Spherical Harmonic Discrete Ordinate Method (SHDOM) for Atmospheric Radiative Transfer

Model Capabilities

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.

What's New

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.


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, 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.


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 .

More Stuff

Results of old tests and examples illustrating how to best use SHDOM are below.

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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