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

Back to SHDOM