Classification of particle effective shape ratios in cirrus
clouds based on the lidar depolarization ratio
Vincent Noel, Helene Chepfer, Guy Ledanois, Arnaud Delaval, and Pierre H. Flamant
A shape classification technique for cirrus clouds that could be applied to future spaceborne lidars is
presented. A ray-tracing code has been developed to simulate backscattered and depolarized lidar
signals from cirrus clouds made of hexagonal-based crystals with various compositions and optical depth,
taking into account multiple scattering. This code was used first to study the sensitivity of the linear
depolarization rate to cloud optical and microphysical properties, then to classify particle shapes in cirrus
clouds based on depolarization ratio measurements. As an example this technique has been applied to
lidar measurements from 15 mid-latitude cirrus cloud cases taken in Palaiseau, France. Results show
a majority of near-unity shape ratios as well as a strong correlation between shape ratios and temperature: The lowest temperatures lead to high shape ratios. The application of this technique to spaceborne measurements would allow a large-scale classification of shape ratios in cirrus clouds, leading to
better knowledge of the vertical variability of shapes, their dependence on temperature, and the formation processes of clouds. © 2002 Optical Society of America
OCIS codes: 080.2720, 010.3920, 280.3640, 010.2940, 290.5890.
1. Introduction
Cirrus clouds have a strong influence on weather and
climate1 because they consistently cover more than
30% of the Earth’s surface.2 To estimate their contribution to the energetic balance, a correct model of
cirrus radiative properties is needed. Such a model
strongly depends on the cloud’s microphysical properties, e.g., particle shape, size, and orientation.
During the past two decades several intensive field
experiments devoted to cirrus clouds have been conducted to document microphysical properties: the
First and Second International Satellite Cloud Climatology Project 共ISCCP兲 Regional Experiment
共FIRE I and FIRE II兲,3,4 the International Cloud Experiment 共ICE兲,5,6 the European Cloud Radiation Experiment 共EUCREX兲,7–9 the Central Equatorial
Pacific Experiment 共CEPEX兲,10 and the Subsonic Aircraft: Contrail and Cloud Effects Special Study
共SUCCESS兲.11 The results of these experiments
confirm the strong dependence of the radiative prop-
V. Noel 共[email protected]兲, H. Chepfer, G. Ledanois, A. Delaval, and P. H. Flamat are with the Laboratoire de
Météorologie Dynamique, Ecole Polytechnique, 91128 Pasaiseau,
France.
Received 3 August 2001; revised manuscript received 4 March
2002.
0003-6935兾02兾214245-13$15.00兾0
© 2002 Optical Society of America
erties of cirrus clouds on their microphysical characteristics. Among those parameters the shape of the
ice crystals is one of the most difficult to study because of its temporal and spatial variability. Owing
to the high altitude of such clouds, the complexity of
in situ measurements makes them casual sources of
information. To extend the coverage of shape retrieval, spaceborne observations have been developed: Baran et al.12 used dual-view along-track
scanning radiometer 共ATSR兲 observations, Baum et
al.13 or Rolland and Liou14 studied the potentiality of
the moderate-resolution imaging spectrometer 共MODIS兲, and Chepfer et al.15 used the polarization and
directionality of the Earth’s reflectance 共POLDER-1兲
polarization capability. Other methods must be investigated to complete the existing studies.
Owing to its sensitivity to optically thin clouds, the
lidar is one of the instruments most suited for retrieving cirrus properties.16 Lidars are active remotesensing devices, also referred to as laser radars.
