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a subjective analysis of MLH. The left-hand frame in Fig.
4.3
shows that the thresh-
old value cannot be kept constant during the diurnal evolution of the boundary layer
in order to get a result, which is comparable to the one from the gradient method
applied in Fig.
4.3
.
Gradient or Derivative Methods
Hayden et al. (
1997
) and Flamant et al. (
1997
) proposed to use the largest negative
peak of the first derivative of the optical attenuated backscatter intensity (
B
(
z
)) for
the detection of
H
4 from LIDAR data (height of gradient minimum H4
GM
),
min
∂
,
B
(
z
)
∂
H
4
GM
=
(4.5)
z
The right-hand frame of Fig.
4.3
demonstrates that this is a very meaningful
assumption. Likewise, Wulfmeyer (
1999
) used the first minimum of the slope to
detect the top of a convective boundary layer from DIAL data. Münkel and Räsänen
(
2004
), Münkel (
2007
), and Schäfer et al. (
2004
,
2005
) applied the gradient method
to ceilometer data. Menut et al. (
1999
) took the minimum of the second derivative
of
B
(
z
) as the indication for MLH,
min
∂
,
2
B
(
z
)
∂
H
4
IPM
=
(4.6)
z
2
This method is called inflection point method (IPM). It usually gives slightly
lower values for
H
4 than the gradient method (
4.5
). A further approach was sug-
gested by Senff et al. (
1996
). They looked for the largest negative gradient in the
logarithm of the backscatter intensity (height of logarithmic gradient minimum
H
4
LGM
),
min
∂
,
ln
B
(
z
)
∂
H
4
LGM
=
(4.7)
z
This approach usually gives the largest value for
H
4. According to Sicard et al.
(
2006
)
H
4
IPM
from (
4.6
) is closest to the MLH derived from radiosonde ascents
via the Richardson method. The other two algorithms (
4.5
) and (
4.7
) give slightly
higher values. The vertical profiles shown in Fig.
4.4
(taken from Emeis et al.
2008
)
give a comparison of the determination of mixing layer heights from eqs. (
4.5
)to
(
4.7
).
In Emeis et al. (
2007b
) the gradient method (
4.5
) has been further refined and
extended to enable the calculation of up to
n
5 lifted inversions. This algorithm,
which has also been used for the MLH analysis shown in Fig.
4.3
, is described
in the following. Prior to the determination of gradient minima, the overlap and
range corrected attenuated backscatter profiles have to be averaged over time and
height to suppress noise-generated artefacts. Therefore, the
H
4 values are deter-
mined in a two-step procedure. Between 140 m and 500 m, height sliding averaging
=
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