VLIDORT User's Guide

Special note regarding Cox-Munk type ocean BRDF kernels:The Cox-Munk kernel uses σ 2 = 0.003 + 0.00512*W where W is the wind speed in meters/secondfor the first parameter. For example, if W = 10, then σ 2 = 0.054200. In contrast, the Giss-Cox-Munk kernel uses 0.5*σ 2 for the first parameter (half the value!). Thus, for this value of W, theGiss-Cox-Munk kernel would a value of 0.5*σ 2 = 0.027100 for its first parameter.Also, the Cox-Munk kernel uses the square of the refractive index for the second parameter. Forexample, if the refractive index is 1.334, then the second parameter would be 1.334*1.334 =1.779556. In contrast, the Giss-Cox-Munk kernel uses just the refractive index itself for thesecond parameter. Thus, the Giss-Cox-Munk kernel would a value of 1.334 for its secondparameter.Table F: File-read Character strings for linearized kernel variables in BRDF Supplement Table CName Kind Character string in Configuration fileDO_KERNEL_FACTOR_WFS LogicalDO_KERNEL_PARAMS_WFS LogicalKernels, indices, # pars, Factor Jacobian flag, Par Jacobian flagsThese quantities are formatted together for each kernel usingFormat (A10,I3,I2,4L). See example below.Example of linearized BRDF inputs: configuration file settings for 3 BRDFkernels as indicated:BRDFSUP - Kernels, indices, # pars, Factor Jacobian flag, Par Jacobian flagsCox-Munk 9 2 T T T FRoss-thin 2 0 T F F FLi-dense 5 2 T T T F6.3.4. Ocean glitter kernel functionWe now turn to descriptions of the individual BRDF kernels. The ocean glitter kernel isdescribed here and the land kernels in the following section. For glitter, we use the well-knowngeometric-optics regime for a single rough-surface redistribution of incident light, in which thereflection function is governed by Fresnel reflectance and takes the form [Jin et al., 2006]:2122ρ ( μ,μ′ , φ φ′, , σ ) ( θ , ). . ( γ , σ ). ( μ,μ′CM− m = rrm P D , σ )4 rμμ′γ. (6.3.5)r2Here, σ is the slope-squared variance (also known as the MSS or mean slope square) of the2Gaussian probability distribution function P ( γ , σ ) which has argument γ (the polar direction ofthe reflected beam); r( θ , m)is the Fresnel reflection for incident angle θ and relative refractive2index m, and ( μ , μ′2D , σ ) is a correction for shadowing. The two non-linear parameters are σand m. We have the usual Cox-Munk empirical relation [Cox and Munk, 1954a]:2σ = 0.003+0.00512W(6.3.6)in terms of the wind speed W in m/s. A typical value for m is 1.33. The MSS Gaussian is:112