They combine a laser that sends a laser beam vertically through the atmosphere and a telescope that
collects light backscattered by atmospheric components. By measuring the time elapsing between
emission of the beam and reception of the signal by
the telescope, the altitude of the backscattering event
can be retrieved. Lidars give information on geometric properties of clouds, such as cloud thickness
and altitude, as well as optical properties 共e.g., optical
thickness兲. They also provide a vertical distribution
20 July 2002 兾 Vol. 41, No. 21 兾 APPLIED OPTICS
4245
of several parameters, such as the backscattering coefficient ␤ 共km⫺1 sr⫺1兲 or the extinction coefficient ␣
共m⫺1兲.17 If the emitted light is linearly polarized in
a plane referred to as the parallel plane, separating
backscattered light intensity between the two polarization planes 共储 and ⬜兲 provides the depolarization
ratio ⌬P:
⌬P ⫽
I⬜
,
I储
(1)
where I⬜ is the light backscattered in the perpendicular plane and I储 is the light backscattered in the
parallel plane. The depolarization ratio is strongly
dependent on the particle shape: Spherical particles lead to ⌬P ⫽ 0, whereas irregularly shaped ice
particles can show values to as great as 0.6.18 As a
consequence the lidar depolarization ratio can be regarded as an indicator of microphysical shape19 as
well as a potential cloud-classification method.
In most lidar analyses single scattering is assumed, that is, light is being scattered only once between its emission and its reception by the telescope.
However, this is clearly not the case in atmospheric
scattering because light can be scattered several
times in the near-forward direction before it returns
to the detector; this phenomenon is called multiple
scattering. The importance of multiple scattering
has been shown in the scattering of clouds20,21 and
even more in spaceborne measurements,22,23 owing to
the large volume of the receiver cone. Several studies have tried to provide an empirical global factor
that corrects this effect.24,25 However, strong disparities remain among all the studies.26
To quantify the information that can be retrieved
from the depolarization ratio and estimate its usefulness for spaceborne measurements, a ray-tracing
code for simulating lidar measurements has been developed, taking into account multiple scattering. In
this paper we present this simulation and the resulting classification of particle shapes in clouds. A selection of atmospheric settings 共clouds composition
and geometry兲 and lidar configurations 共ground-based
and spaceborne兲 is in Section 2. The ray-tracing code
itself is presented in Section 3. Results of simulations
are presented in Section 4 along with the application to
15 lidar cases collected at the ground measurement
site at Palaiseau, France 关Site Instrumental Régional
de Télédection Atmosphérique 共SIRTA兲兴. Finally, results are analyzed in Section 5.
2. Simulation Parameters
A.
Lidar Parameters
In this simulation the lidar laser and telescope are
both located at the origin of the coordinates. The
laser has an infinitely small beamwidth, and the telescope has a field of view of ␪FOV. Both can optionally
bear the same deviation angle ␪0 from the vertical.
Real-life lidar systems are simulated by an appropriate choice of parameters 共Table 1兲: Ground-based
lidar settings are similar to the ground lidar operat4246
APPLIED OPTICS 兾 Vol. 41, No. 21 兾 20 July 2002
Table 1. Lidar Settingsa
Set
␪FOV 共mrad兲
⌬Z 共km兲
␪0 共°兲
Ground-based
Calipso
3.0
0.125
8.0
695.0
0°
0°
a
␪FOV, field of view; ⌬Z, range to cloud layers; ␪0, angle with
vertical direction.
ing at SIRTA 共Subsection 4.B兲, and the spaceborne
settings are similar to the future Cloud Aerosol Lidar
and Infrared Pathfinder Satellite Observations lidar
program27 共in the absence of a fixed value for the
incidence angle, which has been taken as ␪0 ⫽ 0°兲.
B.
Atmosphere Definition
The atmosphere is modeled with horizontal infinite
layers, each with its own geometrical parameters 共altitude and thickness兲 and microphysical parameters
共optical depth and crystal scattering properties兲. To
each layer can be assigned a free number of scatterers
that modify the photon path and determine the
amount of light scattered back to the detector. Scatterers can be either water droplets, atmospheric molecules, or ice crystals.
