Geoscience Reference
In-Depth Information
where
c
1
and
c
2
are empirical constants with values of 0.9 and 30 W m
-2
respectively
(for daily mean values). DeBruin (
1987
) proposed a slightly simpliied version of Eq.
(
7.19
) which is now generally referred to as the Makkink equation:
s
LE
v
=
065
.
K
↓
(7.20)
s
+
γ
Although the original Makkink equation predates the Priestley-Taylor equation, for-
mally it could be derived from it (DeBruin and Lablans,
1998
):
•
For daily mean values the soil heat lux can be neglected (in irst approximation the same
amount of energy enters the soil during the day as leaves the soil at night). Hence in the
Priestley-Taylor equation
Q*
-
G
can be replaced by
Q*
.
For well-watered surfaces the net radiation is roughly 50% of the global radiation. This
•
ixed ratio is due to the well-deined albedo of grass and the moderate difference between
air temperature (important in determining
L
↓
) and surface temperature (determining
L
↑
).
These two steps yield Eq. (
7.20
) from Eq. (
7.18
) with a proportionality constant
of 0.63 rather than 0.65 (which is close enough given the empirical nature of the
Makkink equation).
Question 7.13:
Make a table listing all methods to estimate evapotranspiration pre-
sented in this chapter. For each method, list the assumptions/restrictions, the required
input data and advantage/disadvantage of the method.
7.4 Dewfall
Because the Penman-Monteith equation is based on a combination of the surface
energy balance and a description of atmospheric heat and moisture transport, it should
in principle be able to reproduce dewfall as well. As dewfall generally occurs under
conditions when the amount of incoming solar radiation is small or zero, the sto-
mata will be closed and water vapour is transported to the surface of leaves only. If
we assume that there is some initial thin layer of liquid water on the vegetation, and
if the dynamics of transport of radiation, heat and water vapour
within
the canopy
is ignored, the Penman equation can be used to determine the amount of dewfall
D
(dewfall occurs if
D
< 0):
ρ
c
r
(
)
p
e
e
()
T
−
( )
+
sat
sQ
*
G
a
a
LD
=
+
a
(7.21)
v
s
γ
s
+
γ
Whereas both terms are positive in the case of daytime evaporation, in the case of dew-
fall the irst term will be negative (taking care of the removal of the energy released
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