Accelerated higher order radiative perturbation computation: an application of GDOM

In a previous paper by the authors, the computational expressions for the higher order terms of the radiative perturbation series have been developed, and numerical results have been obtained. In this paper, new computational expressions are developed that use the analytic Green's function and the GDOM code, which were developed recently by Qin and Box. Our analysis and numerical computations indicate that the new scheme dramatically improves the efficiency of the computation (by reducing the CPU-time to less than 2% of that required by the previous scheme), and the huge demand on memory usage has been completely removed. This new scheme allows us to expand the high order perturbation computations to more general cases, for example, to include azimuth dependence, and to use the perturbation theory in more potential applications.     

Computation of Green's function for radiative transfer

In an accompanying paper, we develop the computational expressions for the higher order perturbation of the radiative transfer equation, and present some numerical results for typical cases. In this article, we discuss a number of issues regarding the implementation of the HOP computation: obtaining the Green's function, its expansion as a double series of Legendre polynomials, and obtaining the adjoint radiance of more general sources such as those for the fluxes at arbitrary altitudes. Examples of Green's function and its expansion coefficients are presented.     

Vector Green's function algorithm for radiative transfer in plane-parallel atmosphere

Green's function is a widely used approach for boundary value problems. In problems related to radiative transfer, Green's function has been found to be useful in land, ocean and atmosphere remote sensing. It is also a key element in higher order perturbation theory. This paper presents an explicit expression of the Green's function, in terms of the source and radiation field variables, for a plane-parallel atmosphere with either vacuum boundaries or a reflecting (BRDF) surface. Full polarization state is considered but the algorithm has been developed in such way that it can be easily reduced to solve scalar radiative transfer problems, which makes it possible to implement a single set of code for computing both the scalar and the vector Green's function.     

Extension of the discrete-ordinate algorithm and efficient radiative transfer calculation

As an accurate and efficient algorithm, the discrete-ordinate method (DOM) has been used to solve the radiative transfer problem of plane-parallel scattering atmosphere illuminated by a parallel beam, an idealized case of the sun, from above the atmosphere. In this paper, we extend this algorithm so that radiative problems of more general sources, such as parallel surface sources that illuminate with a parallel beam in any direction from any vertical position, and general surface sources that illuminate continuously in a hemisphere, can be solved. For a problem where intensity distributions are sought for a number of different sources within the same atmosphere-surface system, the intrinsic properties of DOM are used so that the time required for the solution for extra sources is reduced to a substantially small amount. In the case of parallel surface sources, numerical testing has shown that the amount can be reduced to as little as 15% of a full solution. Examples of applications are presented.     

Linearization of radiative transfer with respect to surface properties

The linearization of radiative transfer with respect to surface properties in the UV and visible part of the solar spectrum is presented. The proposed method is a rigorous extension of the radiative perturbation theory with respect to surface properties. Given the forward and adjoint intensity field, analytical expressions are provided for the linearization of any observable related to the radiation field with respect to surface properties characterized by Minnaert's and Lambertian bidirectional reflection distribution function. For the considered surface reflection characteristics, we also discuss an extension of the reduction approach of Chandrasekhar as an alternative linearization method. The suitability of both approaches for the combined retrieval of trace gas and surface properties from the backscattered sunlight in the UV and visible part of the spectrum is discussed. The authors come to the conclusion that the perturbation theory, for this purpose, represents the superior method because of its general applicability to any parameter characterizing the optical properties of the atmosphere and the underlying surface.     

Approximate polarization calculations with scalar radiative transfer theory

The Pomraning phase function can be used to perform approximate polarized Rayleigh transfer calculations with a scalar radiative transfer equation. The approximation is numerically tested for the albedo problem consisting of azimuthally independent radiation incident on a homogeneous semi-infinite atmosphere. The numerical tests were carried out with the same approach used by Viik (JQSRT 68 (2000) 319-326) to numerically test the approximate phase function for solving the Milne problem. Away from the surface the Pomraning phase function gives marginally better results for the diffuse radiation than the usual scalar Rayleigh phase function because it was derived from an asymptotic limit more appropriate for deeper locations in an atmosphere. For optical depths less than unity, though, the scalar Rayleigh approximation is better than the Pomraning approximation.     

