Geoscience Reference
In-Depth Information
θ
(K)
Fig. 2.16 Example of the profile of potential temperature measured with the same radiosonde as that of
the wind shown in Figure 2.15. The solid circle shows the median value of the surface
temperature. The arrow indicates the height of the inversion. (From Brutsaert and Sugita,
1991.)
Until now, no general definitive form has been derived for these functions
B
w
and
C
.An
example of a formulation for unstable conditions, that has produced good results (Brutsaert,
1999), is summarized in what follows. It is based on the assumption of an ABL consisting
of two layers, namely a surface layer, with profiles given by Equations (2.63) and (2.64),
and above it a mixed layer as a slab with uniform profiles; it is further also based on the
assumption explained behind (2.64) regarding the position of the top of the surface layer,
where it meets the mixed layer. For moderately rough terrain, i.e. when
z
0
≤
(
α
t
/β
t
)
h
i
, the
resulting functions are
B
w
=−
ln(
α
t
)
+
m
(
α
t
(
h
i
−
d
0
)
/
L
)
−
m
(
z
0
/
L
)
(2.69)
C
=−
ln(
α
t
)
+
h
(
α
t
(
h
i
−
d
0
)
/
L
)
−
h
(
z
0h
/
L
)
For very rough terrain, when
z
0
>
(
α
t
/β
t
)
h
i
, the functions are
B
w
=
ln ((
h
i
−
d
0
)
/
(
β
t
z
0
))
+
m
(
β
t
z
0
/
L
)
−
m
(
z
0
/
L
)
C
=
ln ((
h
i
−
d
0
)
/
(
β
t
z
0
))
+
h
(
β
t
z
0
/
L
)
−
h
(
z
0h
/
L
)
(2.70)
The similarity functions
B
w
and
C
given by Equations (2.69) and (2.70) are illustrated in
Figures 2.17 and 2.18. In the derivation of Equations (2.69) and (2.70) it was assumed that
the outer region is a perfectly mixed slab layer; this assumption has its limitations. In fact,
