The goal of this paper is to retrieve information about ice particle orientation in cirrus clouds. This is achieved by comparing simulations of sunlight reflection on a cirrus cloud with measurements of polarized radiances from the spaceborne instrument POLDER-1/ADEOS-1. Results show that horizontal orientation of crystals can be spotted by the presence of a local maximum of polarized radiance in the direction of specular reflection. The angular width of the local maximum is shown to contain information on the particle maximum deviation angle, while the maximum intensity can provide information on particle shape and relative concentrations of ice crystals, horizontally and randomly-oriented. The study of 31 ice cloud cases show that in 80 % of them, the deviation angle is less than 3¢ . Also, the relative concentration of horizontally-oriented crystals is less than 21 %, depending on the angular distribution used for crystal deviation.

Introduction

Cirrus clouds cover permanently more than 30% of the Earth's surface (Wylie et al, 1994), and as such have a strong influence on the planet's radiative balance (Stephens et al, 1990). As they are made of ice crystals, their influence strongly depends on their microphysical properties. However, for cirrus clouds such properties show a very high variability, and due to the high altitude of these clouds in situ data is only scarcely available. As a consequence, the overall cirrus radiative impact is still uncertain, with one of the largest sources of uncertainty remaining the microphysical properties, and especially the particles orientation in space.

Usually, studies of crystal properties inside cirrus clouds implicitely assume a random orientation for the particles. This type of model has symmetry properties that allow great simplification in computations of crystals optical properties and radiative transfer. Nowadays, this model is still used in the vast majority of radiative transfer simulations used to parametrize cirrus clouds models. However, it cannot give a satisfactory explanation for all optical displays created by these clouds, and could lead to possible bias when estimating their radiative impact.

First observations of preferential orientation of ice crystals were done through stro-boscopic measurements [START_REF] Magono | On the growth of snow flakes and graupel[END_REF], refined several years later by studying droplets accretion on falling ice particles [START_REF] Ono | The shape and riming properties of ice crystals in natural clouds[END_REF]. These first studies revealed that specific shapes of ice crystals, such as plates, columns and dendrites, oriented themselves while falling, in order to offer maximum resistance to the air. As in-situ observation of this dynamic behavior is not possible, remote sensing was gradually introduced in the studies that followed. Radar [START_REF] Hendry | Radar observations of the alignment of precipitation particles by electrostatic fields in thunderstorms[END_REF] and direct photography [START_REF] Sassen | Remote sensing of planar ice crystals fall attitude[END_REF] were used first, however the instrument that generated the most studies of the orientation phenomenon is the lidar [START_REF] Platt | Some microphysical properties of an ice cloud from lidar observations of horizontally oriented crystals[END_REF][START_REF] Sassen | Remote sensing of planar ice crystals fall attitude[END_REF]Thomas et al, 1990;[START_REF] Sassen | Parry arc : a polarization lidar, ray-tracing, and aircraft case study[END_REF][START_REF] Noel | Analysis of ice clouds lidar measurements at multiple incidence angles[END_REF], thanks to its ability to detect optically thin clouds and its sensitivity to light polarization.

Theoretical and laboratory studies [START_REF] Jayaweera | The behavior of freely falling cylinders and cones in a viscous fluid[END_REF][START_REF] Podzimek | Aerodynamic conditions of ice crystal aggregation[END_REF][START_REF] List | Free-fall behavior of planar snow crystals, conical graupel and small hail[END_REF][START_REF] Lynch | Subsuns, bottlinger's rings and elliptical halos[END_REF][START_REF] Klett | Orientation model for particles in turbulence[END_REF] gave further insight into this behavior. Computer simulations (Takano and Liou, 1989a) showed that oriented crystals could increase the cloud albedo by as much as 30 %, leading to important modifications on the cloud radiative effect (Takano and Liou, 1989b). Recent observations [START_REF] Sassen | Diurnal effects in the composition of cirrus clouds[END_REF] suggest the crystals orientation could even have a potential feedback effect on particle generation inside the cloud. These results confirm the possible impact of this parameter on climate prediction. Unfortunately, the frequency and con-centration of horizontally-oriented crystals at a global scale in ice clouds is still largely unknown.

In order to estimate the overall impact of crystals orientation on cloud radiative effect, studies have to be pursued on a global scale, which is only possible through satellite monitoring. Following this approach, radiances observations from satellite instruments have been found to convey information about cirrus clouds microphysical properties [START_REF] Chepfer | Ice crystal shapes in cirrus clouds derived from polder/adeos-1[END_REF][START_REF] Chepfer | Estimation of cirrus clouds effective ice crystals shapes using visible reflectances from dual-satellite measurements[END_REF][START_REF] Liou | Interpretation of cirrus cloud polarization measurements from radiative transfer theory[END_REF][START_REF] Masuda | Retrieval of cirrus optical thickness and ice-shape information using total and polarized reflectance from satellite measurements[END_REF]. More specifically, POLDER-1 (POLarization and Directionality of the Earth's Reflectance) observations of sunlight scattering upon ice clouds were recently used to estimate the frequency of the preferred orientation of crystals in cirrus [START_REF] Chepfer | Observations of horizontally oriented ice crystals in cirrus clouds with polder-1/adeos-1[END_REF]. The present paper focuses on the cases where oriented crystals were actually observed.

Measurements of normalized polarized radiances are compared to results of ray-tracing simulations to retrieve informations about the crystals orientation behavior.

The observations and the simulations are presented in Sect. 2, followed by the sensivity study of simulated normalized polarized radiances to crystal microphysical properties (Sect. 3). Based on these findings, the horizontally-oriented crystals maximum deviation angle and relative concentrations are retrieved in Sect. 4. Discussion and conclusion are given in Sect. 5.

Observed and simulated radiances

Observed radiances from satellite

The preferential orientation of ice crystals in a cirrus cloud creates physical anisotropy that can be detected with multi-directional observations. For example, in presence of horizontally-oriented plates, bidirectional polarized radiances show a distinctive highintensity peak in the direction of specular reflection. This distinctive behavior has been used to estimate the frequency of horizontal orientation of crystals in cirrus clouds [START_REF] Chepfer | Observations of horizontally oriented ice crystals in cirrus clouds with polder-1/adeos-1[END_REF], using observations of normalized polarized radiances reflected by the atmosphere from the POLDER-1 spaceborne radiometer. POLDER-1 [START_REF] Deschamps | The polder mission : instrument characteristics and scientific objectives[END_REF] flew on the ADEOS-1 satellite from August 96 to June 97 and, up to now, seems the best suited instrument to retrieve information about crystal orientation in cirrus cloud. This radiometer measured normalized radiances £ ¥¤ §¦ © and normalized polarized radiances £ ¤ ! "¦ # $ for a given ground or cloud pixel from up to 14 viewing directions, defined by their zenith and azimuthal angles and [START_REF] Hagolle | Results of polder in-flight calibration[END_REF] :

£ ¤ §¦ # $ % '& )( £ 0¦ © $ 1 2 43 65 87 05 £ ¤ ! "¦ # $ & )( £ 9! "¦ © $ % 1 2 43 65 @7 05 (1)
with 65 the solar zenithal angle and 7 A5 the solar irradiance at the top of the atmosphere.

£ ¥¤ §¦ © and £ ¥¤ ! "¦ # $ 9 % were measured at several visible wavelengths (443nm-865nm).

In order to minimize bias due to molecular scattering, this study uses the 865nm channel.

To simulate £ B¤ §¦ © and £ ¤ ! C¦ # $ , multiple scattering effects have to be consid- ered (Sect. 2.2).

Normalized polarized radiance and multiple scattering

Multiple scattering has been shown to have a significant impact on light scattered by randomly-oriented particles (Trankle and Greenler, 1987). However, in presence of horizontally-oriented particles, its impact on normalized radiances is still not correctly quantified, even if its influence on plane albedo has been estimated (Takano and Liou, 1989b). In such a case, a reasonable guess would be to assume this impact is similar in preferential and random orientation. For this last case, studies of multiple scattering effects on total and polarized radiances [START_REF] Goloub | Analysis of the polder polarization measurements performed over cloud covers[END_REF] have shown that, while the total radiance is strongly affected by multiple scattering, polarized radiance is mainly formed by the first scattering event, with saturation quickly taking place after a few events and no further influence from following events. Hence, if an observed cloud has a optical depth high enough for the polarized radiance to reach saturation, the reflected normalized polarized radiance does not depend on the cloud optical depth anymore.

