TY - JOUR
T1 - Improved δ-Eddington approximation for optically thin clouds
AU - Ren, Tong
AU - Yang, Ping
AU - Tang, Guanglin
AU - Huang, Xianglei
AU - Mlawer, Eli
N1 - Funding Information:
This study was supported by the National Science Foundation ( AGS-1632209 ). T. Ren appreciates his discussions of the results in this work with Dr. Jiachen Ding, Dr. Masanori Saito, and Dr. Steve Schroeder. We also thank the Texas A&M High Performance Research Computing for providing the disk quota and software for the simulations in this study.
Publisher Copyright:
© 2019
PY - 2020/1
Y1 - 2020/1
N2 - The δ-Eddington simulations of broadband shortwave net radiation fluxes at the top of the atmosphere (FTOA) and the surface (FSURF) are evaluated with different parameterizations of the forward fraction of scattering (f), including the square of the asymmetry factor (f = g2), the fraction of the forward single-scattered intensity over the total single-scattered intensity (f = fp), and the cube of the asymmetry factor (f = g3). g2 and g3 are respectively the 2nd and 3rd moments of the Henyey–Greenstein (HG) phase function and hence approximate measures of the variance and skewness of the phase function. The factor fp for spherical droplets is estimated using a truncation angle, which separates the forward peak and diffusive portions of a highly anisotropic phase function. The results show that the simulations of FTOA and FSURF are not improved, if the conventional approach f = g2 is replaced by f = fp in the δ-Eddington approximation for an atmosphere in the presence of liquid clouds. For the optically thick conditions, multiple scattering plays a dominant role in determining the reflectance (R) and transmittance (T) of the cloudy layer; the conventional parameterization f = g2 is most accurate among the three parameterizations. For the optically thin conditions, single scattering dominates over multiple scattering and thus f = g2 results in biased FTOA and FSURF calculations, particularly with low solar elevations. For such cases, f = g3 shows most accurate FTOA and FSURF results for both liquid and ice clouds, though f = g3 also results in smaller cloud layer heating rates in general.
AB - The δ-Eddington simulations of broadband shortwave net radiation fluxes at the top of the atmosphere (FTOA) and the surface (FSURF) are evaluated with different parameterizations of the forward fraction of scattering (f), including the square of the asymmetry factor (f = g2), the fraction of the forward single-scattered intensity over the total single-scattered intensity (f = fp), and the cube of the asymmetry factor (f = g3). g2 and g3 are respectively the 2nd and 3rd moments of the Henyey–Greenstein (HG) phase function and hence approximate measures of the variance and skewness of the phase function. The factor fp for spherical droplets is estimated using a truncation angle, which separates the forward peak and diffusive portions of a highly anisotropic phase function. The results show that the simulations of FTOA and FSURF are not improved, if the conventional approach f = g2 is replaced by f = fp in the δ-Eddington approximation for an atmosphere in the presence of liquid clouds. For the optically thick conditions, multiple scattering plays a dominant role in determining the reflectance (R) and transmittance (T) of the cloudy layer; the conventional parameterization f = g2 is most accurate among the three parameterizations. For the optically thin conditions, single scattering dominates over multiple scattering and thus f = g2 results in biased FTOA and FSURF calculations, particularly with low solar elevations. For such cases, f = g3 shows most accurate FTOA and FSURF results for both liquid and ice clouds, though f = g3 also results in smaller cloud layer heating rates in general.
KW - Forward fraction of scattering
KW - The asymmetry factor
KW - δ-Eddington approximation
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U2 - 10.1016/j.jqsrt.2019.106694
DO - 10.1016/j.jqsrt.2019.106694
M3 - Article
AN - SCOPUS:85073427135
SN - 0022-4073
VL - 240
JO - Journal of Quantitative Spectroscopy and Radiative Transfer
JF - Journal of Quantitative Spectroscopy and Radiative Transfer
M1 - 106694
ER -