ARTICLE IN PRESS Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 www.elsevier.com/locate/jqsrt Sensitivity of depolarized lidar signals to cloud and aerosol particle properties Yu Youa,!, George W. Kattawara, Ping Yangb, Yong X. Huc, Bryan A. Baumc a Department of Physics, Texas A&M University, College Station, TX 77843, USA Department of Atmospheric Sciences, Texas A&M University, College Station, TX 77843, USA c NASA Langley Research Center, Hampton, VA 23681, USA b Abstract Measurements from depolarized lidars provide a promising method to retrieve both cloud and aerosol properties and a versatile complement to passive satellite-based sensors. For lidar observations of clouds and aerosols, multiple scattering plays an important role in the scattering process. Monte Carlo simulations are carried out to investigate the sensitivity of lidar backscattering depolarization to cloud and aerosol properties. Lidar parameters are chosen to be similar to those of the upcoming space-based CALIPSO lidar. Cases are considered that consist of a single cloud or aerosol layer, as well as a case in which cirrus clouds overlay different types of aerosols. It is demonstrated that besides thermodynamic cloud phase, the depolarized lidar signal may provide additional information on ice or aerosol particle shapes. However, our results show little sensitivity to ice or aerosol particle sizes. Additionally, for the case of multiple but overlapping layers involving both clouds and aerosols, the depolarized lidar contains information that can help identify the particle properties of each layer. r 2005 Elsevier Ltd. All rights reserved. Keywords: Space-borne lidar; CALIPSO; Depolarization; Clouds; Particle shape 1. Introduction Data from satellite-based radiometers have been used to determine a variety of cloud properties such as cloud pressure/temperature, thermodynamic phase, optical thickness, and effective particles size . However, in many cases (e.g., mixed-phase clouds or multiple but overlapping cloud layers), the interpretation of passive radiometer measurements is problematic, and often fails to allow an unambiguous determination of cloud phase as well as the predominant shapes of ice-cloud particles, both of which are of great importance in the determination of other cloud properties. The development of polarized lidar techniques over the past three decades provides a complementary way to infer cloud properties. Numerous studies have shown that lidar backscattering depolarization measurements can be used to infer the cloud thermodynamic phase and shape of ice-cloud particles . Through analysis of depolarized lidar backscattering signals, it is possible to classify cloud particle sphericity and thus infer more !Corresponding author. 0022-4073/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jqsrt.2005.11.058 ARTICLE IN PRESS Y. You et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 471 information about the cloud thermodynamic phase. As a simple example, for a lidar with small field of view (FOV), single backscattering dominates. In this case non-polarized backscattering signals imply water (spherical particle) clouds, while highly polarized backscattering signals imply ice (non-spherical particle) clouds. Aerosols tend to have much smaller particles than ice clouds, in general, and their asphericity should also be further investigated. Besides water and ice clouds, atmospheric aerosols also play an important role in climate studies . It is also reasonable to expect that the lidar backscattering depolarization measurements could provide information for shape (aspect ratio) of aerosols. Both ground and aircraft-based depolarization lidars have been studied extensively in previous work [4,5]. One of the available space borne lidars is the Cloud Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) . Unlike ground-based lidar systems, the space-based CALIPSO lidar samples a large horizontal span of the atmospheric volume within its receiver FOV, and thus is likely to detect multiply scattered photons. The multiple scattering in the signal introduces ambiguity in the discrimination between water and ice particles. As a standard polarization-sensitive lidar, the CALIPSO laser beam is linearly polarized, with the Stokes vector fI 0 ; Q0 ; U 0 ; V 0 g ¼ f1; 1; 0; 0g. Other studies have analyzed the backscattering signals by lidar with a right-handed circularly polarized laser beam , for example with fI 0 ; Q0 ; U 0 ; V 0 g ¼ f1; 0; 0; 1g. In this paper, we first briefly show what information can be obtained from depolarization data, and then present model results from Monte Carlo simulations of the multiple scattering process in the depolarized laser beam for clouds and aerosols. Finally, methods are suggested to infer microphysical properties of both clouds and aerosols. As an example, we investigate the behavior of a system in which an ice cloud, consisting of nonspherical particles, overlays an aerosol layer composed of either soot or dust. 2. Lidar depolarization method For randomly oriented particles having a plane of symmetry, the phase matrix (Mueller matrix) has only six parameters and relates the incident and scattered beams