Cloud coverage aspects of the albedo effect

We discuss some details of the cloud coverage aspects of the albedo effect — the pressure of the radiation reflected by the Earth — on the motion of an artificial satellite. We focus on modeling of the Earth's surface reflection and propagation of the radiation through the atmosphere. We adopt analytical models of these phenomena from radiative transfer theory, in contrast to earlier approaches, based on the fitting of satellite photometry data. We perform several computations based on the accepted models for the ERS-1 and MACEK satellites to test the hierarchy of importance of the effects investigated. In the case of the MACEK mission (which carried a precision accelerometer on board) this information might be essential when interpreting the data.     

Radiative transfer in a homogeneous magnetized plasma

On the ground of the proper wave representation the general theory is developed of radiative transfer in a homogeneous plasma with the strong magnetic field ( _B /1). The linear and nonlinear equations are derived which generalize the corresponding equations of scalar radiative transfer theory in isotropic media. The solutions of some problems are given for the cases when the magnetic field is perpendicular to the surface: diffuse reflection of radiation from a semiinfinite medium, provided the sources are placed far from the surface (Milne's problem) and have constant intensity, increase linearly or quadratically with the optical depths, or decrease exponentially from the surface.     

Radiative Transfer in Inhomogeneous Atmospheres. I

This series of papers is devoted to multiple scattering of light in plane parallel, inhomogeneous atmospheres. The approach proposed here is based on Ambartsumyan's method of adding layers. The main purpose is to show that one can avoid difficulties with solving various boundary value problems in the theory of radiative transfer, including some standard problems, by reducing them to initial value problems. In this paper the simplest one dimensional problem of diffuse reflection and transmission of radiation in inhomogeneous atmospheres with finite optical thicknesses is considered as an example. This approach essentially involves first determining the reflection and transmission coefficients of the atmosphere, which, as is known, are a solution of the Cauchy problem for a system of nonlinear differential equations. In particular, it is shown that this system can be replaced with a system of linear equations by introducing auxiliary functions P and S. After the reflectivity and transmissivity of the atmosphere are determined, the radiation field in it is found directly without solving any new equations. We note that this approach can be used to obtain the required intensities simultaneously for a family of atmospheres with different optical thicknesses. Two special cases of the functional dependence of the scattering coefficient on the optical thickness, for which the solutions of the corresponding equations can be expressed in terms of elementary functions, are examined in detail. Some numerical calculations are presented and interpreted physically to illustrate specific features of radiative transport in inhomogeneous atmospheres.     

太阳辐射压摄动计算的新进展

介绍了一种新的建立太阳辐射压摄动模型的方法,即Ｖｏｋｒｏｕｈｌｉｃｋｙ等人提出的方法。该方法以辐射转移方程为基本数学工具,并运用相应的物理概念,通过对太阳辐射场强和辐射流量的计算来求出太阳辐射压摄动。此方法既适用于卫星处于地球半影区内和地球阴影之外的情形,也适用于地球反照辐射压的计算。还介绍了该方法的一些计算结果,并简单评述了其不足之处。     

On some aspects of the albedo effect application to the ERS-1 satellite

Some aspects of the perturbative influence of radiation reflected by the Earth's surface on the motion of an artificial satellite are discussed. We concentrate on consequences of the extreme models with anisotropic reflection on the Earth's surface (specular reflection, clouds with anisotropic phase function). The possible effects of Lála's modification of the Earth's albedo nominal value are investigated. The role of the satellite surface optical properties is pointed out in the context of the albedo effect. All mentioned models are purely numerical. The whole message of the paper can be summarized in the following items

-It is very doubtful that the 10^?8 ÷ 10^?9 m s^?2 level is reached when determining the perturbing accelerations caused by the albedo effect in the case of the ERS-1 satellite due to poorly defined optical characteristics of the Earth's atmosphere, the Earth and the satellite's surface.

-In the general case this albedo effect uncertainty level is about 50% with respect to the averaged values, and probably as high as 100% with respect to the instantaneous values of the perturbing accelerations.

     

A hybrid mode of diffuse and specular reflector for computation of the emergent radiation by the adding method

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.     

