Radiative transfer in a semi-infinite plane parallel atmosphere with an inhomogeneous source function

2007 ◽  
Vol 312 (3-4) ◽  
pp. 239-260 ◽  
Author(s):  
N. A. Silant’ev ◽  
G. A. Alexeeva
Keyword(s):  
Radiative Transfer ◽  
Source Function ◽  
Infinite Plane ◽  
Plane Parallel

The transport equation of radiative transfer with isotropic scattering

1969 ◽  
Vol 65 (1) ◽  
pp. 199-208 ◽  
Author(s):  
G. E. Hunt
Keyword(s):  
Integral Equation ◽  
Radiative Transfer ◽  
Singular Integral Equation ◽  
Transport Equation ◽  
Singular Integral ◽  
Source Function ◽  
Three Dimensional ◽  
Isotropic Scattering ◽  
Plane Parallel ◽  
Homogeneous Plane

AbstractThe kernel of the integral equation for the source function in a three-dimensional homogeneous atmosphere possesses the properties of a Green's function. These properties are used to transform the integral equation into a singular integral equation for the kernel. The particular case of a homogeneous plane parallel atmosphere is discussed and a solution to the kernel equation is obtained at all points of the atmosphere.

scholarly journals Scale dependence of cirrus heterogeneity effects. Part II: MODIS NIR and SWIR channels

2018 ◽  
Vol 18 (16) ◽  
pp. 12105-12121 ◽  
Author(s):  
Thomas Fauchez ◽  
Steven Platnick ◽  
Tamás Várnai ◽  
Kerry Meyer ◽  
Céline Cornet ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Spatial Resolution ◽  
Thermal Infrared ◽  
Radiative Effects ◽  
Ice Clouds ◽  
Plane Parallel ◽  
Wide Range ◽  
The Impact ◽  
Side Illumination

Abstract. In a context of global climate change, the understanding of the radiative role of clouds is crucial. On average, ice clouds such as cirrus have a significant positive radiative effect, but under some conditions the effect may be negative. However, many uncertainties remain regarding the role of ice clouds on Earth's radiative budget and in a changing climate. Global satellite observations are particularly well suited to monitoring clouds, retrieving their characteristics and inferring their radiative impact. To retrieve ice cloud properties (optical thickness and ice crystal effective size), current operational algorithms assume that each pixel of the observed scene is plane-parallel and homogeneous, and that there is no radiative connection between neighboring pixels. Yet these retrieval assumptions are far from accurate, as real radiative transfer is 3-D. This leads to the plane-parallel and homogeneous bias (PPHB) plus the independent pixel approximation bias (IPAB), which impacts both the estimation of top-of-the-atmosphere (TOA) radiation and the retrievals. An important factor that determines the impact of these assumptions is the sensor spatial resolution. High-spatial-resolution pixels can better represent cloud variability (low PPHB), but the radiative path through the cloud can involve many pixels (high IPAB). In contrast, low-spatial-resolution pixels poorly represent the cloud variability (high PPHB), but the radiation is better contained within the pixel field of view (low IPAB). In addition, the solar and viewing geometry (as well as cloud optical properties) can modulate the magnitude of the PPHB and IPAB. In this, Part II of our study, we simulate TOA 0.86 and 2.13 µm solar reflectances over a cirrus uncinus scene produced by the 3DCLOUD model. Then, 3-D radiative transfer simulations are performed with the 3DMCPOL code at spatial resolutions ranging from 50 m to 10 km, for 12 viewing geometries and nine solar geometries. It is found that, for simulated nadir observations taken at resolution higher than 2.5 km, horizontal radiation transport (HRT) dominates biases between 3-D and 1-D reflectance calculations, but these biases are mitigated by the side illumination and shadowing effects for off-zenith solar geometries. At resolutions coarser than 2.5 km, PPHB dominates. For off-nadir observations at resolutions higher than 2.5 km, the effect that we call THEAB (tilted and homogeneous extinction approximation bias) due to the oblique line of sight passing through many cloud columns contributes to a large increase of the reflectances, but 3-D radiative effects such as shadowing and side illumination for oblique Sun are also important. At resolutions coarser than 2.5 km, the PPHB is again the dominant effect. The magnitude and resolution dependence of PPHB and IPAB is very different for visible, near-infrared and shortwave infrared channels compared with the thermal infrared channels discussed in Part I of this study. The contrast of 3-D radiative effects between solar and thermal infrared channels may be a significant issue for retrieval techniques that simultaneously use radiative measurements across a wide range of solar reflectance and infrared wavelengths.

Search for the source function inside a plane-parallel scattering layer from the intensity of emerging radiation

1976 ◽  
Vol 25 (3) ◽  
pp. 1164-1169 ◽  
Author(s):  
N. N. Rogovtsov ◽  
A. M. Samson
Keyword(s):  
Source Function ◽  
Scattering Layer ◽  
Plane Parallel

Non-LTE Line Transfer with Diffusion of Excited Atoms

1977 ◽  
Vol 32 (2) ◽  
pp. 156-159
Author(s):  
D. F. Düchs ◽  
J. Oxenius
Keyword(s):  
Differential Equation ◽  
Low Temperature ◽  
Radiative Transfer ◽  
Spectral Line ◽  
Source Function ◽  
Homogeneous Medium ◽  
Classical Problem ◽  
Temperature Limit ◽  
Excited Atoms ◽  
Line Transfer

The classical problem of radiative transfer in a spectral line, due to two-level atoms, in a homogeneous medium is reconsidered. It is pointed out that the source function used up to now in the literature neglects the diffusion of the excited atoms. In many cases this assumption is not justified. In the low-temperature limit kT ≪ hv, the correct source function, allowing for diffusion of excited atoms, obeys an integro-differential equation

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.

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