Tellus (2009), 61B, 165–179
C
2008 The Authors
Journal compilation
C
2008 Blackwell Munksgaard
Printed in Singapore. All rights reserved
TELLUS
Depolarization ratio profiling at several wavelengths
in pure Saharan dust during SAMUM 2006
By VOLKER FREUDENTHALER
1∗
,MICHAEL ESSELBORN
2
, MATTHIAS WIEGNER
1
,
BIRGIT HEESE
3
,MATTHIAS TESCHE
3
,ALBERT ANSMANN
3
,DETLEF M
¨
ULLER
3
,
DIETRICH ALTHAUSEN
3
,MARTIN WIRTH
2
,ANDREAS FIX
2
,GERHARD EHRET
2
,
PETER KNIPPERTZ
4
,CARLOS TOLEDANO
1
,JOSEF GASTEIGER
1
,
MARKUS GARHAMMER
1
andMEINHARD SEEFELDNER
1
,
1
Meteorological Institute,
Ludwig-Maximilians-Universit
¨
at, Theresienstr. 37, 80333 Munich, Germany;
2
Institute of Atmospheric Physics,
German Aerospace Center (DLR), Oberpfaffenhofen, 82234 Wessling, Germany;
3
Leibniz Institute for Tropospheric
Research, Permoserstr. 15, 04318 Leipzig, Germany;
4
Institute for Atmospheric Physics, Johannes Gutenberg
University, Becherweg 21, 55099 Mainz, Germany
(Manuscript received 2 January 2008; in final form 18 August 2008)
ABSTRACT
Vertical profiles of the linear particle depolarization ratio of pure dust clouds were measured during the Saharan Mineral
Dust Experiment (SAMUM) at Ouarzazate, Morocco (30.9
◦
N, –6.9
◦
E), close to source regions in May–June 2006,
with four lidar systems at four wavelengths (355, 532, 710 and 1064 nm). The intercomparison of the lidar systems is
accompanied by a discussion of the different calibration methods, including a new, advanced method, and a detailed
error analysis. Over the whole SAMUM periode pure dust layers show a mean linear particle depolarization ratio at
532 nm of 0.31, in the range between 0.27 and 0.35, with a mean Ångstr
¨
om exponent (AE, 440–870 nm) of 0.18 (range
0.04–0.34) and still high mean linear particle depolarization ratio between 0.21 and 0.25 during periods with aerosol
optical thickness less than 0.1, with a mean AE of 0.76 (range 0.65–1.00), which represents a negative correlation of
the linear particle depolarization ratio with the AE. A slight decrease of the linear particle depolarization ratio with
wavelength was found between 532 and 1064 nm from 0.31 ± 0.03 to 0.27 ± 0.04.
1. Introduction
Shape, size distribution and composition of aerosol particles
influence their scattering characteristics and thus the radiative
impact. The polarization lidar technique (Schotland et al., 1971;
Sassen, 1991; Sassen, 2005) is a well-established method to
distinguish ice clouds from water clouds and to identify layers
with ice crystals in mixed–phase clouds (e.g. Ansmann et al.,
2005, 2007). Freudenthaler et al. (1996) applied a scanning po-
larization lidar to study the evolution of contrails. The technique
has been used to identify the type of polar stratospheric clouds
(Reichardt et al., 2000; Toon et al., 2000; Sassen, 2005) and
volcanic ash in the troposphere and stratosphere (Hayashida
et al., 1984; Winker and Osborn, 1992; Sassen et al., 2007).
