Geoscience Reference
In-Depth Information
Variance methods
When the data needed for Equation (4.1), and temperature fluctuations
θ
are available, they
can also be used to calculate the variances of the fluctuations
(
q
)
2
w
)
2
θ
)
2
σ
2
q
=
σ
w
=
2
σ
θ
=
2
;
(
;
(
(4.2)
These may then be related to the covariance given in(4.1), i.e. the rate of evaporation, by
means of simple similarity assumptions. These relationships form the basis of the variance
method, which can be used as a complement or as an alternative to the eddy correlation
method to determine turbulent surface fluxes
E
,
u
∗
and
H
. The variance method was prob-
ably first proposed by Tillman (1972) and further elaborated upon by Wesely (1988) and
others (see, for example, Asanuma and Brutsaert, 1999; Eng
et al
., 2003). One disadvantage
of the eddy correlation technique is that (4.1) is very sensitive to the vertical orientation of
the velocity sensor to measure
w
;variance-based techniques do not suffer this drawback.
The dissipation method is another alternative method that makes use of the same kind of tur-
bulence measurements to derive the surface fluxes (see Champagne
et al
., 1977; Brutsaert,
1982).
4.2.2
Methods in terms of mean variables
Over a uniform surface with adequate fetch, formulations in terms of mean variables are
based directly on the similarity principles for the atmospheric boundary layer dis
cu
ssed
in Chapter 2. The word “mean” as used here, refers to the fact that the
q
data
are obtained by averaging over a certaintime period, in the same way as was explained
for the second moments in the previous section. These methods can be classified into
two general types, namely bulk transfer methods and mean profile methods.
,
u
and
θ
Bulk-transfer approach
In this approach the flux is determined by means of equations, whose general form is
givenby(2.33) for water vapor, and by (2.34) and (2.35) for its analogs momentum and
temperature, respectively. One of the more common forms of (2.33) used in practical
applications is as follows
E
=
Ce
ρ
u
1
(
q
s
−
q
2
)
(4.3)
where the subscripts 1 and 2 refer to measurement levels
z
1
and
z
2
above the ground,
the subscript s refers to the ground surface at
z
=
0 and
Ce
can be determined theoreti-
cally or empirically. The specific humidity at the surface
q
s
must be known in Equation
(4.3); therefore it is used mostly over water where
q
s
can be taken simply as
q
∗
(
T
s
), the
saturation value at the temperature of the water surface. The main practical advantage
of this mass-transfer approach, usually with a constant-known coefficient Ce, lies in the
fact that it can be applied on a routine basiswith regular and easily obtainable data of
mean wind speed, water surface temperature and humidity of the air.
As discussed already in Section 2.5.2, Equation (4.3) can be justified readily by the
form of the flux-profile functions (2.41), (2.44), (2.54), (2.55), and (2.56). However,
these functions also show that any empirical mass transfer coefficient Ce for data taken
in the atmospheric boundary layer, can only be constant if the roughness parameters are