Because cirrus clouds are mostly made of ice crystals, we are focusing on such crystals. They can be
found in an almost infinite variety of shapes and sizes.28,29 However, since covering the full range of crystal shapes is beyond the scope of this paper and since
water crystallizes naturally in a hexagonal shape, a
model of hexagonally based shapes was chosen. Even
if it is a fairly simple approximation, several studies
show that these kinds of crystals are often found in
cirrus clouds.30 They are defined by their shape ratio
Q ⫽ l兾共2r兲, where l is the crystal length and r is its base
radius. By browsing Q values from 0.05 to 5, we can
represent ice plates and columns. Molecular scattering was approximated by adding spherical scatterers
with concentrations as defined by Valley.31
A set of physical properties, noted p, is assigned to
each scatterer:
␮p 共km⫺1兲 is the photon mean free path, depending on the considered particle concentration and
optical depth. It defines how often a photon will
interact with particle p 共Section 3兲.
• Mp共⌰兲 is the particle-scattering matrix.32 This
matrix gives the Stokes vector of any light beam scattered by the particle p in direction ⌰. Computation
of this matrix is a separate process that has already
been addressed thoroughly.33–36 For this paper a
separate specific ray-tracing code taking polarization
effects into account has been internally developed,
allowing computations of Mp for a wide range of
particle-shape ratios. This code is based on Scattering Matrix for Oriented Crystals with optimization
for the backscattering angle.37
• Cpd, CpD, and Cp␦ 共␮m2兲, particle cross sections
for each possible interaction 共angular scattering, diffraction, and ␦-function transmission, respectively,
•
Table 2. Atmosphere Definitionsa
Set
Layers
Q
␦
1
2
3
4
5
1
1
1
2
1
0.05
1.00
2.50
0.05, 1.00
0.05, 1.00
1.0
1.0
1.0
1.0
2.0
a
Q, shape factors of scatterers inside the layers; ␦, layer optical
depths.
Section 3兲. These cross sections are obtained as a
side result of the scattering matrix computation.
3. Description of the Ray-Tracing Process
The simulation begins with the emission of a single
light beam into a modeled atmosphere 共Subsection
2.B兲 with an optional deviation angle ␪0 共Subsection
2.A兲. An associated Stokes vector I0 ⫽ 关I Q U V兴
holds all the information on beam intensity and polarization.
The path and the Stokes vector of the light beam
are then modified by successive interactions with atmospheric components. The probability of interaction after a progression of length l is given by P共l 兲 ⫽
exp共⫺␮l 兲␮dl, where ␮ is the mean free path of the
current atmospheric layer 共Subsection 2.B兲. When
the light beam encounters a particle p, an interaction
is selected among angular scattering, diffraction, or
␦-function transmission, based on a random probability weighted by the relevant cross sections Cpd,
CpD, and Cp␦ 共Subsection 2.B兲. In the case of angular scattering, the Stokes vector Is of the transformed
beam is obtained through the scattering matrix Mp of
the encountered scatterer: Is ⫽ Mp共␪兲 䡠 I0, where ␪ is
the angle between the incoming and the transmitted
beams. If diffraction occurs, the transformed beam
is given by Fraunhofer formulas.38 Finally, light
beams undergoing ␦-function transmission36 are regarded as not scattered at all.
Eventually, some of the scattered light has to return to the detector. As in ray-tracing simulations
this is an unlikely event; a technique is used in which
each scattering event contributes to the recorded
light. When a light beam is scattered by a particle p
inside the detector field of view, no matter what direction it is following next, it contributes to detected
light as the Stokes vector Ir ⫽ Mp共⌰兲 䡠 I0, where ⌰ is
the angle between the incoming light beam direction
and the return path to the detector. Once this contribution is recorded, the light beam follows its own
course in a new direction.
4. Results
A.
Theoretical Analysis
Simulations were conducted for both ground-based
and space-based lidar configurations 共Table 1兲 and
atmospheric parameters as defined in Table 2.
