A New Look at the Discrete Ordinate Method for Radiative Transfer Calculations in Anisotropically Scattering Atmospheres. II: Intensity Computations

Abstract The spherical harmonics discrete ordinate method for plane-parallel data assimilation (SHDOMPPDA) model is an unpolarized plane-parallel radiative transfer forward model, with corresponding tangent linear and adjoint models, suitable for use in assimilating cloudy sky visible and infrared radiances. It is derived from the spherical harmonics discrete ordinate method plane-parallel (SHDOMPP, also described in this article) version of the spherical harmonics discrete ordinate method (SHDOM) model for three-dimensional atmospheric radiative transfer. The inputs to the SHDOMPPDA forward model are profiles of pressure, temperature, water vapor, and mass mixing ratio and number concentration for a number of hydrometeor species. Hydrometeor optical properties, including detailed phase functions, are determined from lookup tables as a function of mass mean radius. The SHDOMPP and SHDOMPPDA algorithms and construction of the tangent-linear and adjoint models are described. The SHDOMPPDA forward model is validated against the Discrete Ordinate Radiative Transfer Model (DISORT) by comparing upwelling radiances in multiple directions from 100 cloud model columns at visible and midinfrared wavelengths. For this test in optically thick clouds the computational time for SHDOMPPDA is comparable to DISORT for visible reflection, and roughly 5 times faster for thermal emission. The tangent linear and adjoint models are validated by comparison to finite differencing of the forward model.

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Analytic Green’s Function for Radiative Transfer in Plane-Parallel Atmospheres

Journal of the Atmospheric Sciences ◽

10.1175/jas3532.1 ◽

2005 ◽

Vol 62 (8) ◽

pp. 2910-2924 ◽

Cited By ~ 4

Author(s):

Yi Qin ◽

Michael A. Box

Keyword(s):

Radiative Transfer ◽

Green’S Function ◽

Green's Function ◽

Discrete Ordinate Method ◽

Bidirectional Reflectance Distribution Function ◽

Discrete Ordinate ◽

Bidirectional Reflectance ◽

Plane Parallel ◽

Computing Complexity ◽

Bidirectional Reflectance Distribution

Abstract Green’s function is a widely used approach for boundary value problems. In problems related to radiative transfer, Green’s function has been found to be useful in land, ocean, and atmosphere remote sensing. It is also a key element in higher order perturbation theory. This paper presents an explicit expression of the Green’s function, in terms of the source and radiation field variables, for a plane-parallel atmosphere with either vacuum boundaries or a reflecting [atmosphere–bidirectional reflectance distribution function (BRDF)] surface. A FORTRAN 95 code, Green’s function and discrete ordinate method (GDOM), has been developed to efficiently compute the Green’s function. This code also integrates with an implementation of the discrete ordinate method with several extensions and improvements. Computing complexity of the Green’s function algorithm is analyzed, and validation of the code is discussed.

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