The polarization lidar is also well suited for aerosol profiling
(McNeil and Carswell, 1975; Murayama et al., 1996; Gobbi,
∗
Corresponding author.
e-mail: volker.freudenthaler@meteo.physik.uni-muenchen.de
DOI: 10.1111/j.1600-0889.2008.00396.x
1998; Cairo et al., 1999; Sassen et al., 2007) and allows us
to unambiguously discriminate desert dust from other aerosols
(Gobbi et al., 2000; di Sarra et al., 2001; Sakai et al., 2002; M
¨
uller
et al., 2003; Iwasaka et al., 2003; Murayama et al., 2004). Based
on model calculations, it has been demonstrated that the spectral
dependence of the dust linear depolarization ratio is sensitive to
the size distribution of the nonspherical scatterers (Mishchenko
and Sassen, 1998). Thus, observations of the linear depolar-
ization ratio at several wavelengths may be used in retrieval
schemes (Dubovik et al., 2006) to improve the estimation of
the microphysical properties of dust from optical measurements
(D. M
¨
uller, personal communication, 2008; Wiegner et al.,
2008). First dual-wavelength aerosol polarization lidar measure-
ments were presented by Sugimoto et al. (2002).
The linear depolarization ratio δ is defined as the ratio of
the cross–polarized lidar return signal to the parallel-polarized
backscatter signal. The planes of polarization of the employed
two detectors are parallel and orthogonal to the plane of polar-
ization of the transmitted linearly polarized laser. The method is
discussed in detail in Section 2. Although the polarization lidar
Tellus 61B (2009), 1 165
PUBLISHED BY THE INTERNATIONAL METEOROLOGICAL INSTITUTE IN STOCKHOLM
SERIES B
CHEMICAL
AND PHYSICAL
METEOROLOGY
166 V. FREUDENTHALER ET AL.
technique appears to be rather simple, and thus robust and reli-
able, several sources for systematic errors can have a significant
impact on the result and can introduce large errors. These error
sources are discussed in Section 3. On the other hand, rather ac-
curate values of the depolarization ratio of desert dust (including
the spectral slope of the ratio) are required for further use in the
above mentioned retrieval schemes. An extensive error analysis
is thus as important as the measurement itself. Several papers
(Biele et al., 2000; Reichardt et al., 2003; Alvarez et al., 2006)
show how highly accurate depolarization observations can be
realized. In this paper, a further technique is discussed, which
improves the calibration of the depolarization channels.
We begin with the presentation of the polarization lidar tech-
nique (methodology, lidar setup) in Sections 2 and 3. In Section
4, the observations are discussed. For the first time, dust depo-
larization ratios at four wavelengths were measured. The unique
field site was close to the source of the dust particles so that
the depolarization properties of pure dust could be investigated.
Section 5 summarizes the main findings, and the error analysis
is treated in the Appendix.
2. Polarization lidar method
Measurements of the linear depolarization ratio δ with lidars are
often performed with the aim to just discern between the dry,
the liquid and the ice phase of aerosols and clouds in the profiles
of one lidar system, which requires only a relative measure of
δ with a low accuracy of the absolute values. During Saharan
Mineral Dust Experiment (SAMUM), it was attempted to mea-
sure a possible wavelength dependence of the dust particle linear
depolarization ratio δ
p
, with four different lidar systems at four
wavelengths as inputs for model calculations of δ
p
regarding the
particles shapes and size distribution. Thus, the uncertainty of
the absolute values must be known and should be small com-
pared with the expected natural variance. The total backscattered
power P(r) with their dependence on the distance r from the lidar
is described by the lidar equation
P =
ηβ (r)τ
2
(r)
r
2
, (1)
where η is the system constant, β the backscatter coefficient,
and the factor τ
2
accounts for the atmospheric transmittance
on the way from the lidar to the scattering volume, and back.
For the determination of δ the lidars used in this study measure
the atmospheric backscatter signals in two receiver channels,
parallel- and cross-polarized with respect to the plane of the
linear polarized output of the laser beam. The two polarization
components are separated in the receiver by means of polarizing
beamsplitter cubes (PBC). But this separation is not perfect. Fur-
thermore the polarizing beamsplitter might be misaligned with
respect to the plane of polarization of the emitted laser beam,
and additionally, a rotation of the polarization plane is used for
the relative calibration of the two receiver channels. Therefore,
Fig. 1. Signal power components in a receiver of a depolarization lidar
with a polarizing beamsplitter cube with reflectivities R
p
and R
s
and
transmittances T
p
and T
s
for linearly polarized light parallel (p) and
perpendicular (s) to the incident plane of the polarizing beamsplitter.