by 2 3 2 32 3 P11 P12 I0 0 0 I 6 Q 7 6 P12 P22 6 7 0 0 7 6 7 6 7 6 Q0 7 (1) 6 7¼6 7 :6 7, 0 P33 P34 5 4 U 0 5 4U 5 4 0 0 0 "P34 P44 V0 V where fI 0 ; Q0 ; U 0 ; V 0 g and fI; Q; U; V g are the incident and scattered Stokes vectors, respectively, and fPij g are the elements of the single scattering phase matrix, which are functions of the scattering angle Y . For a linearly polarized incident laser beam, the linear depolarization, dL , is defined by dL ¼ jE ? j2 I " Q . ¼ jE jj j2 I þ Q (2) For spherical particles, P11 ¼ P22 and P12 ð180% Þ ¼ P21 ð180% Þ ¼ 0. And since initially fI 0 ; Q0 ; U 0 ; V 0 g ¼ f1; 1; 0; 0g, we have dL ¼ 0. Thus for spherical particles, the single scattered signals are not depolarized. A Monte Carlo scheme was used to simulate the multiple scattering process. The geometry of a scattering event in the simulation is shown in Fig. 1. Fig. 1(a) shows the definition of DOdish , the solid angle viewing the lidar aperture from the location of the scattering event. For each collision inside the lidar FOV, we estimated the power that directly enters the sensor due to the backscattered photon through the following relationships: i ¼ oDOdish r2 expð"brÞI, where o is the single scattering albedo, DOdish is as defined in Fig. 1(a), b is the extinction coefficient, r, as has been shown in Fig. 1(a), is the distance between the sensor and the location of scattering, and I is the radiance. Note that I represents the power per unit area per unit solid angle, so I multiplied by DOdish r2 is the power that enters the solid angle DOdish . ARTICLE IN PRESS 472 Y. You et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 (a) (b) Fig. 1. Geometry of a lidar system showing the rotation angles from a scattering event in the Monte Carlo simulation. Fig. 1(b) illustrates the rotation of the plane of reference, where ninc and nsca are directions of motion for the incident and scattered beams, respectively, and Y is the scattering angle. For each scattering event, the Stokes vector is given by  2 3 2 3 I0 I 6Q 7 6Q7 6 07 6 7 (3) 7, 6 7 ¼ Lð"F2 ÞPðYÞLð"F1 Þ6 4 U0 5 4U 5 V0 V where PðYÞ is the single scattering phase matrix and Lð"F2 Þ and Lð"F1 Þ (4) are rotation matrices. As has been illustrated in Fig. 1(b), the incident Stokes vector is referenced to the incident meridian plane. It is first rotated from the meridian plane to the scattering plane by a multiplication of Lð"F1 Þ, and then multiplied by PðYÞ to obtain the scattered Stokes vector in the scattering plane. Finally a multiplication by Lð"F2 Þ rotates this scattered Stokes vector from the scattering plane into the scattered meridian plane. Since differences in single scattering phase matrices lead to differences in multiple scattering Mueller matrices, one can expect that the depolarization values may provide useful information about the scattering particles. 3. Model results This study simulates the depolarization of CALIPSO lidar backscattering at a wavelength of 532 nm. The receiver has a 0.13 mrad FOV. The incident Stokes vector is given by fI 0 ; Q0 ; U 0 ; V 0 g ¼ f1; 1; 0; 0g. (5) The anticipated satellite altitude is 705 km, so that the diameter of the field of view is approximately 91 m. For simplicity, we assume that the laser transmitter has zero divergence. In our simulations, a Gamma distribution  NðrÞ ¼ N 0 rm e"Lr (6) is assumed to describe the range of particle sizes within the clouds, where r is the particle radius, N0 is the normalizing parameter, m is the shape parameter, and L is the scale parameter. The effective radius, reff , and effective variance, veff , defined by  ARTICLE IN PRESS Y. You et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 R r2 reff ¼ Rr1r2 r1 veff ¼ R r2 r1 rpr2 NðrÞ dr pr2 NðrÞ dr , ðr " reff Þ2 pr2 NðrÞ dr Rr , r2eff r12 pr2 NðrÞ dr 473 (7) (8) are two important parameters that characterize the distribution. 3.1. Monte Carlo simulations We used the Monte Carlo code developed by Hu et al. , which is applicable to inhomogeneous plane parallel media. The full Mueller matrix was calculated rather than just the Stokes vector. Thus, by using different incident Stokes vectors, the backscattering depolarization could be studied for a variety of cases. This code was tested through comparison with a similar Monte Carlo code developed by Kattawar and Gray , which is only applicable to a homogeneous medium. The number of photons traced was set to n ¼ 6 ' 108 for Hu et al.’s code and n ¼ 1 ' 109 for Kattawar et al.’s code. For all calculations, the averaged values were recorded for the first 0:6n; 0:65n; . . . ; 0:9n; 0:95n and n photons. To obtain results deemed to be reliable, the number of photons was chosen so that the averaged values varied within 71%. Results are shown in Fig. 2 for a test case involving spherical particles having an effective radius of 3 mm and an optical thickness of 4. Here we present the depolarization as a function of optical thickness from the cloud top. Since most lidars attenuate at optical thickness t(3, we only plotted the curve up to t ¼ 3. The comparison shows that two Monte Carlo codes agree within 2%. Since the Monte Carlo method itself introduces a 1% variation, we can claim that these two