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evaluation of wind measurements from high masts. Wieringa (
1989
) has given a
more general overview on this phenomenon. The term ''cross-over'' comes from
plots displaying mean daytime and mean night-time vertical wind profiles. These
two profiles cross each other at the cross-over height. Below this height, the mean
daytime wind speed is larger than the mean nocturnal wind speed while above this
height the opposite is true. This leads to the phenomenon that at cross-over height
the diurnal variation of wind speed is at a minimum. Emeis (
2004
) and Emeis et al.
(
2007b
) have demonstrated this effect from ground-based acoustic soundings with
a SODAR. E.g., Emeis (
2004
) shows the diurnal wind variation at different heights
for a rural area (Fig.
3.10
). Emeis et al. (
2007b
) find a cross-over height of a bit
more than 100 m for spring in Hannover (Germany) (Fig.
3.11
). Lokoshchenko
and Yavlyaeva (
2008
) find a cross-over height from sodar data of 60-80 m for
spring and summer in Moscow.
Daytime wind speeds in both layers below and above the cross-over height are
more or less equal due to the intense vertical mixing in the daytime convective
boundary layer. At night-time the strong stabilisation of the boundary layer due to
the radiative cooling of the ground leads to a decoupling of the winds above and
below the cross-over height. Winds below this height no longer feel the driving
winds from higher layers while winds above this height speed up due to the
missing frictional force from below. This nocturnal speed-up above the cross-over
height leads to the formation of low-level jets.
3.4.1 Vertical Profiles of the Weibull Parameters
The cross-over height, which has been introduced in the preceding section, is
related to the vertical profile of the shape parameter k of Weibull distributions of
the 10 min wind speeds as well (see Appendix A and Wieringa
1989
), as this
parameter is inversely related to the temporal variance of wind speed (see Eq.
(A.28)). Thus, the vertical profile of the shape parameter must have a maximum at
the cross-over height because the diurnal variation of the wind speed is at a
minimum here. Evaluations in Emeis (
2001
) clearly show such maxima in the
shape parameter profiles at heights between 60 and 80 m.
Independent from the wind profile laws which have been introduced in
Sect. 3.1
above and which easily apply to the scale parameter A of the Weibull distribution
as well, several empirical formulas for the vertical variation of the shape parameter
k have been suggested from earlier studies. Justus et al. (
1978
) fitted profile
functions from tower data up to 100 m a.g.l. by:
z
a
z
ref
1
c ln
k
ð
z
Þ¼
k
A
ð
3
:
90
Þ
z
z
ref
1
c ln
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