Geoscience Reference
In-Depth Information
In most applications; a further approximation is made: that the aerodynamic resistances
r
a,V
and
r
a,H
can both be assumed equal to the equivalent resistance for momentum transport in a
well mixed neutral boundary layer
r
a
for which a value can be derived from assumptions about
the wind speed profile. In particular, for a logarithmic wind speed profile, turbulence theory
suggests that
ln
z
−
d
/z
o
2
2
u
z
r
a
=
(B3.1.8)
where
d
is called the zero plane displacement,
z
o
is the roughness height,
u
z
is the wind speed
at the measurement height,
z
, and
is the von Karman constant. This expression assumes
a well mixed boundary layer above the vegetation canopy. Corrections may be required for
stable atmospheric conditions.
After these approximations
1
r
a
+
r
c
a
c
p
E
=
(
e
s
(
T
z
)
−
e
z
+
e
{
T
o
−
T
z
}
)
(B3.1.9)
But from the expression for sensible heat flux
{
T
o
−
T
z
}
=
Cr
a
/
a
c
p
=
r
a
[
H
−
E
]
/
a
c
p
(B3.1.10)
so that
a
c
p
[
H
−
E
]
1
r
a
+
r
c
e
r
a
E
=
(
e
s
(
T
z
)
−
e
z
)
+
(B3.1.11)
Rearranging this equation gives
E
1
e
r
a
(
e
s
(
T
z
)
−
e
z
)
e
r
a
(
r
a
+
r
c
)
1
r
a
+
r
c
a
c
p
+
=
R
n
+
(B3.1.12)
or
e
H
+
a
c
p
(
e
s
(
T
z
)
−
e
z
)
/r
a
E
=
(B3.1.13)
e
+
(1
+
r
c
/r
a
)
This is the Penman-Monteith equation. Use of the equation requires measurements of
temperature, humidity and wind speed at the reference height
z
, available energy
H
, and
estimates of the two resistance coefficients
r
a
and
r
c
. The approximation
H
≈
R
n
is often made.
The equation can be applied with hourly data to provide estimates of the diurnal pattern of
evapotranspiration rates.
The resistance coefficients have an important control on predicted evapotranspiration rates,
particularly when the resistances are low (Beven, 1979a). The variation of predicted evapo-
transpiration with
r
a
and
r
c
for a particular set of meteorological conditions is shown in Figure
B3.1.2. Typical values for a dry grass canopy would be
r
a
=
50
sm
−1
and
r
c
=
50
sm
−1
, while
for a dry tree canopy
r
a
=
50
sm
−1
. The highest actual evapotranspiration
rates will be predicted for a rough canopy (low
r
a
) with intercepted water on the leaf surfaces
(
r
c
=
10
sm
−1
and
r
c
=
0).
