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A New k-Distribution Scheme for Clear-Sky Radiative Transfer Calculations in Earth’s Atmosphere. Part I: Thermal Infrared (Longwave) Radiation

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  • 1 Department of Atmospheric Sciences, National Central University, Taoyuan, Taiwan
  • 2 Research Center for Environmental Changes, Academia Sinica, Taipei, Taiwan
  • 3 Department of Atmospheric and Environmental Sciences, Gangneung-Wonju National University, Gangneung, South Korea
  • 4 Research Center for Atmospheric Environment, Hankuk University of Foreign Studies, Yongin, South Korea
  • 5 Department of Atmospheric and Environmental Sciences, Gangneung-Wonju National University, Gangneung, South Korea
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Abstract

A new k-distribution scheme of longwave radiation without the correlated-k-distribution assumption is developed. Grouping of spectral points is based on the line-by-line (LBL)-calculated absorption coefficient k at a few sets of reference pressure pr and temperature θr, where the cooling rate is substantial in a spectral band. In this new scheme, the range of k(pr, θr) of a band is divided into a number of equal intervals, or g groups, in log10(kr). A spectral point at the wavenumber ν is identified with one of the g groups according to its kν(pr, θr). For each g group, a Planck-weighted k-distribution function Hg and a nonlinearly averaged absorption coefficient k¯g(p,θ) are derived. The function Hg and the absorption coefficient k¯g(p,θ) constitute the new k-distribution scheme. In this k-distribution scheme, a spectral point can only be identified with a g group regardless of pressure and temperature, which is different from the correlated-k distribution scheme. The k-distribution scheme is applied to the H2O, CO2, O3, N2O, and CH4 absorption bands, and results are compared with LBL calculations. To balance between the accuracy and the computational economy, the number of g groups in a band of a given gas is chosen such that 1) the difference in cooling rate is <0.1 K day−1 in the troposphere and <1.0 K day−1 in the stratosphere and 2) the difference in fluxes is <0.5 W m−2 at both the top of the atmosphere and the surface. These differences are attained with 130 g groups, which is the sum of the g groups of all five gases.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Wei-Liang Lee, leelupin@gate.sinica.edu.tw

Abstract

A new k-distribution scheme of longwave radiation without the correlated-k-distribution assumption is developed. Grouping of spectral points is based on the line-by-line (LBL)-calculated absorption coefficient k at a few sets of reference pressure pr and temperature θr, where the cooling rate is substantial in a spectral band. In this new scheme, the range of k(pr, θr) of a band is divided into a number of equal intervals, or g groups, in log10(kr). A spectral point at the wavenumber ν is identified with one of the g groups according to its kν(pr, θr). For each g group, a Planck-weighted k-distribution function Hg and a nonlinearly averaged absorption coefficient k¯g(p,θ) are derived. The function Hg and the absorption coefficient k¯g(p,θ) constitute the new k-distribution scheme. In this k-distribution scheme, a spectral point can only be identified with a g group regardless of pressure and temperature, which is different from the correlated-k distribution scheme. The k-distribution scheme is applied to the H2O, CO2, O3, N2O, and CH4 absorption bands, and results are compared with LBL calculations. To balance between the accuracy and the computational economy, the number of g groups in a band of a given gas is chosen such that 1) the difference in cooling rate is <0.1 K day−1 in the troposphere and <1.0 K day−1 in the stratosphere and 2) the difference in fluxes is <0.5 W m−2 at both the top of the atmosphere and the surface. These differences are attained with 130 g groups, which is the sum of the g groups of all five gases.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Wei-Liang Lee, leelupin@gate.sinica.edu.tw
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