Geoscience Reference
In-Depth Information
Fig. 3.8 Comparison of logarithmic wind profiles from (
3.16
)(thin line, parameters are given in
the first line of the insert) and smooth boundary layer wind profiles from Eq. (
3.65
)(dotted line,
parameters are given in the second and third line of the insert) with measured monthly mean data
(bold line). Left daytime profiles, right night-time profiles, both from SODAR data for August
2002 in Hannover (Germany). (From Emeis et al.
2007b
)
linearly with height in the surface layer, the logarithmic relations (
3.6
) and (
3.16
)
cannot be extended into the Ekman layer. Therefore, two approaches have been
tested to overcome this problem. The first idea is to fit the Prandtl and Ekman profiles
together in such a way that there is a smooth transition in terms of wind speed and
wind shear between both regimes. The second idea is to modify the mixing length in
order to extrapolate the Prandtl layer wind profile into higher layers.
Etling (
2002
) had proposed the first idea by presenting a wind profile
description with a linearly increasing exchange coeffiicient K
M
below the Prandtl
layer height, z
p
and a constant K
M
above this height:
8
<
:
u
=
j ln
ð
z
=
z
0
Þ
for z\z
p
u
g
ð
sin a
0
þ
cos a
0
Þ
for z
¼
z
p
u
g
1
2
2
p
e
c
ð
z
z
p
Þ
u
ð
z
Þ¼
ð
3
:
55
Þ
sin a
0
cos
ð
c
ð
z
z
p
Þþ
p
=
4
a
0
Þ
for z [ z
p
þ
2e
2c
ð
z
z
p
Þ
sin
2
a
0
1
=
2
The vertical wind profile given by Eq. (
3.55
) depends on five parameters: the
surface roughness z
0
, the geostrophic wind speed u
g
, the height of the Prandtl layer
z
p
, the friction velocity u
*
, and the angle between the surface wind and the geo-
strophic wind a
0
. The two variables z
0
and u
g
are external parameters, the other
three of them are internal parameters of the boundary layer. If a fixed value is
chosen for z
p
then two further equations are needed to determine u
*
and a
0
.
Equation (
3.55
) describes a smooth transition of wind speed from the Prandtl layer
to the Ekman layer (see Fig.
3.8
).
Deviating from the original approach of Etling (
2002
) the unified vertical wind
profile should be generated from the more realistic physical requirement that both
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