Fig. 1. Simulated profiles for ground-based lidar: A, backscattered radiance in the parallel plane; B, backscattered radiance in normal
plane; C, depolarization ratio; D, ratio between radiances in multiple and single scattering, in the parallel plane.
20 July 2002 兾 Vol. 41, No. 21 兾 APPLIED OPTICS
4247
Table 3. Increase in Depolarization Ratio Due to Multiple Scattering
Set
Ground-Based
共%兲
Spaceborne
共%兲
Increase
共%兲
1
2
3
4
5
⫹53.8
⫹16.6
⫹14.5
⫹54.0
⫹56.5
⫹53.8
⫹13.75
⫹12.20
⫹36.66
⫹58.11
⫹0.0
⫺1.82
0.0
⫺20.0
⫹1.75
1. Ground-Based Configuration
Results of ground-based lidar simulations are summarized in Fig. 1: 共i兲 backscattered radiances
共Wm⫺2 sr⫺1兲 I储 共Fig. 1A兲 and I⬜ 共Fig. 1B兲, 共ii兲 depolarization ratios ⌬P 共Fig. 1C兲, 共iii兲 the ratio R of
multiple-scattering radiance to single-scattering radiance for a parallel plane 共Fig. 1D兲. Singlescattering results are shown by continuous curves
and multiple-scattering results by dashed curves.
Figure 1 shows an increase in the depolarization ratio
with in-cloud penetration depth, owing to increasing
multiple scattering. For atmospheric case 1 共unity
optical depth and crystals with shape factor Q ⫽ 0.05兲
the depolarization increases by 54% between the
cloud base and top, whereas the increase is only 15%
for the same cloud composed of columns 共case 3兲.
Such coefficients for all atmospheric settings are
shown in Table 3. Based on such results, it appears
that multiple scattering leads to an increase in the
depolarization ratio in most cases, depending on the
cloud optical thickness and particle-shape ratio.
Besides, the R coefficients increase strongly with
in-cloud penetration, showing that the backscattered
radiance in a single polarization state seems even
more difficult to analyze for remote-sensing applications than the depolarization ratio.
To estimate how lidar incidence angle ␪0 affects the
results, scanning lidar measurements were simulated by modifying the incidence angle value from 0°
to 45° for atmospheric set 1. Results in Fig. 2
present a very small dependence on incidence angle.
For example, in both single and multiple scattering
共Figs. 2A and 2B兲 a small decrease in backscattered
radiance can be observed. However, because this
effect is mostly due to the increase in cloud range, I⬜
and I储 are equally influenced and the depolarization
ratio is not affected 共Fig. 2C兲. However, it shows an
increase of 15% on the upper right side of the cloud
共i.e., for higher ranges, Fig. 2D兲 due to the multiplescattering effect.
2. Spaceborne Configuration
Results of spaceborne lidar simulations are shown in
Fig. 3. They are consistent with ground-based simulations 共Fig. 1兲, except that the cloud is seen from
above instead of below.
Following the same approach as ground-based sim-
Fig. 2. Simulated scanning lidar profiles: A, backscattered radiance for the parallel plane in single scattering; B, backscattered radiance
for the parallel plane in multiple scattering; C, depolarization ratio for single scattering; D, depolarization ratio for multiple scattering.
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APPLIED OPTICS 兾 Vol. 41, No. 21 兾 20 July 2002
Fig. 3. Same as Fig. 1 but for spaceborne lidar.
ulations, the increase in depolarization between the
top and the bottom of the cloud is shown in Table 3
along with a comparison with ground-based results.
It shows that the multiple-scattering effect is similar:
The very narrow field of view of the spaceborne lidar,
compared with the ground-based lidar compensates
for its greater distance to the clouds 共Table 1兲. As a
consequence the depolarization ratio holds the same
amount of information for ground-based and spaceborne lidar measurements. We will therefore use
ground-based measurements in the rest of the study,
keeping in mind that the results will be applicable to
spaceborne instruments.
