Geoscience Reference
In-Depth Information
The second derivative of
B
(
z
) in the height
z
is
z
=
z
+
h
/
2
−
z
−
h
/
2
2
B
∂
∂
∂
B
∂
B
/
h
,
(4.9)
z
2
∂
z
∂
z
There is a gradient minimum
H
4
_n
in the height
z
if the second derivative of
B
(
z
)
one range gate below
z
is not positive, if the second derivative of
B
(
z
) in the height
z
is positive, and if the false hit conditions mentioned above are fulfilled:
z
2
z
−
1
≤
z
2
z
>
0and
B
z
z
≤
2
B
2
B
z
,if
∂
0and
∂
−
h
2
B
min
and
∂
B
∂
∂
B
∂
H
4
=
≥
∂
∂
z
z
max
for n
=
1,
...
5.
(4.10)
The MLH from optical remote sensing is taken as the lowest height
H
4
_n
:
MLH
op
=
H
4_1,
(4.11)
Idealized Backscatter Method
A parallel development by Eresmaa et al. (
2006
) using an idealized backscatter
profile, originally described by Steyn et al. (
1999
), is also an extension of the gra-
dient method. MLH is not determined from the observed backscatter profile, but
from an idealized backscatter profile fitted to the observed profile. The robustness
of this technique is founded on utilizing the whole backscatter profile rather than
just the portion surrounding the top of the mixing layer. In this method an idealized
backscattering profile
B
i
(
z
) is fitted to measured profile by the formula
erf
z
,
B
m
+
B
u
B
m
−
B
u
−
h
B
i
(
z
)
=
−
(4.12)
2
2
h
where
B
m
is the mean mixing layer backscatter,
B
u
is the mean backscatter in air
above the mixing layer, and
h
is related to the thickness of the entrainment layer
capping the ABL in convective conditions. Two new parameters
A
1 and
A
2are
defined so that
A
1
2. The value of
A
1is
kept constant during the fitting procedure. A good estimation of
A
1 based on an
initial order-of-magnitude guess for the MLH is crucial for the quality of the result.
=
(
B
m
+
B
u
)
/
2 and
A
2
=
(
B
m
−
B
u
)
/
Wavelet Method
A wavelet method has been developed for the automatic determination of mixing
layer height from backscatter profiles of an LD-40 ceilometer by de Haij et al.
(
2006
). Before that wavelet transforms have been applied in recent studies for
MLH determination from LIDAR observations (e.g. Cohn and Angevine,
2000
;
Davis et al.
2000
; Brooks,
2003
; Wulfmeyer and Janjic
2005
). The most important
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