(6.3.3) (6.3.4) The amplitude derivative is trivial. The parameter derivative (6.3.3) depends on the empirical formulation of the kernel in question, but all kernels in the LIDORT and VLIDORT BRDF schemes are analytically differentiable with respect to their parameter dependencies. The choice of a Lambertian surface is a special case, controlled by a single flag. If this flag is set it is only necessary to specify the Lambertian albedo (between or equal to one of the limit R values 0.0 and 1.0). If the surface weighting function option is also set, then VLIDORT will return the Lambertian weighting function. Table 6.3.1 The BRDF kernel functions for VLIDORT Index Name Size bk Reference Scalar/Vector 1 Lambertian 0 Scalar 2 Ross thin 0 1995 Scalar Wanner et al., 3 Ross thick 0 1995 Scalar Wanner et al., 4 Li sparse 2 1995 Scalar Wanner et al., 5 Li dense 2 1995 Scalar Wanner et al., 6 Hapke 3 1993 Scalar Hapke, 7 Roujean 0 1995 Scalar Wanner et al., 8 Rahman 3 1993 Scalar Rahman et al., 9 Cox-Munk 2 1954 Scalar Cox/Munk, 10 Giss Cox-Munk 2 1997 Vector Mishchenko/Travis 11 Giss Cox-Munk Cri 2 [V. 2010, personal Vector Natraj, communication] 12 BPDF Soil 1 [Maignan 2009] Vector et al., 13 BPDF Vegetation 1 [Maignan 2009] Vector et al., 14 BPDF NDVI 3 [Maignan 2009] Vector et al., 15 New Cox-Munk 3 [A. 2014] Scalar Sayer, In VLIDORT, the BRDF is a 4 x 4 matrix linking incident and reflected Stokes Remark. Most kernels are scalar, so that in VLIDORT, we set the {1,1} element of a 4 x 4 vector kernel k equal to the corresponding scalar kernel function k and all other elements are zero.
(6.3.3) (6.3.4) The amplitude derivative is trivial. The parameter derivative (6.3.3) depends on the empirical formulation of the kernel in question, but all kernels in the LIDORT and VLIDORT BRDF schemes are analytically differentiable with respect to their parameter dependencies. The choice of a Lambertian surface is a special case, controlled by a single flag. If this flag is set it is only necessary to specify the Lambertian albedo R (between or equal to one of the limit values 0.0 and 1.0). If the surface weighting function option is also set, then VLIDORT will return the Lambertian weighting function. Table 6.3.1 The BRDF kernel functions for VLIDORT Index Name Size bk Reference Scalar/Vector 1 Lambertian 0 Scalar 2 Ross thin 0 Wanner et al., 1995 Scalar 3 Ross thick 0 Wanner et al., 1995 Scalar 4 Li sparse 2 Wanner et al., 1995 Scalar 5 Li dense 2 Wanner et al., 1995 Scalar 6 Hapke 3 Hapke, 1993 Scalar 7 Roujean 0 Wanner et al., 1995 Scalar 8 Rahman 3 Rahman et al., 1993 Scalar 9 Cox-Munk 2 Cox/Munk, 1954 Scalar 10 Giss Cox-Munk 2 Mishchenko/Travis 1997 Vector 11 Giss Cox-Munk Cri 2 [V. Natraj, 2010, personal communication] Vector 12 BPDF Soil 1 [Maignan et al., 2009] Vector 13 BPDF Vegetation 1 [Maignan et al., 2009] Vector 14 BPDF NDVI 3 [Maignan et al., 2009] Vector 15 New Cox-Munk 3 [A. Sayer, 2014] Scalar Remark. In VLIDORT, the BRDF is a 4 x 4 matrix linking incident and reflected Stokes Most kernels are scalar, so that in VLIDORT, we set the {1,1} element of a 4 x 4 vector kernel k equal to the corresponding scalar kernel function k and all other elements are zero.
vlidort_2p7_f90userguide_v10_09apr2015.docx