103
Energy balance for the canopy foliage
(28)
Energy balance for the air canopy
k i (Ti _ Ti) t· k(i,i~I)(Ti~l _ Ti) + k(i,i' 1)(T e i -1 - Tei ) = 0
f,c
f
c
'c
c
c
c
(29)
Water balance for the air canopy
(30)
In Eqs. (28)-(30) Si and I RN are the net solar and infrared fluxes at the foliage surface,
respectively, kf,c is a foliage-canopy air heat transfer coefficient, ef,e is a transfer coefficient
for transpiration, L is the latent heat of evaporation, and ke is a heat and water vertical
turbulent transfer coefficient within the canopy.
The third and fourth terms in Eq. (28) and the first terms in Eqs. (29)-(30) are the
sensible and latent heat (or water vapor) exchanges between canopy foliage and canopy
air. Similar to the surface-atmosphere exchanges discussed in section 2, these fluxes can be
expressed as the product of a transfer coefficient times a difference in potential, therefore
the transfer coefficients can also be interpreted as the inverse of resistances. The second
and third terms in Eqs. (29)-(30) are the energy and water exchanges between canopy air
layers.
At i = 1 (next to the ground) Eq. (28) remains unaltered, while Eqs. (29)-(30) become
k i (Ti _ Ti) + k(i,itl)(T H1 _ Ti) + k (1' - Ti) = 0
j.e
f c c
c
c
e,g
9
c
(31 )
i ((Ti)
i) + k(i,i+l) ( i~ 1 i) + k (3 ( (]') i) _ ()
e f,e qs f - qc
c
qe - qc
'C,g 9 qs g - qo -
(32)
where ke,g is the exchange coefficient between ground and lowest canopy layer (assumed
to be the same for heat and moisture) and {3g is a ground wetness factor. For i = N v (top
canopy layer)
(33)
i ((Ti)
i) k(i,i-l)( i-I
i) t- k (
i) - 0
e f,e q8 f - qe + e
qo - qe' e,a qa - qe -
(34)
where ke,a is the exchange coefficient between the top canopy layer and the bottom AM
level. In addition, Eqs. (28)-(34) need be coupled with an equation for the surface ground
temperature underlying the canopy
where Sg and I RN,g are the solar and infrared net fluxes at the ground surface and T8 ,1 is
the temperature of the top layer of a soil model (see section 3.2.1).
Energy balance for the canopy foliage
(28)
Energy balance for the air canopy
k i (Ti _ Ti) t· k(i,i~I)(Ti~l _ Ti) + k(i,i' 1)(T e i -1 - Tei ) = 0
f,c
f
c
'c
c
c
c
(29)
Water balance for the air canopy
(30)
In Eqs. (28)-(30) Si and I RN are the net solar and infrared fluxes at the foliage surface,
respectively, kf,c is a foliage-canopy air heat transfer coefficient, ef,e is a transfer coefficient
for transpiration, L is the latent heat of evaporation, and ke is a heat and water vertical
turbulent transfer coefficient within the canopy.
The third and fourth terms in Eq. (28) and the first terms in Eqs. (29)-(30) are the
sensible and latent heat (or water vapor) exchanges between canopy foliage and canopy
air. Similar to the surface-atmosphere exchanges discussed in section 2, these fluxes can be
expressed as the product of a transfer coefficient times a difference in potential, therefore
the transfer coefficients can also be interpreted as the inverse of resistances. The second
and third terms in Eqs. (29)-(30) are the energy and water exchanges between canopy air
layers.
At i = 1 (next to the ground) Eq. (28) remains unaltered, while Eqs. (29)-(30) become
k i (Ti _ Ti) + k(i,itl)(T H1 _ Ti) + k (1' - Ti) = 0
j.e
f c c
c
c
e,g
9
c
(31 )
i ((Ti)
i) + k(i,i+l) ( i~ 1 i) + k (3 ( (]') i) _ ()
e f,e qs f - qc
c
qe - qc
'C,g 9 qs g - qo -
(32)
where ke,g is the exchange coefficient between ground and lowest canopy layer (assumed
to be the same for heat and moisture) and {3g is a ground wetness factor. For i = N v (top
canopy layer)
(33)
i ((Ti)
i) k(i,i-l)( i-I
i) t- k (
i) - 0
e f,e q8 f - qe + e
qo - qe' e,a qa - qe -
(34)
where ke,a is the exchange coefficient between the top canopy layer and the bottom AM
level. In addition, Eqs. (28)-(34) need be coupled with an equation for the surface ground
temperature underlying the canopy
where Sg and I RN,g are the solar and infrared net fluxes at the ground surface and T8 ,1 is
the temperature of the top layer of a soil model (see section 3.2.1).