In such cases, it is possible to write a single-scattering approximation of normalized polarized radiance from the general radiative transfer equation [START_REF] Goloub | Analysis of the polder polarization measurements performed over cloud covers[END_REF] :

£ ¥¤ ! "¦ © $ % '& 1 %2 43 65 D ¦ 1 2 43 65 9E 1 2 43 CF G IH E QP H E SR H (2)
with G , P and R are the second, third and fourth elements of the scattered Stokes vector ( Van de Hulst, 1957). This approximation has already been widely used in the litterature [START_REF] C-Labonnote | Modeling of light scattering in cirrus clouds with inhomogeneous hexagonal monocrystals. comparison with in situ and adeos-polder measurements[END_REF][START_REF] C-Labonnote | Polarized light scattering by inhomogeneous hexagonal monocrystals: Validation with adeos-polder measurements[END_REF][START_REF] Goloub | Cloud phase detection from polder/adeos[END_REF][START_REF] Riedi | Global distribution of cloud top phase from polder/adeos-i[END_REF][START_REF] Riedi | Comparison of polder cloud phase retrievals to active remote sensors measurements at the arm sgp site[END_REF]. In order to ensure its validity, all the cases selected for the present paper (Sect. 4) show a high optical depth.

Simulated radiances from modeled crystals

Following Eq. 2, the scattered Stokes vectors are sufficient to simulate normalized polarized radiances £ ¤ ! "¦ # $ for any viewing direction in space. The Stokes vectors were simulated using a ray-tracing code [START_REF] Noel | Computation of a single-scattering matrix for nonspherical particles randomly or horizontally oriented in space[END_REF], for clouds composed of preferentially oriented crystals.

As a first approximation, the modelled ice crystals were shaped as hexagonal-based plates with variable aspect ratios T & U H WV (with X the crystal length and Y the radius of the hexagonal base). This simple shape seems to accurately reproduce the scattering behavior of cirrus clouds [START_REF] Heymsfield | A parametrization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content[END_REF]. The plates are also the particles more likely to exhibit an preferential orientation with a specific optical signature [START_REF] Ono | The shape and riming properties of ice crystals in natural clouds[END_REF][START_REF] Sassen | Parry arc : a polarization lidar, ray-tracing, and aircraft case study[END_REF]. Preferential orientation is taken into account in the model through the deviation angle `from the horizontal plane . As the general distribution of `is still unknown, a gaussian and a square probability functions are considered, both centered on

`& ba , with a standard deviation dc fe @g . In this framework, hc Be ig gives an indication of the average deviation of ice crystals from the horizontal plane, with pc fe @g & ba ¢ meaning a perfect horizontal orientation.

Once the crystals parameters T and dc fe ig are chosen, and the solar zenithal angle 65

is fixed, the ray-tracing simulation delivers the entire D rq sD scattering matrix t ¦ #ï u $ 9 % of the modelled crystal for any viewing direction in space. As incident sunlight is unpolarized (i.e. its Stokes vector is v & w¦ @x 4 ya a a 4 ), the Stokes vector of the scattered light (Van de Hulst, 1957) is easily obtained by :

v ¦ # $ % '& t ¦ # $ % B "¦ @x u a a ya ¥& t ¦ # $ % (3)
Normalized polarized radiances are then easily calculated using Eq. 2.

3 Study of simulated polarized radiances

Sensitivity study

For the sake of simplicity, in this sensitivity study scattering is considered in the pri- Similar computations using a gaussian distribution for the deviation angle `give a similar shape for £ B¤ ! and have not been plotted in Fig. 1 for readability. However, properties of the simulated curves depend strongly on the chosen distribution (square or gaussian) and on the value of dc fe @g . Similarly, the particle aspect ratio has a strong influence.

Sensitivity to crystal maximum deviation angle

The general shape of the curve is strongly dependent on the crystal maximum deviation angle pc fe @g (Fig. 1). For crystals with small deviations, the curve shows a very narrow peak of high intensity in the direction of specular reflection. If the crystals deviation increase, the maximum intensity quickly decreases, while its angular width increases. This behavior reaches its limit for randomly-oriented crystals : the local maximum totally disappears.

The peak angular width, at half-maximum intensity, is plotted in Fig. 2 as a function of the crystal maximum deviation angle c Be ig for three different aspect ratios : 0.05, 0.2 and 0.5. For square distributions of the deviation angle `, very small deviations (pc Be ig hg x ¢ ) show a local maximum with a i ¢ angular width. This width increases very quickly with crystal deviation, gaining approximately ¢ for a i ¢ increase in pc Be ig . For gaussian distributions the angular widths are smaller (i.e. the peaks are narrower) by

x 4d f ¢ in average, due to the higher probability given to smaller angular deviations. If the deviations are too small (i.e. dc Be ig kj a ld m ¢ ), the angular width becomes too narrow to be measured. With both distributions, the curve is monotonic for small deviations (pc Be ig j on 4¢ , angular width up to g x p ¢ ). The maximum deviation angle pc fe ig can then be linked to the angular width of the local maximum, independently from the aspect ratio.

The curve maximum intensity is plotted in Fig. 3 as a function of crystal aspect ratio T for three maximum deviation angle c Be ig : 1, 2 and ¢ . The maximum intensity is very sensitive to the crystal deviations : small deviations lead to high intensities, and a

x ¢ -increase in pc Be ig leads to a ua q fall in maximum intensity. In addition, the effect of crystal aspect ratio T is more apparent on the maximum intensity (Fig. 3) than on the peak angular width (Fig. 2).

Sensitivity to crystal shape

The crystal aspect ratio T has a more subtle impact on the polarized radiance. For small crystal deviations (dc fe ig up to n ¢ ), the aspect ratio has almost no influence on the curve angular width (Fig. 2). When deviations get larger (rc fe @g ts Qn ¢ ), the crystal aspect ratio begins to influence the curve angular width. This is equally valid without regard to the distribution chosen for `.

The influence of crystal shape is more obvious when looking at the curve maximum intensity. For square distributions, low aspect ratios (T uj a d vx p ) lead to high normalized polarized radiances £ ¥¤ ! s )w (Fig. 3). When the aspect ratio increases, the polarized radiances decreases, with a threshold for a d i xj yT zj a d due to consecutive scattering events inside the crystal. There can be a factor 10 between local maximum intensities for very low (T uj a d ea ) and very high (T {g x ) aspect ratios. For a gaussian distribution, the same behavior is observed; however, the maximum intensities are significantly increased, up to 400% for pc fe @g & |x ¢ . This will have important consequences on the retrieved microphysical properties (Sect. 3.2).

Sensitivity to Crystal concentrations

Until this point of the study, clouds were assumed to be only composed of horizontallyoriented crystals. However, it is possible that only a fraction of crystals are closely aligned with the horizontal plane, while the remaining crystals are randomly oriented.

If a cloud is defined as a mix of horizontally-oriented crystals (noted by the subscript h) and randomly-oriented crystals (noted by the subscript r), the normalized polarized radiance £ ¤ ! scattered by the entire cloud will be given by [START_REF] Sassen | A midlatitude cirrus cloud climatology from the facility for atmospheric remote sensing. part ii : microphysical properties derived from lidar depolarisation[END_REF] :

£ ¥¤ ! }& )d £ ¥¤ ! 6 E ~V £ ¥¤ ! 6 V d E ~V (4)
where ~is the relative concentration of each particle bearing the relevant orientation, and £ ¤ ! the related radiance (Eq. 2). For randomly-oriented crystals there is no max- imum of normalized polarized radiance in the direction of specular reflection, thus

£ ¥¤ ! V £ ¥¤ ! (typically, for a solar zenithal angle %5 & D ¢ , £ ¤ ! V j a d fa lx D in the direction of specular reflection). If
£ f¤ ! V is neglected, the total normalized polarized radiance is given by

£ B¤ ! & ¤ 6 ¤ ¤ £ ¥¤ ! .
The local maximum of normalized polarized radiance will linearly decrease as the quantity of randomly-oriented particles increase.

