The Light Environment of Plant Canopies
like cylinders have a hemi-surface area index equal to n / 2 times the
silhouette leaf area index. Silhouette or "projected" leaf area index is
not consistent in canopies with leaves that have complex shapes because
the details of the projection are important and often not recorded. For
example, some needles are shaped like hemicylinders and are twisted
along their length a variable number of rotations, and others may have a
cross section like 114 of a cylinder and lay flat on a planimeter with more
than one orientation. Throughout this chapter we consider flat leaves and
use the terms HSAI and LA1 interchangeably. At the top of the canopy,
L = 0. With increasing depth into the canopy, L increases and is equal
to the total leaf area index of the canopy L, below the canopy. For a given
canopy there exists a relationship between L and the physical distance
one would measure in the canopy, but the relationship is not necessarily
a simple one.
Much can be learned about the role of canopy architecture in determining the relation between leaf radiative properties and canopy radiative
properties by considering canopies to consist of a statistical distribution
of flat leaves. You may recall from Ch. 11 that leaves typically have
absorptivities of about 0.5 (Table 11.4) and canopies typically have absorptivities of about 0.8 (Table 11.2); this difference is related to the
architecture of the canopy. Separating the effects of leaf spectral properties from the effect of canopy architecture is important because most
leaves have similar reflectance and transmittance spectra, even though
they depend on wavelength, but canopy architecture can vary widely with
species, environmental condition, and time.
An idealized canopy can be constructed above some horizontal ground
area of size A by randomly placing horizontal, black (leaves that do not
reflect or transmit radiation) leaves each of area a above the ground. If
one black leaf is randomly placed over the area A the probability that
a random ray will hit this leaf is a/A. The fraction of the area A that
would be in shadow by a uniform light beam at the zenith is also a/A.
If this incident beam of light is thought of as being composed of a great
many very small rays of light, then a fraction a / A of these tiny rays
would intersect the leaf and the fraction 1 - a / A would pass by the
leaf unintercepted. If a second leaf is placed randomly over the area A
the probability that a light ray will not be intercepted by either leaf is
(1 - u/A)', because the placement of the second leaf is independent of
the placement of the first leaf. If N leaves are placed randomly above the
area A then the probability that none of the leaves will intercept a light ray
is (1 - U I A ) ~ .
This describes a binomial distribution and accommodates
the fact that many of the shadows of these horizontal leaves will overlap
on the ground surface, A. The quantity (1 - a/A) can be thought of as
the transmittance of light from the zenith through this canopy of black,
horizontal, randomly-distributed leaves. Alternatively, (1 - u / A ) ~ can be
considered to be the fraction of the ground area illuminated by the incident
beam. At this point, it is important to recognize that these probabilities
apply to both transmittances and area fractions. Binomial probability
like cylinders have a hemi-surface area index equal to n / 2 times the
silhouette leaf area index. Silhouette or "projected" leaf area index is
not consistent in canopies with leaves that have complex shapes because
the details of the projection are important and often not recorded. For
example, some needles are shaped like hemicylinders and are twisted
along their length a variable number of rotations, and others may have a
cross section like 114 of a cylinder and lay flat on a planimeter with more
than one orientation. Throughout this chapter we consider flat leaves and
use the terms HSAI and LA1 interchangeably. At the top of the canopy,
L = 0. With increasing depth into the canopy, L increases and is equal
to the total leaf area index of the canopy L, below the canopy. For a given
canopy there exists a relationship between L and the physical distance
one would measure in the canopy, but the relationship is not necessarily
a simple one.
Much can be learned about the role of canopy architecture in determining the relation between leaf radiative properties and canopy radiative
properties by considering canopies to consist of a statistical distribution
of flat leaves. You may recall from Ch. 11 that leaves typically have
absorptivities of about 0.5 (Table 11.4) and canopies typically have absorptivities of about 0.8 (Table 11.2); this difference is related to the
architecture of the canopy. Separating the effects of leaf spectral properties from the effect of canopy architecture is important because most
leaves have similar reflectance and transmittance spectra, even though
they depend on wavelength, but canopy architecture can vary widely with
species, environmental condition, and time.
An idealized canopy can be constructed above some horizontal ground
area of size A by randomly placing horizontal, black (leaves that do not
reflect or transmit radiation) leaves each of area a above the ground. If
one black leaf is randomly placed over the area A the probability that
a random ray will hit this leaf is a/A. The fraction of the area A that
would be in shadow by a uniform light beam at the zenith is also a/A.
If this incident beam of light is thought of as being composed of a great
many very small rays of light, then a fraction a / A of these tiny rays
would intersect the leaf and the fraction 1 - a / A would pass by the
leaf unintercepted. If a second leaf is placed randomly over the area A
the probability that a light ray will not be intercepted by either leaf is
(1 - u/A)', because the placement of the second leaf is independent of
the placement of the first leaf. If N leaves are placed randomly above the
area A then the probability that none of the leaves will intercept a light ray
is (1 - U I A ) ~ .
This describes a binomial distribution and accommodates
the fact that many of the shadows of these horizontal leaves will overlap
on the ground surface, A. The quantity (1 - a/A) can be thought of as
the transmittance of light from the zenith through this canopy of black,
horizontal, randomly-distributed leaves. Alternatively, (1 - u / A ) ~ can be
considered to be the fraction of the ground area illuminated by the incident
beam. At this point, it is important to recognize that these probabilities
apply to both transmittances and area fractions. Binomial probability