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At least 163 records · Page 9

Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media

The transfer of monochromatic radiation in a scattering, absorbing, and emitting plane-parallel medium with a specified bidirectional reflectivity at the lower boundary is considered. The equations and boundary conditions are summarized. The numerical implementation of the theory is discussed with attention given to the reliable and efficient computation of eigenvalues and eigenvectors. Ways of avoiding fatal overflows and ill-conditioning in the matrix inversion needed to determine the integration constants are also presented.

Stamnes, Knut↗

Aerosol analysis with the Coastal Zone Color Scanner - A simple method for including multiple scattering effects

A method for studying aerosols over the ocean using Nimbus-7 CZCS data is proposed which circumvents having to perform radiative transfer computations involving the aerosol properties. The method is applied to the CZCS band 4 at 670 nm, and yields the total radiance (L sub t) backscattered from the top of a stratified atmosphere containing both stratospheric and tropospheric aerosols and the the Rayleigh scattered radiance (L sub r). The radiance which the aerosol would produce in the single scattering approximation is retrieved from (L sub t) - (L sub r) with an error of not greater than 5-7 percent.

Gordon, Howard R.↗

Numerical Simulations of Single and Multiple Scattering by Fractal Ice Clusters

We consider the scattering model in the form of a vertically and horizontally homogeneous particulate slab of an arbitrary optical thickness composed of widely separated fractal aggregates built of small spherical ice monomers. The aggregates are generated by applying three different approaches, including simulated cluster-cluster aggregation (CCA) and diffusion-limited aggregation (DLA) procedures. Having in mind radar remote-sensing applications, we report and analyze the results of computations of the backscattering circular polarization ratio obtained using efficient superposition T-matrix and vector radiative-transfer codes. The computations have been performed at a wavelength of 12.6 cm for fractal aggregates with the following characteristics: monomer refractive index m=1.78+i0.003, monomer radius r=1 cm, monomer packing density p=0.2, overall aggregate radii R in the range 4<=R<=10 cm and fractal dimensions D(sub f) 2.5 and 3. We show that for aggregates generated with simulated CCA and DLA procedures, the respective values of the backscattering circular polarization ratio differ weakly for D(sub f) 2.5, but the differences can increase somewhat for D(sub f)3, especially in case of an optically semi-infinite medium. For aggregates with a spheroidal overall shape, the dependence of the circular polarization ratio on the cluster morphology can be quite significant and increases with increasing the aspect ratio of the circumscribing spheroid.

Dlugach, Janna M.↗

Demystifying Piecewise and Localized Scatter Correction Methods

Multiplicative scatter is a common source of noise in near-infrared spectroscopy and other related instrumental techniques. A wide variety of methods are commonly used for the correction of multiplicative scatter. However, the majority of such methods assume that the parameters that describe the scatter are constant throughout the measured spectrum, which is often not the case. This work investigates a family of methods that perform scatter correction using local regions of neighboring wavelengths in order to better account for wavelength-dependent scattering. The methods in question are piecewise standard normal variate, localized standard normal variate, piecewise multiplicative scatter correction, and localized multiplicative scatter correction. This work describes the theoretical and algorithmic foundations of the family of local region-based scatter correction methods and compares their application and optimization at a qualitative and quantitative level using several datasets.

NIR spectroscopy↗

Calculation of the angular radiance distribution for a coupled atmosphere and canopy

The radiative transfer equations for a coupled atmosphere and canopy are solved numerically by an improved Gauss-Seidel iteration algorithm. The radiation field is decomposed into three components: unscattered sunlight, single scattering, and multiple scattering radiance for which the corresponding equations and boundary conditions are set up and their analytical or iterational solutions are explicitly derived. The classic Gauss-Seidel algorithm has been widely applied in atmospheric research. This is its first application for calculating the multiple scattering radiance of a coupled atmosphere and canopy. This algorithm enables us to obtain the internal radiation field as well as radiances at boundaries. Any form of bidirectional reflectance distribution function (BRDF) as a boundary condition can be easily incorporated into the iteration procedure. The hotspot effect of the canopy is accommodated by means of the modification of the extinction coefficients of upward single scattering radiation and unscattered sunlight using the formulation of Nilson and Kuusk. To reduce the computation for the case of large optical thickness, an improved iteration formula is derived to speed convergence. The upwelling radiances have been evaluated for different atmospheric conditions, leaf area index (LAI), leaf angle distribution (LAD), leaf size and so on. The formulation presented in this paper is also well suited to analyze the relative magnitude of multiple scattering radiance and single scattering radiance in both the visible and near infrared regions.

Liang, Shunlin↗

Intermediate energy proton-deuteron elastic scattering

A fully symmetrized multiple scattering series is considered for the description of proton-deuteron elastic scattering. An off-shell continuation of the experimentally known twobody amplitudes that retains the exchange symmeteries required for the calculation is presented. The one boson exchange terms of the two body amplitudes are evaluated exactly in this off-shell prescription. The first two terms of the multiple scattering series are calculated explicitly whereas multiple scattering effects are obtained as minimum variance estimates from the 146-MeV data of Postma and Wilson. The multiple scattering corrections indeed consist of low order partial waves as suggested by Sloan based on model studies with separable interactions. The Hamada-Johnston wave function is shown consistent with the data for internucleon distances greater than about 0.84 fm.

Wilson, J. W.↗

Inverse atmospheric radiative transfer problems - A nonlinear minimization search method of solution

The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.

Fymat, A. L.↗