scholarly journals On the property of ”statistical identity” of solutions to some classical problems of the radiative transfer theory

2021 ◽  
pp. 502-508
Author(s):  
H. V. Pikichyan
Keyword(s):  
Radiative Transfer ◽  
Diffusion Process ◽  
Diffuse Reflection ◽  
Isotropic Scattering ◽  
Probabilistic Interpretation ◽  
Temporal Dependence ◽  
Absorbing Medium ◽  
Direct Transformation ◽  
Nonhomogeneous Media ◽  
Random Events

A probabilistic interpretation of the classical solution of the diffuse reflection problem (DRP) of radiation from a semi-infinite homogeneous scattering-absorbing medium on the language of random events in the simple case of monochromatic and isotropic scattering is constructed. A certain property of the so-called ”statistical identity” is specially defined. By using these two circumstances, it is possible to construct a simple symbolic scheme for the direct transformation of the solution mentioned above in the particular case of DRP into solutions to more general cases of DRP, which taking into account the anisotropy and incoherence of scattering, as well as the temporal dependence of the task on the act of absorption. Moreover, some generalization of the primary scheme makes it possible to directly obtain solutions of the DRP also for nonhomogeneous media and for general case of time dependence (on absorption acts and free flights between them) for the quanta diffusion process. At the same time, both the well-known results of the DRP decisions and some new ones were obtained.

scholarly journals APOLLO_NG – a probabilistic interpretation of the APOLLO legacy for AVHRR heritage channels

2015 ◽  
Vol 8 (10) ◽  
pp. 4155-4170 ◽  
Author(s):  
L. Klüser ◽  
N. Killius ◽  
G. Gesell
Keyword(s):  
Radiative Transfer ◽  
Probabilistic Approach ◽  
Retrieval Algorithm ◽  
Probabilistic Interpretation ◽  
Cloud Detection ◽  
Processing Scheme ◽  
Cloud Property ◽  
Cloud Processing ◽  
Wide Range ◽  
Physical Principles

Abstract. The cloud processing scheme APOLLO (AVHRR Processing scheme Over cLouds, Land and Ocean) has been in use for cloud detection and cloud property retrieval since the late 1980s. The physics of the APOLLO scheme still build the backbone of a range of cloud detection algorithms for AVHRR (Advanced Very High Resolution Radiometer) heritage instruments. The APOLLO_NG (APOLLO_NextGeneration) cloud processing scheme is a probabilistic interpretation of the original APOLLO method. It builds upon the physical principles that have served well in the original APOLLO scheme. Nevertheless, a couple of additional variables have been introduced in APOLLO_NG. Cloud detection is no longer performed as a binary yes/no decision based on these physical principles. It is rather expressed as cloud probability for each satellite pixel. Consequently, the outcome of the algorithm can be tuned from being sure to reliably identify clear pixels to conditions of reliably identifying definitely cloudy pixels, depending on the purpose. The probabilistic approach allows retrieving not only the cloud properties (optical depth, effective radius, cloud top temperature and cloud water path) but also their uncertainties. APOLLO_NG is designed as a standalone cloud retrieval method robust enough for operational near-realtime use and for application to large amounts of historical satellite data. The radiative transfer solution is approximated by the same two-stream approach which also had been used for the original APOLLO. This allows the algorithm to be applied to a wide range of sensors without the necessity of sensor-specific tuning. Moreover it allows for online calculation of the radiative transfer (i.e., within the retrieval algorithm) giving rise to a detailed probabilistic treatment of cloud variables. This study presents the algorithm for cloud detection and cloud property retrieval together with the physical principles from the APOLLO legacy it is based on. Furthermore a couple of example results from NOAA-18 are presented.

The SKN Approximation for Solving Radiative Transfer Problems in Absorbing, Emitting, and Linearly Anisotropically Scattering Plane-Parallel Medium: Part 2

2002 ◽  
Vol 124 (4) ◽  
pp. 685-695 ◽  
Author(s):  
Zekeriya Altac¸
Keyword(s):  
Radiative Transfer ◽  
Incident Energy ◽  
Radiative Heat ◽  
Isotropic Scattering ◽  
Benchmark Problems ◽  
Scattering Medium ◽  
Second Order Differential Equations ◽  
Plane Parallel ◽  
Kernel Approximation ◽  
Transfer Problems

The SKN (Synthetic Kernel) approximation is proposed for solving radiative transfer problems in linearly anisotropically scattering homogeneous and inhomogeneous participating plane-parallel medium. The radiative integral equations for the incident energy and the radiative heat flux using synthetic kernels are reduced to a set of coupled second-order differential equations for which proper boundary conditions are established. Performance of the three quadrature sets proposed for isotropic scattering medium are further tested for linearly anisotropically scattering medium. The method and its convergence with respect to the proposed quadrature sets are explored by comparing the results of benchmark problems using the exact, P11, and S128 solutions. The SKN method yields excellent results even for low orders using appropriate quadrature set.

An Iterative Solution for Anisotropic Radiative Transfer in a Slab

1979 ◽  
Vol 101 (4) ◽  
pp. 695-698 ◽  
Author(s):  
W. H. Sutton ◽  
M. N. O¨zis¸ik
Keyword(s):  
Radiative Transfer ◽  
Iterative Method ◽  
Integral Form ◽  
Iterative Solution ◽  
Single Scattering ◽  
Anisotropic Scattering ◽  
Initial Guess ◽  
Isotropic Scattering ◽  
Wide Range ◽  
Reflecting Boundaries

An iterative method is applied to solve the integral form of the equation of radiative transfer for the cases of isotropic scattering, highly forward, and backward anisotropic scattering in plane-parallel slab with reflecting boundaries. Calculations are performed for the values of single scattering albedo from ω = 0.7 to 1.0 where the convergence was previously reported to be poor. It is found that the convergence is significantly improved for most cases if the P-1 approximation of the spherical harmonics method is used for the initial guess. Results are presented for the hemispherical reflectivity and transmissivity of the slab over a wide range of parameters.

scholarly journals Analytical solution of the simple nonlinear radiative transfer problem

2018 ◽  
pp. 364-372
Author(s):  
H. V. Pikichyan
Keyword(s):  
Radiative Transfer ◽  
Analytical Solution ◽  
Transfer Problem ◽  
Internal Field ◽  
Field Problem ◽  
Radiative Transfer Problem ◽  
Absorbing Medium ◽  
One Dimensional ◽  
Radiation Beams ◽  
Finite Optical Thickness

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.

Transient Radiative Transfer of Light Pulse Propagation in Three-Dimensional Scattering Media With Finite Volume Method and Integral Equation Model

2003 ◽  
Author(s):  
Xiaodong Lu ◽  
Pei-Feng Hsu ◽  
John C. Chai
Keyword(s):  
Integral Equation ◽  
Radiative Transfer ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Light Pulse ◽  
Three Dimensional ◽  
Equation Model ◽  
Isotropic Scattering ◽  
Scattering Media ◽  
Volume Method

The transient radiative transfer process is studied with a finite volume method (FVM) and an integral equation (IE) model. Propagation of a short light pulse in the three-dimensional absorbing and isotropic scattering media is considered. Collimated irradiation enters at one side of the rectangular medium. The other five boundaries are cold and black, nonparticipating surfaces. The spatial and temporal distributions of the integrated intensity and radiative flux are obtained.

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