Doubling-Adding Method for Delta-Four-Stream Spherical Harmonic Expansion Approximation in Radiative Transfer Parameterization

AbstractThough the single-layer solutions have been found for the δ-four-stream spherical harmonic expansion method (SHM) in radiative transfer, there is lack of a corresponding doubling–adding method (4SDA), which enables the calculation of radiative transfer through a vertically inhomogeneous atmosphere with multilayers. The doubling–adding method is based on Chandrasekhar's invariance principle, which was originally developed for discrete ordinates approximation. It is shown that the invariance principle can also be applied to SHM and δ-four-stream spherical harmonic expansion doubling–adding method (δ-4SDA) is proposed in this paper. The δ-4SDA method has been systematically compared to the δ-Eddington doubling–adding method (δ-2SDA), the δ-two-stream discrete ordinates doubling–adding method (δ-2DDA), and δ-four-stream discrete ordinates doubling–adding method (δ-4DDA). By applying δ-4SDA to a realistic atmospheric profile with gaseous transmission considered, it is found that the accuracy of δ-4SDA ...

[1]  J. Landgraf,et al.  Actinic Flux and Net Flux Calculations in Radiative Transfer—A Comparative Study of Computational Efficiency , 2001 .

[2]  Robert D. Cess,et al.  The Effect of Tropospheric Aerosols on the Earth's Radiation Budget: A Parameterization for Climate Models , 1983 .

[3]  K. Stamnes,et al.  Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. , 1988, Applied optics.

[4]  T. Ackerman,et al.  A simple formulation of the delta-four-stream approximation for radiative transfer parameterizations , 1988 .

[5]  K. Liou.  Analytic Two-Stream and Four-Stream Solutions for Radiative Transfer , 1974 .

[6]  T. Vesala.  Radiative Transfer in the Atmosphere and Ocean , 2003 .

[7]  Max J. Suarez,et al.  A Solar Radiation Parameterization for Atmospheric Studies , 2013 .

[8]  Q. Fu,et al.  Multiple Scattering Parameterization in Thermal Infrared Radiative Transfer , 1997 .

[9]  M. Chou,et al.  A Solar Radiation Model for Use in Climate Studies , 1992 .

[10]  Q. Fu.  Parameterization of radiative processes in vertically nonhomogeneous multiple scattering atmospheres , 1991 .

[11]  Michael D. King,et al.  Comparative accuracy of selected multiple scattering approximations , 1986 .

[12]  Qiang Fu,et al.  Test of Mie-based single-scattering properties of non-spherical dust aerosols in radiative flux calculations , 2009 .

[13]  Jiangnan Li,et al.  A comparison of two-stream DISORT and Eddington radiative transfer schemes in a real atmospheric profile , 2009 .

[14]  Jiangnan Li,et al.  Accounting for unresolved clouds in a 1‐D solar radiative‐transfer model , 2005 .

[15]  A. Uchiyama,et al.  Accuracy of the delta-four-stream approximation in inhomogeneous scattering atmospheres , 1992 .

[16]  Xiuji Zhou,et al.  On the relationship between direct and diffuse radiation , 2013 .

[17]  K. Salzen,et al.  Simulation of mineral dust aerosol with Piecewise Log-normal Approximation (PLA) in CanAM4-PAM , 2011 .

[18]  S. Gong,et al.  Implementing the Delta-Four-Stream Approximation for Solar Radiation Computations in an Atmosphere General Circulation Model , 2008 .

[19]  R. Dickinson,et al.  Four-stream isosector approximation for canopy radiative transfer , 2007 .

[20]  G. Rybicki.  Radiative transfer , 2019, Climate Change and Terrestrial Ecosystem Modeling.

[21]  Q. Fu,et al.  On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres , 1992 .

[22]  L. J. Cox.  Optical Properties of the Atmosphere , 1979 .

[23]  Q. Fu,et al.  Parameterization of the Radiative Properties of Cirrus Clouds , 1993 .

[24]  Xiuji Zhou,et al.  Analytical Delta-Four-Stream Doubling-Adding Method for Radiative Transfer Parameterizations , 2013 .

[25]  Four-Stream Spherical Harmonic Expansion Approximation for Solar Radiative Transfer , 1996 .

[26]  K. Stamnes,et al.  A reliable and efficient two-stream algorithm for spherical radiative transfer: Documentation of accuracy in realistic layered media , 1995 .

[27]  Jiangnan Li,et al.  Four-stream isosector approximation for solar radiative transfer , 1998 .

[28]  C. Knight,et al.  Drop Freezing in Clouds , 1974 .

[29]  Kuo-Nan Liou,et al.  Radiation and Cloud Processes in the Atmosphere: Theory, Observation and Modeling , 1992 .