Heterogeneous Canopies
15.1 2 Canopy Reflectivity (Emissivity) versus
Leaf Reflectivity (Emissivity)
Canopy reflectance is less than leaf reflectance because some of the radiation incident on leaves is transmitted deeper into the canopy where
multiple interactions between the radiation and leaves causes additional
absorption of the radiation. In effect, the canopy behaves as a trap for
the radiation that is absorbed at the deeper depths in the canopy or at the
soil surface. Either Eq. (15.7) or Eq. (15.8) can be used to illustrate this
trapping phenomenon. For a deep canopy with PAR reflectivity pp = 0.1
and PAR transmissivity t , = 0.1, the canopy reflectance pgy = 0.056.
In the thermal wavelength band, if the leaf emissivity E L = 0.95, then the
leaf reflectivity pL = 0.05 because t~ = 0. Using Eq. (1 5.7) for a deep
canopy, p ~ , , , = 0.013 so the emissivity of this deep canopy is 0.987.
Therefore a deep canopy is much closer to a blackbody than the leaves
that make it up, and this explains why dense canopies often are assumed
to have thermal emissivities of 0.99 even though leaves may have lower
emissivities.
15.1 3 Heterogeneous Canopies
The simplified radiative exchange principles described in this chapter
apply to vegetative canopies with leaves that are randomly distributed
throughout the canopy space. Such canopies of randomly-positioned
leaves are often referred to as homogeneous because the probability of
finding a leaf anywhere in the canopy space is independent of horizontal
position. When leaves are not randomly distributed in space, the canopy
is considered heterogeneous; and the character of the heterogeneity can
take many forms. We briefly consider two approaches to characterizing
heterogeneity.
1. Incorporate a clumping factor in the exponential extinction equations
by replacing L with a (+) L; where (@) is the clumping factor that
depends on zenith angle.
2. Assume leaves to be randomly distributed within the confines of
some appropriate geometric volumes, which we refer to as canopy
envelopes, to represent widely-spaced tree crowns or crop rows.
The clumping-factor approach has the advantage of making it possible
to extend the previous equations for random canopies discussed earlier in
this chapter to heterogeneous cases. For random canopies a(+) = 1,
clumped foliage has a(+) < 1, and if foliage is more nearly miformly spaced, a(+) > l. For forest canopies, which tend to be the
most strongly clumped, the dependence of clumping factor on + can be
15.1 2 Canopy Reflectivity (Emissivity) versus
Leaf Reflectivity (Emissivity)
Canopy reflectance is less than leaf reflectance because some of the radiation incident on leaves is transmitted deeper into the canopy where
multiple interactions between the radiation and leaves causes additional
absorption of the radiation. In effect, the canopy behaves as a trap for
the radiation that is absorbed at the deeper depths in the canopy or at the
soil surface. Either Eq. (15.7) or Eq. (15.8) can be used to illustrate this
trapping phenomenon. For a deep canopy with PAR reflectivity pp = 0.1
and PAR transmissivity t , = 0.1, the canopy reflectance pgy = 0.056.
In the thermal wavelength band, if the leaf emissivity E L = 0.95, then the
leaf reflectivity pL = 0.05 because t~ = 0. Using Eq. (1 5.7) for a deep
canopy, p ~ , , , = 0.013 so the emissivity of this deep canopy is 0.987.
Therefore a deep canopy is much closer to a blackbody than the leaves
that make it up, and this explains why dense canopies often are assumed
to have thermal emissivities of 0.99 even though leaves may have lower
emissivities.
15.1 3 Heterogeneous Canopies
The simplified radiative exchange principles described in this chapter
apply to vegetative canopies with leaves that are randomly distributed
throughout the canopy space. Such canopies of randomly-positioned
leaves are often referred to as homogeneous because the probability of
finding a leaf anywhere in the canopy space is independent of horizontal
position. When leaves are not randomly distributed in space, the canopy
is considered heterogeneous; and the character of the heterogeneity can
take many forms. We briefly consider two approaches to characterizing
heterogeneity.
1. Incorporate a clumping factor in the exponential extinction equations
by replacing L with a (+) L; where (@) is the clumping factor that
depends on zenith angle.
2. Assume leaves to be randomly distributed within the confines of
some appropriate geometric volumes, which we refer to as canopy
envelopes, to represent widely-spaced tree crowns or crop rows.
The clumping-factor approach has the advantage of making it possible
to extend the previous equations for random canopies discussed earlier in
this chapter to heterogeneous cases. For random canopies a(+) = 1,
clumped foliage has a(+) < 1, and if foliage is more nearly miformly spaced, a(+) > l. For forest canopies, which tend to be the
most strongly clumped, the dependence of clumping factor on + can be