Remote Sensing of Boundary Layer Structure and Height - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 178

200 9 10 -9 m -1 sr -1 in the lower layer and 250 9 10 -9 m -1 sr -1 in the upper
layer. Additionally the vertical gradient value qB/qz max of a lifted inversion must
be more negative than -0.30 9 10 -9

m -2 sr -1

in the lower layer and more

negative than -0.60 9 10 -9 m -2 sr -1

in the upper layer.

B.2.3 Idealised Backscatter Method

A parallel development by Eresmaa et al. (2006) using an idealised backscatter
profile, originally described by Steyn et al. ( 1999 ), is also an extension of the
gradient method. MLH is not determined from the observed backscatter profile,
but from an idealised backscatter profile fitted to the observed profile. The
robustness of this technique is founded on utilising the whole backscatter profile
rather than just the portion surrounding the top of the mixed layer. In this method
an idealized backscattering profile B i (z) is fitted to measured profile by the
formula:

B i ð z Þ¼ B m þ B u
2

B m B u
2

z h
Dh

erf ð B : 4 Þ

where B m is the mean mixed layer backscatter, B u is the mean backscatter in air
above the mixed layer and Dh is related to the thickness of the entrainment layer
capping the ABL in convective conditions.

B.2.4 Wavelet Method

A wavelet method has been developed for the automatic determination of mixed
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 Janji´ 2005 ). The most important
advantage of wavelet methods is the decomposition of the signal in both altitude as
well as vertical spatial scale of the structures in the backscatter signal.
The wavelet algorithm in de Haij et al. ( 2006 ) is applied to the 10 min averaged
range and overlap corrected backscatter profile B(z) within a vertical domain of
90-3,000 m. For each averaged profile the top of two significant aerosol layers are
detected in order to detect MLH as well as the top of a secondary aerosol layer,
like e.g., an advected aerosol layer or the residual layer. This wavelet MLH
method uses the scale averaged power spectrum profile W B (z) of the wavelet
transform with 24 dilations between 15 and 360 m and step size 15 m. The top of
the first layer, H4_1, is detected at the first range gate at which the scale averaged
power spectrum W B (z) shows a local maximum, exceeding a threshold value of
0.1. This threshold value is empirically chosen, based on the analysis of several