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.

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

Remote sensing from satellite or airborne platforms of land or sea surfaces in the visible and near infrared is strongly affected by the presence of the atmosphere along the path from Sun to target (surface) to sensor. This paper presents 6S (Second Simulation of the Satellite Signal in the Solar Spectrum), a computer code which can accurately simulate the above problems. The 6S code is an improved version of 5S (Simulation of the Satellite Signal in the Solar Spectrum), developed by the Laboratoire d'Optique Atmospherique ten years ago. The new version now permits calculations of near-nadir (down-looking) aircraft observations, accounting for target elevation, non lambertian surface conditions, and new absorbing species (CH/sub 4/, N/sub 2/O, CO). The computational accuracy for Rayleigh and aerosol scattering effects has been improved by the use of state-of-the-art approximations and implementation of the successive order of scattering (SOS) algorithm. The step size (resolution) used for spectral integration has been improved to 2.5 nm. The goal of this paper is not to provide a complete description of the methods used as that information is detailed in the 6S manual, but rather to illustrate the impact of the improvements between 5S and 6S by examining some typical remote sensing situations. Nevertheless, the 6S code has still limitations. It cannot handle spherical atmosphere and as a result, it cannot be used for limb observations. In addition, the decoupling the authors are using for absorption and scattering effects does not allow to use the code in presence of strong absorption bands.

Second Simulation of the Satellite Signal in the Solar Spectrum, 6S: an overview

This paper reviews scattering theory required for analysis of light reflected by planetary atmospheres. Section 1 defines the radiative quantities which are observed. Section 2 demonstrates the dependence of single-scattered radiation on the physical properties of the scatterers. Section 3 describes several methods to compute the effects of multiple scattering on the reflected light.

Light scattering in planetary atmospheres

We present an integral equation which generalizes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient new technique for a wide variety of monte carlo procedures. The resulting rendering algorithm extends the range of optical phenomena which can be effectively simulated.

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The rendering equation

Preface How to Get the Software Part I. Linear Equations. 1. Basic Concepts and Stationary Iterative Methods 2. Conjugate Gradient Iteration 3. GMRES Iteration Part II. Nonlinear Equations. 4. Basic Concepts and Fixed Point Iteration 5. Newton's Method 6. Inexact Newton Methods 7. Broyden's Method 8. Global Convergence Bibliography Index.

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Subrahmanyan Chandrasekhar

Papers

Radiative Transfer