P
R
and P
T
are the measured quantities in the reflected and transmitted
path, respectively, and V
R
and V
T
are the corresponding amplification
factors including the optical transmittances.
we show the necessary equations of the angle ϕ between the
plane of polarization of the laser and the incident plane of the
polarizing beamsplitter cube, according to Fig. 1.
The backscatter powers before the PBC are (skipping the
range dependence in the following for convenience)
P
⊥
=
η
⊥
β
p
⊥
+ β
m
⊥
τ
2
r
2
,
P
=
η
β
p
+ β
m
τ
2
r
2
,
(2)
with the system constants η
||
and η
⊥
including here only the laser
power and the telescope aperture, assuming negligible diattenu-
ation of the optics before the PBC, for example, a telescope or
dichroic beamsplitters. The backscatter coefficient β is split up
in the parallel- (β
) and cross-polarized (β
⊥
) components of the
backscatter from particles (β
p
) and from molecules (β
m
). The
total backscatter power P and the total backscatter coefficient β
are the sum of both polarized components:
P = P
+ P
⊥
. (3)
The ratio of the total backscatter coefficient to the molecular
component is called the backscatter ratio R
R =
β
m
+ β
p
β
m
, (4)
and the ratio of the total cross- to the total parallel-polarized
backscatter coefficient is called the linear volume depolarization
ratio δ
v
:
δ
v
=
β
⊥
β
=
P
⊥
P
. (5)
Tellus 61B (2009), 1
DEPOLARIZATION RATIO PROFILING IN PURE SAHARAN DUST 167
The power components with respect to the incident plane of
the PBC are
P
s
(ϕ) = P
sin
2
(ϕ) + P
⊥
cos
2
(ϕ),
P
p
(ϕ) = P
cos
2
(ϕ) + P
⊥
sin
2
(ϕ).
(6)
The subscripts p and s denote the planes parallel and perpen-
dicular to the incident plane of the PBC (see Fig. 1), respectively,
and ϕ is the angle between the plane of polarization of the laser
and the incident plane of the PBC. Depending on this angle, the
cross polarized signal P
⊥
can be measured in the reflected (for
ϕ = 0
◦
) or in the transmitted path (ϕ = 90
◦
). Hence, we denote
the power measured in the reflected and transmitted paths with
the subscripts R and T, respectively. Behind the PBC the total
reflected (P
R
) and transmitted (P
T
) power components are
P
R
(ϕ) = [P
p
(ϕ)R
p
+ P
s
(ϕ)R
s
]V
R
,
P
T
(ϕ) = [P
p
(ϕ)T
p
+ P
s
(ϕ)T
s
]V
T
.
(7)
The amplification factors V
R
and V
T
include the optical trans-
mittances of the receiver and the electronic amplification in each
channel. P
R
and P
T
are the quantities we actually record with the
data acquisition. For the following it is convenient to introduce a
relative amplification factor V
∗
and the measured signal ratio δ
∗
δ
∗
(ϕ) =
P
R
(ϕ)
P
T
(ϕ)
,V
∗
=
V
R
V
T
. (8)
With eqs. (6)–(8), we achieve
δ
∗
(ϕ) = V
∗
[1 + δ
v
tan
2
(ϕ)]R
p
+ [tan
2
(ϕ) + δ
v
]R
s
[1 + δ
v
tan
2
(ϕ)]T
p
+ [tan
2
(ϕ) + δ
v
]T
s
. (9)
2.1. Calibration
To retrieve the total backscatter power P and δ
v
from the mea-
surements P
R
and P
T
with eqs. (3)–(7), we need V
∗
, which we
can get from calibration measurements in different ways and
using eq. (9) in the following form
V
∗
=
[1 + δ
v
tan
2
(ϕ)]T
p
+ [tan
2
(ϕ) + δ
v
]T
s
[1 + δ
v
tan
2
(ϕ)]R
p
+ [tan
2
(ϕ) + δ
v
]R
s
δ
∗
(ϕ). (10)
For ϕ = 0
◦
, it follows from eq. (10)
V
∗
=
T
p
+ δ
v
T
s
R
p
+ δ
v
R
s
δ
∗
(
0
◦
)
. (11)
With known δ
v
in some range of the lidar signal, we can
determine V
∗
already from a regular measurement with eq.
