Assessment of influence of urban aerosol vertical profile on clear-sky diffuse radiance pattern

Aerosol particles spread in the atmosphere play an important role in solar light scattering and thus co-determine the sky radiance/luminance pattern as well as diffuse irradiances/illuminances at the ground. The particular influence is given by their optical properties and by their distribution in the atmosphere. The dependence of the aerosol extinction coefficient on altitude is usually described by the exponential law, which results from averaging of a large amount of aerosol realizations. This is also frequently the case of simulating of the solar diffuse radiance/luminance distribution over the sky, when it is based on solving the radiative transfer problem. However, the aerosol vertical profile can sometimes be significantly different from the exponential one. Mainly in the urban environment, the aerosol is often well-mixed within the atmospheric boundary layer, so its volume extinction coefficient is almost constant there. This work investigates how such different profiles affect the clear sky radiance pattern and consequently also the ground-based horizontal diffuse irradiance. The numerical simulations reveal that the discrepancies are negligible in practice. So it appears that the aerosol vertical distribution does not play any important role in sky radiance calculations and the standard exponential law is general enough to cover also various specific aerosol conditions.

Discontinuities in numerical radiative transfer

Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of the stationary radiative transfer equation is particularly challenging in such situations, because standard numerical methods may perform very inefficiently in the absence of local smoothness. However, a rigorous investigation of the numerical treatment of the radiative transfer equation in discontinuous media is still lacking. The aim of this work is to expose the limitations of standard convergence analyses for this problem and to identify the relevant issues. Moreover, specific numerical tests are performed. These show that discontinuities in the atmospheric physical parameters effectively induce first-order discontinuities in the radiative transfer equation, reducing the accuracy of the solution and thwarting high-order convergence. In addition, a survey of the existing numerical schemes for discontinuous ordinary differential systems and interpolation techniques for discontinuous discrete data is given, evaluating their applicability to the radiative transfer problem.

Monte-Carlo methods for NLTE spectral synthesis of supernovae

We present JEKYLL, a new code for modelling of supernova (SN) spectra and lightcurves based on Monte-Carlo (MC) techniques for the radiative transfer. The code assumes spherical symmetry, homologous expansion and steady state for the matter, but is otherwise capable of solving the time-dependent radiative transfer problem in non-local-thermodynamic-equilibrium (NLTE). The method used was introduced in a series of papers by Lucy, but the full time-dependent NLTE capabilities of it have never been tested. Here, we have extended the method to include non-thermal excitation and ionization as well as charge-transfer and two-photon processes. Based on earlier work, the non-thermal rates are calculated by solving the Spencer-Fano equation. Using a method previously developed for the SUMO code, macroscopic mixing of the material is taken into account in a statistical sense. To save computational power a diffusion solver is used in the inner region, where the radiation field may be assumed to be thermalized. In addition, a statistical Markov-chain model is used to sample the emission frequency more efficiently, and we introduce a method to control the sampling of the radiation field, which is used to reduce the noise in the radiation field estimators. Except for a description of JEKYLL, we provide comparisons with the ARTIS, SUMO and CMFGEN codes, which show good agreement in the calculated spectra as well as the state of the gas. In particular, the comparison with CMFGEN, which is similar in terms of physics but uses a different technique, shows that the Lucy method does indeed converge in the time-dependent NLTE case. Finally, as an example of the time-dependent NLTE capabilities of JEKYLL, we present a model of a Type IIb SN, taken from a set of models presented and discussed in detail in an accompanying paper. Based on this model we investigate the effects of NLTE, in particular those arising from non-thermal excitation and ionization, and find strong effects even on the bolometric lightcurve. This highlights the need for full NLTE calculations when simulating the spectra and lightcurves of SNe.

Analytical solution of the simple nonlinear radiative transfer problem

Exploring the "Principle of invariance" and the method of "Linear images", the simple nonlinear conservative problem of radiative transfer is analyzed. The solutions of nonlinear reection-transmission and internal field problems of one dimensional scattering-absorbing medium of finite optical thickness are obtained, whereas both boundaries of medium illuminated by powerful radiation beams. Using two different approaches - a direct and inverse problem, the analytical solution of the internal field problem is derived.

A Microstructure-Based Monte Carlo Investigation on the Anisotropic Radiative Transfer in Porous Ceramics

Thermal barrier coatings provide excellent thermal insulation for metal components of gas turbines. Although the relationships between microstructures and mechanical properties as well as thermal conductivity of various TBCs have been extensively studied, there still exists a deficiency of a full understanding on microstructural-related thermal radiation transport inside them, which becomes more and more crucial for advanced gas turbine applications requiring higher operating temperatures. This study aims at presenting a microstructure-based numerical investigation on radiative transfer in the air plasma sprayed (APS) TBC. In this study, the microstructures of APS TBCs are quantitatively reconstructed based on the Ultra-Small-Angle X-Ray Scattering (USAXS) measurement by the Stony Brook University group, in which the microscale interlamellar pores, intrasplat cracks and globular voids are regarded as oblate spheroids with different sizes and aspect ratios, with a specific distribution of orientations. This is a typical anisotropic medium, in which the physical properties vary with the observing direction. The anisotropic feature of radiative properties including the scattering coefficient and phase function is for the first time demonstrated using the discrete dipole approximation (DDA) method. A modified Monte Carlo method is proposed and implemented to solve the anisotropic radiative transfer problem in such medium. The spectral normal-hemispherical reflectance and transmittance of the coating are thus obtained and further compared with the experimental data from literature as well as our group to validate this numerical method. This work provides a versatile numerical framework for the study of the anisotropic radiative transfer mechanism in APS thermal barrier coatings based on microstructure charaterization.

Formation of polarized spectral lines in atmospheres with horizontal inhomogeneities

We study the problem of the generation and transfer of spectral line intensity and polarization in models of stellar atmospheres with horizontal plasma inhomogeneities. We solve the non-LTE radiative transfer problem in full 3D geometry taking into account resonant scattering polarization and its modification by magnetic fields via the Hanle effect. We show that horizontal fluctuations of the thermodynamical conditions of stellar atmospheres can have a significant impact on the linear polarization of the emergent spectral line radiation and its center-to-limb variation.