3. Depolarization Ratio Study
To compare lidar measurements with theoretical values, simulations were conducted for a ground-based
lidar considering a single ice cloud of variable optical
thickness. The depolarization ratio ⌬Psim was calculated for shape factor ratios Q ranging from 0.01 to
10 and for a cloud optical thickness ␦ ranging between 0 and 3. The resulting function, ⌬Psim ⫽ f 共Q,
␦兲, is shown in Fig. 4. The global shape of this curve
is consistent with the results of Del Guasta.39
Higher depolarization ratios are associated with
higher shape ratios 共columns兲 and low depolarization
ratios with lower shape ratios 共plates兲. The increase
in optical thickness leads to a steady increase in the
depolarization ratio, which is more important for low
shape ratios.
Figure 4 shows that for a Q smaller than 0.05 and
Q between 0.7 and 1.05, Q and ⌬P can be linked by a
bijective relationship for any given value of optical
depth. On the contrary, for Q between and 0.05 and
0.7 and Q greater than 1.05, several shape ratios
can lead to the same depolarization ratio. Based
on these statements, four classes of shape ratios
were chosen: 共Q ⬍ 0.05兲, 共0.05 ⬍ Q ⬍ 0.7兲, 共0.7 ⬍
Q ⬍ 1.05兲, and 共Q ⬎ 1.05兲, noted as classes I, II, III,
and IV in Fig. 4. It appears that there is a global
increase in the depolarization ratio while the optical depth increases, although the class boundaries
stay constant.
Using Fig. 4 for a given value of cloud optical thickness, we can select a shape ratio class based on a
depolarization measurement. This technique will
be applied in Subsection 4.B to lidar measurements of
the depolarization ratio, each vertical profile being
independently processed to retrieve a value of optical
thickness.20
B.
Application to Experimental Measurements
In this section the lidar simulation presented in Section 4 is used to derive an estimate of the ice crystal
shape ratio from lidar depolarization ratio observations. The lidar data were taken by the Nd:YAG
lidar located on SIRTA. The laser source, operating
at a 0.532-␮m wavelength, is polarized in the parallel
plane. Clouds limits were detected by setting a signal threshold for each lidar profile, and the depolar20 July 2002 兾 Vol. 41, No. 21 兾 APPLIED OPTICS
4249
Fig. 4. Evolution of the depolarization ratio ⌬P as a function of the shape ratio Q and the cloud optical thickness ␦ for single and multiple
scattering.
ization ratio ⌬Pex was defined as ⌬Pex ⫽ 共I⬜兾I储兲
共Section 1兲. This ratio was normalized to the molecular depolarization ratio 关2.79% Ref. 共40兲兲兴 in a region
free of clouds and aerosols.
Fifteen experimental cases were selected between
27 April 1999 and 5 December 1999, representing
roughly 127 h of data. For each case, lidar profiles
are averaged over 1 min, and the vertical resolution is
15 m. The characteristics of each case, including
altitude, average temperature, and its standard deviation, are presented in Table 4. Temperatures
were provided by radiosoundings launched at
Trappes meteorological station 共15 km from Palaiseau兲. The optical depth was calculated profilewise, but as an indication the average and maximum
values are provided.