(11), which we call the ‘0
◦
-calibration’. The linear depolar-
ization ratio δ
m
of air molecules is well known (Behrendt and
Nakamura, 2002), and thus, we could use an aerosol-free li-
dar range in the free troposphere were δ
v
= δ
m
. But already
a very low amount of strong depolarizing aerosols, like dust
or ice crystals in the assumed clean range, causes large er-
rors of δ
v
and thus of V
∗
. Furthermore, several instrumental
Fig. 2. Relative errors of V
∗
over the calibration angle error γ (see
text) calculated using eqs. (9), (10), (12) and (13), with T
p
=0.95, R
p
=
0.05, R
s
= 0.99 and T
s
= 0.01 for δ
v
= 0.0036 (clean air) and δ
v
=
0.30 (desert dust). The ±45
◦
-calibration errors are multiplied by a
factor of 100.
uncertainties can add large errors, especially with this cali-
bration method as described in the Appendix. More reliable
calibration methods use the fact that tan
2
(±45
◦
) = 1, which
makes P
p
= P
s
in eq. (6), and from eq. (9) we get for
ϕ =+45
◦
or ϕ = –45
◦
,
V
∗
=
T
p
+ T
s
R
p
+ R
s
δ
∗
(
±45
◦
)
, (12)
which is independent of δ
v
. We call this method the ‘45
◦
-
calibration’. However, it is difficult to measure the exact angle
of the plane of polarization of a laser beam and the alignment
relative to the polarizing beamsplitter cube. An error γ from
ϕ =±45
◦
, of the order of 1
◦
, has to be assumed causing a large
error in V
∗
depending on δ
v
(see Fig. 2). But if we calculate V
∗
from two subsequent measurements at exactly 90
◦
difference,
that is, ϕ =+45
◦
+ γ and ϕ = –45
◦
+ γ :
V
∗
=
T
p
+ T
s
R
p
+ R
s
δ
∗
(
+45
◦
)
× δ
∗
(
−45
◦
)
, (13)
it can be shown that the errors compensate each other very well
over a large range of γ (see Fig. 2). We call this method the
‘±45
◦
-calibration’. The exact 90
◦
difference can be achieved
with high accuracy by means of, for example, mechanical limit
stops (portable lidar system, POLIS; Deutsches Zentrum f
¨
ur
Luft- und Raumfahrt, High Spectral Resolution Lidar, DLR-
HSRL) or a motorized rotation mount (multichannel lidar sys-
tem, MULIS).
The 45
◦
-calibration is based on the fact that P
p
= P
s
are made
equal, which can also be achieved by using a polarizing sheet
filter in front of the PBC at ϕ =+45
◦
or −45
◦
(see Fig. 3). If
the polarizing filter has a negligible small transmission in the
cross-polarized plane (k2 < 10
−4
), eqs. (12) and (13) are still
valid, and the calibration errors are similar to those in Fig. 2.
Tellus 61B (2009), 1
168 V. FREUDENTHALER ET AL.
Fig. 3. Signal power components in a receiver of a depolarization lidar
with an additional linear analyser (polarizing sheet filter) with
transmittances parallel (k1) and perpendicular (k2) to the incident
linear polarized light. The other components are as described in Fig. 1.
MULIS and POLIS used the advanced two-angle ±45
◦
-
calibration method with different techniques for the rotation
of the polarization, and the DLR-HSRL used the one angle
45
◦
-calibration method. For Backscatter Extinction lidar–Ratio
Temperature Humidity profiling Apparatus (BERTHA), the 45
◦
-
calibration with a polarizing sheet filter was applied.
