SHDOM: Boundary Conditions

The upper boundary condition is open, i.e. there is no reflection from the top of the domain. Isotropic incident radiance at the top boundary may be specified.

There are currently four types of surface reflection: Lambertian, Fresnel, RPV (Rahman, Pinty, Verstraete, 1993: J. Geophys. Res., 98, 20791), and Ocean. It is simple to add other surface types (see Source Code Options ). A Lambertian surface reflects radiance isotropically, and is specified with the surface albedo. A Fresnel surface reflects specularly, and is specified with the index of refraction of the surface dielectric (e.g. water). The RPV parameterization is used to model the general bidirectional reflectance function (BRF) characteristics of land surfaces (soils and vegetation) with three parameters (rho0, k, Theta). The Ocean BRDF parameterization models the glint specular reflection averaged over wave facets and the internal reflection from sea water, and is specified by the wind speed and chlorophyl-alpha pigment concentration. The Ocean reflectance model is obtained from the 6S model and modified by Norman Loeb at NASA Langley. High SHDOM angular resolution (Nmu, Nphi) is needed at low wind speeds to resolve the broadened specular reflection peak, so it is a good idea to do a test with increasing angular resolution until the reflection is stable.

See the SURFACE FILE FORMAT section for how to specify the parameters. The temperature and reflection properties of these models may vary arbitrarily across the surface.

There are two options for the horizontal boundary conditions. The first is periodic and the second is open. These are specified for X and Y directions independently using the BCFLAG: bit 0 for X and bit 1 for Y. Thus BCFLAG=0 is periodic in X and Y, BCFLAG=1 is open in X and periodic in Y, and BCFLAG=3 is open in X and Y. The independent pixel flag (IPFLAG) overrides the boundary condition flag, since an independent pixel does not have a horizontal boundary condition.

Periodic boundaries mean that when rays exit one side they wrap around to enter the opposite side. The periodic domain size is NX*DELX by NY*DELY; for example if NX=64 and DELX=0.050 km, then X=3.2 km is equivalent to X=0 km (left hand side).

The open horizontal boundary condition means that radiation leaving the sides does not wrap around and is not reflected back in. However, there may be radiation entering the sides. For open BCs the property file grid points on the edges are used in independent pixel mode to compute the boundary radiation. For example, in 2D (X and Z) the first and last X property grid columns are computed with plane-parallel (IPA) radiative transfer. These grid columns then provide the boundary radiances for the interior of the domain. The interior domain is (NX-1)*DELX wide. In 3D the four corner columns are computed with 1D (plane-parallel) radiative transfer, while the four side slices are done with 2D radiative transfer. If you want the boundary columns to produce plane-parallel results, simply make sure the input optical properties for the columns on the boundaries are the same. The radiance output calculation can be done for locations beyond the horizontal domain; this is the purpose of the "X and Y offsets" in the radiance output specification. For the open boundary conditions the rays are traced back through the regions beyond the domain using plane-parallel radiative transfer, and then may enter the domain. This allows the lower part of the domain to be seen through the domain "sides" for slanted paths.