Phase matrix induced symmetrics for multiple scattering using the matrix operator method

Entirely rigorous proofs of the symmetries induced by the phase matrix into the reflection and transmission operators used in the matrix operator theory are given. Results are obtained for multiple scattering in both homogeneous and inhomogeneous atmospheres. These results will be useful to researchers using the method since large savings in computer time and storage are obtainable

An explicit form of the Mie phase matrix for multiple scattering calculations in the I, Q, U, and V representation

An explicit expression is obtained for the phase matrix in the I, Q, U, and V Stokes vector representation for a system containing a polydispersion of spherical particles. All of the symmetry relations derived by Hovenier using general arguments are established explicitly. Convenient algorithms are given for the computation of the phase matrix for a spherical polydispersion. Since this theory is so vitally important in radiative transfer, many researchers will need to compute these functions for realistic aerosols distributions. Therefore, results are presented for a haze L distribution so that other researchers will have a way of checking their programs which compute these quantities

Radiance, polarization, and ellipticity of the radiation in the earth's atmosphere

The complete radiation field including polarization is calculated for a model of the real atmosphere by the matrix operator method. The radiance, direction and amount of polarization, and ellipticity are obtained at the top and bottom of the atmosphere for three values of the surface albedo (0; 0.15 0.90) and five solar zenith angles. Scattering and absorption by molecules (including ozone) and by aerosols are taken into account together with the variation of the number density of these substances with height. All results are calculated for both a normal aerosol number and a distribution which is one-third of the normal amount at all heights. The calculated values show general qualitative agreement with the available experimental measurements. The position of the neutral points of the polarization in the principal plane is a sensitive indicator of the characteristics of the aerosol particles in the atmosphere, since it depends on the sign and value of the single scattered polarization for scattering angles around 20 deg and 160 deg for transmitted and reflected photons respectively

Multiple scattered radiation emerging from continental haze layers. 2: Ellipticity and direction of polarization

The ellipticity and the direction of polarization are calculated for radiation that has undergone multiple scattering from plane parallel layers. Both the radiation emerging from the top of the layer and that transmitted through the bottom are considered. Two different phase functions are used for the scattering layer: Rayleigh and haze L. The direction of polarization of the reflected radiation shows little variation as the optical depth of the layer increases, while there is a much larger variation for the transmitted radiation. When the optical thickness is small, the direction of polarization for haze L varies rapidly with zenith angle near those angles at which the single scattered polarization is zero. The ellipticity of the radiation from haze L layers increases at first in direct proportion to the optical thickness of the layer. In general the ellipticity of the transmitted radiation is considerably greater than that of the reflected because of the greater average number of photon collisions in the former case

Multiple scattered radiation emerging from continental haze layers. 1: Radiance, polarization, and neutral points

The complete radiation field is calculated for scattering layers of various optical thicknesses. Results obtained for Rayleigh and haze scattering are compared. Calculated radiances show differences as large as 23% compared to the approximate scalar theory of radiative transfer, while the same differences are approximately 0.1% for a continental haze phase function. The polarization of reflected and transmitted radiation is given for various optical thicknesses, solar zenith angles, and surface albedos. Two types of neutral points occur for aerosol phase functions. Rayleigh-like neutral points arise from zero polarization that occurs at scattering angles of 0 deg and 180 deg. For Rayleigh phase functions, the position of these points varies with the optical thickness of the scattering layer. Non-Rayleigh neutral points are associated with the zeros of polarization which occur between the end points of the single scattering curve, and are found over a wide range of azimuthal angles

Self-unloading, reusable, lunar lander project

In the early 21st century, NASA will return to the Moon and establish a permanent base. To achieve this goal safely and economically, B&T Engineering has designed an unmanned, reusable, self-unloading lunar lander. The lander is designed to deliver 15,000 kg payloads from an orbit transfer vehicle (OTV) in a low lunar polar orbit and an altitude of 200 km to any location on the lunar surface

Personal Computer-Based Model for Cool Storage Performance Simulation

A personal computer based hourly simulation model was developed based on the CBS/ICE routines in the DOE-2.1 mainframe building simulation software. The menu driven new model employs more efficient data and information handling than the previous model, thus reducing the amount of input to basic system information required from the user. A comparison of results between the new model and CBS/ICE shows good agreement, indicating that the new model may be used with confidence

Radiation transfer through the earth's atmosphere using the matrix operator method

The matrix operator method of solving radiation transfer problems is extended to include polarization. The reflection and transmission operators are presented with continuous variables. An explicit expression for the phase matrix for spherical particles is obtained from the Mie theory in a form applicable to the matrix operator method. The symmetry relations derived by Hovenier from symmetry arguments for the phase matrix are rigorously demonstrated. The symmetry relations for the reflection and transmission operator in both the homogenous and inhomogenous cases are rigorously proven from the symmetry properties of the phase matrix. The reflection and transmission opperators are Fourier decomposed in azimuth and the resulting equations are discretized, yielding the usual discrete equations of the matrix operator method. Intensity, polarization, and direction of polarization results are given for a conservative Rayleigh atmosphere with optical depths ranging from the very small to the semi-infinite limit. The position of the babinet, and Brewser/Arago neutral points are given as a function of optical depth for the reflected and transmitted radiation. The change in the direction of polarization from single scattering is given for the reflected radiation for various depths. The change in the direction of polarization increases with optical depth to depths slightly greater than one. The change then decreases to the semi-infinite limit