scholarly journals Modified analytic expression for the single-scattering phase function

2017 ◽  
Vol 66 (18) ◽  
pp. 180201
Author(s):  
Shi Ze-Lin ◽  
Cui Sheng-Cheng ◽  
Xu Qing-Shan
Keyword(s):  
Phase Function ◽  
Single Scattering ◽  
Scattering Phase ◽  
Analytic Expression ◽  
Scattering Phase Function

scholarly journals Spectrally Invariant Approximation within Atmospheric Radiative Transfer

2011 ◽  
Vol 68 (12) ◽  
pp. 3094-3111 ◽  
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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