codes agree very well. 3.2. Results for both water and ice clouds Depolarization profiles were simulated for water clouds consisting of spherical droplets and for ice clouds consisting of nonspherical particles. The refractive indices of water and ice at 532 nm are 1:3343 þ 1:53 ' 10"9 i and 1:3117 þ 2:57 ' 10"9 i , respectively. For water clouds, we assumed an effective variance of 0.1 and a range of effective radii. For ice clouds, we used in situ data obtained from field experiments to derive the Fig. 2. Comparison of two Monte Carlo codes, for spherical particles with effective radii reff ¼ 3:0 mm and optical thickness t ¼ 4, as well as the fractional relative error. ARTICLE IN PRESS 474 Y. You et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 parameters and then calculated the effective variance and effective radius. Mie theory was used to provide single scattering phase matrices for water clouds. The results are as shown in Fig. 3. Since for spheres P22 ¼ P11 and P44 ¼ P33 , they are not shown in Fig. 3. We also assume a homogeneous medium with optical thickness t ¼ 4 and a cloud geometric thickness of 300 m. Fig. 4shows that for water clouds, the backscattering signal gradually depolarizes from 0 to (0.25 as the pulse moves from the cloud top toward the cloud bottom due to multiple scattering effects. Note that the depolarization profiles are almost linear in the highly depolarized region. For a given optical thickness, the Fig. 3. Single scattering phase matrices for water cloud droplets with different values of effective radii. Fig. 4. Depolarization profiles for water-droplets clouds, with optical thickness t ¼ 4, physical thickness 300 m, and various effective radii. ARTICLE IN PRESS Y. You et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 475 depolarization ratio decreases as the effective particle size increases. Although the discrepancies are small, they provide a possible approach to discriminate the effective sizes for water cloud particles. For ice clouds, the particle habits assumed for the derivation of single scattering and bulk scattering properties are presented in Fig. 5. For ice clouds, the single scattering phase matrices were calculated by the geometric optics method (GOM). The semi-width and length of the various ice particles (3D bullet rosettes, aggregates, hexagonal columns, hexagonal plates, and droxtals) are given by . The results are as shown in Fig. 6. Hu et al.  studied the sensitivity of depolarized lidar signals to ice particle habits. Only three ice habits (3D bullet rosettes, aggregates and hexagonal columns) were included in their study. In Fig. 2 of , one can see that although the depolarization profiles vary for three ice particle shapes, they are similar to each other, and have almost the same value of slope, because ‘‘the difference is due primarily to differences in the single scattering d’’. In this paper, we include two more ice particle habits (droxtals and plates), and tried to find another way to discriminate 3D bullet rosettes, aggregates and hexagonal columns. Aggregate 3D Bullet Rosette Plate Solid Column Droxtal Fig. 5. Shapes of ice crystals. Fig. 6. Single scattering phase matrices for ice crystal clouds, with different shapes. ARTICLE IN PRESS 476 Y. You et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 In Fig. 7, we present the depolarization profiles calculated with the assumption of a linearly polarized incident laser beam for ice clouds composed entirely of individual ice particle habits. As before, we only show the profiles for to3. For comparison, we also include a water cloud in this figure. First, it is clear that we can easily discriminate water clouds from ice clouds. Furthermore, there is an indication that it should be possible to discriminate droxtals, hexagonal plates and 3D bullet rosettes from each other. One can see that profiles for these three habits have different starting values and different slopes, which imply that both single scattering and multiple scattering processes affect the depolarization profiles. By contrast, the profiles for 3D bullet rosettes, aggregates and hexagonal columns are so similar that they cannot provide enough information to discriminate particle shape. Fig. 7. Depolarization profiles for three types of ice-crystal clouds, with optical thickness of t ¼ 4, a cloud geometric thickness of 300 m, with various particle shapes, compared with the profile of a water-droplet cloud. Fig. 8. Depolarization profiles for three types of ice-crystals clouds, with optical thickness of t ¼ 4, a cloud geometric thickness of 300 m, and various particle shapes. The incident beam is circularly polarized. ARTICLE IN PRESS Y. You et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 477 We now turn our attention to the discrimination of the other three shapes: 3D bullet rosettes, aggregates and hexagonal columns. Since a linearly polarized incident laser beam does not have much sensitivity, we explored the use of a right-handed circularly polarized incident laser beam. In this case, the incident Stokes vector is fI 0 ; Q0 ; U 0 ; V 0 g ¼ f1; 0; 0; 1g. As has been stated in , this can be accomplished by inserting a quarter-wave