Retrieval of cloud microphysical properties

Following the sensivity study (Sect. 3.1), microphysical properties of the studied cloud can be retrieved using observed normalized polarized radiances.

In a first step, the crystal maximum deviation angle c fe ig can be retrieved from the angular width of the polarized radiance local maximum (Sect. 3.1.1), provided the deviations are less than n ¢ wide. As gaussian distributions lead to slightly thinner peaks for a given hc Be ig (Fig. 2), stronger deviations will be required to produce a given angular width.

Once 9c fe ig is known, the intensity of the polarized radiance local maximum can be estimated as a function of crystal aspect ratio T and relative concentration of horizontally- oriented particles r (Sect. 3.1.2 and 3.1.3). Gaussian distribution leads to higher in- tensities (Fig. 3), so lower concentrations will be required to produce a given intensity.

These two values are correlated, and sets of possible values can be retrieved based on the actual polarized radiances measurements.

As an example, the maximum intensity of

£

Retrieval of the crystal maximum deviation angle

The angular width of the peak at half maximum intensity is approximately

Retrieval of horizontally-oriented crystals shape and relative concentration

When considering a local maximum of normalized polarized radiance created by horizontallyoriented crystals, its intensity is linked to the shape and relative concentration of these crystals with respect to the angular distribution of the crystal deviation (Sect. 3.1.3). As the crystals maximum deviation is obtained independently (Sect. 4.2), the shape and relative concentration of these crystals can be retrieved.

The retrieved crystal maximum deviations for the actual case are a d n 6¢ and i d x ¢ (Sect.

4.2). Using the retrieved pc Be ig and the exact POLDER observation angle, local maxi- mums of polarized radiances are simulated for different aspect ratios. For each aspect ratio, the relative concentration of horizontally-oriented particles ~ is estimated (Sect.

3.2). These concentrations are shown in table 1 for both square and gaussian angular distributions.

Even if the relative concentration ~ shows high variations for different crystal shapes (the retrieved concentration is between 5 and 6 times higher for T & a d m than for T & ba d ea , depending on the deviation distribution), the concentration values stay over- all very low, below 4 %. As was expected (Sect. 3.2), the use of gaussian distribution leads to lower concentrations.

Multiple cases

The same analysis is conducted on 30 more cases where POLDER measurements show a local maximum of normalized polarized radiance, and there are enough measurements to determine the angular width. For each case, normalized polarized radiances are simulated for the exact observation angles $ , until the simulated peak width is consistent with the measured values.

The frequencies of retrieved maximum deviation angles are shown in Fig. 6 for square and gaussian distributions of deviation angles, with respective average values

x ¢ and x ud w 4¢ . In more than 80 % of the cases, the retrieved maximum deviation angle is less than ¢ . It follows that, in most cases, the ice crystals are almost perfectly horizontally-oriented, with slightly larger deviations more frequent for gaussian distributions (g D a 4q of cases show x ¢ j Qpc Be ig j ¢ , against g x p 4q for square distributions).

Following the previous case study (Sect 4.3), once the maximum deviation angle is retrieved for a given case, polarized radiances are simulated for several aspect ratios T , estimating for each one the relative concentrations of horizontally-oriented ice crystals d . These values are shown for square (Fig. 7.a) and gaussian (Fig. 7.b) distributions of deviation angles, with average relative concentrations given in Table 2. The frequency of horizontally-oriented crystals is between 6.2 and 21.4 % if a square distribution is assumed, and between 5.4 and 8.6 % if a gaussian distribution is assumed. Moreover, for any aspect ratios the relative concentration of horizontally-oriented crystals has more than 60 % probability to be under 10 %. The second highest frequency (Fig. 7.a and b) is for a relative concentration between 10 and 20 %, but it is much lower (below 20 %). The chosen angular distribution has only a small influence here.

Discussion and conclusion

The present study shows that, in presence of horizontally-oriented crystals within a cirrus cloud, their maximum deviation angle can be retrieved from spaceborne measurements of polarized radiances. This angle is generally very low, below ¢ in most cases, with little influence from the deviation angle distribution. Previous studies used other ground-based observations to retrieve this parameter : [START_REF] Sassen | Remote sensing of planar ice crystals fall attitude[END_REF], through a statistical analysis of direct photography, found oriented ice crystals in cirrus clouds were more likely to bear a gaussian angular distribution, with a half-width angle below 1.4¢ for most particle shapes and an maximum value of 2.5¢ . Later, most studies took advantage of the rapid variation of the lidar signal near the zenith direction in presence of oriented crystals : looking at the backscattered intensity, [START_REF] Platt | Some microphysical properties of an ice cloud from lidar observations of horizontally oriented crystals[END_REF] found a maximum deviation near 0.5¢ , while Thomas et al (1990), by studying the more sensitive depolarization ratio, found a deviation angle no higher than 0.3¢ . However, these studies were mostly ground-based, and their conclusions are local. The present study draws consistent results from 31 cloud cases observed from satellite. Moreover, the concentration of oriented particles relative to the entire population of crystals, a

parameter still unknown at this point, was found to be under 10 % in most of the studied clouds. The application of this procedure to a high number of spaceborne measurements (from e.g. POLDER-2 or PARASOL) could give helpful insight into the orientation behavior of ice crystals in cirrus clouds, information that is otherwise very hard to get and still largely unknown.

However, there are still some limitations with this technique. For example, future progress in radiative transfer computations may show that the influence of multiple scattering effects can not be considered similar in isotropic and anisotropic media, as was assumed in the present study (Sect. 2.2). Moreover, oriented ice crystals were taken as plates, which is the most likely hypothesis. However, oriented hollow columns can produce specific optical signatures similarly to plate crystals [START_REF] Sassen | Parry arc : a polarization lidar, ray-tracing, and aircraft case study[END_REF], and in the future the way to discriminate these two shapes has to be investigated. Also, POLDER-1 measurements themselves have inherent limitations, the more important one being their spatial resolution of 6x6 km. Even if still being able to witness a signature of crystals orientation at such a large scale confirms the potential radiative implications of this phenomenon, there could be large variations in §c Be ig over an area so large. By analyzing smaller cloud areas through other techniques, the spatial variability of crystal orientations could be established at smaller scales, assessing the representativity of POLDER-1 retrievals. Another problem occurs when the polarized radiances saturate the POLDER-1 sensors for some contiguous pixels. In such cases the retrieval is still possible, but the peak angular width is measured with a lower accuracy, which has an impact on the retrieved maximum deviation angle. Finally, the procedure shown in this paper only provides a range of correlated values : the relative concentration and aspect ratio (Sect 4.3). Although the variation of concentration with the supposed aspect ratio is quite small (less than 5%), any external retrieval of crystal shapes would significantly increase the reliability and credibility of the concentration results. When considering future observations from the PARASOL instrument, the collocated CALLIOPE lidar from the CALIPSO mission (Winker and Wielicki, 1999) could provide useful information about particle shape, thus constraining the retrieval.

Even with these limitations, valuable information can be gained about crystals orientation in cirrus clouds from spaceborne polarized radiometric measurements. Up to now, it remains the only known technique for retrieving this property on a global scale. As a next step to this study, the retrieval technique presented in this article could be applied to data from two new spaceborne instruments. First, the POLDER-2 instrument, located on ADEOS-2, which is already in orbit, has begun as of January 2003 to take measurements. Second, the PARASOL mission, scheduled for launch in 2004, will provide another source of spaceborne POLDER measurements. Its location in the the constellation a satellites named Aqua-Train will allow interaction with other spaceborne instruments, with potential improvements to the retrieval technique discussed in the present article. These results will greatly improve our understanding of the physical behavior of cirrus particles over the planet.

physical and radiative properties of cirrus clouds to climate and climate feedback. J.

of Atmos. Sci., 47: 1742-1753, 1990. editors, Sensors, Systems, and Next Generation Satellites, SPIE, pp. 26-36, 1999.

  mary scattering plane ( p & f5 & a ), with a solar incidence angle arbitrarily fixed at 65 & D ¢ . For actual case studies (Sect. 4) the exact scattering plane and incidence angle measured by POLDER will be used. As an example, the simulated normalized polarized radiance £ ¤ ! reflected by the cloud is plotted in Fig. 1 as a function of the zenith angle , for three square distribu- tions of deviation angles with c fe ig & x 4 $ ¢ , and two crystal aspect ratios T & a d ea and a d f . The comparatively low £ f¤ ! for randomly-oriented crystals is plotted in bold line. In these curves, £ ¥¤ ! shows a local maximum in the direction of specular reflection ( A& D ¢ ), which is not present for randomly-oriented particles.

