The iterative method is equivalent to a successive order approach. For each iteration 1) the source function is transformed to discrete ordinates at every grid point, 2) the integral form of the radiative transfer equation is used to compute the discrete ordinate radiance at every grid point, 3) the radiance is transformed back to spherical harmonics, and 4) the new source function is computed from the radiance in spherical harmonics. As with all order of scattering methods the number of iterations increases with the single scattering albedo and optical depth. A sequence acceleration method is used to speed up convergence, which is typically achieved in under 50 iterations. During the solution process, the grid cells with the integral of the source function difference above a certain limit are split in half, generating new grid points. The number of spherical harmonic terms kept at each grid point also changes as the iterations proceed (i.e. adaptive spherical harmonic truncation).

- SHDOM now can perform polarized radiative transfer for randomly oriented particles and includes particle scattering codes that output polarized optical property input files for SHDOM.
- SHDOM can make visualization output images using multiple processors with MPI.

A brief description of the polarization implementation in SHDOM and
1D comparisons validating SHDOM polarization output are described in
Emde, C., V. Barlakas, C. Cornet, F. Evans, S. Korkin, Y. Ota,
L.C.-Labonnote, A. Lyapustin, A. Macke, B. Mayer, M. Wendisch,
2015: IPRT polarized radiative transfer model intercomparison
project -- Phase A. * J. Quant. Spectros. Radiat. Trans.,*
** 164,** 8-36. doi: 10.1016/j.jqsrt.2015.05.007 .
The SHDOM text discusses artifacts around viewing zenith angles of
0° and 180° for highly peaked phase functions (e.g. clouds),
which are seen in the comparisons.

The mathematics of including polarization in SHDOM is described in
Doicu, A., D. Efremenko, T. Trautmann, 2013: A multi-dimensional
vector spherical harmonics discrete ordinate method for atmospheric
radiative transfer. *J. Quant. Spectrosc. Radiat. Transfer,*
** 118,** 121-131.

The Pincus and Evans 2009
article describes the parallelization of SHDOM and performance
comparisons with the I3RC Community Monte Carlo model. The reference is

Pincus, R., and K. F. Evans, 2009: Computational cost and accuracy in
calculating three-dimensional radiative transfer: Results for new
implementations of Monte Carlo and SHDOM. *J. Atmos. Sci.,*
**66,** 3131-3146.

A conference paper (PDF) from the ARM science team meeting (2003) describes and gives examples for the new optical property generation system and the SHDOM visualization output.

A journal article on the SHDOM algorithm is available as a
PDF file (though the figures are poor).
The reference is

Evans, K. F., 1998: The spherical harmonic discrete ordinate method
for three-dimensional atmospheric radiative transfer.
* J. Atmos. Sci.,* ** 55,** 429-446.

SHDOM is distributed as a gzipped Unix tar file (675K). If you have trouble downloading the distribution from the Web, you can try the anonymous ftp site (ftp://nit.colorado.edu/pub/shdom/). SHDOM output from three of the example scripts (run_polarized, run_mono_les, run_brdf) is also available. The old unpolarized SHDOM distribution is available here (2.2M).

Several scientists have used SHDOM for 1D modeling, so a plane-parallel version, called SHDOMPP, has been developed. SHDOMPP is optimized for plane-parallel radiative transfer, making it faster and more accurate. More information and a distribution file is available .

This material is based upon work supported by the National Science Foundation under Grant ATM-9421733. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author) and do not necessarily reflect the views of the National Science Foundation. Updates to SHDOM from 1997 to 2004 were funded by the Atmospheric Radiation Measurement program of the Department of Energy under grant DE-A1005-90ER61069. The update to SHDOM adding multiple processor capability was funded by NASA Radiation Sciences Program under award NNX07AQ84G. The polarization upgrade to SHDOM was funded by NASA Remote Sensing Theory program under award NNX11AJ94G.

Last modified: September 7, 2015