VLIDORT User's Guide

for a 2-parameter Gamma-function size distribution with an effective radius of 1.05 µm, aneffective variance of 0.07 µm, and a refractive index of 1.43+ ???An additional test is performed to compare the results of VLIDORT with those found in Siewert(2000c). In this test and in that work, the optical property data set "Problem IIA" of Wauben andHovenier (1992) is used. This benchmark test considers a 1-layer "slab" problem with scatteringby randomly-oriented oblate spheroids with an aspect ratio of 1.999987, a size parameter of 3,and refractive index of 1.53-0.006i. The tables of results generated by VLIDORT for this casemay then be compared with Tables 2-9 of Siewert (2000c).6.3. BRDF SupplementHere, the bidirectional reflectance distribution function (BRDF) supplement is described. TheBRDF supplement is a separate system of VLIDORT-based software that has the purpose ofproviding total BRDF inputs for the main VLIDORT programs. In other words, we wish to fill upthe BRDF inputs in Tables C2 and G2 in sections 6.1.1.3 and 6.1.1.7, respectively. We note thatthe supplement also has the observational geometry facility like VLIDORT itself.In section 6.3.1, we give an overview of BRDF construction and discuss the available options.Next, a sample calling sequence for the supplement is given in section 6.3.2. The supplementinputs and outputs are given in tables in section 6.3.3. Following this, descriptions of the oceanand land kernels (both scalar and polarized) are given in sections 6.3.4-6.3.6. Lastly, the sectionis closed with some comments on surface emission in section 6.3.7.6.3.1. BRDFs as a sum of kernel functionsA scalar 3-kernel bidirectional reflectance distribution function (BRDF) scheme wasimplemented in LIDORT [Spurr, 2004]; a similar scheme is implemented in VLIDORT. Herewe confine ourselves to a scalar description. The BRDF ρ ( μ,μ′, φ − φ′total) is specified as alinear combination of (up to) three semi-empirical kernel functions:3∑ρ ′ − ′ =′ − ′total( μ,μ , φ φ ) Rkρk( μ,μ , φ φ ; bk) . (6.3.1)k = 1Here, ( θ , φ)indicates the pair of incident polar and azimuth angles, with the prime indicating thereflected angles. The R k are linear combination coefficients or “kernel amplitudes”, while thekernels ρk( θ,θ ′,φ − φ′; bk) are derived from semi-empirical models of surface reflection for avariety of surfaces. For each kernel, the geometrical dependence is known, but the kernelfunction depends on the values taken by a vector b k of pre-specified parameters.A well-known example is the single-kernel Cox-Munk BRDF for glitter reflectance from theocean [Cox and Munk, 1954a, 1954b]; the kernel is a combination of a Gaussian probabilitydistribution function for the square of the wave facet slope (a quantity depending on wind-speedW), and a Fresnel reflection function (depending on the air-water relative refractive index m rel ). Inthis case, vector b k has two elements: b k = {W, m rel }. For a Lambertian surface, there is onekernel: ρ 1 ≡ 1 for all angles, and coefficient R 1 is just the Lambertian albedo.104