104
The first difficulty which arises in the solution of the system (28)-(35) is the specification of the various radiative and turbulence transfer terms appearing in it. The net
solar and infrared contributions Si and I R~ can be calculated once the thermal infrared
emission and the solar extinction coefficients are know for each vegetation layer. The
emissions can be expressed as exponential functions of the leaf area index in a layer, L i ,
as Ei = 1_e- Lil 'ZJi (Sellers et al. 1986), where /i is the average inverse diffuse optical depth.
Once the emissivities are known, the terms I R'N in Eqs. (28)-(35) can be calculated from
the absorption-emissions of the different layers.
A common approach to the calculation of solar fluxes within the canopy has been to use
a two-stream approximation accounting for multiple reflections by leaves and radiation
trapping by dense canopies (Dickinson 1983, Sellers et al. 1986). The system of twostream equations regulating the upward and downward solar fluxes are
dS T
G
- / i - + (1 - (1 - I)W )ST - wIS 1 = wlo/i- Doe- GLI !"
dL
p,
(36)
dS 1
G
/ i - + (1 - (1 -/)w)Sl - WiST = w(l -Io)/i-Doe-GLI!"
dL
p,
(37)
where ST and Sl are the hemispheric upward and downward diffuse fluxes, p, is the cosine
of the incident direct beam and Do is its intensity, G(p,) is the relative projected leaf area
in direction p" W is a leaf scattering coefficient and I, 10 are the backscatter parameters
of a leaf for diffuse and direct beam, respectively. The intensity of the direct beam is
Doe-GxLAJI!". The various parameters appearing in Eqs. (36)-(37) can be calculated as
described in Dickinson (1983) and Sellers et al. (1986).
With the boundary conditions Sl = S[O at the canopy top (L = 0) and ST =
adDoe-GLAI I!" + a l S 1 (where ad and al are the direct and diffuse surface albedoes) at the
canopy bottom (L = LA!) the solutions to the system (36)-(37) are
(38)
(39)
where al - a7 are algebraic combinations of the coefficients of the equations (Sellers 1985).
Once the upward and downward fluxes are calculated as a function of leaf area index, the
term Si in Eq. (28) is given by the net flux absorbed by each layer. Note that Eqs
(36)-(39) can be used to calculate the canopy albedo once ST (0) and Sl(O) are known.
More difficult is the treatment of turbulent transfer coefficients appearing in Eqs.
(28)-(30). The canopy-to-atmosphere transfer coefficient is usually expressed in terms
of the bulk drag coefficient and the wind speed at the atmospheric reference level, i.e.
kc,a = CdVa (see Eqs. (14)-(19)). Therefore, in the presence of a vegetative canopy
The first difficulty which arises in the solution of the system (28)-(35) is the specification of the various radiative and turbulence transfer terms appearing in it. The net
solar and infrared contributions Si and I R~ can be calculated once the thermal infrared
emission and the solar extinction coefficients are know for each vegetation layer. The
emissions can be expressed as exponential functions of the leaf area index in a layer, L i ,
as Ei = 1_e- Lil 'ZJi (Sellers et al. 1986), where /i is the average inverse diffuse optical depth.
Once the emissivities are known, the terms I R'N in Eqs. (28)-(35) can be calculated from
the absorption-emissions of the different layers.
A common approach to the calculation of solar fluxes within the canopy has been to use
a two-stream approximation accounting for multiple reflections by leaves and radiation
trapping by dense canopies (Dickinson 1983, Sellers et al. 1986). The system of twostream equations regulating the upward and downward solar fluxes are
dS T
G
- / i - + (1 - (1 - I)W )ST - wIS 1 = wlo/i- Doe- GLI !"
dL
p,
(36)
dS 1
G
/ i - + (1 - (1 -/)w)Sl - WiST = w(l -Io)/i-Doe-GLI!"
dL
p,
(37)
where ST and Sl are the hemispheric upward and downward diffuse fluxes, p, is the cosine
of the incident direct beam and Do is its intensity, G(p,) is the relative projected leaf area
in direction p" W is a leaf scattering coefficient and I, 10 are the backscatter parameters
of a leaf for diffuse and direct beam, respectively. The intensity of the direct beam is
Doe-GxLAJI!". The various parameters appearing in Eqs. (36)-(37) can be calculated as
described in Dickinson (1983) and Sellers et al. (1986).
With the boundary conditions Sl = S[O at the canopy top (L = 0) and ST =
adDoe-GLAI I!" + a l S 1 (where ad and al are the direct and diffuse surface albedoes) at the
canopy bottom (L = LA!) the solutions to the system (36)-(37) are
(38)
(39)
where al - a7 are algebraic combinations of the coefficients of the equations (Sellers 1985).
Once the upward and downward fluxes are calculated as a function of leaf area index, the
term Si in Eq. (28) is given by the net flux absorbed by each layer. Note that Eqs
(36)-(39) can be used to calculate the canopy albedo once ST (0) and Sl(O) are known.
More difficult is the treatment of turbulent transfer coefficients appearing in Eqs.
(28)-(30). The canopy-to-atmosphere transfer coefficient is usually expressed in terms
of the bulk drag coefficient and the wind speed at the atmospheric reference level, i.e.
kc,a = CdVa (see Eqs. (14)-(19)). Therefore, in the presence of a vegetative canopy