Development of a Network Analogy and Evaluation of Mean Beam Lengths for Multidimensional Absorbing/Isotropically Scattering Media

1990 ◽  
Vol 112 (2) ◽  
pp. 408-414 ◽  
Author(s):  
W. W. Yuen
Keyword(s):  
Radiative Transfer ◽  
Flux Density ◽  
Optical Thickness ◽  
Numerical Results ◽  
Beam Length ◽  
Scattering Media ◽  
Limiting Behavior ◽  
Isothermal Medium ◽  
Mathematical Behavior ◽  
Large Optical Thickness

Based on Hottel’s zonal formulation, a network analogy is developed for the analysis of radiative transfer in general multidimensional absorbing/isotropically scattering media. Applying the analogy to the analysis of an isothermal medium and assuming that the incoming and outgoing flux density is homogeneous within the medium, the effect of scattering on the evaluation of mean beam lengths is illustrated. Two concepts of mean beam length, an absorption mean beam length (AMBL) and an extinction mean beam length (EMBL), are introduced and shown to be important for the analysis of radiative transfer in practical systems. Both mean beam lengths differ significantly from the conventional mean beam length in systems of moderate and large optical thickness. Relations between AMBL and EMBL and their limiting behavior are developed analytically. Numerical results for a sphere radiating to its surface and an infinite parallel slab radiating to one of its surfaces are presented to demonstrate quantitatively the mathematical behavior of the two mean beam lengths.

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>

Transient Radiative Transfer in Anisotropically Scattering Media Using Monotonicity-Preserving Schemes

2000 ◽  
Author(s):  
M. Sakami ◽  
K. Mitra ◽  
P.-F. Hsu
Keyword(s):  
Radiative Transfer ◽  
Research Work ◽  
Discrete Ordinates ◽  
Scattering Media ◽  
Discrete Ordinates Method ◽  
Piecewise Parabolic ◽  
Phase Functions ◽  
Monotonicity Preserving ◽  
Made In ◽  
Thick Medium

Abstract This research work deals with the analysis of transient radiative transfer in one-dimensional scattering medium. The time-dependant discrete ordinates method was used with an upwind monotonic scheme: the piecewise parabolic scheme. This scheme was chosen over a total variation diminishing version of the Lax-Wendroff scheme. These schemes were originally developed to solve Eulerian advection problem in hydrodynamics. The capability of these schemes to handle sharp discontinuity in a propagating electromagnetic wave front was compared. The accuracy and the efficiency of the discrete ordinates method associated with the piecewise parabolic advection scheme were studied. Comparisons with Monte Carlo and integral formulation methods show the accuracy and the efficiency of this proposed method. Parametric study for optically thin and thick medium, different albedos and phase functions is then made in the unsteady state zone.

scholarly journals Influence of Leaf Specular Reflection on Canopy Radiative Regime Using an Improved Version of the Stochastic Radiative Transfer Model

2018 ◽  
Vol 10 (10) ◽  
pp. 1632 ◽  
Author(s):  
Bin Yang ◽  
Yuri Knyazikhin ◽  
Donghui Xie ◽  
Haimeng Zhao ◽  
Junqiang Zhang ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Flux Density ◽  
Vegetation Index ◽  
Radiation Flux ◽  
Specular Reflection ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Remotely Sensed Data ◽  
Wide Range ◽  
Radiative Regime

Interpreting remotely-sensed data requires realistic, but simple, models of radiative transfer that occurs within a vegetation canopy. In this paper, an improved version of the stochastic radiative transfer model (SRTM) is proposed by assuming that all photons that have not been specularly reflected enter the leaf interior. The contribution of leaf specular reflection is considered by modifying leaf scattering phase function using Fresnel reflectance. The canopy bidirectional reflectance factor (BRF) estimated from this model is evaluated through comparisons with field-measured maize BRF. The result shows that accounting for leaf specular reflection can provide better performance than that when leaf specular reflection is neglected over a wide range of view zenith angles. The improved version of the SRTM is further adopted to investigate the influence of leaf specular reflection on the canopy radiative regime, with emphases on vertical profiles of mean radiation flux density, canopy absorptance, BRF, and normalized difference vegetation index (NDVI). It is demonstrated that accounting for leaf specular reflection can increase leaf albedo, which consequently increases canopy mean upward/downward mean radiation flux density and canopy nadir BRF and decreases canopy absorptance and canopy nadir NDVI when leaf angles are spherically distributed. The influence is greater for downward/upward radiation flux densities and canopy nadir BRF than that for canopy absorptance and NDVI. The results provide knowledge of leaf specular reflection and canopy radiative regime, and are helpful for forward reflectance simulations and backward inversions. Moreover, polarization measurements are suggested for studies of leaf specular reflection, as leaf specular reflection is closely related to the canopy polarization.

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