Geoscience Reference
In-Depth Information
−
Wind speed (m s
−
1
)
Fig. 2.15 Example of a wind profile measured above moderately hilly prairie terrain (
z
0
=
1
.
05 m,
d
0
=
26
.
9 m) in Kansas at 1500 CDT on August 14, 1987, by means of a radiosonde; the circles
represent the wind speed, and the triangles and squares represent the
x
- and
y
-components of
the wind velocity, respectively. The arrow indicates the height of the inversion. (From Brutsaert
and Sugita, 1991).
The more recent implementations (see, for example, Brutsaert, 1999) have been mostly
for unstable conditions with mean values of the variables in the mixed layer, and with the
wind speed as a scalar. The rationale for this choice of bulk variables is that, indeed, as
illustrated in Figure 2.15, owing to convection with vertical mixing the
y
-component of
the velocity is nearly negligible, so that the
x
-component is practically equal to the wind
speed; moreover, wind speed measurements aloft can be noisy, so that a height-averaged
value is likely to be more robust. Figure 2.16 shows the corresponding temperature profile.
Thus, with this choice of variables, the formulation for momentum and sensible heat can
be written as
u
k
V
m
=
[ln ((
h
i
−
d
0
)
/
z
0
)
−
B
w
]
(2.67)
w
θ
0
ku
∗
θ
s
−
θ
m
=
[ln ((
h
i
−
d
0
)
/
z
0h
)
−
C
]
(2.68)
in which
V
m
and
θ
m
are the mean wind speed and potential temperature, respectively, in the
mixed layer of the unstable ABL;
h
i
is the height of the top of the mixed layer, that is the
bottom of the inversion above the ground, and
B
w
has been given a subscript w to indicate
that the wind speed
V
is used, instead of the wind velocity components
u
and
v
.