  B¤ ! is shown in Fig. 4 as a function of crystal aspect ratio T and horizontally-oriented crystals relative concentration ũ , for a square distribution of deviation angles with rc fe @g & x ¢ . Using this figure, an observed polarized radiance maximum intensity can be linked to a range of correlated values for T and d . In this specific case, cloud areas showing polarized radiances values greater than should contain more than 30 % of horizontally-oriented crystals, the exact value depending on their shape. Each case must be studied for the actual viewing angles $ $ , for which the azimuth angle o f5 is rarely constant. Therefore, polarized radiances are considered as a function of the angle between the direction of specular reflection and the actual scat- tering direction. The local maximum of polarized radiance is therefore centered on & {a ¢ . The case studied in this section was measured by the POLDER-1 radiometer at coordinates 60.25N, 25.15W, through orbit 7352 over sea. In this case, sunlight reflected on an ice cloud with incident angle of 5 '& D i u¢ . Measurements of normalized polarized radiance are shown in Fig. 5 as a function of . They show a local maximum of £ p¤ ! g a d f in the direction of specular reflection (for g a ¢ ), while staying relatively low for other scattering directions. This behavior suggests the presence of horizontallyoriented crystals in the studied cloud. Measurements of polarized radiances are very similar to results from ray-tracing simulations (Fig. 1). More specifically, the angular width and intensity of the local maximum lie within the same range. It should then be possible to retrieve the maxi-mum deviation angle and relative concentration of the horizontally-oriented crystals present in the cloud, following the steps shown in Sect. 3.2.

x

  4d m ¢ . When considering normalized polarized radiance, the angular width of a local maximum is linked to the maximum deviation angle of horizontally-oriented crystals in the cloud, with little regard to the quantity or shape of these crystals (Sect. 3.1.1). To retrieve the maximum deviation angle, simulations are first conducted with an arbitrary large crystal deviation (typically c Be ig & n a ¢ ). The simulated normalized polarized radiances are then compared to the actual observations, with respect to the exact scattering direction given by the angles $ (Sect. 2.3). Based on the width difference between the simulated polarized radiances and the measured ones, an adjusted value of the crystal maximum deviation angle is used in a new round of simulations. This whole process is repeated until convergence is reached. The crystal maximum deviation angle is the one giving the best agreement between the simulated and measured radiances. For the actual case, the retrieved crystal maximum deviation is a d n ¢ considering a square angular distribution and i d x ¢ considering a gaussian distribution.

  Takano, Y. and K. N. Liou, Solar radiative transfer in cirrus clouds. part 1 : Singlescattering and optical properties of hexagonal ice crystals. J. ofAtmos. Sci., 46: 3-18, 1989a. Takano, Y. and K. N. Liou, Solar radiative transfer in cirrus clouds. part 2 : Theory and computation of multiple scattering in an anisotropic medium. J. of Atmos. Sci., 46: 20-36, 1989b. Thomas, L., J. C. Cartwright and D. P. Wareing, Lidar observations of the horizontal orientation of ice crystals in cirrus clouds. Tellus, 42B: 211-216, 1990. Trankle, E. and R. G. Greenler, Multiple-scattering effects in halo phenomena. J. Opt. Soc. Am., 4(3): 591-599, 1987. Van de Hulst, H. C., Light scattering by Small Particles. Dover Publications Inc., New York, 1957. Winker, D. and B. Wielicki, The picasso-cena mission. In H. Fujisada and J. B. Lurie,

Figure 1 :

 1 Figure 1 : Normalized polarized radiance as a function of zenithal angle .

Figure 2 :

 2 Figure 2 : Local maximum as a function of maximum deviation angle rc fe @g .

Figure 3 :

 3 Figure 3 : Maximum normalized polarized radiance intensity as a function of crystal aspect ratio T .

Figure 4 :

 4 Figure 4 : Normalized polarized radiance local maximum as a function of crystal aspect ratio T and horizontally-oriented crystals relative concentration ~ .

Figure 5 :

 5 Figure 5 : Normalized polarized radiance as a function of the angle between the

Figure 6 :

 6 Figure 6 : Frequency of maximum deviation angles c Be ig

Figure 7 :

 7 Figure 7 : Distribution of horizontally-oriented crystals concentrations ~ for (a) square distribution of crystal deviation and (b) gaussian distribution of crystal deviation.

  Figure 2:

  Figure 4:

Table Captions Table 1 :

 Captions1 Relative concentrations of horizontally-oriented crystals for different aspect ratios

Table 2 :

 2 Average concentrations of horizontally-oriented crystals for different aspect ratios

Acknowledgements. The results presented in this paper were obtained using data from CNES's POLDER instrument onboard NASDA's ADEOS platform. The authors are grateful to F.-M. Breon for processing the POLDER-1/Level-0 data. 25

Relative concentration ~ (gaussian) % 0.5 0.6 0.7 1.0 1.3 3.1 Table 1: aspect ratio T 0.05 0.1 0.2 0.3 0.4 0.5 Average relative concentration ~ (square) % 6.2 7.1 9.6 9.9 13.6 21.4

Average relative concentration ~ (gaussian) % 5.4 6.0 6.7 7.2 8.0 8.6 Table 2:


Vincent Noel
email: v.r.noel@larc.nasa.gov

This paper presents a study of the orientation of ice crystals in cirrus and midlevel clouds, based on the analysis of several cases of scanning polarization lidar observations. The maximum angle that crystals deviate from the horizontal plane is inferred at consecutive altitude levels, by fitting angle-dependent measurements of linear depolarization ratio and backscattered intensities to a theoretical model with a Gaussian distribution of tilt angles. The average deviation angle is linked to the angular variation of backscatter. A rare observation of so-called Parry-oriented columns is also given to highlight the different backscattering behavior with lidar angle. For planar crystals, two orientation modes are found that depend on cloud temperature. High level cold (<~-30C) clouds show a maximum deviation angle of ~1.0, while for warmer (>~-20C) midlevel clouds this angle averages ~2.0. This difference is caused by variations in particle shape and fall attitude that depend on temperature, likely involving a transition from simple plates to more widely fluttering dendrites at the warmer temperatures. Polarization lidar scans are clearly uniquely suited for the study of ice crystal orientations in clouds.

Introduction

Cirrus clouds permanently cover as much as 40 % of the Earth surface [START_REF] Liou | Influence of cirrus clouds on weather and climate processes: A global perspective[END_REF], and as such represent an important part of the global radiative budget [START_REF] Stephens | The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback[END_REF]). Unfortunately, their study is generally difficult due to their high altitude and semi-transparency, and requires development of analysis techniques based on remote sensing. Their unique composition of ice crystals, which can adopt an infinite variety of shapes and sizes, grants them with unusual microphysical and radiative properties. Properties of these crystals are still poorly known, and this leads to inconsistencies in their parametrization in Global Circulation Models. Due to these uncertainties, cirrus clouds remain an important source of errors in climate prediction.

Traditionally, most radiative models of cirrus suppose a random orientation of crystals (e.g. [START_REF] Takano | The effect of small ice crystals on cirrus infrared radiative properties[END_REF]), an assumption shared by most algorithms and analysis techniques applied to ice clouds. However, experimental studies of ice crystal riming properties and some unusual optical displays, such as arcs and sun pillars, has led to the discovery that ice crystals tend to orient themselves horizontally [START_REF] Ono | The shape and riming properties of ice crystals in natural clouds[END_REF][START_REF] Sassen | Remote sensing of planar ice crystals fall attitude[END_REF]. This phenomenon is difficult to study with current in situ devices, while the platform itself can disturb the particles spatial ordering. [START_REF] Takano | Solar radiative transfer in cirrus clouds. Part 2: Theory and computation of multiple scattering in an anisotropic medium[END_REF] showed that the presence of oriented ice crystals in a cirrus cloud could increase its hemispherical albedo by as much as 30 %. Moreover, particle orientation can lead to high uncertainties in the retrieval of cirrus properties from satellite observations, leading in certain cases to optical depths overestimated by 100 % [START_REF] Masuda | Influence of particle orientation on retrieving cirrus cloud properties by use of total and polarized reflectances from satellite measurements[END_REF]. As a recent study of polarized radiances from the POLDER satellite radiometer has found evidence for oriented crystals in 40 % of observed high clouds, this phenomenon could therefore have a strong influence on the global radiative impact of cirrus clouds [START_REF] Chepfer | Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1[END_REF].

