Geoscience Reference
In-Depth Information
values of
E
A
with equations like (4.25), to a first approximation the wind speed at 2 m
can be estimated by assuming a power dependency on height, or
z
r
)
1
/
7
u
2
=
u
r
(2
/
(4.26)
where
z
r
is the height (inm)atwhich the available wind data are measured.
A more fundamental approach to determine the wind function is based on turbulence
similarity. Thus in terms of the bulk water vapor transfer coefficient as defined, for
example, in(4.3), inwhich
z
1
is the height of the measurement of
u
1
and
z
2
that of
e
a
,
one obtains by virtue of (4.6), the wind function
p
−
1
Ce
u
1
f
e
(
u
1
)
=
0.622
ρ
(4.27)
Ce can be determined by means of the similarity profile functions of Chapter 2. Under
neutral conditions, on account of Equations (4.4), (4.6) and (4.7) this is (to a good
approximation)
622
k
2
u
1
0
.
f
e
(
u
1
)
=
(4.28)
R
d
T
a
ln [(
z
2
−
d
0
)
/
z
0v
]ln[(
z
1
−
d
0
)
/
z
0
]
where, again,
z
1
is the level of the wind speed measurement and
z
2
that of the water
vapor pressure.
When Penman's equation is applied to calculate mean values of
E
over periods of a day
or longer, the use of wind functions like (4.25), (4.27) or (4.28) may be adequate. However,
when hourly values are required, the effect of atmospheric stability, which varies through
the day, may be important. It is possible to include the effect of the atmospheric stability in
the wind function, by writing the drying power of the air(4.24) in a form similar to (2.56)
(see also Brutsaert, 1982) as follows
E
A
=
ku
∗
ρ
(
q
a
−
q
a
)
ln
z
a
−
−
v
z
a
−
L
−
1
+
v
z
0v
d
0
d
0
(4.29)
z
0v
L
where
q
a
and
q
a
are the specific humidity of the air and the saturation specific humidity at air
temperature, respectively. The problem can be solved by the following iteration procedure.
An initial value of
E
is calculated in the usual way by means of Equation (4.23) using a
neutral
E
A
, say (4.24) with (4.28); it is also possible to use (4.29) with
0, and
u
∗
is
calculated by means of (2.54) with
m
=
0. The initial value of
E
is used to obtain
H
by
means of (4.13). These initial values of
E
,
u
∗
and
H
provide a first estimate of the Obukhov
length
L
by means of (2.46). This value of
L
allows now the calculation of a second estimate
of
u
∗
by means of (2.54) and a second estimate of
E
A
by means of (4.29), which produces
a second estimate of
E
by means of (4.23), and so on. An example of the application of this
method has been presented by Katul and Parlange (1992).
v
=
Evaporation from wet surfaces in the absence of advection
The two-term structure of Equation (4.23) suggests an interpretation which may serve
as an aid in understanding the effect of regional or large-scale advection. When the air
has been in contact with a wet surface over a very long fetch, it could be argued that it
may tend to become vapor saturated, so that
E
A
, shown in(4.24), should tend to zero.