2.2. Retrieval of the linear volume depolarization
ratio δ
v
Once V
∗
is known, we get δ
v
with eqs. (5) and (6), for a regular
measurements at ϕ = 0
◦
:
δ
v
=
P
⊥
P
=
P
s
P
p
,ϕ= 0
◦
. (14)
As for commercial PBCs, R
s
is usually much closer to 1 than
T
p
, the noise and error caused by the cross-talk from the strong
parallel-polarized signal to the weaker cross-polarized signal are
reduced if the parallel polarized signal is detected in the reflected
s-branch of the PBC. For this setup ϕ = 90
◦
, and we get
δ
v
=
P
⊥
P
=
P
p
P
s
,ϕ= 90
◦
. (15)
From eqs. (5)–(8) follows
P
s
P
p
=
δ
∗
V
∗
T
p
− R
p
R
s
−
δ
∗
V
∗
T
s
(16)
and
P = P
p
+ P
s
=
V
∗
R
s
− R
p
P
T
+
T
p
− T
s
P
R
V
R
T
p
R
s
− R
p
T
s
. (17)
The knowledge of V
R
is not necessary, as we only need a
relative signal for the lidar signal inversion with the Fernald/Klett
retrieval (Klett, 1985; Fernald, 1984), and thus we can set it to
V
R
= 1. In case the parameters of the polarizing beamsplitter
cube are
T
s
= 1 − R
s
,R
p
= 1 − T
p
, (18)
which can be assumed for commercial PBCs, the total signal P
is retrieved from
P = P
p
+ P
s
= V
∗
P
T
+ P
R
. (19)
2.3. Retrieval of the linear particle depolarization
ratio δ
p
The δ
p
can be calculated from eqs. (2)–(5) using
δ
p
=
β
p
⊥
β
p
=
(
1 + δ
m
)
δ
v
R − (1 + δ
v
)δ
m
(1 + δ
m
)R − (1 + δ
v
)
(20)
(Biele et al., 2000), with the height in dependent linear depolar-
ization ratio of air molecules:
δ
m
=
β
m
⊥
β
m
, (21)
which can be determined with high accuracy (Behrendt and
Nakamura, 2002). The backscatter ratio R can be retrieved from
the total signal P using, for example, the Fernald/Klett inversion
with a reference value β
p
(r
0
) at a reference range r
0
and known
range-dependent lidar ratios S
S =
β
P
α
p
, (22)
where α
p
is the particle extinction coefficient. S(r) must
be retrieved by an additional measurement, for example,
with a Raman channel (Tesche et al., 2008) or a HSRL
(Esselborn et al., 2008). The values of δ
v
and R are subject to
systematic and statistical (noise) errors. A detailed error propa-
gation analysis can be found in the Appendix.
3. Polarization lidar in SAMUM
The linear depolarization ratio of the dust particles was mea-
sured during SAMUM with four lidar systems at four wave-
lengths:MULIS at 532 nm;POLIS at 355 nm (both from
Munich);BERTHA at 710 nm (Leipzig) and the airborne DLR
HSRL at 532 and 1064 nm. MULIS and BERTHA were located
at the airport of Quarzazate (1133 m a.s.l., 30.938
◦
N, –6.907
◦
E)
about 10 m apart from each other and POLIS at about 100 m
distance. All three ground based systems can change the zenith
angle of the sounding (scanning capability), which possibility
was used frequently. We assume that the profiles of the different
lidar systems are well comparable as orographical effects of the
surrounding are negligible and the dust layer was mostly suf-
ficiently homogeneous over the considered periods. The DLR-
HSRL was installed on board the DLR Falcon airplane, which
flew several times over the ground based lidars, with high spa-
tial accuracy. For the temporal averaging of these measurements,
care was taken to consider only sections of the time-series with
comparably small changes in the lidar profiles. Owing to a lack of
adequate reference sources, MULIS and POLIS are described in
Tellus 61B (2009), 1
DEPOLARIZATION RATIO PROFILING IN PURE SAHARAN DUST 169