In the present study, observations of horizontally oriented ice crystals using a scanning lidar are analyzed. The deviation of the crystals from the horizontal plane is retrieved as a function of cloud altitude, by fitting the lidar angle-dependent observations with a Gaussian model of crystal tilt angles. Different fall attitude modes are explained by considering the off-zenith angle linear depolarization ratios. In Section 2, the phenomenon of crystal orientation in cirrus is placed in its context and possible observation techniques are discussed. Section 3 briefly describes the lidar dataset. A first case study showing oriented crystals is presented in Section 4 and used to illustrate the analysis process. A singular case of oriented columns is presented in Section 5 to highlight the differences with oriented plates and ensure the two shapes can be identified with certainty. Multiple cases of oriented plates are then studied in Section 6, and results discussed in Section 7.

Oriented crystals in ice clouds a Crystal orientation behavior

The first study of crystal orientation in ice clouds was conducted by [START_REF] Magono | On the growth of snow flakes and graupel[END_REF], who used stroboscopic observations of particles to show that, under some hydrodynamic conditions, platetype snow crystals fall with their major axis horizontal. Later, [START_REF] Ono | The shape and riming properties of ice crystals in natural clouds[END_REF] generalized this statement by studying ice crystal riming properties, to conclude that free-falling ice crystals (including plates, columns, and dendrites) in a calm atmosphere orient themselves to present the maximum resistance to the air, with a possible slight oscillation about the equilibrium position.

Particle size was also shown to have an impact on particle orientation : depending on their Reynolds number, thick plates would adopt a orientation close to horizontal for diameters above 100μm, when thin plates would require a diameter above 150μm [START_REF] Sassen | Remote sensing of planar ice crystals fall attitude[END_REF]. Since then, it has been shown that turbulence effects could make particles wobble around the horizontal plane [START_REF] Cho | On the orientation of ice crystals in a cumulonimbus cloud[END_REF], and theoretical models suggest that smaller particles (diameter of ~30 μm) could also adopt a preferential orientation, but with a wider tilt angle (10-20°) from the horizontal plane [START_REF] Klett | Orientation model for particles in turbulence[END_REF]. Early densitometer scans of photographic observations of light pillars in ice clouds [START_REF] Sassen | Remote sensing of planar ice crystals fall attitude[END_REF] showed a Gaussian evolution of light intensities in horizontal cross-sections, leading to the conclusion that crystal tilt angles follow a Gaussian distribution. This hypothesis was later confirmed by further observations compared to numerical simulations [START_REF] Sassen | Polarization and brewster angle properties of light pillars[END_REF] and, more recently, by a heuristic model of particle dynamics in turbulence based on their shapes [START_REF] Klett | Orientation model for particles in turbulence[END_REF].

b. Studies of crystals orientation by lidar

While the first studies of ice crystal orienations in the atmosphere used direct photography (e.g., [START_REF] Sassen | Remote sensing of planar ice crystals fall attitude[END_REF], the lidar polarization technique was soon found to provide quite useful information. Owing to its high sensitivity to optically thin cloud layers, this instrument has been extensively used to study cirrus clouds. Lidars with polarization capabilities emit (usually vertically) a light beam linearly polarized in a given plane. The linear depolarization ratio  is then defined as = P ⊥ P ∥ , with P ∥ and P ⊥ powers returned to the lidar receiver, which are, respectively, parallel and orthogonal to the plane of the power transmitted [START_REF] Schotland | Observations by lidar of linear depolarization ratios by hydrometeors[END_REF]. This quantity, which is sensitive to the shape and orientation of the particles probed by the lidar, was shown at first to provide unambiguous cloud phase discrimination [START_REF] Pal | Polarization properties of lidar backscattering from clouds[END_REF][START_REF] Liou | Laser sensing of cloud composition : A backscattered depolarization technique[END_REF], and later distinguish between crystal shapes [START_REF] Sassen | Ice crystal habit discrimination with the optical backscatter depolarization technique[END_REF].

In the presence of oriented crystals in clouds, the lidar returns display very low values of  and high backscattered intensities [START_REF] Platt | Lidar backscatter from horizontal ice crystal plates[END_REF]. This specific signature can be attributed either to planar crystals with their main faces aligned horizontally, or more rarely to columns with their main axis aligned horizontally and a pair of prism faces parallel to the ground. This phenomenon is distinguished from water cloud backscattering, which also lead to low values of , by tilting the lidar pointing direction, or lidar angle. When oriented crystals are present,  increases rapidly as the lidar beam moves away from the zenith direction [START_REF] Platt | Some microphysical properties of an ice cloud from lidar observations of horizontally oriented crystals[END_REF]), a behavior reproduced by simulations [START_REF] Mishchenko | T-matrix computations of zenith-enhanced lidar backscatter from horizontally oriented ice plates[END_REF]). This has led to several lidar-based studies of crystal orientation, showing for example that horizontally-oriented crystals are present in any temperature range [START_REF] Thomas | Lidar observations of the horizontal orientation of ice clouds in cirrus clouds[END_REF]). Scanning lidars are the logical progression of this technique, and lead to graphic observations of oriented crystals and particles in clouds [START_REF] Roy | Retrieval of droplet-size density distribution from multiple field-of-view cross-polarized lidar signal: theory and experimental validation[END_REF]Sassen and Takono 2000). With such instruments, the change in  can be closely monitored while the lidar incidence angle on the cloud changes continuously. Recently, the angular evolution of the lidar depolarization ratio was shown to contain significant information on the orientation behavior of plate-like crystals [START_REF] Noel | Analysis of ice clouds lidar measurements at multiple incidence angles[END_REF]: when plotting  as a function of the incidence angle, the inflexion point where the change is fastest (i.e., the derivative reaches a maximum) gives an approximation of the maximum deviation angle of the ice plates. Although it is principally planar ice crystals that produce this angular dependence with lidar, the observations from [START_REF] Sassen | Parry arc: A polarization lidar, ray-tracing, and aircraft case study[END_REF] have shown that rare occurrence of horizontally-oriented columns crystals falling with a pair of prism faces parallel to the ground can also generate a backscattering maximum in the zenith direction. However, this condition, which produces the rare Parry arc from refracted sunlight, leads to unique strong lidar depolarization as the lidar is scanned a few degrees off the zenith, and so has a very different signature than horizontally oriented plates crystals.

The FARS Scanning Lidar Dataset

The present paper uses observations of cirrus and midlevel clouds from the scanning Polarization Diversity Lidar or PDL [START_REF] Sassen | Advances in polarization diversity lidar for cloud remote sensing[END_REF]. This dual-wavelength (0.532 and 1.06 m)

lidar records atmospheric profiles of backscattered intensity and depolarization ratio with a maximum resolution of 1.5 m and a maximum scanning of 5 s -1 . Depolarization ratio is calibrated by taking into account the difference between receiver channel gains, and alignment variations by fixing the depolarization ratio at δ~0.02 in mid-to upper-tropospheric signals believe to contain to significant aerosols or cloud backscattering [START_REF] Young | Revised depolarization corrections for atmospheric extinction[END_REF].

The dataset analyzed here was collected at the Facility for Atmospheric Remote Sensing (FARS, see [START_REF] Sassen | A midlatitude cirrus cloud climatology from the facility for atmospheric remote sensing. Part II: Microphysical properties derived from lidar depolarization[END_REF] in Salt Lake City, Utah, between 1994 and 2000. Note that although efforts were made to orient the laser table to the zenith direction for these scans using an electronic level, positioning errors of 0.5 -1.0 can occur due to slight movements of the truck containing the PDL. Of the 37 distinct periods of consecutive 10 scans around the zenith direction (at a 1.0 s -1 scan rate) examined in this study, a total of six cases of oriented plate-like crystals in clouds showed consistently strong angle-dependent effects and were selected for detailed study. Some of these observations were made in response to indications of oriented crystal effects by the PDL or polarization ruby lidar at FARS. Although this scanning dataset is too small to draw conclusions on the overall frequency of oriented ice crystal effects in cirrus clouds, more climatologically-representative results can be found in [START_REF] Sassen | A midlatitude cirrus cloud climatology from the facility for atmospheric remote sensing. Part II: Microphysical properties derived from lidar depolarization[END_REF].

