Question 8.4: A canopy of a shrub species with hairy leaves is sufficientl...
A canopy of a shrub species with hairy leaves is sufficiently dense and deep for the assumptions of isotropic multiple scattering of solar radiation to apply. Assume that the individual leaves have reflection (ρ) and transmission (τ ) coefficients both of 0.15 for PAR:
a. What is the absorption coefficient (α_{p}) for PAR of the leaves?
b. What is the reflection coefficient (ρ_{c}^∗ ) of the canopy for PAR?
c. Repeat the calculations of (a) and (b) for near-infra-red (NIR) radiation assuming leaf properties ρ = τ = 0.40 for this waveband.
d. If the PAR and NIR bands each contain half the energy in the solar spectrum at the surface, what is the value of ρ_{c}^∗ for the whole solar spectrum?
Given: ρ = τ = 0.15 for PAR,
a. absorption coefficient
α_{p} = 1 − τ − ρ= 1 − 2(0.15)
= 0.70.
b. Reflection coefficient of the canopy (PAR),
p^{*}_{c} = (1 − α^{0.5} _{p} )/(1 + α^{0.5} _{p} ) = 0.09.
c. Repeat (a) and (b) for NIR when ρ = τ = 0.40,
α_{p} = 1 − 0.40 − 0.40 = 0.20,
p^{*}_{c} = (1 − α^{0.5} _{p} )/(1 + α^{0.5} _{p} ) = 0.38.
d. Calculate p^{*}_{c} for the whole solar spectrum,
p^{*}_{ctotal} = 0.5 × (p^{*}_{cPAR} ) + 0.5 × (p^{*}_{cNIR}) = 0.24