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1.
The vector equation of radiative transfer is solved both for conservative and non-conservative planetary atmospheres using the method of discrete ordinates. The atmosphere, bounded by a Lambert bottom, is considered plane-parallel and homogeneous. The scattering in the atmosphere obeys the Rayleigh or Rayleigh-Cabannes law. The compiled package of FORTRAN codes allows us to find the Stokes parameters for such an atmosphere at arbitrary optical depth.  相似文献   

2.
We present measurements of ratios of elements of the scattering matrix of martian analogue palagonite particles for scattering angles ranging from 3° to 174° and a wavelength of 632.8 nm. To facilitate the use of these measurements in radiative transfer calculations we have devised a method that enables us to obtain, from these measurements, a normalized synthetic scattering matrix covering the complete scattering angle range from 0° to 180°. Our method is based on employing the coefficients of the expansions of scattering matrix elements into generalized spherical functions. The synthetic scattering matrix elements and/or the expansion coefficients obtained in this way, can be used to include multiple scattering by these irregularly shaped particles in (polarized) radiative transfer calculations, such as calculations of sunlight that is scattered in the dusty martian atmosphere.  相似文献   

3.
The vector equation of radiative transfer is solved for non-conservative homogeneous plane-parallel atmosphere using the method of discrete ordinates. The scattering processes in the atmosphere bounded by a Lambert bottom are described by the Rayleigh-Cabannes phase matrix. The primary radiation field is generated by constant internal sources. A package of FORTRAN subroutines is compiled to find the axial radiation field for such an atmosphere at arbitrary optical depth.  相似文献   

4.
We have considered six scalar equations which are obtained from the vector transport equation for radiative transfer to the problem of diffuse reflection and transmission in finite plane-parallel Rayleigh scattering atmosphere. By use of the Laplace transform and the theory of linear singular operators these equations have been solved exactly to get the angular distribution of the intensity diffusely reflected from the surface and diffusely transmitted below the surface.  相似文献   

5.
Scattering of starlight by dust, molecules and electrons in spiral galaxies will produce a modification of the direct intensity and a polarization in the observed light. We treat the case where the distribution of scatterers can be considered to be optically thin, and derive semi-analytic expressions for the resolved intensity and polarized intensity for Thomson, Rayleigh, and more general scattering mechanisms. These expressions are applied to a parametric model for spiral galaxies. It is further shown that in the case of Thomson and Rayleigh scattering, and when scatterers and stars are distributed with rotational symmetry, the total polarized flux depends on the inclination, i , of the galactic axis to the line of sight according to a simple sin2  i law. This generalizes the well-known result for point-like and spherical light sources. By using a method based on spherical harmonics, we generalize this law for more general mechanisms, and show that to good approximation, the sin2  i law still holds for the class of models considered.  相似文献   

6.
The H N method, employed for studies in neutron transport theory, is used to establish numerical results basic to the vector equation describing the transfer of polarized light in a Rayleigh scattering atmosphere with true absorption. The method has been applied to the classical Milne problem. The exit distribution is defined as a series in powers of the zenith observation angle. The numerical results are computed and compared with exact values obtained using the exit distribution in terms of the H-matrix. The numerical results are in good agreement with previously published findings.  相似文献   

7.
Atmospheric density profiles as well as several light absorption and scattering processes depend on geographic position and are generally time-variable. Their impact on the atmospheric Cherenkov technique in general (imaging or non-imaging) is investigated. Different density profiles lead to differences in Cherenkov light density of up to 60%. Seasonal variations at mid-latitude sites are of the order of 15–20%. The quest for improved energy calibration of Cherenkov experiments also shows the need for improved transmission calculations, taking all relevant processes into account and using realistic profiles of absorbers. Simulations including the scattering mechanisms also reveal the relevance of Rayleigh and Mie scattering for atmospheric Cherenkov experiments. Refraction and the differences between treating the atmosphere in plane-parallel or spherical geometry are also investigated.  相似文献   