The effect of surface characteristics on diffuse reflection radiation at λ=0.40 μm

The diffuse radiation in the upward direction at the top and at an internal level of an inhomogeneous atmosphere is computed at =0.40 m. The surface is assumed to reflect light in accordance with a hybrid mode of a diffuse and specular reflector. The objective is to estimate the effect of underlying surface characteristics in terms of the diffuse radiation field. By making use of these results, accuracy in monitoring the atmospheric aerosols would be increased for the use of remote sensing satellite techniques. Junge power lawv ^*=3 is adopted for the size distribution of aerosols (1963), while the data given by McClatchyet al. (1971) is used for the number density of aerosols with height distribution. It is noted from the computations that the diffuse reflection radiation is affected by the surface characteristics, even if the albedo of the surface is a fixed constant and very small.On leave from the Meterological Research Institute, Tokyo, Japan.bl]References     

Exact solution of the equation of transfer with planetary phase function

We have considered the transport equation for radiative transfer to a problem in semi-infinite atmosphere with no incident radiation and scattering according to planetary phase function w(1 + xcos ). Using Laplace transform and the Wiener-Hopf technique, we have determined the emergent intensity and the intensity at any optical depth. The emergent intensity is in agreement with that of Chandrasekhar (1960).     

Emergent radiation from the atmosphere bounded by the two half Lambert surfaces composed of different albedo,II

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.     

Exact solution of the transport equation for radiative transfer with scattering albedo ωO < 1 using the Laplace transform and the Wiener-Hopf technique and an expression ofH-function

We have considered the transport equation for radiative transfer to a problem in semi-infinite non-conservative atmosphere with no incident radiation and scattering albedo ₀ < 1. Usint the Laplace transform and the Wiener-Hopf technique, we have determined the emergent intensity and the intensity at any optical depth. We have obtained theH-function of Dasgupta (1977) by equating the emergent intensity with the intensity at zero optical depth.     

Radiation transfer in a diffuse and specular reflecting slab with Rayleigh scattering

A method of analysis is presented for solving the radiative transfer problem in an absorbing, emitting, inhomogeneous, and anisotropically scattering plane-parallel medium with specular and diffuse reflecting boundaries and internal source (problem 1). Exact relations for the radiation heat flux at the boundaries of problem 1 are obtained in terms of the radiation density and albedos of the corresponding source-free medium with specular reflecting boundaries (problem 2). Two coupled integral equations for the radiation density and the second moment of the radiation intensity for problem 2 with Rayleigh phase functions are obtained. The Galerkin method is used to solve these equations. Albedos of problem 2 are compared with theF _n method. Numerical results for radiation heat fluxes at the boundaries of problem 1 are tabulated for different forms of the internal source.     

Radiation hydrodynamics of high-luminosity accretion into black holes

To extend Shapiro's (1973a, b) calculations of black hole accretion to the regimes of interstellar gas densities and of black hole masses for which emergent luminosities are expected to be high, the radiation hydrodynamics of spherically symmetric gas flows in static isotropic metrics is discussed. Since for the more luminous objects the optical depth of the accretion volume becomes large, particular attention has to be paid to radiative transfer through non-Euclidean spaces, and a method for solving the full transfer problem is presented. The method is applied to accretion into black holes of mass between 10M and 10⁵ M , under the conservative assumption that all other heat sources, like dissipation of magnetic or turbulent energy, can be neglected in comparison to the compressional work term,p dV. In the interstellar gas parameter range of interest, the radiation field is then dominated by emission and absorption of synchrotron radiation from inner zones of the flow. Temperature stratifications, luminosities and emergent spectra resulting from these processes are calculated.     

The Spatial Angular Function of Thermal Emission of the Moon

New satellite measurements of the lunar-surface radiation temperature are used to construct the spatial angular function of thermal radiation of the Moon in the infrared (10.5–12.5 m) spectral range. The basic material for investigations is the scanned cosmic spectrozonal images of the lunar surface transmitted by the first Russian geostationary artificial meteorological satellite GOMS. The formulas for calculating the angular parameters are given, and the photometric function of thermal radiation of the Moon is plotted as a function of the incidence angle, the reflection angle, and the azimuthal angle between the planes of the incident and reflected rays.     

X-ray resonance scattering in a spherically symmetric coronal model

In the solar corona the opacities of some of the prominent X-ray emission lines are on the order of 1 over typical coronal path lengths. We present and discuss a particular solution of the radiative transfer problem involving an extended, spherically symmetric coronal shell radiating isotropic, homogeneous emission in which single-scattering also takes place. Within the context of this simplified model we find that scattered radiation is an important contribution to the total emergent resonance line flux and that for the He-like family of resonance (r), intercombination (i), and forbidden (f) lines, the ratio G=(f + i)/r would decrease as a function of optical depth for disk-center emission in an extended spherically symmetric corona.     