Table 1. System parameters of the depolarization channels of the lidar systems
POLIS MULIS BERTHA DLR-HSRL
Laser/Receiver Biaxial Biaxial Coaxial Coaxial
Laser Brilliant Ultra Continuum, Surelite II Ti:Saphire, Solar TII Ltd. CF 125 Nd:YAG
Wavelengths (nm) 355 532 710 1064, 532
Pulse energy (mJ) 7.8 50 20 220, 100
Repetition rate (Hz) 20 10 30 100
Beam divergence (mrad) 0.69 0.6 <0.3 0.5
Telescope Dall-Kirkham Cassegrain Cassegrain Cassegrain
Diameter (m) 0.2 0.3 0.53 0.35
Focal length (m) 1.2 0.96 3 5
Field stop (mrad) 2.5 0 to 3, adjustable 0.6 1
Receiver optics
Interference filter bandwidth (nm) 1.0, fwhm 1.1, fwhm 0.4, fwhm 1.0, fwhm
PBC T
p
0.9521 0.9831 0.95 1
PBC R
s
0.9985 0.9965 0.999 1
Depol.-calibration method ±45
◦
manual ±45
◦
wave plate 45
◦
polarizer 45
◦
manual
more detail in the following. For the DLR-HSRL and BERTHA,
the details regarding the depolarization measurements comple-
ment the descriptions in the references mentioned below. Table 1
gives a summary of the relevant lidar system parameters.
3.1. MULIS
MULIS is a mobile, five wavelength lidar system with backscat-
ter channels at 355, 532 and 1064 nm and Raman channels at
387 and 607 nm. The Nd:YAG laser fundamental wavelength is
frequency doubled and tripled by means of Potassium Dideu-
terium Phosphate (KD
∗
P) crystals, and the output at 532 nm is
assumed to be perfectly linear polarized. The adjustable filed
stop (TS in Fig. 4) is used to decrease the field of view and with
that, the signal power in the near range during the calibration
measurements, because at ϕ =±45
◦
(Fig. 1), the signal in the
cross-polarized channel can increase by an order of magnitude.
Such a high signal exceeds the linear range of the data acquisi-
tion, especially that of the preamplifier, which would introduce
signal distortions and errors in V
∗
, which are very difficult to
assess. To minimize diattenuation and polarization effects of the
dichroic beamsplitters, all optical coatings are custom-designed
(Laseroptik, Germany). For the same reason, the beamsplitters
BS1toBS4areusedat30
◦
reflection angle (see Fig. 4). To re-
duce cross-talk, the custom-made PBC (Optarius, UK) has high
transmittance T
p
and high reflection R
s
,andP
is detected in the
reflected branch P
R
of the PBC (see eq. 15). A cemented, true
zero-order half-wave plate at 532 nm (Casix, China) is used in
front of the PBC to rotate the plane of polarization with a verified
accuracy and repeatability of better than 0.1
◦
. The accuracy of
the ϕ = 0
◦
position is better than ±0.2
◦
,anda±45
◦
-calibration
was performed every time the lidar setup had been changed. The
detectors are Hamamatsu R7400 PMTs in the depolarization
Fig. 4. Optical setup of the MULIS receiver with analog backscatter
channels at 355 nm, 532 nm parallel- and cross- polarized, 1064 nm
and Raman channels at 387 and 607 nm. TS, tilted slit diaphragm; L1,
collimating lens; BS#, dichroic beamsplitters (BS3, 6 and 7 are used as
mirrors); IFF#, interference filter; PBC, polarizing beamsplitter cube at
532 nm and HWP, half-wave plate at 532 nm for the calibration of the
depolarization channels.
channels. The sensitivity of individual channels was adjusted
with absorbing neutral density filters (Schott). The preampli-
fier stages of the 12 bit (P
R
, P
) and 14 bit (P
T
) ADC-boards
(Spectrum GmbH, Germany) were optimized regarding signal
Tellus 61B (2009), 1