Cover classification map distinguishing the following biomes types: (1) grasses
and cereal crops, (2) shrubs, (3) broadleaf crops, (4) savannas, (5) evergreen
broadleaf forests, (6) deciduous broadleaf forests, (7) evergreen needle leaf forests,
(8) deciduous needle leaf forests. The biome map reduces the number of unknowns
of the inverse problem through the use of simplifying assumptions (e.g., biomespecific models of leaf orientation distributions; Knyazikhin et al. 1998) and
standard constants (e.g., biome-specific leaf and soil optical properties at given
wavelengths). Over 11 years of Terra MODIS and about 10 years of Aqua
MODIS LAI/FPAR products have been generated with this algorithm. Figure 2.1
shows global fields of annual average LAI and FPAR derived from 10 years of
Terra MODIS Collection 5 data.
A consistent retrieval of LAI/FPAR from different sensors depends on the
parameterization of the physically-based algorithm by adjusting for sensor-specific
features of the BRF measurements (spatial resolution, bandwidth, calibration,
atmospheric correction, information content, etc.). The theory of canopy spectral
invariants provides the required BRF parameterization via a small set of welldefined measurable variables that specify the relationship between the spectral
response of vegetation canopy bounded be biome-specific canopy architecture low
by a non-reflecting surface to the incident radiation at the leaf and canopy scales
(Huang et al. 2007; Yuri Knyazikhin et al. 2011; Lewis and Disney 2007; Smolander and Stenberg 2005). The core theory provides a more easy and efficient way
of simulating wavelength dependent BRFs as a function of biome-specific canopy
structural attributes. The first order approximation of the BRF for a vegetation
canopy bounded below by a non-reflecting surface (Ganguly et al. 2008b; Huang
et al. 2007) is approximated as:
BRF BS;k X
ð Þ ¼ x k R 1 X
ð Þ þ
x
2
k
1 À px k
R 2 X
ð Þ;
ð2:1Þ
where x k is the leaf single scattering albedo, R 1 and R 2 are escape probabilities
expressed relative to the number of incident photons and p refers to the recollision
probability, which is defined as the probability that a photon scattered by a foliage
element in the canopy will interact within the canopy again. The spectral
absorptance, a BS,k of the vegetation canopy with non-reflecting background can be
expressed as:
a BS;k ¼
1 À x k
1 À px k
i 0 ;
ð2:2Þ
where i 0 is the probability of initial collisions, or canopy interceptance, defined as
the portion of photons from the incident beam that are intercepted, i.e., collide with
phytoelements for the first time. The FPAR is a weighted integral of Eq. (2.2) over
the photosynthetically active radiation (PAR) spectral region (Knyazikhin et al.
1998). The formulation in Eq. (2.1) permits decoupling of the structural and
radiometric components of any optical sensor signal, and requires a set of sensorspecific values of configurable parameters, namely the ‘‘single scattering albedo’’
2 Green Leaf Area and Fraction of Photosynthetically
47
and cereal crops, (2) shrubs, (3) broadleaf crops, (4) savannas, (5) evergreen
broadleaf forests, (6) deciduous broadleaf forests, (7) evergreen needle leaf forests,
(8) deciduous needle leaf forests. The biome map reduces the number of unknowns
of the inverse problem through the use of simplifying assumptions (e.g., biomespecific models of leaf orientation distributions; Knyazikhin et al. 1998) and
standard constants (e.g., biome-specific leaf and soil optical properties at given
wavelengths). Over 11 years of Terra MODIS and about 10 years of Aqua
MODIS LAI/FPAR products have been generated with this algorithm. Figure 2.1
shows global fields of annual average LAI and FPAR derived from 10 years of
Terra MODIS Collection 5 data.
A consistent retrieval of LAI/FPAR from different sensors depends on the
parameterization of the physically-based algorithm by adjusting for sensor-specific
features of the BRF measurements (spatial resolution, bandwidth, calibration,
atmospheric correction, information content, etc.). The theory of canopy spectral
invariants provides the required BRF parameterization via a small set of welldefined measurable variables that specify the relationship between the spectral
response of vegetation canopy bounded be biome-specific canopy architecture low
by a non-reflecting surface to the incident radiation at the leaf and canopy scales
(Huang et al. 2007; Yuri Knyazikhin et al. 2011; Lewis and Disney 2007; Smolander and Stenberg 2005). The core theory provides a more easy and efficient way
of simulating wavelength dependent BRFs as a function of biome-specific canopy
structural attributes. The first order approximation of the BRF for a vegetation
canopy bounded below by a non-reflecting surface (Ganguly et al. 2008b; Huang
et al. 2007) is approximated as:
BRF BS;k X
ð Þ ¼ x k R 1 X
ð Þ þ
x
2
k
1 À px k
R 2 X
ð Þ;
ð2:1Þ
where x k is the leaf single scattering albedo, R 1 and R 2 are escape probabilities
expressed relative to the number of incident photons and p refers to the recollision
probability, which is defined as the probability that a photon scattered by a foliage
element in the canopy will interact within the canopy again. The spectral
absorptance, a BS,k of the vegetation canopy with non-reflecting background can be
expressed as:
a BS;k ¼
1 À x k
1 À px k
i 0 ;
ð2:2Þ
where i 0 is the probability of initial collisions, or canopy interceptance, defined as
the portion of photons from the incident beam that are intercepted, i.e., collide with
phytoelements for the first time. The FPAR is a weighted integral of Eq. (2.2) over
the photosynthetically active radiation (PAR) spectral region (Knyazikhin et al.
1998). The formulation in Eq. (2.1) permits decoupling of the structural and
radiometric components of any optical sensor signal, and requires a set of sensorspecific values of configurable parameters, namely the ‘‘single scattering albedo’’
2 Green Leaf Area and Fraction of Photosynthetically
47