The Light Environment of Plant Canopies
angle is not exact but it is close. For example, the spherical leaf angle
distribution has a true mean leaf inclination angle of 57", rather than 60".
The fraction of beam radiation that is transmitted through the canopy
without interception tb(@) is given by Eq. (15.1) with Kbe(@) from
Eq. (15.4) (or one of the simpler equations for Kb(@) if the distribution is horizontal, vertical, or spherical) using the appropriate sun zenith
angle (Eq. (1 1.1)).
15.3 Transmission of Diffuse Radiation
The diffuse radiation comes from all directions, and is attenuated differently from beam radiation, which comes from just one direction. Diffuse
radiation can be thought of as many beams and a diffuse transmission
coefficient for the canopy can be calculated from
t d = 2
tb(@) sin@ COS @ d$f.
r2
(15.5)
For horizontal leaves, t b (@) is not dependent on +, and so t b = td, but for
the other leaf angle distributions tb (+) does depend on @ and the integration in Eq. (1 5.5) must be carried out numerically. When the integration is
done numerically, it is found that t d does not decrease exponentially with
L, as it does for beam radiation (except for horizontal leaves). In order
to obtain a useful approximation for models, an exponential equation can
be fit to the values obtained and allow Kd, the extinction coefficient for
black leaves in diffuse radiation, to vary with leaf area index. Figure 15.4
shows the result based on a numerical integration of Eq. (15.5), assuming
1
Leaf Area Index
FIGURE 15.4. Apparent extinction coefficient for diffuse radiation in canopies
differing in leaf angle distribution.