Radiative perturbation theory for polarized radiances: 1. Theory

Radiative perturbation theory has proven to be a useful tool in radiative transfer calculations, especially in situations where repeated solution of the radiative transfer equation is required. So far however, its use has been restricted to non-polarized situations, including such applications as surface fluxes, UV indices, and the inversion of satellite radiance observations. Here, we extend the structure of radiative perturbation theory to incorporate the full Stokes formalism of polarization, to obtain the relevant equations for the first order term. This formalism will be applied to fluxes in a follow-up paper, and eventually to satellite observations.     

基于辐射传输理论和分形理论的云场景仿真

 基于云的边缘特征和天空亮度分布特征，对有云天空场景的仿真方法进行了研究。分析了云对天空亮度影响，并据此提出了一种基于分形原理的云场景仿真方法。通过辐射传输理论，给出了有无云天空的光谱亮度分布计算方法。在分析了云边缘具有自相似分形特征基础上，利用有云天空亮度分布特征、二次随机法和分形几何的Diamond-Square算法设计了云纹理生成算法。利用混合修正δ-Eddington近似计算出了观察视场2°×2°内640×480单元的2维天空亮度数组。利用该理论模型得到有云天空的2维亮度数组，并用VC++实现了云场景的动态仿真，得到了较为逼真的结果。     

ARTS, the atmospheric radiative transfer simulator

ARTS is a modular program that simulates atmospheric radiative transfer. The paper describes ARTS version 1.0, which is applicable in the absence of scattering. An overview over all major parts of the model is given: calculation of absorption coefficients, the radiative transfer itself, and the calculation of Jacobians. ARTS can be freely used under a GNU general public license.Unique features of the program are its scalability and modularity, the ability to work with different sources of spectroscopic parameters, the availability of several self-consistent water continuum and line absorption models, and the analytical calculation of Jacobians.     

Scaling algorithms for the calculation of solar radiative fluxes

We derived new scaling formulae based on the method of successive orders of scattering to calculate solar radiative flux. In this report, we demonstrate a multiple scaling method, in which we introduce scaling factors for each scattering order independently. The formula of radiative transfer by the method of successive orders of scattering cannot be solved rapidly except in the case of optically thin atmospheres. Then we further derived a double scaling method, which scales the ordinary radiative transfer equation by two scaling factors. We applied the double scaling method to two-stream and four-stream approximations of the discrete ordinates method. Comparing the results of the double scaling method with those of the delta-M method, we found that the double scaling method improved the accuracy of radiative fluxes at large solar zenith angles, especially in the optically thin region, and that in the region where multiple scattering dominates, its accuracy was comparable to that of the delta-M method. Once we determined the scaling factors appropriately, the double scaling method calculated radiative fluxes as rapidly as the delta-M method in the two-stream and four-stream approximations. This method, therefore, is useful for accurate computation of solar radiative fluxes in general circulation models.     

Noninvasive determination of tissue optical properties based on radiative transfer theory

We present a feasibility study of a new method for determining the tissue optical properties, including the absorption and scattering coefficients and the scattering asymmetry factor. A state-of-the-art radiative transfer model for the coupled air/tissue system, based on rigorous radiative transfer theory, is used in our forward modeling simulations. The concept of the effective photon penetration depth is introduced and used to help determine the depth below, which information about the tissue will not be available through noninvasive imaging of a biological tissue using reflected diffuse light. Simulation results show that for accurate determination of tissue optical properties, one can use radiative transfer theory in conjunction with measurements of reflected radiances as well as other existing techniques.     

Fast multilevel radiative transfer

The vast majority of recent advances in the field of numerical radiative transfer relies on approximate operator methods better known in astrophysics as Accelerated Lambda-Iteration (ALI). A superior class of iterative schemes, in term of rates of convergence, such as Gauss-Seidel and successive overrelaxation methods were therefore quite naturally introduced in the field of radiative transfer by Trujillo Bueno and Fabiani Bendicho [A novel iterative scheme for the very fast and accurate solution of non-LTE radiative transfer problems. Astrophys J 1995;455:646]; it was thoroughly described for the non-LTE two-level atom case. We describe hereafter in details how such methods can be generalized when dealing with non-LTE unpolarised radiation transfer with multilevel atomic models, in monodimensional geometry.     

