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water vapour
heat
e
a
T
a
r
ae
r
ah
T
s
r
c
e
sat
(
T
s
)
Figure 7.2
The 'big leaf' approach: vegetation replaced by one leaf, with one stoma-
tal cavity. Water vapour transport experiences an extra resistance,
r
c
(canopy resis-
tance). Note that the aerodynamic resistances are those for scalar transport, not for
momentum.
Now the derivation of the Penman equation can be revisited to include the extra resis-
tance. Equation (
7.9
) becomes:
c
eT
rr
−
()
e
p
a
LE
=−
ρ
γ
sat
s
(7.14)
v
+
ae
c
Subsequently, Eq. (
7.12
) becomes
ρ
γ
ρ
γ
c
ee
rr
−
()
T
rr
−
+
T
T
p
L
v
E
=−
a
a
a
sat
+
s
()
T
s
a
+
ae
c
ae
c
(7.15)
c
e
−
e
rr
()
()
r
T
s
T
p
a
=
−
a
sat
+
a
ah
H
+
γ
r
+
r
ae
c
ae
c
Finally, in combination with the energy balance equation, this gives the Penman-
Monteith equation (along the same derivation as for Eq. (
7.13
)):
ρ
c
r
(
)
p
e
()
−
e
T
( )
a
a
sQ
*
G
sat
LE
=
+
a
(7.16)
v
r
r
r
r
s
++
γ
1
c
s
++
γ
1
c
a
a
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