## SHDOM Validation Testing

### Independent pixel - linear optical depth

The first series presented here is a test of the independent pixel mode
of operation and a demonstration of the adaptive grid approach. The
input file of optical properties specifies a 2D medium that is
vertically uniform but has optical depth increasing from 0 on the left
to 20 on the right. The independent pixel mode treats the input columns
separately, so each has the plane-parallel solution. Monochromatic
solar transfer for two sun angles and thermal radiative transfer are
shown. The single scattering albedo and Henyey-Greenstein (g=0.85) phase
function are fixed. The upwelling flux from the top of the medium is
compared with results from a
doubling-adding
model . The initial "base grid" used by SHDOM has only one grid
cell vertically, and so the adaptive grid algorithm is used to achieve
reasonable accuracy. A depiction of the final adaptive grid cells is
shown in the figures below.
These figures give some idea of the accuracy achieved with various cell
splitting criterion. The actual accuracy depends on the type of transfer
(solar or thermal), the sun angle, and the medium as well as the splitting
accuracy. In 1D the adaptive grid cell generation can be relied upon to
provide the necessary spatial resolution, but this is not the case for 2D
or 3D (see the accuracy example).
#### 3D Gaussian

The second series are tests of 3D radiative transfer with a gaussian
extinction field. The extinction field for these tests is a 3D gaussian
with a peak optical depth of 2 in a Nx=20,Ny=20,Nz=11 domain. A color
plot of the extinction field shows the
X-Y map view of the optical depth and the X-Z cross section through the
center. Results are shown for solar radiative transfer at 1.65 micron
wavelength with a sun angle of 45 degrees and for thermal radiative
transfer at 10.7 micron wavelength. The optical properties are computed
with Mie scattering theory for liquid cloud droplets with an effective
radius of 10 micron and effective variance of 0.1 for each wavelength.
The upwelling flux and radiance from the top are shown here compared
with results from a 3D backward Monte Carlo radiative transfer code. The
optical depth in this example is relatively small in order to obtain
high accuracy from the Monte Carlo code. The results shown are for the
base grid with no adaptive cell generation, which is not needed for this
high resolution base grid.
The Gaussian comparison results are also shown in the form of a table listing the SHDOM accuracy for
cases with various angular and spatial resolutions. These results show
that relatively high angular resolution (Nmu > 8) is required to get
1% to 2% accuracy in this case.

Last modified: June 20, 1997
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