Editorial Type:
Article
Article Type:
Research Article

Spectrally Invariant Approximation within Atmospheric Radiative Transfer

A. Marshak Climate and Radiation Branch, NASA Goddard Space Flight Center, Greenbelt, Maryland

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Y. Knyazikhin Department of Geography and Environment, Boston University, Boston, Massachusetts

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J. C. Chiu Department of Meteorology, University of Reading, Reading, United Kingdom

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W. J. Wiscombe Climate and Radiation Branch, NASA Goddard Space Flight Center, Greenbelt, Maryland

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Print Publication:
01 Dec 2011
DOI:
https://doi.org/10.1175/JAS-D-11-060.1
Page(s):
3094–3111
Restricted access

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.

Corresponding author address: Alexander Marshak, Climate and Radiation Branch, NASA Goddard Space Flight Center, Greenbelt, MD 20771. E-mail: alexander.marshak@nasa.gov

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.

Corresponding author address: Alexander Marshak, Climate and Radiation Branch, NASA Goddard Space Flight Center, Greenbelt, MD 20771. E-mail: alexander.marshak@nasa.gov
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