The grid spacing needed is determined by some assumptions of SHDOM: 1) the variation in the extinction and the product of the source function and extinction across a grid cell is linear, 2) the source function across a grid face is accurately interpolated with the bilinear method, and 3) the radiance across a grid face is accurately interpolated with the bilinear method. The first and second assumptions should be satisfied by the source function based adaptive cell splitting algorithm, and also would be by having the optical depth across the grid cells small compared to one. The third assumption is satisfied by not using too coarse a base grid, and probably only matters as it affects the computation of the source function. It can make sense to have a coarse base grid where there is little scattering (clear sky), but then the output fluxes in those regions will be of low accuracy, though the output radiances (computed by tracing back) will be good. Because the accuracy can be compromised if the optical depth across a grid cell is too large, a warning is given if the property grid has cells with optical depth larger than 2. It is the internal grid that matters, but most people have the same grid so the check is done there. There are pathological cases in which a completely erroneous solar radiative transfer solution can occur if the optical depth across the cloud top grid cell is very large.
The accuracy is also determined by the angular resolution, specified by the number of discrete ordinates (NMU and NPHI). To a lesser degree the adaptive spherical harmonic truncation parameter SHACC also determines the angular resolution. Most of the benefit from the adaptive truncation occurs for low values of SHACC, so it is recommended to keep this parameter small. A value of SHACC=0 still gives the benefit of not allocating source function spherical harmonic terms where there is no scattering. Then NMU and NPHI will determine the angular resolution. The angular resolution needed depends on the desired output: for solar beam problems, net flux convergence (heating rates) requires the least, followed by hemispheric fluxes, and then radiances. For heating rates Nmu=8, Nphi=16 is enough, for hemispheric fluxes Nmu=8, Nphi=16 is often adequate, and radiances may need Nmu=16, Nphi=32 or more depending on the phase function.
Choosing the cell splitting accuracy: Remember that the adaptive parameters are in absolute units, not relative! The actual accuracy is not linearly related to the cell splitting accuracy. The cell splitting accuracy usually should be set substantially higher than the desired absolute flux accuracy. Look at the examples in the journal paper for guidance.
The only sure way to know how to set the spatial and angular resolution is to test how the desired solution behaves with increasing resolution, or make selected comparisons with an independent radiative transfer method. It is not useful to increase the angular and spatial accuracy much beyond one another. Tests have shown that the accuracy is not controlled by the cell splitting accuracy alone; both the base grid (NX,NY,NZ) and the splitting accuracy (SPLITACC) have to be considered. Thus, setting the splitting accuracy so small that there are many more adaptive grid points than base grid points, will probably not achieve any higher accuracy. See the convergence examples on the SHDOM Web site and refer to the journal article.
Unlike for plane-parallel situations, the delta-M method does not assure high accuracy for downwelling solar flux in 2D and 3D as it does for 1D, thus the distribution of downwelling solar flux may not be accurate for highly peaked phase functions unless high angular resolution is used. This is because in 3D, sharp variations in the extinction field mean that the downwelling solar flux is not averaged over all angles in the same way as for a uniform medium. This limitation appears to not affect upwelling flux, upwelling radiance, or heating rates.
Because of the thresholding nature of the cell splitting and the spherical harmonic truncation, very small changes in the inputs can amplify into larger changes in the output results. For example, running the same case on different machines can lead to noticeably different results. These variations, however, should be within the overall accuracy of the results governed by the angular and spatial resolution.
Upwelling hemispheric fluxes are slightly more accurately computed by using the double Gaussian quadrature discrete ordinate set. This is choosen by setting ORDINATESET=3 in SOLVE_RTE. With this option, radiances, heating rates, and net fluxes may be slightly less accurate.