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1.
Tsutomu Takashima 《Earth, Moon, and Planets》1985,33(1):59-97
A procedure of computing the radiance and the polarization parameters of radiation diffusely reflected and transmitted by an inhomogeneous, plane-parallel terrestrial atmosphere bounded by a ruffled ocean surface is discussed with the aid of the adding method. If the atmosphere and the ocean are simulated by a number of homogeneous sublayers, the matrices of radiation reflected and transmitted diffusely by the atmosphere-ocean system can be expressed in terms of these matrices of sublayers by using only a couple of iterative equations in which the polarity effect of radiation is included. Furthermore, the upwelling radiance and the polarization degree of radiation at the top of the atmosphere can be calculated by using a single iterative equation without requiring the equation for the diffuse transmission matrix of radiation. The ruffled ocean surface can be treated as an interacting interface, where the transmitted radiation from beneath the ocean surface into the atmosphere is also taken into account into the derivation of equations. Finally, sample computations of the upwelling radiance and the polarization degree of radiation from the top of the atmosphere are carried out at the wavelength of 0.60 micron. 相似文献
2.
A method of computing the diffuse reflection and transmission radiation by an inhomogeneous, plane-parallel planetary atmosphere with internal emission source is discussed by use of the adding method. If the atmosphere is simulated by a number of homogeneous sub-layers, the radiation diffusely reflected or transmitted by the atmosphere can be expressed in terms of the reflection and transmission matrices of the radiation of sub-layers. The diffusely transmitted radiation due to the internal emission source can be also easily computed in the same manner. These equations for the emergent radiation are in a quite general form and are applicable to radiative transfer in the atmosphere in the region from ultraviolet to infrared radiation. With this method, the tiresome treatment due to the polarity effect of radiation is overcome. 相似文献
3.
A method of computing the diffuse reflection and transmission radiation from an inhomogenous, plane-parallel planetary atmosphere bounded by the hybrid surface of a diffuse and specular reflector is discussed by using the addition method. If the atmosphere is simulated by a number of homogeneous sublayers, the radiation diffusely reflected and transmitted by the atmosphere can be expressed in terms of the diffuse reflection and transmission matrices of radiation of sublayers (Laciset al., 1974; Takashima, 1973, 1975). With this method (Takashima, 1975), the troublesome treatment due to the effect of polarity of radiation is overcome. Moreover, if the surface reflects radiation in accordance with the Lambert law as well as a quite arbitrary phase matrix (Takashima, 1974), the addition method can be easily extended. It is shown in this paper that the addition method is suitable for numerical computation even if the surface reflects light according to the hybrid mode of the diffuse and specular law (Uenoet al., 1974; Mukai, 1976).On leave from the Meterological Research Institute, Tokyo, Japan. 相似文献
4.
Tsutomu Takashima 《Astrophysics and Space Science》1974,30(2):309-313
If the atmosphere is simulated by a number of homogeneous sublayers, it was shown (Takashima, 1973a) that the intensity and polarization parameters emerging from any boundary of internal sublayer's field can be determined, provided that the diffuse reflection and transmission matrices of radiation of sublayers are known. Furthermore, if the surface (ground) is assumed to reflect light in accordance with the Lambert law, it is shown in this paper that the internal radiation field at boundary of any sublayer can be also computed in terms of the diffuse radiation matrices of sublayers rather than in terms of that of the entire atmosphere (Sekera, unpublished). The effect of polarization is included. 相似文献
5.
Tsutomu Takashima 《Astrophysics and Space Science》1973,23(1):201-204
Suppose that the atmosphere consists of homogeneous sublayers whose scattering and transmission matrices are known, then it is shown in this paper how to determine the intensity and polarization parameters of internal radiation field by the matrix method. 相似文献
6.
