The Light Environment of Plant Canopies
reliable estimate. Equation (15.6) accommodates multiple scattering in
the canopy and is only appropriate where reflectivity and transmissivity
are constant with wavelength. If the reflection coefficient is averaged over
a wavelength band where spectral reflectivity (and transmissivity) varies
considerably with wavelength, (as it does for leaves in the visible and nearinfrared portions of the solar spectrum) then Eq. (1 5.7) is unreliable. This
can best be understood with a simple example; shown as Example 15.1.
Example 15.1. Estimate the transmission of solar radiation through two
filters, stacked on top of each other, using the following two methods.
1. Assume an average transmission for the solar wavelength band (ts),
2. Use visible (VIS) and near-infrared (NIR) transmissions separately.
Assume 112 of the solar radiation is NIR and 112 is VIS, the visible
transmittance (tv) is 0.0, and near-infrared transmittance (zN) is 0.9.
Solution.
1. using ts:
ts = 0.5(0) + 0.5(0.9) = 0.45
t ( 2 filters) = tsts = 0.45 x 0.45 = 0.20.
2. Using tv and tN with tv = 0 and tN = 0.9:
visible
t(2 filters) = 0.0 x 0.0 = 0.0
near-infrared
t(2filters) = 0.9 x 0.9 = 0.81
solar
t ( 2 filters) = 0.5(0.) + 0.5(0.81) = 0.40.
Therefore averaging multiple transmissions or reflections, as happens in
plant canopies, over wavelength bands with different spectral properties
causes errors; in this example a factor of two.
From Example 15.1, the visible and near-infrared wavelength bands
should be treated separately because their spectral properties are so different. Thus a better estimate of the solar albedo is given by P&,~ =
0.5(0.056) + 0.5(0.38) = 0.22, a value 29 percent larger than is obtained by substituting the average solar absorptivity into Eq. (15.7). This
is one of the reasons that solar radiation must be divided into visible
and near-infrared wavelength bands in environmental biophysics. Fortunately about one-half of the irradiance is in each band so approximate
partitioning is simple.
reliable estimate. Equation (15.6) accommodates multiple scattering in
the canopy and is only appropriate where reflectivity and transmissivity
are constant with wavelength. If the reflection coefficient is averaged over
a wavelength band where spectral reflectivity (and transmissivity) varies
considerably with wavelength, (as it does for leaves in the visible and nearinfrared portions of the solar spectrum) then Eq. (1 5.7) is unreliable. This
can best be understood with a simple example; shown as Example 15.1.
Example 15.1. Estimate the transmission of solar radiation through two
filters, stacked on top of each other, using the following two methods.
1. Assume an average transmission for the solar wavelength band (ts),
2. Use visible (VIS) and near-infrared (NIR) transmissions separately.
Assume 112 of the solar radiation is NIR and 112 is VIS, the visible
transmittance (tv) is 0.0, and near-infrared transmittance (zN) is 0.9.
Solution.
1. using ts:
ts = 0.5(0) + 0.5(0.9) = 0.45
t ( 2 filters) = tsts = 0.45 x 0.45 = 0.20.
2. Using tv and tN with tv = 0 and tN = 0.9:
visible
t(2 filters) = 0.0 x 0.0 = 0.0
near-infrared
t(2filters) = 0.9 x 0.9 = 0.81
solar
t ( 2 filters) = 0.5(0.) + 0.5(0.81) = 0.40.
Therefore averaging multiple transmissions or reflections, as happens in
plant canopies, over wavelength bands with different spectral properties
causes errors; in this example a factor of two.
From Example 15.1, the visible and near-infrared wavelength bands
should be treated separately because their spectral properties are so different. Thus a better estimate of the solar albedo is given by P&,~ =
0.5(0.056) + 0.5(0.38) = 0.22, a value 29 percent larger than is obtained by substituting the average solar absorptivity into Eq. (15.7). This
is one of the reasons that solar radiation must be divided into visible
and near-infrared wavelength bands in environmental biophysics. Fortunately about one-half of the irradiance is in each band so approximate
partitioning is simple.