8.
A numerical solution to the integral equation for radiative transfer by resonance reradiation in an isothermal spherical atmosphere is described. The method presented is 100 times more efficient than earlier spherical radiative transfer models. The new model can accommodate density variations in the full three dimensional space and includes effects due to the presence of pure absorbers. Complete frequency redistribution is assumed for photon scattering. Applications of this model to the problem of solar photons scattered by atomic hydrogen in the atmospheres of Venus, Earth and Mars are described, and limb and disk profiles, as well as equivalent mean disk intensities for Venus, Earth and Mars, are presented.  相似文献   

9.
Accurate photometric and kinematic modelling of disc galaxies requires the inclusion of radiative transfer models. Because of the complexity of the radiative transfer equation (RTE), sophisticated techniques are required. Various techniques have been employed for the attenuation in disc galaxies, but a quantitative comparison of them is difficult, because of the differing assumptions, approximations and accuracy requirements that are adopted in the literature. In this paper, we present an unbiased comparison of four methods to solve the RTE, in terms of accuracy, efficiency and flexibility. We apply them all to one problem that can serve as a first approximation of large portions of disc galaxies: a one-dimensional plane-parallel geometry, with both absorption and multiple scattering taken into account, with arbitrary vertical distributions of stars and dust and an arbitrary angular redistribution of the scattering. We find that the spherical harmonics method is by far the most efficient way to solve the RTE, whereas both Monte Carlo simulations and the iteration method, which are straightforward to extend to more complex geometries, have a cost that is about 170 times larger.  相似文献   

10.
Richard W. Zurek 《Icarus》1978,35(2):196-208
This paper examines the solar heating of the Martian atmosphere during the 1971 global dust storm observed by Mariner 9. Radiative scattering as well as absorption is included by utilizing the delta-Eddington approximation to the full radiative transfer equation. The necessary optical parameters are generated by a Mie program which uses a size distribution and a complex refractive index inferred from a number of sources, particularly from recent analyces of Mariner 9 UVS and TV observations. Assuming uniform mixing of the dust, the solar heating per unit mass during a Martian global dust storm is remarkably uniform with height for small solar zenith angles. Heating rates may reach 80°K day? for overhead sunlight. Overall, 20% of the direct insolation is absorbed by the dust-laden atmosphere. Even optically thin widespread dust hazes may produce heating rates of several degrees Kelvin per day.  相似文献   

11.
TheF N method is used to solve, in a concise manner, the complete problem concerning the diffusion of polarized light in a plane-parallel Rayleigh and isotropically scattering atmosphere.  相似文献   

12.
A solution of the transfer equation for coherent scattering in stellar atmosphere with Planck's function as a nonlinear function of optical depth, viz., $$B_v (T) = b_0 + b_1 {\text{ }}e^{ - \beta \tau } $$ is obtained by the method of discrete ordinates originally due to Chandrasekhar.  相似文献   

13.
L.A. Sromovsky 《Icarus》2005,173(1):284-294
Solar radiation reflected by the atmospheres of Neptune and Uranus is dominated by Rayleigh scattering at visible wavelengths, and thus subject to the effects of polarization. Ignoring these effects can lead to errors in reflected intensity of more than 9% in a clear atmosphere. But solving the full vector equation of transfer is computationally very costly, forcing approximations with limitations that are not well understood and not generally applicable to spatially resolved observations and complex atmospheric structures. Using accurate vector radiation transfer calculations, it is here shown that differences between vector and scalar results near zero phase angle have systematic dependencies on optical depth, single scattering albedo, and angle, that provide a basis for accurate approximation of the reflected intensities. With little computational cost, it is possible to calculate corrected spatially resolved scalar intensities that closely match vector intensities, with individual errors rarely exceeding 1%, and mean and RMS errors generally within a few tenths of 1%. The correction method accounts for the attenuating effects of clouds and molecular absorption.  相似文献   

14.
Radiative transfer   总被引：1，自引：0，他引：1  
Chandrasekhar’s work in radiative transfer theory began in 1944 and culminated with the publication of his influential treatiseRadiative Transfer in 1950. In this review his major contributions to radiative transfer will be recounted and evaluated. These include his development of the discrete ordinates method, the invariance principles, and his formulation and solution of the transfer equation for polarized light.  相似文献   