For the evaluation of the effect of the non-uniform surface albedo on the emergent radiation from the atmosphere, the emergent radiation from the atmosphere bounded by the two half Lambert surfaces composed of different albedo is computed. This paper is the improved version of the previous paper (Takashima and Masuda, 1991). The atmosphere is assumed to be homogeneous, which is composed of aerosol, molecules, and absorbent gases. Their optical thicknesses are (1) 0.25, 0.23, and 0.02, and (2) 0.75, 0.23, and 0.02, respectively. The model aerosol is of the oceanic and water soluble types.In the computational procedure, the emergent radiation is calculated approximately by the contributions due to the multiple scattering in the atmosphere, and due to the diffusely or directly transmitted radiation through the atmosphere which is reflected by the surfaces once (4 interactive radiative modes between atmosphere and surface). Furthermore, to perform the hemispherical integration processing the radiative interaction, the transmission function based on the single scattering in the atmosphere is introduced and then the transmission function is averaged over the hemisphere with weighting function. The numerical simulation exhibits the extraordinary effect near the two half surface boundary of different albedoes. The effect decreases exponentially with the distance from the boundary. The effect depends on the atmospheric aerosol type, optical thickness, and surface albedo. The present version enables us to quantitatively discuss the radiative transfer trend near the boundary of two half surfaces. The upward radiance would simply be evaluated using the present scattering approximation method if the surface albedo is less than 0.3. The present method is thought of as a first step extending the one-dimensional radiative transfer model to two-dimensional using the doubling-adding method. 相似文献
7.
K. L. Coulson 《Planetary and Space Science》1959,1(4):265-276
S. Chandrasekhar's solution of the equation of radiative transfer m a medium scattering according to Rayleigh's law has been used for an extensive series of computations of the scattered and diffusely reflected radiation directed outward from the top of a plane stratified model of the atmosphere. The results are discussed in two parts, the first of which deals with the intensity, degree of polarization, plane of polarization and the neutral points of the scattered and diffusely reflected radiation. Part II (see following article) will be a discussion of the upward flux, integrated over the hemisphere, as a function of wavelength of the incident radiation, and of the albedo of the atmospheric model for an energy distribution of the incident light similar to that of the extra-terrestrial solar spectrum. The results are compared with similar quantities for the diffusely scattered radiation from the sunlit sky. 相似文献
8.
Rabindra Nath Das 《Astrophysics and Space Science》1979,60(1):221-232
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
9.
K. L. Coulson 《Planetary and Space Science》1959,1(4):277-284
The solution of the equation of radiative transfer in a medium exhibiting Rayleigh scattering, as developed by S. Chandrasekhar, has been used for an extensive series of computations(3) of the characteristics of the scattered and diffusely reflected radiation emerging from the top of an atmospheric model which corresponds in many respects to the sunlit portion of the earth's atmosphere. The first part of this two-part discussion dealt with the intensity, degree of polarization, plane of polarization and the neutral points of the emergent light as functions of sun elevation, direction in the downward hemisphere, optical thickness of the model atmosphere and reflectivity of the underlying surface. This second part is concerned with the upward flux obtained by an integration of the intensity over the entire hemisphere, for the incident radiation (a) being independent of wavelength or (b) having the spectral distribution of the extra-terrestrial solar radiation. Integration with respect to wavelength in the latter case, together with an approximation for the sphericity of the atmosphere, yields a value of 7.6 per cent for the earth's planetary albedo due to scattering by the clear atmosphere. An approximation for ozone absorption decreases the computed albedo to 6.9 per cent. 相似文献
10.
Rabindra Nath Das 《Astrophysics and Space Science》1979,60(2):321-327
We have considered the transport equation for the problem of diffuse reflection and transmission on Rayleigh's phase function and obtained the exact solution of this equation for angular distributions of the intensities diffusely reflected from the surfacet=0 and diffusely transmitted below the surfacet=t
0 of a finite atmosphere of optical deptht=t
0 using the Laplace transform and the theory of singular operators. This is an exact method. 相似文献
11.
