Editorial Type:
Article
Article Type:
Research Article

A Flexible Parameterization for Shortwave Optical Properties of Ice Crystals

Bastiaan van Diedenhoven Center for Climate System Research, Columbia University, and NASA Goddard Institute for Space Research, New York, New York

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Andrew S. Ackerman NASA Goddard Institute for Space Research, New York, New York

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Brian Cairns NASA Goddard Institute for Space Research, New York, New York

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Ann M. Fridlind NASA Goddard Institute for Space Research, New York, New York

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Print Publication:
01 May 2014
DOI:
https://doi.org/10.1175/JAS-D-13-0205.1
Page(s):
1763–1782
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Abstract

A parameterization is presented that provides extinction cross section σe, single-scattering albedo ω, and asymmetry parameter g of ice crystals for any combination of volume, projected area, aspect ratio, and crystal distortion at any wavelength in the shortwave. Similar to previous parameterizations, the scheme makes use of geometric optics approximations and the observation that optical properties of complex, aggregated ice crystals can be well approximated by those of single hexagonal crystals with varying size, aspect ratio, and distortion levels. In the standard geometric optics implementation used here, σe is always twice the particle projected area. It is shown that ω is largely determined by the newly defined absorption size parameter and the particle aspect ratio. These dependences are parameterized using a combination of exponential, lognormal, and polynomial functions. The variation of g with aspect ratio and crystal distortion is parameterized for one reference wavelength using a combination of several polynomials. The dependences of g on refractive index and ω are investigated and factors are determined to scale the parameterized g to provide values appropriate for other wavelengths. The parameterization scheme consists of only 88 coefficients. The scheme is tested for a large variety of hexagonal crystals in several wavelength bands from 0.2 to 4 μm, revealing absolute differences with reference calculations of ω and g that are both generally below 0.015. Over a large variety of cloud conditions, the resulting root-mean-squared differences with reference calculations of cloud reflectance, transmittance, and absorptance are 1.4%, 1.1%, and 3.4%, respectively. Some practical applications of the parameterization in atmospheric models are highlighted.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JAS-D-13-0205.s1.

Corresponding author address: Bastiaan van Diedenhoven, 2880 Broadway, New York, NY 10025. E-mail: bastiaan.vandiedenhoven@nasa.gov

Abstract

A parameterization is presented that provides extinction cross section σe, single-scattering albedo ω, and asymmetry parameter g of ice crystals for any combination of volume, projected area, aspect ratio, and crystal distortion at any wavelength in the shortwave. Similar to previous parameterizations, the scheme makes use of geometric optics approximations and the observation that optical properties of complex, aggregated ice crystals can be well approximated by those of single hexagonal crystals with varying size, aspect ratio, and distortion levels. In the standard geometric optics implementation used here, σe is always twice the particle projected area. It is shown that ω is largely determined by the newly defined absorption size parameter and the particle aspect ratio. These dependences are parameterized using a combination of exponential, lognormal, and polynomial functions. The variation of g with aspect ratio and crystal distortion is parameterized for one reference wavelength using a combination of several polynomials. The dependences of g on refractive index and ω are investigated and factors are determined to scale the parameterized g to provide values appropriate for other wavelengths. The parameterization scheme consists of only 88 coefficients. The scheme is tested for a large variety of hexagonal crystals in several wavelength bands from 0.2 to 4 μm, revealing absolute differences with reference calculations of ω and g that are both generally below 0.015. Over a large variety of cloud conditions, the resulting root-mean-squared differences with reference calculations of cloud reflectance, transmittance, and absorptance are 1.4%, 1.1%, and 3.4%, respectively. Some practical applications of the parameterization in atmospheric models are highlighted.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JAS-D-13-0205.s1.

Corresponding author address: Bastiaan van Diedenhoven, 2880 Broadway, New York, NY 10025. E-mail: bastiaan.vandiedenhoven@nasa.gov

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