Calculation of the spectrum of the integral equation of radiative transfer. II. Plane layer of finite optical thickness

Astrophysics ◽  
1980 ◽  
Vol 15 (3) ◽  
pp. 324-330 ◽  
Author(s):  
D. I. Nagirner
Keyword(s):  
Integral Equation ◽  
Radiative Transfer ◽  
Optical Thickness ◽  
Plane Layer ◽  
Finite Optical Thickness

A Parametric Numerical Study of Radiative Transfer in Thermotropic Materials

2013 ◽  
Author(s):  
Adam C. Gladen ◽  
Susan C. Mantell ◽  
Jane H. Davidson
Keyword(s):  
Particle Size ◽  
Radiative Transfer ◽  
Optical Thickness ◽  
Parametric Study ◽  
Volume Fraction ◽  
Numerical Study ◽  
Anisotropic Scattering ◽  
Index Of Refraction ◽  
Spherical Particles ◽  
Size Parameter

A thermotropic material is modeled as an absorbing, thin slab containing anisotropic scattering, monodisperse, spherical particles. Monte Carlo ray tracing is used to solve the governing equation of radiative transfer. Predicted results are validated by comparison to the measured normal-hemispherical reflectance and transmittance of samples with various volume fraction and relative index of refraction. A parametric study elucidates the effects of particle size parameter, scattering albedo, and optical thickness on the normal-hemispherical transmittance, reflectance, and absorptance. The results are interpreted for a thermotropic material used for overheat protection of a polymer solar absorber. For the preferred particle size parameter of 2, the optical thickness should be less than 0.3 to ensure high transmittance in the clear state. To significantly reduce the transmittance and increase the reflectance in the translucent state, the optical thickness should be greater than 2.5 and the scattering albedo should be greater than 0.995. For optical thickness greater than 5, the reflectance is asymptotic and any further reduction in transmittance is through increased absorptance. A case study is used to illustrate how the parametric study can be used to guide the design of thermotropic materials. Low molecular weighted polyethylene in poly(methyl methacrylate) is identified as a potential thermotropic material. For this material and a particle radius of 200 nm, it is determined that the volume fraction and thickness should equal 10% and 1 mm, respectively.

Consistent retrieval of cloud/aerosol single scattering properties and surface reflectance

2021 ◽  
Author(s):  
Marta Luffarelli ◽  
Yves Govaerts
Keyword(s):  
Radiative Transfer ◽  
Optical Thickness ◽  
Solution Space ◽  
Single Scattering ◽  
Aerosol Optical Thickness ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Surface Reflectance ◽  
Earth System ◽  
System Components

<p>The CISAR (Combined Inversion of Surface and AeRosols) algorithm is exploited in the framework of the ESA Aerosol Climate Change Initiatiave (CCI) project, aiming at providing a set of atmospheric (cloud and aerosol) and surface reflectance products derived from S3A/SLSTR observations using the same radiative transfer physics and assumptions. CISAR is an advance algorithm developed by Rayference originally designed for the retrieval of aerosol single scattering properties and surface reflectance from both geostationary and polar orbiting satellite observations.  It is based on the inversion of a fast radiative transfer model (FASTRE). The retrieval mechanism allows a continuous variation of the aerosol and cloud single scattering properties in the solution space.</p><p> </p><p>Traditionally, different approaches are exploited to retrieve the different Earth system components, which could lead to inconsistent data sets. The simultaneous retrieval of different atmospheric and surface variables over any type of surface (including bright surfaces and water bodies) with the same forward model and inversion scheme ensures the consistency among the retrieved Earth system components. Additionally, pixels located in the transition zone between pure clouds and pure aerosols are often discarded from both cloud and aerosol algorithms. This “twilight zone” can cover up to 30% of the globe. A consistent retrieval of both cloud and aerosol single scattering properties with the same algorithm could help filling this gap.</p><p> </p><p>The CISAR algorithm aims at overcoming the need of an external cloud mask, discriminating internally between aerosol and cloud properties. This approach helps reducing the overestimation of aerosol optical thickness in cloud contaminated pixels. The surface reflectance product is delivered both for cloud-free and cloudy observations.  </p><p> </p><p>Global maps obtained from the processing of S3A/SLSTR observations will be shown. The SLSTR/CISAR products over events such as, for instance, the Australian fire in the last months of 2019, will be discussed in terms of aerosol optical thickness, aerosol-cloud discrimination and fine/coarse mode fraction.</p>

scholarly journals Feasibility study of multi-pixel retrieval of optical thickness and droplet effective radius of inhomogeneous clouds using deep learning

