Consider a sparse forest canopy with the following characteristics: Leaf area index L = 1.0. Theoretical attenuation coefficient Kb = 1.0 (assuming black leaves). Soil reflection coefficient ρs = 0.15. Leaf reflection coefficient (PAR) ρp = 0.10. Leaf transmission coefficient (PAR) τp = 0.10.

Question

Consider a sparse forest canopy with the following characteristics:

Leaf area index L = 1.0.

Theoretical attenuation coefficient [latex]\mathcal{K}_{b}[/latex] = 1.0 (assuming black leaves).

Soil reflection coefficient [latex]ρ_{s}[/latex] = 0.15.

Leaf reflection coefficient (PAR) [latex]ρ_{p}[/latex] = 0.10.

Leaf transmission coefficient (PAR) [latex]τ_{p}[/latex] = 0.10.

Calculate:

a. The canopy attenuation coefficient [latex]\mathcal{K}[/latex] for PAR.

b. The canopy reflection and transmission coefficients ([latex]ρ_{c}[/latex] and [latex]τ_{c}[/latex]) for PAR, assuming that second-order terms can be ignored.

c. The absorption coefficient of the canopy ([latex]α_{c}[/latex]) for PAR

d. The ratio of absorption ([latex]α_{c}[/latex]) to interception (1 − [latex]τ_{c}[/latex]) of PAR by the canopy.

Accepted Answer

a. [latex] \alpha _{p} = 1- au _{p} - ho _{p} [/latex]

= 1 − 0.10 − 0.10

= 0.80,

[latex] \mathcal{K} = \alpha ^{0.5}_{p} \mathcal{K}_{b} [/latex]

= [latex] (0.80^{0.5} ) imes 1 [/latex]

= 0.89.

b. Neglecting second-order terms,

[latex] ho _{c} = ho ^{*}_{c} - ( ho ^{*}_{c} - ho _{s} )\exp (-2 \mathcal{K}L) [/latex]

and [latex] ho ^{*}_{c} [/latex] = (1 − [latex] \alpha ^{0.5}_{p} [/latex] )/(1 + [latex] \alpha ^{0.5}_{p} [/latex] ) = 0.056

so [latex] ho _{c} [/latex] = 0.056 − (0.056 − 0.15) exp (−2 × 0.89 × 1)

= 0.072,

[latex] au _{c} = \exp (−\mathcal{K}L)[/latex]

= exp (−0.89 × 1)

= 0.41.

c. [latex] \alpha _{c} = 1- ho_{c}- au_{c} (1- ho _{s} ) [/latex]

= 1 − 0.072 − 0.41(1 − 0.15)

= 0.58.

d. Interception is defined as (1 - [latex] au _{c} [/latex] ), so [latex]\alpha _{c} [/latex]/(1 − [latex] au _{c} [/latex]) = 0.98. Thus 98% of the PAR radiation intercepted by the sparse canopy is absorbed. If the problem had been set up for total solar radiation, the ratio would have been closer to 0.75.

Question 8.5: Consider a sparse forest canopy with the following character...

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