Geoscience Reference
In-Depth Information
ln(
z
−
d
0
)
Fig. 2.9
Schematic illustration
of the
m
ean
w
ind
profile
u
=
u
(
z
)inthe
dynamic sublayer and
in the atmospheric
surface layer (ASL,
also called the surface
sublayer).
unstable
neutral
stable
Surface
sublayer
(ASL)
Dynamic
sublayer
ln(
z
0
)
Mean velocity,
u
Once again, integration yields a logarithmic profile as follows,
ln
z
2
−
E
ku
∗
ρ
d
0
q
1
−
q
2
=
(2.43)
z
1
−
d
0
This result, combined with Equations (2.33) and (2.37), produces a mass transfer coeffi-
cient for water vapor; in the case where wind speed and specific humidity are measured
at the same two levels
z
1
and
z
2
one obtains Ce
2
;itis
remarkable that this transfer coefficient has the same form as that for momentum, i.e.
Ce
={
k
/
ln[(
z
2
−
d
0
)
/
(
z
1
−
d
0
)]
}
Cd, as derived above. The fact, that under certain conditions transfer coefficients
of different admixtures in turbulent flow are the same, is also referred to as the
Reynolds
analogy
. The alternative form of Equation (2.43), when one of the specific humidity
values is taken at the surface,
z
=
=
0, is
ln
z
−
E
ku
∗
ρ
d
0
z
0v
q
s
−
=
q
(2.44)
where
q
s
is the value of
q
at the surface and
z
0v
is the (scalar) roughness for
water vapor (see Figure 2.10). In this case the transfer coefficient can be written as
Ce
k
2
, in which the subscript 2 refers to the height
of the wind measurement and the subscript 1 refers to that of the specific humidity. In this
formulation Ce would be equal to Cd only if the two roughness parameters
z
0
and
z
0v
have the same value, which is rarely the case above land.
It would be possible to define a similar logarithmic relationship between the tem-
perature and the surface sensible heat flux
H
; however, since under neutral conditions
the temperature differences and the sensible heat flux are relatively small, this is not
very meaningful. In what follows under non-neutral conditions the scalar roughness for
sensible heat in the temperature profile will be denoted by
z
0h
.
=
/
{
ln[(
z
2
−
d
0
)
/
z
0
]ln[(
z
1
−
d
0
)
/
z
0v
]
}
