the model itself as well as proper inversion techniques, robust to noise in the data and an inadequate ability of the model to describe natural variability in the data. The problem of non-linear effects is addressed, as it has been demonstrated to be a major source of error in the numerical values retrieved by more simple, linear-based approaches. Non-linear effects are especially critical for the retrieval of surface parameters where both scattering and absorption effects are coupled, as well as in the cases of significant multiple-scattering contributions. However, sophisticated modeling approaches can handle such non-linear effects, which are especially important over vegetated surfaces. All the data used in this study were acquired during the 1991 Multisensor Airborne Campaign (MAC-Europe), as part of the European Field Experiment on a Desertification-threatened Area (EFEDA), carried out in Spain in June-July 1991.
Reliable descriptions of the optical properties of clouds and aerosols are essential for studies of radiative transfer in planetary atmospheres. The scattering algorithms provide accurate estimates of these properties for spherical particles with a wide range of sizes and refractive indices, but these methods are not valid for non-spherical particles (e.g., ice crystals, mineral dust, and smoke). Even though a host of methods exist for deriving the optical properties of nonspherical particles that are very small or very large compared with the wavelength, only a few methods are valid in the resonance regime, where the particle dimensions are comparable with the wavelength. Most such methods are not ideal for particles with sharp edges or large axial ratios. We explore the utility of an integral equation approach for deriving the single-scattering optical properties of axisymmetric particles with large axial ratios. The accuracy of this technique is shown for spheres of increasing size parameters and an ensemble of randomly oriented prolate spheroids of size parameter equal to 10.079368. In this last case our results are compared with published results obtained with the T-matrix approach. Next we derive cross sections, single-scattering albedos, and phase functions for cylinders, disks, and spheroids of ice with dimensions extending from the Rayleigh to the geometric optics regime. Compared with those for a standard surface integral equation method, the storage requirement and the computer time needed by this method are reduced, thus making it attractive for generating databases to be used in multiple-scattering calculations. Our results show that water ice disks and cylinders are more strongly absorbing than equivalent volume spheres at most infrared wavelengths. The geometry of these particles also affects the angular dependence of the scattering. Disks and columns with maximum linear dimensions larger than the wavelength scatter much more radiation in the forward and backward directions and much less radiation at intermediate phase angles than equivalent volume spheres.
This analysis of MGS-TES data from the recent global dust storm allows dust optical properties, optical depth, particle size distribution, and surface temperatures to be derived for multiple-scattering atmospheres using radiative transfer methods. Additional information is contained in the original extended abstract.
Hapke's photometric model has been widely used in solar system remote sensing applications for nearly two decades. Recently, Hapke extended his model to describe the coherent-backscatter opposition effect and multiple-scattering by particles with anisotropic single particle phase functions (SPPF's). A practical difficulty for retrieving Hapke's model parameters from typical planet, satellite, and asteroid photometry data sets is that the model employs a large number of adjustable parameters (at least eight) that can be reliably constrained only for a small number of planetary data sets in which both disk-resolved and whole-disk observations are available from opposition to very large phase angles. The present work aims to reduce the number of adjustable parameters and preserve (or even enhance) the model's accuracy and usefulness by expressing Hapke's parameters in terms of more fundamental physical properties on which they mutually depend. The most difficult part of this task, described here, is to develop a simple method for computing the effective SPPF for structurally complex regolith grains from optical constants, grain-size distribution, and average regolith porosity. The development of light-scattering models for irregularly shaped particles is a large, complex subject and many sophisticated methods, such as Discrete Dipole Approximation (DDA) and Monte-Carlo simulations, have been explored elsewhere. Many of these methods are computationally intensive and probably impractical for routine substitution in Hapke's model. Here, progress is reported in developing a practical, semi-empirical method for estimating the directional scattering behavior (i.e. SPPF) of irregular regolith grains. The method employs Optical Transfer Function (OTF) techniques to model how the structural complexity of regolith particles broaden and attenuate the angular distribution of scattered light relative to that expected from ideal spherical particles of equivalent size and composition.
For over 25 years, NASA has supported the development of space radiation transport models for shielding applications. The NASA space radiation transport model now predicts dose and dose equivalent in Earth and Mars orbit to an accuracy of plus or minus 20%. However, because larger errors may occur in particle fluence predictions, there is interest in further assessments and improvements in NASA's space radiation transport model. In this paper, we consider the effects of the isotopic composition of the primary galactic cosmic rays (GCR) and the isotopic dependence of nuclear fragmentation cross-sections on the solution to transport models used for shielding studies. Satellite measurements are used to describe the isotopic composition of the GCR. Using NASA's quantum multiple-scattering theory of nuclear fragmentation (QMSFRG) and high-charge and energy (HZETRN) transport code, we study the effect of the isotopic dependence of the primary GCR composition and secondary nuclei on shielding calculations. The QMSFRG is shown to accurately describe the iso-spin dependence of nuclear fragmentation. The principal finding of this study is that large errors (plus or minus 100%) will occur in the mass-fluence spectra when comparing transport models that use a complete isotope grid (approximately 170 ions) to ones that use a reduced isotope grid, for example the 59 ion-grid used in the HZETRN code in the past, however less significant errors (less than 20%) occur in the elemental-fluence spectra. Because a complete isotope grid is readily handled on small computer workstations and is needed for several applications studying GCR propagation and scattering, it is recommended that they be used for future GCR studies.