Spherical Harmonic Discrete Ordinate Method (SHDOM)
for Atmospheric Radiative Transfer
This implementation of SHDOM computes polarized monochromatic or
spectral band radiative transfer in a one, two, or three-dimensional
medium for either collimated solar and/or thermal emission sources of
radiation. The properties of the medium can be specified completely
generally, i.e. the extinction, single scattering albedo, coefficients
of the scattering phase matrix, and temperature for the particular
wavelength or spectral band may be specified at each input grid point.
SHDOM is superior to Monte Carlo radiative transfer methods when many
radiative quantities are desired, e.g. the radiance field across the
domain top. Radiances in any direction, hemispheric fluxes, net fluxes,
mean radiances, and net flux convergence (related to heating rates) may
be output anywhere in the domain. For highly peaked phase functions the
delta-M method may be chosen, in which case the radiance is computed
with an untruncated phase function single scattering correction. A
correlated k-distribution approach is used for the integration over a
spectral band. There may be uniform or spatially variable Lambertian
reflection and emission from the ground surface. Several types of
bidirectional reflection distribution functions (BRDF) for the surface
are implemented, and more may be added easily. SHDOM may be run on a
single processor or on multiple processors (e.g. an SMP machine or a
cluster) using the Message Passing Interface (MPI). SHDOM may be run
efficiently for unpolarized (scalar) radiative transfer by choosing
NSTOKES=1, or for polarized (vector) radiative transfer problems with
NSTOKES=3 or 4 Stokes parameters. SHDOM is implemented in Fortran, and
a Fortran 90 compiler is now required.
Method in Brief
The SHDOM uses an iterative process to compute the source function
(including the scattering integral) on a grid of points in space. The
angular part of the source function is represented with a spherical
harmonic expansion. Solving for the source function instead of the
radiance field saves memory, because there are often parts of a medium
where the source function is zero or angularly very smooth (hence few
spherical harmonic terms). The other reason for using spherical
harmonics is that the scattering integral is more efficiently computed
than in discrete ordinates. A discrete ordinate representation is used
in the solution process because the streaming of radiation is more
physically (and correctly) computed in this way. An adaptive grid that
chooses where to put grid points is useful in atmospheric radiative
transfer because the source function is usually rapidly varying in
some regions and slowly varying in others.
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).
When to Use SHDOM
SHDOM is the most capable explicit representation (or deterministic) 3D
atmospheric radiative transfer model developed so far. However, it
cannot handle all modeling situations, and Monte Carlo methods are often
superior. SHDOM is appropriate for atmospheric media in which the
radiative transfer can be resolved; i.e. the optical depth across the
adaptive grid cells is small compared to unity. If many of the input
grid cells in a 3D medium have optical depth greater than 1, then SHDOM
is likely to prove computationally infeasible. This typically implies
that the SHDOM grid spacing needs to be 100 meters or smaller for
simulations of 3D clouds. Monte Carlo methods are also faster and more
accurate than SHDOM for simulations in which there are relatively few
radiative quantities output. For example, SHDOM is a poor choice when
horizontal domain average quantities are desired. SHDOM is a good
choice when it resolves the radiative transfer and many radiative
quantities are desired, e.g. the radiance field across the domain top.
See the Pincus and Evans 2009
article in J. Atmos. Sci. for detailed performance comparisons
between SHDOM and the I3RC Community Monte Carlo model.
A major new release of the SHDOM distribution was made available on 7
March 2014. The new features are
The input parameter list has changed somewhat with the new release of
SHDOM. The latest bug fix release was 13 May 2015.
- 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.
See shdom.txt and propgen.txt in the distribution file for details
on how to run the code.
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,
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.,
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
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.
The model is being freely distributed via this Web page. The
distribution README lists the files in the
distribution. A list of the changes
in the update releases is also available.
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 .
Results of old tests and examples illustrating how to best use SHDOM are
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
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