The detailed FARS case study of 11 January 1999 will first be illustrated, before the analysis is applied to the entire dataset. The rare case featuring column crystals [START_REF] Sassen | Parry arc: A polarization lidar, ray-tracing, and aircraft case study[END_REF] will also be presented to highlight the different observations resulting from particle shape and fall variations.

The 11 January 1999 Case Study a. Lidar observations

Between 2122 and 2330 UTC on 11 January 1999, a cirrus cloud located between 7.0 and 8.6 km (above mean sea level, MSL) was observed by the scanning lidar at the FARS location. The observations at the zenith angle tend to show  <~0.15, while ~0.45 is measured in the surrounding cloud (Fig. 1a). In the zenith column between 7.0 and 7.5 km, much lower values of <0.05 are indicated. As altitude increases above 7.5 km, this minimum becomes less marked and becomes narrower, but is still visible up to ~8.0 km. Conversely, the relevant backscattered intensity (Fig. 1b) shows a marked increase in the same central region.

Observed values of  in the horizontal cloud layer between 7.1 and 7.2 km are plotted in Fig. 2a (top) as a function of the lidar angle from the zenith  (with =0 being the zenith direction).

Outside the central region ( > 4.0),  is gathered around 0.3. Closer to the zenith, the depolarization ratio depends strongly on , with many data points decreasing to near zero in the zenith angle. Values of  show a high variability when viewed at these small spatial scales due to the effects of signal noise and the small cloud volumes sensed. This variability can be reduced by averaging the parallel and perpendicular lidar signals before computation of the ratio, although by averaging over too large scales most of the microphysical meaning of the depolarization ratio is lost, so this should be done with great care.

As also apparent in Fig. 1b, the backscatter intensity follows the opposite behavior, with a marked maximum in the zenith direction (Fig. 2b). Compared to lidar depolarization, these values are less scattered and the central peaked region is noticeably more narrow. This last difference can be explained by looking at how both values (depolarization ratio and backscattered intensities) depend on the number of horizontally-oriented crystals with respect to the entire population of crystals. Linear depolarization ratio in presence of horizontally-oriented particles can be written as

= r /[1 N h / N r   h /  r ] (1)
where  r refers to the linear depolarization ratio for randomly-oriented particles, and N and β are the relative concentrations and backscattering coefficients for horizontally (h) and randomly (r) oriented particles [START_REF] Sassen | A midlatitude cirrus cloud climatology from the facility for atmospheric remote sensing. Part II: Microphysical properties derived from lidar depolarization[END_REF]. As Eq. 1 was initially developed for zenithpointing lidar, when considering a scanning lidar the h subscript needs to be extended to include all planar particles with their hexagonal faces orthogonal to the lidar beam direction. Using  r =0.33 for randomly oriented particles, =0.06 at zenith (as Fig. 2a shows) and  h /  r = 360:1, as reported by [START_REF] Sassen | Ice crystal habit discrimination with the optical backscatter depolarization technique[END_REF], in Eq. 1 leads to N r / N h =80:1 at zenith.

Using the same notations, the backscattered intensity can be written as :

=[  h /  r ]/ [1 N r / N h ] (2)
As generally N r / N h ≫1 , and  h /  r is a constant, it follows that N h / N r is directly proportional to β. As N h / N r describes particles with hexagonal faces orthogonal to the lidar beam direction, basic geometry shows that the angular half-width of this ratio, and therefore of β, should be linked to the average deviation angle of horizontally-oriented crystals. This is coherent with observations, that show the angular half-width to be smaller for β (correlated with the average deviation angle, Fig. 2b), than for δ (correlated with the maximum deviation angle, Fig. 2a). Normalizing the backscattered intensity to =1 at zenith, Figure 3 shows that backscattered intensity decreases much faster than depolarization ratio increases. A noticeable impact on backscattered intensity requires a much lower ratio N r / N h (hence an incidence angle closer to zenith) than for depolarization ratio, leading to a narrower peak on angle-dependent observations.

However, the backscattered intensity, unlike the depolarization ratio, is attenuated by the cloud optical depth. Considering oriented crystals at a given altitude, the length of the laser path will increase with the lidar incidence angle θ, and more particles will contribute to laser attenuation.

Due to the inhomogenous distribution of particle concentrations in the cloud, this change in attenuation is difficult to quantify. The depolarization ratio is not affected by this problem, and seems more adapted to the current method of analysis.

b. Analytical model and retrieval technique

The lidar depolarization ratio display of Fig. 2a suggests that the angular evolution of  in a given cloud height layer can be described with three parameters :

• The linear depolarization ratio value in the zenith direction  zen ,

• The linear depolarization ratio value outside the central region  off ,

• The angular half-width of the central peak .

In agreement with earlier studies, our observations strongly suggest a Gaussian function, so by taking into account the three parameters  zen ,  off and , a possible analytical model for the depolarization ratio is given by the function :

 sim = off -exp   2 2 2   off - zen  (3)
It is important to note that in this model the Gaussian function standard deviation  is also the angular half-width of the central peak and marks the inflexion point of the evolution of angular  values. As the observed inflexion point is linked to the angular deviation of crystals, retrieving  using this model will directly quantify the maximum deviation of crystals from the horizontal plane in the each cloud. A near-perfect horizontal orientation of plate crystals will produce a narrow peak of  in the zenith direction and a low value of .

To fit the simulated function  sim () to actual observations, only complete lidar scans are considered. In each scan,  is considered in horizontal layers defined by consecutive altitude bins (the data shown in Fig. 2 is a good example). First approximations for  zen and  off are obtained by considering near-zenith ( < 0.5) and off-zenith ( > 5.0) observations in each altitude range.

These values are used as a starting point for a Levenberg-Marquardt least-square minimization fitting technique. Stopping the process after 700 iterations was found to provide stable results.

Variations of 0.2 around the mean values were allowed for  zen and  off , while a variation range betwen 0 and 10 is allowed for . For the retrieved parameters to be considered as part as an oriented crystal area, three conditions must be fulfilled.

i. High off-zenith depolarization ratio

To ensure the presence of an ice cloud in the considered horizontal layer, high values of offzenith depolarization ratio  off are required (typically,  off > 0.05 was found to be sufficient). For the 11 January 1999 case,  off (Fig. 4) slowly increases from 0.3 at the cloud base (6.9 km) to 0.38 at the cloud top (8.6 km). The higher value above 8.6 km implies a difference in ice particle shapes.

ii. Significantly lower zenith depolarization ratio High values of  off and low values of zenith depolarization ratio zen are a strong indication of oriented ice crystals. However, variations in  with the incidence angle could also come from other spatial microphysical changes in the cloud. To ensure the presence of oriented ice crystals, a significant decrease in depolarization ratio between off-zenith and zenith is required (typically, a 10 % decrease was found to be sufficient). For the 11 January 1999 case, the vertical profile of  zen (dashed line in Fig. 4) stays below 0.2 between 6.9 km (the cloud base) and 7.5 km, i.e. a more than 30 % decrease from the off-zenith values. For altitudes above 7.5 km,  zen is higher but still low enough to warrant the detection of oriented crystals. This increase in  zen could be explained either by a lower relative concentration of horizontally-oriented crystals [START_REF] Sassen | A midlatitude cirrus cloud climatology from the facility for atmospheric remote sensing. Part II: Microphysical properties derived from lidar depolarization[END_REF], or by a change in orientation behavior due to different particle shapes or sizes. As the horizontal extent for the present case is small enough (<1.0 km) to consider the particle shape to be horizontally homogeneous, the increase in  off implies a change in particle shape.

iii. Low deviation from the Gaussian Model Even when conditions (i) (high values of  off ) and (ii) (low values of  zen ) are fulfilled, the fitting technique is sometimes not applicable : horizontal in-cloud variations of particle shape can also lead to such conditions resembling the signature of horizontally oriented plate crystals. To filter out these situations, the average difference is computed between the gaussian model and the actual observations. If this difference is higher than 20%, the retrievals are not considered to be representative of oriented crystals.