Table 4. Presentation of Lidar Experimental Casesa
Date
Time
Tav
Tstd
zmin
zmax
␦av
␦max
I 共%兲
II 共%兲
III 共%兲
IV 共%兲
19990427
19990503
19990510
19990513
19990514
19990519
19990521
19990601
19990618
19991015
19991018
19991112
19991128
19991129
19991205
1195–1328
0900–1081
1115–1341
0791–1223
0828–0966
0843–1028
1210–1436
0953–1098
1273–1673
0838–1293
0715–1170
0748–1588
1125–1639
0740–1348
1751–2191
⫺46.46
⫺50.01
⫺32.00
⫺44.34
⫺31.78
⫺39.96
⫺51.91
⫺35.38
⫺54.46
⫺42.99
⫺47.09
⫺42.20
⫺49.96
⫺50.45
⫺51.11
4.39
5.14
12.09
7.61
5.65
4.32
2.46
10.38
4.18
7.07
5.46
2.06
16.43
10.28
8.09
7.49
6.90
5.50
5.10
4.99
6.49
8.30
4.50
9.51
7.20
7.71
5.80
5.50
7.11
3.70
10.51
11.99
11.01
11.50
10.00
9.21
11.79
11.01
12.70
11.61
11.50
9.51
13.30
13.49
13.49
0.10
0.40
0.16
0.11
0.26
0.01
0.05
0.40
0.14
0.50
0.09
0.11
0.39
0.49
0.29
0.61
2.42
2.55
4.63
1.58
1.55
1.03
3.11
2.42
2.71
0.33
1.98
1.72
3.05
4.06
19.02
35.62
21.00
23.53
37.66
27.20
69.11
34.68
30.23
23.73
20.62
36.47
11.78
7.74
7.02
79.02
47.95
36.43
59.21
41.19
56.50
25.30
41.53
33.64
34.76
39.22
30.83
34.17
19.17
19.85
1.95
13.53
39.18
11.98
14.68
8.34
5.51
13.43
13.09
32.46
36.34
23.22
46.95
57.46
41.95
0.00
2.90
3.38
5.28
6.48
7.96
0.08
10.36
23.05
9.05
3.82
9.48
7.10
15.62
31.18
a
Tav, average temperature; Tstd 共°C兲, its standard deviation; zmin, zmax 共km兲, cloud altitude boundaries; ␦av, average optical depth; ␦max,
maximum optical depth, percentages of retrieved classes.
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APPLIED OPTICS 兾 Vol. 41, No. 21 兾 20 July 2002
Fig. 5. Experimental depolarization ratios for 5 December 1999 case.
1. 5 December 1999 Case
As an example the evolution of experimental depolarization ratios as a function of time and altitude
for 5 December 1999 are shown in Fig. 5. This case
features a rather inhomogeneous cloud evolving
from a 11-km altitude at 1800 UTC down to a 6-km
altitude at 2400 UTC. This cloud shows a strong
depolarization 共to as high as 0.6兲. Temperature
and relative humidity profiles from radiosoundings
launched at 1121 UTC are shown in Fig. 6. The
Fig. 6. Temperature and humidity profiles collected at 1121 UTC.
20 July 2002 兾 Vol. 41, No. 21 兾 APPLIED OPTICS
4251
Fig. 7. Retrieved shape ratios separated in four classes from, light gray, Class I 共Q ⬍ 0.05兲, to, black, Class IV 共Q ⬎ 1.05兲.
cloud temperature ranges between ⫺60 and
⫺35 °C, and the relative humidity is below 20%.
The crystal shape ratio was retrieved by the classification technique presented in Subsection 4.A.3:
The cloud optical depth was calculated for each lidar
profile with a maximum uncertainty of ⫾0.1. Based
on this value, a specific curve ⌬Psim ⫽ f 共Q, ␦兲 was
selected on which the measured depolarization ratios
⌬Pex were reported. The retrieved shape ratio
classes are shown in Fig. 7. The higher and colder
cloud layer, between 10 and 12 km, shows a majority
of shape ratios greater than 1.05 共Class IV兲. The
lower cloud layer 共after 2300 UTC兲 shows a global
decrease in the shape ratio that could be explained by
both platelike shapes 共Q ⬍ 0.05兲 or mixed-phase crystals leading to increased sphericity and a lower average depolarization ratio in the probed cloud
volume.
Fig. 8. Same as Fig. 5 but for 28 November 1999.