Thermosolutal instability of a radiating partially-ionized plasma in a porous medium

The thermosolutal instability of a radiating two-component plasma, in a porous medium in the presence of a uniform vertical magnetic field, is examined with respect to the effects of collision frequency and radiative transfer. A combination of the Bestman and Chandrasekar methods is used to solve the eigenvalue problem with two-dimensional disturbances for the case of stationary convection. Radiation present on the onset of instability is found to have a destabilizing effect for even a very small radiation parameter, of the order(0.1). concentration gradient on the other hand has a stabilizing effect on the system. The effect of collision on the onset of stationary cells diminishes for the optical thin non-grey plasma-near equilibrium. This is of paramount importance in cosmic ray physics, as the interaction between the ionized and neutral gas components represents a state which often exists in the universe.     

Radiative transfer equation in spherically-symmetric non-scattering media

We solved the equation of radiative transfer in spherically-symmetric shells with arbitrary internal sources. We integrated the equation of transfer on the discrete grid of angle and radius given by [_j–1, _j] [r_i–1, r_i]. The size in the angle coordinates is determined by the roots of a quadrature formula where as the size in the radial coordinate is determined by the non-negativity of the reflection and transmission operators. We considered two cases of variation of the Planck function. (1) Constant throughout the medium and (2) varying as 1/r ². We find that in the inner shells, the radiation directed toward the centre of the sphere is more than that directed away from the centre of the sphere. In the outer shells the converse is true.     

Source vector in Rayleigh-Cabannes scattering atmosphere: the nonconservative milne problem

We consider the radiative transfer in a nonconservative homogeneous plane-parallel semi-infinite planetary atmosphere where the scattering processes are described by the Rayleigh-Cabannes phase matrix and where the primary sources are in infinitely deep layers. If we use the superposition principle we derive the Cauchy problem for the source vector.As a by-product the external field of radiation for the problem described is obtained using the principle of invariance by Chandrasekhar. The respective formulae for the radiation field in the deep layers and for the extrapolation distance are given. It is shown that the Rubenson degree of polarization even in the case of near-conservative atmospheres reaches the asymptotic regime at rather small values of the optical depth. The-plane reliefs of the characteristic equation, extrapolation distance and the normalized components of the source vector at the boundary are given along with a sample of zeros of the characteristic equation.     

A New Method of Numerical Solution of Nonsteady Problems in the Theory of Radiative Transfer

A new method is proposed for the numerical solution of nonsteady problems in the theory of radiative transfer. In this method, if the solution at some time t (such as the initial time) is known, then by representing the radiation intensity and all time-dependent quantities (level populations, kinetic temperature, etc.) in the form of Taylor series expansions in the vicinity of t, one can, from the transfer equation and the equations accompanying it (population equations, energy-balance equation, etc.), find all derivatives of that solution at the given time from certain recursive equations. From the Taylor series one can then calculate the solution at some later time t + t, and so forth. The method enables one to analyze nonsteady tradiative transfer both in stationary media and in media with characteristics that vary with time in a given way. This method can also be used to solve nonlinear problems, i.e., those in which the radiation field significantly affects the characteristics of the medium. No iterations are used for this: everything comes down to calculations based on recursive equations. Several problems, both linear and nonlinear, are solved as examples.     

Group-theoretical description of radiative transfer in one-dimensional media

Group theory is used to describe a procedure for adding inhomogeneous absorbing and scattering atmospheres in a one-dimensional approximation. The inhomogeneity originates in the variation of the scattering coefficient with depth. Group representations are derived for the composition of media in three different cases: inhomogeneous atmospheres in which the scattering coefficient varies continuously with depth, composite or multicomponent atmospheres, and the special case of homogeneous atmospheres. We extend an earlier proposal to solve problems in radiative transfer theory by first finding global characteristics of a medium (reflection and transmission coefficients) and then determining the internal radiation field for an entire family of media without solving any new equations. Semi-infinite atmospheres are examined separately. For some special depth dependences of the scattering coefficients it is possible to obtain simple analytic solutions expressed in terms of elementary functions. An algorithm for numerical solution of radiative transfer problems in inhomogeneous atmospheres is described.     

Formation of the solar Hα profile

A series of non-LTE radiative transfer solutions for H was computed using the integrodifferential equation technique of Athay and Skumanich (1967). A model hydrogen atom consisting of three bound levels and a continuum was assumed. It was found that increasing the temperature of the chromosphere at the height of line formation decreases the central intensity of the line. The density structure of the atmosphere primarily affects the optical depth scale rather than the source function. The temperature minimum region of the atmosphere was found to be transparent to H radiation, so that the radiation in some part of the line will arise from two distinct layers of the atmosphere, one above the temperature minimum and one below it. The computed H profile was found to be highly sensitive to the assumed 2–3 collisional cross-section.