These remarks also hold true when considering observations of backscattered intensities (Fig. 2b). Taking into account that intensities are increasing in the zenith region instead of decreasing, the same technique can be applied.

c. Model retrieved parameters

As an example, fitting the function in Eq. 3 to 11 January 1999 observations for altitude range 7.1 to 7.2 km in Fig. 2 leads to retrieved parameters  zen =0.09,  off =0.32 and =1.96°. The resulting function (bold line over the observations in Fig. 2a) follows very closely the angular evolution of observations. This retrieval technique was applied to all horizontal layers for each consecutive lidar scan of the 11 January 1999 case. Retrieved angular widths plotted as a function of altitude (symbols in Fig. 5a, averaged in full line) shows 1.4° at cloud bottom (near 7.0 km), decreasing to as low as 0.4° at mid-cloud (7.5 km), and increasing again up to 1° at higher levels. The absence of valid retrievals above 8.1 km is due to the uncertainties becoming too large to ensure a good fit between the observations and the analytical model. These results reflect closely the vertical changes in the vertical column of low  shown in Fig. 1.

A similar analysis was conducted on the corresponding observations of backscattered intensities. For the horizontal cloud layer shown in Fig. 2b, a value of =0.90° was found for the angular half-width. The vertical profile of retrieved angular widths (Fig. 5b) shows that results are only retrieved in the 7.0 -7.5 km altitude range, and that successful retrievals are fewer than when studying the linear depolarization ratio. The disappearance of the central peak for higher altitude is also apparent in the scanning image (Fig. 1b). The fitting technique is overall less successful than with depolarization ratio. However, it should be noted that in this limited altitude range, the peaks of high intensities in the zenith area are narrower (generally  < 1°) than their depolarization counterparts (0.7° <  < 1.4° in Fig. 5a).

A singular case of Parry-oriented columns

On 16 November 1998, a cirrus producing an upper Parry Arc was probed by the scanning PDL for more than 6 minutes, revealing unusual observations of angle-dependent  [START_REF] Sassen | Parry arc: A polarization lidar, ray-tracing, and aircraft case study[END_REF]. The example in Fig. 6 shows an off-zenith depolarization ratio 0.35< off <0.45, with a much lower 0.2 in the zenith direction, following the plate crystal behavior. However, for a small tilt angles from the zenith, extremely high values of depolarization ratio (>0.8) are observed, which is clearly different from the behavior of oriented plate-like crystals showed in case 1 (Sect. 4).

Values of  in the horizontal cloud layer between 8.1 and 8.2 km, plotted as a function of the lidar angle from zenith  (Fig. 7), reveal a slight asymmetry (the minimum  is found at  =+0.5°), which can be attributed to a small error in the level of the PDL system. Taking this offset into account, the maximum values of   1.2 are found at incidence angles 1.5 off the zenith. This rare angular evolution of  was explained in Sassen and Takono (2000) by the presence of column crystals with a pair of prism faces parallel to the ground (the so-called Parryorientation). To produce the observed displays, these crystals should bear an almost perfect horizontal orientation (deviation from horizontal below 0.5). This case highlights the strong sensitivity of scanning observations of depolarization ratios to the crystal fall behavior, and

shows that angular-dependent observations are a powerful way to discriminate between particle shapes.

This unusual behavior was only observed once in the cases analyzed for the present study, and as such is an exception. Cases presented in the rest of this paper follow the behavior described earlier, and are classified as plate-like crystals.

Retrieval of deviation angles for additional cases

The properties of six cases of oriented crystals observed in cirrus and midlevel clouds by scanning lidar are summarized in Table 1, including the thickness and temperature ranges of oriented crystal layers. Oriented crystals can be observed for time periods as long as 25 minutes.

Example scans for cases 2 to 6, similar to the one shown in Fig. 1 for case 1, are given in Fig. 8.

The fitting technique using Eq. 3 was applied, with the three criterias (Sect. 4.b) being fulfilled in 13.5% of all horizontal layers. In each case, the three parameters,  zen ,  off and  were retrieved.

However, the layers of horizontally oriented crystals do not share the same altitudes. To allow for the study of the vertical evolution of retrieved parameters, the observations are analyzed as a function of therelative penetration depth into the layer of oriented crystals (0 % meaning layer bottom and 100 % layer top). In all cases, ice clouds continued to be probed above the oriented crystals layer.

The particle orientation behavior mostly depends on the particle shape [START_REF] Klett | Orientation model for particles in turbulence[END_REF]. In absence of a preferential orientation of crystals, the lidar depolarization ratio is indicated to convey meaningful information about the shape of crystals probed by polarized laser light [START_REF] Sassen | The polarization lidar technique for cloud research: A review and current assessment[END_REF]. Thus  off can reveal possible differences in crystal shape between the studied cases. Plotting  off as a function of layer penetration (symbols in Fig. 9, averaged profiles in thick lines) seperates the cases into two groups centered around  off  0.25 (cases 3, 4 and 5, diamonds and full line in Fig. 9) and  off  0.35 (cases 1, 2 and 6, crosses and dashes line in Fig. 9). Table 1 shows that T>-20°C for oriented crystals in the first group (warm clouds), and T<-30°C for the second group (cold clouds). This seperation can be explained by the strong influence of temperature on the crystal growth process, and therefore on their shape, which controls the orientation behavior. In the following sections, retrieved parameters will be seperated into these two groups, to highlight possible different orientation behavior modes based on particle shape.

The fact that no oriented crystals are found below -40°C is a consequence of the limited dataset, as crystal orientation is present at all temperatures [START_REF] Thomas | Lidar observations of the horizontal orientation of ice clouds in cirrus clouds[END_REF].

a. Vertical profiles of angular widths

Angular widths for the warmer clouds (Fig. 10a) are very scattered with altitude. However, the average profile for all cases (bold line) stays between 1.5 and 2.1 for a penetration depth below 75 %. For higher penetration depths,  then decreases to reach 1.1 at relative cloud top. Angular widths retrieved for the colder clouds (Fig. 10b) follow a behavior similar to the 11 January 1999 case (Fig. 5). The average profile for all cases (bold line) shows a maximum angular width ( 1.3) located at the layer bottom. We believe that when oriented crystal effects are present near cloud base, the angular widths of the near-zenith depolarization trough (and the backscattering peak) characteristically increase as a result of the effects of ice crystal evaporation, which reduces ice crystal size and thus increases the fall instability [START_REF] Sassen | Remote sensing of planar ice crystals fall attitude[END_REF]. The angular width then decreases with increasing altitude, with a minimum value (0.6) reached at 40 % penetration depth. Finally  increases again, with a second maximum 0.8 observed around 80 % penetration.

b. Angular frequencies

Overall, valid angular half-widths highlighting the presence of oriented crystals were retrieved in 27.6 % of the cloud layer bins for the 6 selected case studies. This frequency should not be extended to all ice clouds, however, because the dataset was selected to favour oriented crystal observations, and the analysis method used here rejects weak orientation effects. It shows, though, that when oriented crystals are present, their coverage can extend on average to a third of the cloud layer.

In the studied warmer cloud cases, oriented crystals were detected in 22.5 % of the probed altitude ranges. Retrieved angles for these clouds (Fig. 11a) follow a rather smooth distribution, with maximum frequencies for half-width angles 1.75 <  < 2.25, and 54 % of them between 1.0 and 3.0. Frequencies decrease as angles move away from this range : 18 % of angles are below 1.0, with a minimum 6 % reached for angles below 0.25; 28 % of angles are above 3.0, with frequencies decreasing slowly to 4 % for angles > 4.75.

