scholarly journals Linearizations of the Spherical Harmonic Discrete Ordinate Method (SHDOM)

Atmosphere ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 292 ◽  
Author(s):  
Adrian Doicu ◽  
Dmitry S. Efremenko
Keyword(s):  
Radiative Transfer ◽  
Spherical Harmonics ◽  
Spherical Harmonic ◽  
Adaptive Grid ◽  
Test Problems ◽  
Discrete Ordinate Method ◽  
Discrete Ordinate ◽  
Adjoint Approach ◽  
Transfer Problems

Linearizations of the spherical harmonic discrete ordinate method (SHDOM) by means of a forward and a forward-adjoint approach are presented. Essentially, SHDOM is specialized for derivative calculations and radiative transfer problems involving the delta-M approximation, the TMS correction, and the adaptive grid splitting, while practical formulas for computing the derivatives in the spherical harmonics space are derived. The accuracies and efficiencies of the proposed methods are analyzed for several test problems.

SHDOMPPDA: A Radiative Transfer Model for Cloudy Sky Data Assimilation

2007 ◽  
Vol 64 (11) ◽  
pp. 3854-3864 ◽  
Author(s):  
K. Franklin Evans
Keyword(s):  
Radiative Transfer ◽  
Data Assimilation ◽  
Spherical Harmonics ◽  
Forward Model ◽  
Radiative Transfer Model ◽  
Computational Time ◽  
Transfer Model ◽  
Discrete Ordinate Method ◽  
Discrete Ordinate ◽  
Plane Parallel

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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