2017 ◽  
Vol 10 (12) ◽  
pp. 4747-4759 ◽  
Author(s):  
Rintaro Okamura ◽  
Hironobu Iwabuchi ◽  
K. Sebastian Schmidt
Keyword(s):  
Deep Learning ◽  
Radiative Transfer ◽  
Optical Thickness ◽  
Cloud Droplet ◽  
Effective Radius ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Optical Remote Sensing ◽  
Transfer Effects ◽  
Cloud Properties

Abstract. Three-dimensional (3-D) radiative-transfer effects are a major source of retrieval errors in satellite-based optical remote sensing of clouds. The challenge is that 3-D effects manifest themselves across multiple satellite pixels, which traditional single-pixel approaches cannot capture. In this study, we present two multi-pixel retrieval approaches based on deep learning, a technique that is becoming increasingly successful for complex problems in engineering and other areas. Specifically, we use deep neural networks (DNNs) to obtain multi-pixel estimates of cloud optical thickness and column-mean cloud droplet effective radius from multispectral, multi-pixel radiances. The first DNN method corrects traditional bispectral retrievals based on the plane-parallel homogeneous cloud assumption using the reflectances at the same two wavelengths. The other DNN method uses so-called convolutional layers and retrieves cloud properties directly from the reflectances at four wavelengths. The DNN methods are trained and tested on cloud fields from large-eddy simulations used as input to a 3-D radiative-transfer model to simulate upward radiances. The second DNN-based retrieval, sidestepping the bispectral retrieval step through convolutional layers, is shown to be more accurate. It reduces 3-D radiative-transfer effects that would otherwise affect the radiance values and estimates cloud properties robustly even for optically thick clouds.

The SKN Approximation for Solving Radiative Transfer Problems in Absorbing, Emitting, and Isotropically Scattering Plane-Parallel Medium: Part 1

2002 ◽  
Vol 124 (4) ◽  
pp. 674-684 ◽  
Author(s):  
Zekeriya Altac¸
Keyword(s):  
Integral Equation ◽  
Radiative Transfer ◽  
Differential Equations ◽  
Order Approximation ◽  
High Order ◽  
High Order Approximation ◽  
One Dimensional ◽  
Second Order Differential Equations ◽  
Plane Parallel ◽  
Transfer Problems

A high order approximation, the SKN method—a mnemonic for synthetic kernel—is proposed for solving radiative transfer problems in participating medium. The method relies on approximating the integral transfer kernel by a sum of exponential kernels. The radiative integral equation is then reducible to a set of coupled second-order differential equations. The method is tested for one-dimensional plane-parallel participating medium. Three quadrature sets are proposed for the method, and the convergence of the method with the proposed sets is explored. The SKN solutions are compared with the exact, PN, and SN solutions. The SK1 and SK2 approximations using quadrature Set-2 possess the capability of solving radiative transfer problems in optically thin systems.

Differential Approximation to Radiative Transfer in Semitransparent Media

1985 ◽  
Vol 107 (2) ◽  
pp. 478-481 ◽  
Author(s):  
F. H. Azad
Keyword(s):  
Integral Equation ◽  
Radiative Transfer ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Exact Formulation ◽  
Differential Approximation ◽  
Reflection And Refraction ◽  
Integrated Intensity ◽  
Dielectric Interfaces ◽  
Semitransparent Medium

Radiative transfer in a semitransparent medium is treated using the differential approximation. Boundary conditions are formulated to accommodate direction-dependent reflection and refraction at a dielectric interfaces. The approximate results are compared to numerical solution of the exact integral equation. Also, a modification based on the exact formulation of the integrated intensity at the interface is presented that significantly improves the accuracy of the differential approximation in the optically thin regimes.

On a non-linear integral equation occurring in diffraction theory

1966 ◽  
Vol 62 (2) ◽  
pp. 249-261 ◽  
Author(s):  
R. F. Millar
Keyword(s):  
Functional Equation ◽  
Integral Equation ◽  
Radiative Transfer ◽  
Plane Wave ◽  
Admissible Solution ◽  
Diffraction Theory ◽  
Linear Integral Equation ◽  
Non Linear Equation ◽  
Non Linear ◽  
Linear Integral

AbstractThe problem of diffraction of a plane wave by a semi-infinite grating of iso-tropic scatterers leads to the consideration of a non-linear integral equation. This bears a resemblance to Chandrasekhar's integral equation which arises in the study of radiative transfer through a semi-infinite atmosphere. It is shown that methods which have been used with success to solve Chandrasekhar's equation are equally useful here. The solution to the non-linear equation satisfies a more simple functional equation which may be solved by factoring (in the Wiener-Hopf sense) a given function. Subject to certain additional conditions which are dictated by physical considerations, a solution is obtained which is the unique admissible solution of the non-linear integral equation. The factors and solution are found explicitly for the case which corresponds to closely spaced scatterers.

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