15.
The problem of monoenergetic radiative transfer in a finite planar stochastic atmospheric medium with polarized (vector) Rayleigh scattering is proposed. The solution is presented for an arbitrary absorption and scattering cross sections. The extinction function of the medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The joint probability distribution function of these Gaussian random variables is used to calculate the ensemble-averaged quantities, such as reflectivity and transmissivity, for an arbitrary correlation function. A modified Gaussian probability distribution function is also used to average the solution in order to exclude the probable negative values of the optical variable. Pomraning-Eddington approximation is used, at first, to obtain the deterministic analytical solution for both the total intensity and the difference function used to describe the polarized radiation. The problem is treated with specular reflecting boundaries and angular-dependent externally incident flux upon the medium from one side and with no flux from the other side. For the sake of comparison, two different forms of the weight function, which introduced to force the boundary conditions to be fulfilled, are used. Numerical results of the average reflectivity and average transmissivity are obtained for both Gaussian and modified Gaussian probability density functions at the different degrees of polarization.  相似文献   

16.
The general formalism, presented in a previous paper of this series (Landi Degl'Innocenti, 1983a), is particularized to deduce the radiative transfer equations for polarized radiation and the statistical equilibrium equations for a multi-level atom in the zero-magnetic field, collisionless regime. The formulae are developed both in the standard representation and in the representation of the statistical tensors. For resonance scattering in a two-level atom, in the limiting case of complete depolarization of the ground level, we recover the classical results for Rayleigh scattering and we derive the expression of the phase matrix in terms of ordinary rotation matrices. The law of scattering is then generalized to take properly into account the influence of the anisotropy of the radiation field on the atomic polarization of the ground level (depopulation pumping).  相似文献   

17.
The limiting polarization of a resonance line is examined for standard radiative transfer of polarized radiation in a semi-infinite scattering atmosphere with complete frequency redistribution. Two families of profiles of the line absorption coefficient, which are generalizations of Lorentz and Doppler profiles, are examined. It is shown that for both families this parameter approaches the Sobolev-Chandrasekhar limit when the fraction of absorption within the frequency interval (expressed in appropriate units) from −1 to 1 relative to the total absorption in the line approaches unity.  相似文献   

18.
The polarized radiative transfer equation is solved when angle-dependent partial redistribution and non-coherent electron scattering are included as line-scattering mechanisms. A static atmosphere with plane parallel symmetry is assumed. Test calculations are used to illustrate the effects of the electron-scattering coefficient, the thermalization parameter and the continuous absorption coefficient on the line polarization. Results of angle-averaged and angle-dependent redistribution functions are compared and it is shown that angle-dependent functions should be used to model the wing polarization of optically thin lines. The lower the continuous absorption compared with the electron scattering, the higher the wing polarization.  相似文献   

19.
C. Devaux  M. Herman 《Icarus》1975,24(1):19-27
We have used the measurements of the solar flux obtained by the Venera 8 spacecraft inside the atmosphere of Venus and the values of the Venus spherical albedo to deduce the characteristics of the clouds and of the ground. The method used is the exponential kernel approximation and the results have been tested by exact computations with the spherical harmonics method.A cloud layer with an optical thickness τ1 ? 144, an albedo for single scattering ω0 = 0.9998 in the rear infrared, above a Rayleigh layer between 0 and 32 km and a ground of reflectivity ? = 0.4, gives a good agreement with the experimental results. A model with two cloud layers is also discussed.  相似文献   

20.
Fluorescent emissions from nitric oxide appear imposed upon the Rayleigh backscattered spectrum of the earth's atmosphere between 250 and 300 nm in wavelength. Satellite instruments designed to monitor the global ozone distribution can routinely observe these signals although techniques for exploiting the data are not yet available. Application of a radiative transfer equation developed for an atmosphere including absorption by ozone, molecular scattering, and nitric oxide fluorescence shows the three most prominent NO emissions relative to the 250–300 nm backscattered sunlight to be the (1,4), (1,6), and (0,3) gamma bands. Analysis of the contribution function for each emission band indicates that the fluorescent signals can provide useful information on the magnitude and variability of nitric oxide between 40 and 140 km in altitude.  相似文献   

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