Fluctuation theory for radiative transfer in random media

We consider the effect of small scale random fluctuations of the constitutive coefficients on boundary measurements of solutions to radiative transfer equations. As the correlation length of the random oscillations tends to zero, the transport solution is well approximated by a deterministic, averaged, solution. In this paper, we analyze the random fluctuations to the averaged solution, which may be interpreted as a central limit correction to homogenization.With the inverse transport problem in mind, we characterize the random structure of the singular components of the transport measurement operator. In regimes of moderate scattering, such components provide stable reconstructions of the constitutive parameters in the transport equation. We show that the random fluctuations strongly depend on the decorrelation properties of the random medium.     

Many polarized radiative transfer models

This note is an introduction to the reprint of the 1991 JQSRT article “A new polarized atmospheric radiative transfer model” by K.F. Evans and G.L. Stephens. We discuss the significance of the article, how our two plane-parallel polarized radiative transfer codes came about, how our codes have been used, and more recent developments in polarized radiative transfer modeling.     

Nanorod near-field radiative heat exchange analysis

A theoretical method for cylinder-to-cylinder radiative heat exchange is formulated. The method utilized was a modified version of a previously published numerical method for near-field sphere-to-sphere radiative exchange. Modifications were made to the numerical procedure to make it applicable to cylindrical geometry of nanorods. Nanorods investigated had length to diameter ratios of 3:1 and 7:1. The heat exchange of nanorods is plotted vs. gap to assess the impact of near-field radiative transfer as gap decreases. Graphical results of energy vs. nanorod radii are also presented. A nanorod-to-plane configuration is estimated utilizing a nanorod asymptotic method. The nanorod-to-nanorod method approximates a nanorod-to-plane geometric configuration when one nanorod radii is held constant, and the second nanorod radii is iteratively increased until the corresponding radiative exchange converges.     

Stability of explicit radiation-material coupling in radiative transfer calculations

We show that explicit radiation-material coupling, which is essentially always stable for infrared radiative transfer is conditionally stable in the high energy density regime. A linearized stability analysis is first performed for a simple infinite-medium problem that yields both a criterion for unconditional stability, a time-step restriction that applies for conditional stability, and a time-step criterion that always applies for non-oscillatory solutions. This analysis is then extended to include space dependence with the result that the system is always conditionally stable, but with a time step restriction somewhat different from the infinite-medium case. Nonetheless, the time step restriction for non-oscillatory solutions remains the same. Computations are presented that confirm the predictions of our analysis, and conclusions are given.     

Generalized form of the direct and adjoint radiative transfer equations

The main goal of this paper is to give a rigorous derivation of the generalized form of the direct (also referenced as forward) and adjoint radiative transfer equations. The obtained expressions coincide with expressions derived by Ustinov [Adjoint sensitivity analysis of radiative transfer equation: temperature and gas mixing ratio weighting functions for remote sensing of scattering atmospheres in thermal IR. JQSRT 2001;68:195-211]. However, in contrast to [Ustinov EA. Adjoint sensitivity analysis of radiative transfer equation: temperature and gas mixing ratio weighting functions for remote sensing of scattering atmospheres in thermal IR. JQSRT 2001;68:195-211] we formulate the generalized form of the direct radiative transfer operator fully independent from its adjoint. To illustrate the application of the derived adjoint radiative transfer operator we consider the angular interpolation problem in the framework of the discrete ordinate method widely used to solve the radiative transfer equation. It is shown that under certain conditions the usage of the solution of the adjoint radiative transfer equation for the angular interpolation of the intensity can be computationally more efficient than the commonly used source function integration technique.     

Screened perturbation theory at four loops

We study the thermodynamics of massless ⁴-theory using screened perturbation theory, which is a way to systematically reorganise the perturbative series. The free energy and pressure are calculated through four loops in a double expansion in powers of g² and m/T, where m is a thermal mass of order gT. The result is truncated at order g⁷. We find that the convergence properties are significantly improved compared to the weak-coupling expansion.     

Variational method for solving radiative transfer problems

The variational principle is used to solve two problems of radiative transfer. The first one is the temperature distribution and radiative heat flux for a plane layer of ceramic material. While the second is the calculation of the integral blankness degree of a sphere filled with dust of an arc steel-melting furnace. Numerical results obtained shows good agreement with the published data.