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APPLIED OPTICS 兾 Vol. 41, No. 21 兾 20 July 2002
Fig. 9. Same as Fig. 6 but for 28 November 1999.
2. 28 November 1999 Case
As a second example, the evolution of experimental
depolarization ratios as a function of time and altitude for 28 November 1999 are shown in Fig. 8.
This case features two continuous layers, one be-
tween 6.5 and 8 km and another between 11 and 13
km, from 1100 to 1630 UTC. The upper layer shows
strong depolarization patches, whereas the lower
layer shows a wider range of depolarization values.
Temperature and relative-humidity profiles are
Fig. 10. Same as Fig. 7 but for 28 November 1999.
20 July 2002 兾 Vol. 41, No. 21 兾 APPLIED OPTICS
4253
shows patches of high shape ratios surrounded by low
shape ratios 共Classes I and II兲. Again, this low
shape ratio can be interpreted as either plates or
mixed-phased crystals. Owing to the relatively high
temperature of the lower layer, the mixed-phased
hypothesis can be considered as the most probable.
Fig. 11. Frequency of occurrence of the different effective shape
classes for the 15 cases that were studied.
shown in Fig. 9. For the upper layer the temperature ranges between ⫺60 and ⫺72 °C with a relative
humidity of ⬃25%. For the lower one the cloud temperature ranges between ⫺35 and ⫺25 °C with a relative humidity between 25% and 55%.
The retrieved shape ratios are shown in Fig. 10.
The upper layer shows broken patches of high shape
ratios 共Classes III and IV兲, whereas the lower layer
3. Summary of Retrievals
The 15 selected cases have been processed in the
same way, and a histogram of the classes of retrieved
shape ratios for all cases is shown in Fig. 11. Class
percentages for single cases are presented in Table 4.
The upper limit for the last class has been taken as
Q ⫽ 4, since almost all retrieved shape ratios are
found below that value. It shows that most particle
ratios can be found in Class III, that is, Q between 0.7
and 1.05 共⬃35%兲, with another peak for Class II, that
is, Q between 0.05 and 0.7 共⬃32%兲. Note that these
results are significant only for the mid-latitude thin
cirrus cases that were studied and not applicable to
all cirrus clouds. Besides, histograms of temperatures for each shape-ratio class are presented in Fig.
12, assuming that the temperature profiles stay constant during the observation. These charts show a
global shift of dominant temperatures from one class
៮ ⬃ ⫺40 °C兲 for
to another, from a high temperature 共T
៮ ⬃
low shape ratios 共Q ⬍ 0.05兲 to low temperatures 共T
⫺60 °C兲 for the highest shape ratios 共Q ⬎ 1.5兲.
Fig. 12. Temperature histograms for each class of a shape ratio.
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APPLIED OPTICS 兾 Vol. 41, No. 21 兾 20 July 2002
5. Analysis
When the presented results are considered, several
shortcomings that could lead to bias in the results
should be stressed:
• The retrieval technique implies that clouds are
made exclusively of pure hexagonal-based ice crystals. Occurrences of mixed-phase clouds containing
water under ice and the liquid phase could lead to
biased results: Near-spherical shapes lead to a low
depolarization ratio and are wrongly counted as plate
crystals 共i.e., low shape ratios兲. However, only the
first shape ratio class is affected by this phenomenon,
and its importance can be limited by a careful selec៮ ⬍ 40°兲.
tion of unambiguous cases 共T
• However, in its current state the simulation
focuses on hexagonal-based particle shapes. Using
more complex shapes is possible, leading to potentially different depolarization ratios as long as the
particle-scattering matrix Mp is known 共Subsection
2.B兲. Calculation of these matrices for a wide variety of ice crystals has been thoroughly addressed.41
• Moreover, ray-tracing by design cannot take
into account particle size, where as studies42,43 have
shown that the presence of small particles 共with an
effective radius r ⬍ 6 ␮m兲 could lead to strong depolarization ratios 共⌬P ⬎ 0.7兲.44 This size effect cannot
be accounted for with ray-tracing models, but, since
such high values were not noticed in current measurements, this phenomenon should not apply here.