plate in front of the input beam. For this case, the backscattering circular depolarization, dC , is defined by dC ¼ jE L j2 I " V , ¼ jE R j2 I þ V (9) where EL and ER are the left-handed and right-handed circularly polarized components of the electric field, respectively. Presented in Fig. 8 are depolarization profiles for three ice particle habits. Unlike the results for a linearly polarized incident laser beam, these depolarization profiles show marked differences in slopes. Effects of multiple scattering processes also show up in these profiles, and act to magnify the differences between each of them. It is clear that a right-handed circularly polarized incident laser beam leads to a better discrimination between these three ice particle habits than does the linearly polarized incident beam. It should be noted that we introduced dC only for the purpose of discriminating these three ice particle habits. In the next section, we will switch back to dL , since the linearly backscattered signals can create the discrimination we are seeking in this study. 3.3. Dust and soot aerosols The backscattering signal caused by the presence of aerosols is quite interesting. In our simulations, we chose three cases of aerosols, including dust and soot [15–17]. The values of effective radius, effective variance and refractive index in each case are given in Table 1. To study both spherical and non-spherical (spheroidal) aerosol particles, we simulated the backscattering signals for aerosols with various ratios of horizontal to rotational axes (aspect ratio). Simulations were performed for a mineral-based type of aerosol. We used the T-matrix method  to calculate the single scattering phase matrices for spherical and spheroidal aerosol particles. A standard gamma distribution was again assumed to describe the particle sizes. The results are shown in Fig. 9. As above, we first assumed a homogeneous layer of aerosol particles with optical thickness t ¼ 4 and a geometrical thickness of 300 m. In this section, we switch back to dL . Fig. 10 shows that the backscattering depolarization profiles contain enough information to determine the aspect ratio in all cases. However, the situation is not quite the same for dust and soot aerosol particles. Figs. 10(a) and (b) imply that for dust particles, which have a small absorbing part of the refractive index, multiple scattering considerably affects the depolarization profile. For prolate spheroidal aerosol particles (aspect ratio o1), the depolarization has a relatively large initial value, and then continues to increase gradually as the beam penetrates the layer. For oblate spheroidal aerosol particles (aspect ratio 41), the depolarization has a relatively large initial value, but then decreases slightly before again increasing in value as the beam traverses the layer. The non-vanishing initial depolarization value is attributed to the particle asphericity. For spherical aerosol particles, the single scattering is simply Mie scattering, and thus the Table 1 Values of effective radius, effective variance and refractive index in each case Case Eff. radius (mm) Variance Refractive index (a) Dust (b) Dust (c) Soot 2.0 1.0 0.1 0.1 0.2 0.2 1:53 þ 0:5 ' 10"2 i 1:53 þ 0:5 ' 10"2 i 1:75 þ 0:435i ARTICLE IN PRESS 478 Y. You et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 (a) (b) (c) Fig. 9. Single scattering phase matrices for cases (a), (b) and (c), respectively, with various values of aspect ratio. ARTICLE IN PRESS Y. You et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 (a) 479 (b) (c) Fig. 10. Depolarization profiles for aerosol particles, for cases (a), (b) and (c), respectively, with optical thickness t ¼ 4, physical thickness 300 m, and various ratios of apect ratio. depolarization profile is similar to that of a water cloud. As such, the depolarization value is initially zero and increases gradually. Fig. 10(c) indicates that for soot particles, depolarization profiles are basically determined by the single scattering; multiple scattering does not have much influence on the profiles. This is a result of absorption, which leads to a smaller single scattering albedo for soot aerosol particles. Unfortunately, with highly absorbing aerosol types, the depolarization lidar does not provide information about whether the soot particles are prolate or oblate since they lead to similar depolarization profiles. However, perhaps one could attempt to discriminate spheroidal particles from spherical ones based upon whether the initial value is zero or non-zero at the top of the cloud. To show how multiple scattering influences the results, we present in Fig. 11 the ratio of backscattered radiance I due to multiple scattering over that due to single scattering. ARTICLE IN PRESS 480 Y. You et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 Fig. 11. Ratio of backscattered radiance due to multiple scattering over that due to single scattering, as a function of the optical thickness. 