### 2.5.1 - BRFDs

The measured surface reflectance depends on the
configuration: *sun position – observation geometry*.

First think of a geostationary satellite, located at fixed position above the Earth. For each individual pixel only the Sun geometry varies from slot to slot.

For the case of polar orbiters, (normally sun-synchronous) it is mainly the satellite observation angles that change between observation slots of the same region.

This means that reflectance values measured with
geostationary or polar satellites need to be corrected for directional
effects. Such corrections may be easily performed if the *Bidirectional
Reflectance Distribution Functions (BRDF) *are known. The BRDF model
describes reflection behavior for all possible combinations of
sun-viewing geometries. The characteristics of the BRDF will determine
what "type" of material the viewer thinks the displayed object is
composed of.

Among the several *Bi-directional Reflectance
Distribution Functions* proposed by different authors,
the one by Roujean et al. (1992) has been extensively used for
vegetation parameters estimations:

ρ (θ_{s}, θ_{v}, φ) = K_{0} + K_{1} x F_{1}(θ_{s},
θ_{v}, φ) + K_{2}
x F_{2}(θ_{s},
θ_{v}, φ)

F_{1}
and F_{2} are functions, called kernels, which only
depend on the angular configuration of aquisition:

- θ
_{s}is the sun zenith angle; - θ
_{v}is the satellite zenith angle - φ is the relative azimuth angle between sun and satellite

The *K *coefficients quantify
the respective contribution of each kernel to the whole BRDF and are
derived by model inversion.

*K*corresponds to_{0}*isotropic*reflectance, i.e. reflectance values directionally normalised to reference illumination and observation zenith angles of 0°. This geometry leads to a minimum of the shadow proportion (hotspot geometry);*K*and_{1}*K*represent angular distribution related to_{2}*geometric*(caused by diffuse reflectors) and*volumetric*(caused by volume scatter reflectors) surface scattering processes.

The isotropic, geometric and volumetric components of surface reflectance are intrinsically linked to the amount and state of vegetation, canopy structure and to the leaf and soil optical properties, as you will see in more detail in chapter 5.