In the studied cases of colder clouds, oriented crystals were detected in 35.8 % of the probed altitude ranges. Retrieved half-width angles for these clouds (Fig. 11b) follow a more narrow distribution, centered on lower angles ranging from 0.75 <  < 1.25. Only 18.5 % of angles are above 1.75, with that number falling under 7 % above 3.0. Small angles are dominant, with 81.5 % of angles below 1.75, compared to 36.5 % for warmer clouds (Fig. 11a).

c. Angles retrieved from analysis of backscattered power

The angular variations of observed backscattered intensities were also fitted to the model in Eq. 3 for all cases. However, as noted earlier, results from the analysis of backscattered intensities often have higher uncertainties than when studying depolarization ratios. For cases when angle retrieval was possible using  scans, only 5 % of the cases analyzed using backscattered intensities gave confident results. For those cases, the retrieved angular deviations  pow are plotted in Fig. 12 as a function of the corresponding angular deviation  retrieved from the  analysis. When the depolarization ratio analysis leads to angular deviations between 0.25 and 3.0 , the associated  pow lies between 0.2 and 2.0. Least-square fitting on a second-order polynomial (dotted line) shows that for an increase from 0.25 to 0.3 in ,  pow slowly increases from 0.2 and reaches saturation around 2.0. As the half-widths from backscattered power are linked to the average deviation angle (Sect. 4a), this shows that the maximum deviation angle increases faster than the average deviation angle. As the variability of angles retrieved from backscattered intensities seems to be lower than from analysis of depolarization ratios, this suggests the angular evolution of the lidar depolarization ratio is more sensitive to changes in microphysical properties, and is better suited for studies of crystal orientation.

Discussion and Conclusions

A technique aimed at estimating the maximum deviation angle of horizontally-oriented plate crystals was presented, fitting the variation of depolarization ratio with the lidar incidence angle to a Gaussian model. The model reproduces observations of  for plate-like particle cases. A very rare case of oriented columns exhibits a strongly contrasting behavior, which prevents confusion between the two crystal shapes.

Planar crystals in warm (>~-20C) midlevel clouds show overall a higher half-width angle, centered on an average 2.0 and distributed smoothly between 0 and 5.0 (Fig. 11a). For crystals in cold (<~-30C) cirrus clouds, more than half of the retrieved angles below 1.0 (Fig. 11b). As the half-width is related to the maximum deviation angle, crystals appear more closely oriented with the horizontal planes in cold clouds. This difference must come from different particle shapes, as suggested by the difference in  off between cold and warm clouds (Fig. 9). The most plausible explanation is that the differences in temperature have favored the growth of large and more widely fluttering dendritic ice crystals at >~-20C, although the  values for dendrites have not yet been estimated from theory. An analog exists, however, in terms of observations : the sun pillar optical phenomenon, which is caused by the reflections from fluttering ice crystals off the setting/rising sun. The angular height of the pillar increases as the crystal wobble angle from the horizontal plane increases, and extended observations show that proper sun pillars are rare in cirrus clouds, but often spectacular in the ice crystals falling below mixed phase clouds at warmer temperatures [START_REF] Sassen | A midlatitude cirrus cloud climatology from the Facility for Atmospheric Remote Sensing: IV. Optical displays[END_REF]. Similarly, the tendency for the deviation angles to increase significantly at cloud base also reflects wider fluttering motions, which in this case seem to be due to the effects of crystal evaporation that decrease crystal size and fall atitude stability. These different orientation behaviors could also be explained by atmospheric dynamics : more laminar air motions in higher, colder clouds, would lead to almost-horizontal orientations, while more turbulent motions in lower, warmer clouds, unable to destroy the orientation itself [START_REF] Cho | On the orientation of ice crystals in a cumulonimbus cloud[END_REF], would nethertheless lead to an increase in crystal deviation from the horizontal plane.

Among the six studied cases, crystals in cold clouds are more closely aligned with the horizontal plane, and their angular half-width is smaller by 1.0 than in warm clouds, so the maximum deviation angle should follow the same trend. Moreover, the relative frequency of oriented crystals is higher in cold ( 35 %) clouds than warm ( 22 %) clouds. If this behavior holds true for more robust sample sizes, it may have noticeable radiative consequences.

Horizontally oriented particles increase the hemispherical albedo effect of a given cirrus cloud, and the more closely aligned are the particles, the higher the increase. The impact of particle alignment on the radiative properties has to be quantified, but if results from the present study are representative of most ice clouds, oriented crystals would influence more the radiative balance of cirrus clouds than other ice clouds. As changes in high cloud albedo directly impact the transfer of radiation through the troposphere at visible wavelengths, this phenomenon could have important consequences for the global radiative budget. To estimate these effects, large-scale studies of crystal orientation in cirrus clouds are required. This could be possible through application of similar analysis to multi-angle satellite observations. For instance, polarized radiances from the POLDER instrument have been shown to contain valuable information on oriented particles [START_REF] Chepfer | Observations of horizontally oriented ice crystals in cirrus clouds with POLDER-1/ADEOS-1[END_REF][START_REF] Noel | Study of ice crystal orientation in cirrus clouds based on satellite polarized radiance measurements[END_REF]. However, as was shown in the present paper, scanning lidar not only allows an analysis of the crystal orientation, but also

Figure 1

 1 Figure 1. a. PDL scanning observations of linear depolarization ratio at 10 zenith angle on 11 January 1999. b. Same as 'a' but for backscattered intensities.

Figure 2

 2 Figure 2. a. Observations of linear depolarization ratio as a function of the lidar incidence angle between 7.1 and 7.2 km. b. Same as 'a' but for backscattered intensities.

Figure 3 .

 3 Figure 3. Model results showing the dependence of the linear depolarization ratio and backscattered intensity on the ratio of randomly to horizontally oriented plate ice crystals.

Figure 4 .

 4 Figure 4. Profile of off-zenith linear depolarization ratio.

Figure 5

 5 Figure 5. a. Retrieved half-width angles  for Gaussian functions fitted to depolarization ratios as a function of altitude. b. Same as 'a' but fitted to backscattered intensities.

Figure 6 .

 6 Figure 6. Same as Fig. 1 but for the 16 November 1999 case.

Figure 7 .

 7 Figure 7. Same as Fig. 2 but for 16 November 1999 case between 8.1 and 8.2 km.

Figure 8 .

 8 Figure 8. Same as Fig. 1 but for cases 2 to 6.

Figure 9 .

 9 Figure 9. Profiles of off-zenith linear depolarization ratios for all cases.

Figure 10

 10 Figure 10. a. Retrieved half-width angles  for gaussian functions fitted to depolarization ratios as a function of altitude, for warmer clouds. Dashed lines are averages for each single case, and the full line is the total average. b. Same as 'a' but for colder clouds.

Figure 11

 11 Figure 11. a. Histogram of retrieved half-width angles  for warmer clouds. b. Same as 'a' but for colder clouds.

Figure 12 .

 12 Figure 12. Deviation angles retrieved from analysis of backscattered intensities plotted as a function of the corresponding angles retrieved from analysis of linear depolarization ratio.

Table Captions Table 1 :

 Captions1 Properties of the layers of Oriented Crystals (OC) observed in cirrus clouds by scanning lidar in the studied cases.

	Case	Date	Time [min]	Cloud altitude [km]	OC Layer Thickness [km]	OC Freq. [%]	Top T°[ °C]	Bottom T°[ °C]
	1	1999-01-11 12	6.9 -8.6	0.9	50.9	-32.6	-26.8
	2	1999-01-11	8	6.3 -8.3	0.8	35.7	-32.0	-26.8
	3	2000-11-22 25	4.8 -6.4	0.6	20.7	-22.6	-17.8
	4	2001-04-27 12	4.2 -6.5	0.4	25.0	-16.7	-13.4
	5	2000-03-27 17	4.0 -5.0	0.4	22.0	-7.9	-6.8
	6	1998-11-16 12	7.4 -10.0	0.8	25.8	-36.3	-30.3
					Table 1:

Acknowledgements. This research was supported in part by NASA-Langley Research Center, under contract NAS1-02058. The FARS data used in this study has been collected and analyzed under support from NFS grants ATM-9528287 and ATM-0296190. The PDL system was developed under DOE grant DEFG-0394ER747 from the Atmospheric Measurement Program.

The authors would like to thank Dave M. Winker for his support, and the reviewers for their useful comments.

provides ways to correlate the retrieved properties with their synoptic and microphysical context.

The presence of such an instrument on a spaceborne platform [START_REF] Winker | The CALIPSO Mission : Spaceborne Lidar for observations of Aerosols and Clouds[END_REF], with a smaller scanning angle (e.g. 1°) to compensate for the high altitude, would greatly improve the current knowledge of cirrus clouds microphysics in general.