Geoscience Reference
In-Depth Information
eTe eTe
ER c
(())(())
−−
−
l
l
(21.26)
l
=−
r
sat
s
sat
n
a p
Δ
H
or:
(())
eTe
−
D
(21.27)
Ec
l
sat
s
Rc
l
lr
+
=
+
r
ap
n
p
Δ
R
Δ
R
H
H
where
D
is the vapor pressure deficit of the air outside the boundary layer of the
leaf.
Substituting Equation (21.22) into Equation (21.27) and rearranging gives:
r
cD
ap
l
Δ+
R
n
R
(21.28)
l
l
E
=
H
Rr
R
+
Δ+
g
v
ST
H
If it is then assumed that the boundary-layer resistances for latent and sensible
heat are equal and represented by
R
(i.e., that
R
=
R
H
=
R
V
), then Equation (21.28)
becomes:
r
cD
l
ap
Δ+
R
n
R
E
l
(21.29)
l
=
⎛
r
⎞
Δ+
g
1
+
ST
⎜
⎟
⎝
R
⎠
This equation is the well-known and much used
Penman-Monteith equation
(Monteith, 1965), which is the basis for much of the description of evaporation in
hydrometeorology. In this case the equation is applied to the energy balance for
unit area of leaf.
Energy budget of a dry canopy
Early research into how best to represent the complexity of exchanges in vegetation
canopies involved two general approaches. One approach (e.g., Waggoner and
Reifsnyder, 1968; 1969) was to build multi-layer computer models of the interaction.
Such models (see Fig. 21.6a) represent the capture of radiant energy at several levels
in the canopy, and the heat exchanges between leaves and air at these levels is
calculated from the level-average stomatal resistance to water vapor flow and the
level-average leaf boundary-layer resistance to momentum, water vapor and sensible
heat flow. Multi-layer models also often describe the aerodynamic resistance to
energy flow between each level using a form of K Theory.