For the evaluation of the effect of the nonuniform surface albedo to the emergent radiation from the atmosphere, the emergent radiation from the atmosphere bounded by the two-halves of the Lambert surface with different albedos is computed. The principal plane is assumed to be perpendicular to the boundary of surfaces. The atmosphere is assumed to be homogeneous, which is composed of aerosol, molecules, and absorbent gases. Their optical thicknesses are 0.25, 0.23, and 0.02, respectively. The model aerosol is of the oceanic and water soluble types.In the computational procedure, the emergent radiation is approximated by the contributions due to the multiple scattering in the atmosphere, directly attenuated radiation, and radiation due to single scattering in the atmosphere which is reflected by the Lambert surface (up to 4 interactive radiative modes between atmosphere and surface). For quantitative analysis, results are compared with those of the atmosphere-uniform surface model, where the multiple scattering is considered. The numerical simulation exhibits the extraordinary effect near the surface boundary of different albedos. The effect decreases exponentially with the distance from the boundary. It is a function of the observational position, difference of surface albedos, optical thickness and aerosol type.The upward radiance would simply be evaluated using the present scattering approximation method if the atmosphere is in clear condition. Whereas in hazy condition, the effect of multiple scattering in the atmosphere should be considered more precisely, since the upward radiance exhibit a strong dependence on observational nadir angles due to multiple scattering in the atmosphere. Furthermore, it depends on the optical characteristics of aerosols. 相似文献
12.
Tõnu Viik 《Astrophysics and Space Science》1995,232(1):49-64
The determination of the average path-length of photons emerging from a finite planeparallel atmosphere with molecular scattering is discussed. We examine the effects of polarisation on the average path-length of the emergent radiation by comparing the results with those obtained for the atmosphere where the scattering obeys the scalar Rayleigh function. Only the axial radiation field is considered for both cases.To solve this problem we have used the integro-differential equations of Chandrasekhar for the diffuse scattering and transmission functions (or matrices). By differentiation of these equations with respect to the albedo of single scattering we obtain new equations the solution of which gives us the derivatives of the intensities of the emergent radiation at the boundaries.As in the case of scalar transfer the principles of invariance by Chandrasekhar may be used to find an adding scheme to obtain both the scattering and transmission matrices and their derivatives with respect to the albedo of single scattering. These derivatives are crucial in determining the average path length.The numerical experiments have shown that the impact of the polarisation on the average pathlength of the emergent radiation is the largest in the atmospheres with optical thickness less than, or equal to, three, reaching 6.9% in the reflected radiation. 相似文献
13.
Knut Stamnes 《Planetary and Space Science》1982,30(7):727-732
By appealing to the reciprocity principle simple expressions are derived for the plane albedo and the transmissivity of a vertically inhomogeneous, plane parallel atmosphere. The plane albedo is shown to equal the angular distribution of the reflected intensity for isotropie Illumination of unit intensity incident at the top of the atmosphere, while the transmissivity equals the angular distribution of the transmitted intensity for isotropie illumination of unit Intensity incident at the bottom of the atmosphere. Chandrasekhar's solution of the planetary problem (including a Lambert reflecting lower boundary) in terms of the solution to the standard problem (no reflecting ground) is extended to apply to an inhomogeneous atmosphere resting on a surface that reflects radiation anisotropically but with no dependence on the direction of incidence (anisotropic Lambert reflector). The computational aspects are discussed and a procedure for computing the planetary albedo and transmissivity Is outlined for a vertically inhomogeneous, anisotropically scattering atmosphere overlying a partially reflecting surface. Numerical verification and illustration are also provided and it is shown that the assumed vertical variation of the single scattering albedo strongly affects the plane albedo but only weakly the transmissivity. 相似文献
14.
The Mariner 9 ultraviolet spectrometer observed the brightness of a region on the south polar cap centered at approximately ?87°S, 10°W. Measurements taken at various incidence and emission angles (i and ?) show that the brightness increased with decreasing air mass, ≈(sec i + sec ?). The observed intensity consists primarily of a component reflected from the cap and twice-attenuated by the atmosphere and a component diffusely reflected from the atmosphere. The diffusely reflected component was determined from nearby observations of non-polar regions at the same incidence and emission angles and was substrated from the total intensity. Inversion of the intensity difference using a formula analogous to the Bouger-Langley law yielded the optical thickness of the atmosphere. The dust cloud over the polar cap was moderately thick between November 26 and December 2, 1971. At this time the optical thickness was near unity, and it decreased approximately linearly with time, reaching a value close to that of a Rayleigh atmosphere by mid-February. The optical thickness showed little dependence on the wavelength during the early orbital observations. As the dust storm cleared, the atmospheric optical thickness exhibited increasingly strong inverse wavelength dependence. Particles large compared with the wavelength dominated the Martian dust storm. These particles are estimated to have a mean radius of about 2 μm. 相似文献
15.
