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Fig. 2.4 Comparison of different wind profile descriptions with measured sodar data for daytime
unstable conditions ( left ) and night-time stable stratification ( right ). The thin full lines give the
logarithmic profile with stability correction (upper eq. in (2.27)), the bold full line theprofilefrom
the lower eq. in (2.27). The dashed profile is computed from eq. ( 2.33 )andthe dash-dotted profile
from eq. ( 2.32 )
m from eq. ( 2.26 ). For
details the reader is referred to Gryning et al. ( 2007 ) and Peña et al. ( 2009 ). A com-
parison of wind profiles from eqs. ( 2.27 ), ( 2.32 ), and ( 2.33 ) is shown in Fig. 2.4 .
Temperature is decreasing with height at least by the adiabatic lapse rate, in a
shallow super-adiabatic layer near the surface even stronger. The standard deviations
of the wind components in the Prandtl layer (below z p ) now depend on the ABL
height z i or the height z (Panofsky et al. 1977 ,Arya 1995 ):
with a complex stability correction function T ( z
/
L
) and
12
1 / 3
σ u , v
u
0.5 z i
L
=
,
(2.34)
1.3 1
1 / 3
σ w
u
3 z
L
=
.
(2.35)
For the Ekman layer above z p ,Arya( 1995 )gives
σ u , v , w =
0.6 w
,
(2.36)
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