Boundary-layer height detection with a ceilometer at a coastal ... - Orbit

90/(10 8 m srad), respectively). For very low aerosol concentrations these values may still
prove too high, and β crit is set to 40/(10 8 m srad).
The values of β crit and β m are somewhat arbitrary, and may be chosen differently. Here
the values are chosen after exploring the sensitivity of the method in a variety of aerosol
backscatter profiles.
4.3 Fitting an idealized aerosol backscatter profile
Under ideal cloudless conditions, when the ABL is well mixed, the observed backscatter profile
will show a shape that resembles an error function. Steyn et al. (1999) developed a method
that exploits this resemblance.
The method involves minimizing the differences between an idealized backscatter profile
B(z) and the observed backscatter profile β(z). The idealized backscatter, B, at height z is
given as
1400
β profile 14/06/2010 10:40
1200
1000
Height [m]
800
600
400
200
0
−100 0 100 200 300
Backscatter [1/(10 8 *srad*m)]
Figure 11: The vertical backscatter profile and the idealized profile. The profile parameters
are: B m =218, B u =16 and s=79. Dashed line indicates the BLH estimate, z m = 553 m. Data
from the ceilometer on June 14 2010.
B(z) = B m + B u
2
− B (
m − B u z − zm
erf
2
s
where B m is the mean backscatter in the mixed layer, B u is the mean backscatter above
the mixed layer, z m the mixed layer height and s is a normalization constant related to the
entrainment zone thickness (EZT). The EZT is defined here to be the area where backscatter
values drop from 0.95B m to 0.05B m . The profile parameters are determined by a nonlinear
curve fitting procedure, minimizing the least squares between β(z) and B(z).
min
B m,B u,z m,s
∑
i
)
(
)
B(B m , B u , z m , s, z i ) − β(z i )
(24)
(25)
24 DTU Wind Energy Master Thesis M-0039