11km 10km I – Icecloud : ! = 0.5, " = 0.5 II 5km III – Aerosol: ! = 1.0, " = 0.2 0km Ground Fig. 12. Configuration of the ice over aerosol layers. The extinction coefficient b and the optical thickness t of each layer are as shown in the figure. From this figure, one can see that for dust particles, multiple scattering plays a more important role as the optical thickness increases. This confirms our previous statement. We now present results for a more realistic case in which an ice cloud layer overlays a dust aerosol layer (case (b)). Fig. 12 shows the physical configuration. In regions I and III, there are ice cloud and aerosol layers, respectively. While in region II, there is clear atmosphere. Note that at the 532 nm wavelength, the extinction coefficient for clear atmosphere is b(0.01 km"1 , so the optical thickness in region II is t(0:05, which is by far smaller than those for the other two regions. Thus for simplicity, we can assume that there is no scattering in region II. In Fig. 13, we plot the depolarization as a function of geometrical thickness from the cloud top. Here we can see that in regions I and II, the three depolarization profiles are almost the same, as expected. Note that in region II, all profiles oscillate sharply. In this region, there are few photons backscattered from the particles; hence the stability of the Monte Carlo simulation becomes poor. In region III, the profiles differ from each other. For spherical aerosol particles, the depolarization sharply drops to zero, and then increases very slowly. For spheroidal aerosol particles, the depolarization drops to the non-vanishing single scattering value (compare with profiles in Fig. 10), and then remains at this value. Fig. 13 implies that lidar backscattering ARTICLE IN PRESS Y. You et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 481 Fig. 13. Depolarization profiles for overlapping layers, with ice cloud over aerosol, with various values of aspect ratio. The optical thickness and extinction coefficient of each layer are as shown in Fig. 11. depolarization signals can provide useful information about the aerosol particles even if a relatively thin ice cloud layer overlays it. 4. Summary We have shown that lidar backscattering polarization measurements can provide important information about cloud and aerosol particle properties. For the CALIPSO spaceborne lidar, multiple scattering must be considered because of the relatively large field of view. To simulate this multiple scattering process, a Monte Carlo scheme is proposed. Water clouds, ice clouds, and aerosols are included in this investigation. The detailed results are as follows: (a) For spherical particles (e.g., water cloud), the depolarization profile has an initial value of 0 and increases rapidly because of multiple scattering. The lidar backscattered signals indicate some sensitivity to the effective particle size. The results also show that for a given value of optical thickness, the depolarization ratio decreases as the effective particle size increases. (b) For non-spherical particles (e.g., ice cloud), the depolarization profile is shown to have considerable sensitivity to particle habit. We suggest that a linearly polarized incident laser beam can be used to discriminate droxtals and plates from bullet rosettes. It is also suggested that a circularly polarized incident laser beam can be used to discriminate aggregates and columns from bullet rosettes. (c) For aerosol particles, the depolarization profile is sensitive to the particle asphericity. If the particles are not highly absorbing (i.e., the imaginary portion of the refractive index has a low value, e.g., dust particles), one can even reasonably discriminate between prolate and oblate particles. (d) For a more complex case involving an optically thin ice cloud overlying an aerosol layer, it should be possible to infer useful particle information for each layer by studying the depolarization profiles. Based on the above results, we conclude that space-borne lidar backscattering depolarization measurement can provide important information for the determination of particle shapes and cloud thermodynamic phase not only for a homogeneous medium, but also for multiple-layered plane parallel media. However, we need to simulate more complex scenarios such as cloud layers that are composed of both ice and water phase particles ARTICLE IN PRESS 482 Y. You et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 100 (2006) 470–482 as well as a cloud layer with heavy aerosol contamination, such as from volcanic ash, dust, or smoke. We also need to compare the computed results with those measured by remote sensing observations, and then select models that describe more realistic cloud and aerosol properties. Acknowledgements George Kattawar acknowledges the support from the Office of Naval Research (N00014-02-1-0478). Ping Yang acknowledges the support from the National Science Foundation (ATM-0239605), the support from Science Applications International Corporation (Contract no. 4400053274 and 4400101412), and a subcontract from the University of Maryland at Baltimore County (CG0235A). We would like to thank Dr. Deric Gray for authorizing us to use his Monte Carlo code to double-check the validity of our code. References  Baum BA, Soulen P, Strabala KI, King MI, Ackerman SA, Menzel WP, et al. 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