Normalization method of highly forward-peaked scattering phase function using the double exponential formula for radiative transfer

Radiative transfer is the process of energy transfer during the propagation of electromagnetic radiation through a medium. The processes of extinction, due to absorption and scattering, and thermal emission are described. It is shown how they can be represented by wavelength-dependent optical thickness, due to absorption or emission cross sections and the number of absorbers, emitters, or scatterers. Cloud optical thickness and conservative scattering are described. The scattering phase function is introduced. Next, the general form of radiative transfer is given, and its applicability to the details of planetary atmospheric radiation shown.

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Spectrally Invariant Approximation within Atmospheric Radiative Transfer

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-11-060.1 ◽

2011 ◽

Vol 68 (12) ◽

pp. 3094-3111 ◽

Cited By ~ 9

Author(s):

A. Marshak ◽

Y. Knyazikhin ◽

J. C. Chiu ◽

W. J. Wiscombe

Keyword(s):

Radiative Transfer ◽

Phase Function ◽

Single Scattering ◽

Atmospheric Conditions ◽

Water Vapor Absorption ◽

Mathematical Basis ◽

Invariant Approximation ◽

Scattering Phase ◽

Atmospheric Radiative Transfer ◽

Scattering Phase Function

Abstract Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These “spectrally invariant relationships” are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accurately describe the extinction and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

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Semi-Analytic Monte Carlo Model for Oceanographic Lidar Systems: Lookup Table Method Used for Randomly Choosing Scattering Angles

Applied Sciences ◽

10.3390/app9010048 ◽

2018 ◽

Vol 9 (1) ◽

pp. 48 ◽

Cited By ~ 3

Author(s):

Peng Chen ◽

Delu Pan ◽

Zhihua Mao ◽

Hang Liu

Keyword(s):

Monte Carlo ◽

Radiative Transfer ◽

Phase Function ◽

Geometric Model ◽

Airborne Lidar ◽

Cumulative Distribution ◽

Lookup Table ◽

Transfer Model ◽

Scattering Phase ◽

Scattering Phase Function

Monte Carlo (MC) is a significant technique for finding the radiative transfer equation (RTE) solution. Nowadays, the Henyey-Greenstein (HG) scattering phase function (spf) has been widely used in most studies during the core procedure of randomly choosing scattering angles in oceanographic lidar MC simulations. However, the HG phase function does not work well at small or large scattering angles. Other spfs work well, e.g., Fournier-Forand phase function (FF); however, solving the cumulative distribution function (cdf) of the scattering phase function (even if possible) would result in a complicated formula. To avoid the above-mentioned problems, we present a semi-analytic MC radiative transfer model in this paper, which uses the cdf equation to build up a lookup table (LUT) of ψ vs. P Ψ ( ψ ) to determine scattering angles for various spfs (e.g., FF, Petzold measured particle phase function, and so on). Moreover, a lidar geometric model for analytically estimating the probability of photon scatter back to a remote receiver was developed; in particular, inhomogeneous layers are divided into voxels with different optical properties; therefore, it is useful for inhomogeneous water. First, the simulations between the inverse function method for HG cdf and the LUT method for FF cdf were compared. Then, multiple scattering and wind-driven sea surface condition effects were studied. Finally, we compared our simulation results with measurements of airborne lidar. The mean relative errors between simulation and measurements in inhomogeneous water are within 14% for the LUT method and within 22% for the inverse cdf (ICDF) method. The results suggest feasibility and effectiveness of our simulation model.

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