BRDF Applications in Semiarid Grassland Monitoring with the AVHRRs
Summary of the Roujean et al (1992a) BRDF Model
Full details of the derivation of the BRDF model are given in Roujean et
al (1992a). Briefly, it is expressed as
where R is the bidirectional reflectance in a given channel for the solar
zenith, view zenith and relative azimuth angles
respectively. f1 and f2 are simple analytic functions
of the solar and viewing angles; specifically, f1 accounts for the geometric
scattering and shadowing component (neglecting mutual shadowing of protrusions
from the surface) and is expressed as
while f2 accounts for the volume scattering component from an infinite discrete
medium of randomly-located facets, assuming the single scattering approximation
and an isotropic facet distribution function. It is expressed as
where E is the phase or scattering angle, related to conventional angles by
In the derivation of the model the surface parameters are dependent on the
three-dimensional structure and optical properties of a canopy and its
background. Specifically, k0 represents the bidirectional reflectance
viewing a (possibly heterogeneous) surface at nadir with the overhead sun
(sun zenith = view zenith = 0), while k1 and k2 measure the relative
contributions of the geometric/shadowing and volume scattering components
in total reflectance, respectively. Thus k1 should be a function of the
three-dimensional structure of a canopy while k2 is a function of facet
reflectance and facet area index:
where h and l are the height and length of surface protrusions, S is the
horizontal surface associated with each protrusion, r is facet
reflectance, F is facet area index (LAI), alpha is a fraction of total
background and protrusion reflectance and b is a constant which represents
a rough average of (1/2) / (cos(sunzen) + cos(viewzen)).
Use back button | Index | Disclaimer