T. Takashima 《Earth, Moon, and Planets》1994,64(1):39-46
To evaluate the effect of the cliff on the radiation field, the upwelling radiation at the top of the atmosphere is computed over the cliff using the reflection and transmission functions derived from the doubling-adding method. The model is defined by the plane-parallel homogeneous atmosphere, which is composed of aerosol and molecules, and is bounded by the top level surface, cliff and low level surface. These surfaces may be assumed to be the Lambertian.In the computational procedure, the equation for the emergent radiation is expanded into a series of radiative interaction modes among atmosphere, surfaces and the cliff. In respective modes, probabilities of respective interactions are firstly evaluated. With the aid of these probabilities, the emergent radiation is calculated using the doubling-adding method for the model atmosphere bounded by the surfaces and cliff, where the above radiative interactions are considered upto twice as large to obtain the enough accuracy of simulation. The multiple scattering is considered. 相似文献
16.
A new way is adopted for the evaluation of the upwelling radiation from atmosphere bounded by two half-Lambert surfaces. The atmosphere is assumed to be homogeneous, and is composed of aerosol, molecules, and absorbent gases, where the model aerosol is of the oceanic and water soluble types.In the computational procedure, an iterative doubling-adding equation is expanded into a series of the radiative interaction modes between atmosphere and surface. Next, a probability of radiation interacting with respective half surfaces is calculated based on the assumption of single-scattering in the atmosphere. On the basis of this probability, the emergent radiation at the top of the atmosphere is approximately calculated by considering the radiative intractions to be twice as large. The effect of the multiple-scattering is fully taken into account. A numerical simulation exhibits the extraordinary effect near the two half-surface boundary of different albedoes. The effect of the other half-surface on the radiance decreases monotonically with the distance from the boundary. The present new version enable us to quantitatively discuss radiative transfer near the boundary of two half-surfaces even if the optical thickness is large and (or) surface albedo is great. 相似文献
17.
The orbit of the balloon satellite, Explorer 19, is analysed to determine the effects of direct solar radiation pressure over one revolution of the satellite (111 min) for MJD 42822 and MJD 42966. At the earlier date, the satellite entered the Earth's shadow, presenting an opportunity to examine the effectiveness of two different shadow models. The reflectivity of the surface of the satellite was estimated from analysis of the variations in orbital eccentricity over a period of 236 days.Although many of the parameters associated with the shape and orientation of the satellite are unknown, the theory for a non-spherical satellite is applied using trial and error methods to determine the parameters of best fit. The paper concludes with an examination of the perturbations in orbital eccentricity and inclination due to incident, specularly reflected, and diffusely reflected radiation. 相似文献
18.
N. J. McCormick 《Astrophysics and Space Science》1980,71(1):235-238
A procedure is developed to determine the single-scattering albedo from polarization measurements of the angle-dependent intensity at two locations within, or on the boundaries of, a homogeneous finite atmosphere which scatters radiation according to Rayleigh's law with true absorption. The density of the atmosphere need not be known. 相似文献
19.
The law of limb darkening has been calculated when the atmosphere of the primary component is illuminated by the extended
surface of the secondary component in a binary system. The specific intensities calculated at infinity show marked changes
when the plane-parallel approximation is replaced by the assumption of spherical symmetry. The middle portions of the illuminated
surface reflect maximum radiation while the innermost and outermost layers show lesser amount of reflected radiation. 相似文献
20.
In this paper we consider the time-dependent diffuse reflection and transmission problems for a homogeneous anisotropically-scattering atmosphere of finite optical depth and solve it by the principle of invariance. Also we consider the time-dependent diffuse reflection and transmission of parallel rays by a slab consisting of two anisotropic homogeneous layers, whose scattering and transmission properties are known. It is shown how to express the time-dependent reflected and transmitted intensities in terms of their components. In a manner similar to that given by Tsujita (1968), we assumed that the upward-directed intensities of radiation at the boundary of the two layers are expressed by the sum of products of some auxiliary functions depending on only one argument. Then, after some analytical manipulations, three groups of systems of simultaneous integral equations governing the auxiliary functions are obtained. 相似文献