Geoscience Reference
In-Depth Information
8
1E5
3E4
1E4
6
C
4
2
0
0
100
200
300
400
-
(h
i
-
d
0
)/L
Fig. 2.18 Dependence of the bulk similarity function
C
on [
−
(
h
i
−
d
0
)
/
L
] for three example values of
[(
h
i
−
d
0
)
/
z
0h
], as obtained with Equation (2.69) for moderately rough terrain. The values of
10
4
and 10
5
are indicated at the curves; clearly,
C
is not very
sensitive to this variable and also the values obtainable for very rough terrain with Equation
(2.70) fall mostly inside the outermost curves shown here. It is assumed that
α
t
=
0
.
12 and
β
t
=
120.
z
0h
], namely 10
4
,3
[(
h
i
−
d
0
)
/
×
less meaningful to use the average specific humidity
q
m
. The approach has only been used
with
q
b
=
q
i
, the value of
q
at
z
=
h
i
, as follows
w
q
0
ku
∗
q
s
−
q
i
=
[
ln ((
h
i
−
d
0
)
/
z
0v
)
−
D
]
(2.71)
where, as before in the case of
B
w
and
C
,
D
is a function of a number of variables; the only
one that has been considered so far is (
h
i
−
d
0
)
/
L
, but beside this effect, Equation (2.71)
has been studied very little (see Brutsaert, 1982).
2.6
SURFACE BOUNDARY CONDITION: THE ENERGY
BUDGET CONSTRAINT
The turbulent fluxes of water vapor and sensible heat near the Earth-atmosphere interface
are linked not only by similarity relationships in the turbulent air, but also by the energy
budget. Indeed, both evaporation
E
, as a latent heat flux, and the related sensible heat
flux
H
require the supply of some other form of energy. Therefore their magnitudes
are constrained by this available energy. The question can be treated quantitatively by
considering the energy budget for a layer of surface material. Depending on the nature
of the surface, this layer may consist of water, or of some other substrate like soil,
plant canopy or snow; although this layer can be taken to be infinitesimally thin, it may
