Geoscience Reference
In-Depth Information
This shows that the vapor pressure
e
is closely proportional to the specific humidity
q
.
The introduction of the additional constant
a
in(4.5) may be viewed as a means of improv-
ing the curve-fit between the mean wind speed and the rate of evaporation. Although
their theoretical justification is marginal, equations like Stelling's (4.5) have been found
useful to describe evaporation from water or wet surfaces. Some examples for various
problems and surfaces can be found in papers by Penman (1948, 1956), Brutsaert and Yu
(1968), Shulyakovskiy (1969) and Neuwirth (1974) among many others. Mass-transfer
equations, in terms of the vapor pressure difference, are sometimes written in a more
general form as follows
E
=
f
e
(
u
1
)(
e
s
−
e
2
)
(4.7)
where, as before, the subscripts refer to the levels above the surface
z
1
and
z
2
at which the
measurements are made, and
f
e
(
u
) is called the wind function, which can be obtained
experimentally or from similarity; obviously, in the case of (4.5), one has
f
e
(
u
)
=
a
+
bu
.
Mean profile methods
The available flux-profile functions for the boundary layer given in Section 2.5.2 allow
the calculation of the surface fluxes from measurements of mean concentration at two
or more levels. The specific form of the profile functions depends on the level above the
surface, i.e. the specific sublayer, where the measurements are made (see Figure 2.6).
Profile methods are most useful in the atmospheric surface layer, where they can be
based on the Monin-Obukhov similarity. Recall that the surface sublayer is the fully
turbulent layer, located between a height
z
sb
,which is well above the surface roughness
elements - say at least four to five times theirheight
h
0
-andaheight
z
st
,which is
roughly of the order of one tenth of the thickness of the boundary layer; a more precise
estimate of the extent of the surface layer is presented in Section 2.5.2. The profiles inthis
layer are given by Equations (2.50)-(2.52) (or (2.54)-(2.56)). The subscripts 1 and 2 in
th
e
se
equ
at
ions refer to a lower and upper level at which the respective measurements of
q
,
u
and
θ
are made; clearly, these elevations need not be the same in all three equations.
The
-functions appearing in(2.50)-(2.52) are given in(2.58), (2.59), (2.63) and (2.64).
In this approach, the flux of any admixture, be it
E, u
∗
o
r
H
,
c
ann
o
t be calculated simply
from measurements of its corresponding concentration,
q
,
θ
, only; indeed, except
under neutral conditions, each of Equations (2.50)-(2.56) contains also the momentum
flux
u
∗
, and the Obukhov length
L
, defined in(2.46), which, in turn, contains the three
fluxes. In practice there are two alternative methods of closing a flux determination
problem.
The first method consists of the simultaneous solution of Equations (2.50)-(2.52)
(or (2.54)-(2.56)) for the three unknown surface fluxes
u
∗
,
H
and
E
,with known mea-
surements at least at two levels of mean specific humidity, mean wind speed and mean
temperature. This numerical problem may be solved indifferent ways. One simple way
isbyiteration, as follows; it is assumed initially that the profiles are logarithmic, i.e. that
L
u
or
-functions are zero. This permits the calculation of a first estimate of
the fluxes with (2.50)-(2.52) (or (2.54)-(2.56)), from which a first estimate can be made
=∞
so that the