• Finally, until now all calculations were conducted for randomly-oriented particles. The next
logical step would be to implement an anisotropic
media 共i.e., particles with a preferential plane of orientation兲,45,46 which could potentially lead to higher
values of ⌬Psim for low shape ratios.47 However, recent papers48,49 show that an efficient study of anisotropic media would require multiple incidence-angle
measurements, which are seldomly available at this
point. Furthermore spaceborne lidar measurements of this kind will not be available in the near
future.
6. Conclusions
We have presented a technique for retrieving information on particle shapes in ice clouds, taking advantage of the strong sensitivity of light polarization
to microphysical properties. The potential application to this technique to spaceborne lidar measurements has been studied. A ray-tracing simulation of
lidar backscattering and depolarization profiles has
been developed, taking into account multiple scattering. Several atmospheric models were processed
with different cloud microphysical and optical settings from either a ground-based or a spaceborne
point of view. Lidar simulations show that the
multiple-scattering effect, although strongly dependent on particle shape and optical depth, stays in the
same range for either ground-based or spaceborne
lidar, owing to the very narrow field of view of the
spaceborne configuration. Simulated depolariza-
tion ratios were used to retrieve effective shape ratios
from experimental depolarization ratios. The 15
cases of lidar observations for mid-latitude cirrus
clouds were studied to separate the effective shape
ratios into four different classes. Results show a
majority of near-unity shape ratios on average for the
cases that were studied. Moreover the proportion of
low temperatures is higher for high effective shape
ratios 共Subsection 4.B.3兲.
A comparison of such results with previous studies
is difficult for the following reasons: 共i兲 The number
of existing studies of particle shapes in ice clouds is
very limited for the time being. 共ii兲 Passive satellite
retrievals are integrated from the cloud top over a
variable penetration depth, depending on the type of
measurement 共wavelength, viewing direction, etc.兲,
whereas the lidar provides information on the vertical distribution. 共iii兲 The existing studies do not
cover seasonal variation at mid-latitude areas such
as the Palaiseau ground site. Nevertheless an analysis of ATSR dual-view observations collected above
tropical cirrus clouds12 led to the conclusion that near
the top of such clouds, columns 共high shape ratios兲
and polycrystals are more frequent. Moreover the
POLDER-1 analysis,15 in which bidirectional polarized observations were used showed that columns
and polycrystals are dominant at the cloud top for
mid-latitude cirrus clouds. Those results are consistent with the current study, since the higher colder
particles show higher shape ratios.
Note that these results could be biased owing to
several assumptions that are described in detail in
Section 5: 共i兲 monodisperse size distribution, 共ii兲
hexagonal particle shape, 共iii兲 randomly oriented particles. However, in the absence of large-scale climatological studies of shape factor, this retrieval method
could be applied on already operational ground-based
lidar measurements. Since a great number of cirrus
cases are available through the globe, this method
could lead to potential preliminary statistical studies
of the effective shape ratios of cirrus clouds and their
vertical variability. As an example, in the first step
the whole cirrus lidar database of SIRTA could be
used to estimate the representation of the effective
shapes in cirrus clouds in northern France.
In addition, the application of this retrieval method
to spaceborne lidar measurements could lead to studies of shape factors at the global scale. This could
allow cirrus clouds of different latitudes to be discriminated. Coupled with the vertical variability allowed by lidar measurements, several aspects of
crystal shape evolution and cloud formation processes could be studied.
The authors thank the Centre National d’Etudes
Spatiales and the Sodern Company for financial support. Thanks are extended to Laurent Sauvage for
providing the data acquisition. The authors are
grateful to the anonymous reviewer for useful comments.
The authors would like to thank SIRTA for providing the lidar data.
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