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Abstract
The backscattering coefficient (β), lidar ratio (S), and depolarization ratio (δ) of ice particles were estimated over a wide range of effective radii to interpret spaceborne 355-nm high-spectral-resolution lidar data from the ATLID sensor onboard the EarthCARE satellite. Five randomly oriented ice particle shapes (3D ice) and two quasi-horizontally oriented particle types (2D ice) were analyzed using five effective angles. The size dependence of β, S, and δ was examined using physical optics and geometrical optics integral equation methods. Differences in β for the same effective radius and ice water content among particle types exceeded one order of magnitude. S-δ relations are useful for inferring ice particle habit and orientation using ATLID data from EarthCARE.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Clouds are the greatest contributor to variations in climate change predictions [1]. Ice clouds affect Earth’s radiation budget but are poorly represented in climate model simulations; for example, simulated ice water paths differ up to 20-fold among general circulation models. Global observations of the vertical structures of cloud phases and microphysics are key to future climate prediction [2].
The Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) mission was launched on 28 April 2006 and has been in operation for more than 12 years. The Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) instrument onboard the CALIPSO satellite measures the total attenuated backscattering coefficient (${\beta _{att}}$) at 1064nm, ${\beta _{att}}$ and its perpendicular component at 532 nm, from which the depolarization ratio ($\delta $) can be obtained [3]. The combinations of vertically-integrated ${\beta _{att}}$ and $\delta $ [4] or vertically-resolved $\delta $ and attenuation (KU-type product) [5] have been applied in algorithms to obtain global distributions of cloud phase and ice orientation using CALIOP. A retrieval algorithm has been formulated for the synergetic use of CALIOP and the cloud radar of CloudSat to estimate ice microphysical characteristics such as effective radius, water content, and the mixing ratios of horizontally and randomly oriented ice particles using the attenuated backscattering coefficient and depolarization ratio from CALIOP and the radar reflectivity factor from CloudSat as input parameters (KU-micro product) [6,7].
After CALIOP, Aeolus was launched in August 2018. Aeolus uses the high-spectral-resolution lidar (HSRL) technique to measure the horizontally projected wind velocity, true backscattering coefficient ($\beta $) and extinction coefficient (${\sigma _{ext}}$) at 355 nm in clouds and aerosols [8]. The Earth Clouds, Aerosol and Radiation Explorer (EarthCARE) satellite, which is a joint mission of the Japanese Aerospace Exploration Agency (JAXA) and the European Space Agency (ESA) scheduled to be launched in 2021, will carry an HSRL (atmospheric lidar: ATLID) at 355 nm and has depolarization capability, a Doppler cloud profiling radar, a multi-spectral imager, and a broadband radiometer [9]. Because ATLID will measure, ${\sigma _{ext}}$, and $\delta $ at 355 nm, it will offer a unique opportunity to study the relationship between the lidar ratio S (${\sigma _{ext}}/\beta $) and $\delta $ of ice clouds.
Several ground-based lidar studies have reported on S and $\delta $ in ice clouds using Raman lidar. The temperature dependence of this relation has been reported; namely, that differences in ice particle habits at different temperatures led to observed differences in S and $\delta $ at 355 nm [10]. It was also reported [11] that S increases as $\delta $ increases at 532 nm based on Raman lidar. Airborne HSRL experiments resulted in two-dimensional projections of S and $\delta $ as well as of S and the spectral dependence of $\delta $ for ice particles and aerosols [12].
The analysis of CALIOP data revealed that the mean value of S is 33.5 [sr] at 532 nm for semitransparent ice clouds when transmission is used as a constraint [13]. When CALIPSO and Infrared Imager Radiometer (IIR) data were analyzed while inferring the lidar ratio, S was estimated to range from approximately 20 to 50 [sr] [14].
The interpretation of such features is necessary to establish theoretical relationships between ice microphysics and the parameters observed with lidar. The geometrical optics (GO) method has been widely applied to analyses that use visible and infrared wavelengths [15], as ice particle size is generally much larger than the wavelengths of interest. However, this method has serious drawbacks for use with lidar due to convergence of the solutions in the direction of backscattering [16]. Several efforts have been made to improve GO, including development of the geometrical optics integral equation (GOIE) method [16–18] and a physical optics (PO) method based on a modified Kirchhoff approximation [19,20] to overcome the limitations of conventional GO. PO has been applied to the calculation of lidar backscattering for horizontally oriented ice particles in analyses of specular reflection [21,22]. The S and $\delta $ values of randomly oriented and distorted columns at 532 nm and 1,064 nm were shown to increase after distortion [23]. The size dependences of $\delta $ and S for randomly oriented columns, plates, bullets, and droxtals can be studied using PO [24]. PO is employed in the retrieval algorithm for ice microphysics using CALIPSO and CloudSat data [6,7]. Additionally, lidar backscattering properties of quasi-horizontally oriented ice plates have been theoretically estimated under CALIOP specification [22].
We conducted a comprehensive analysis of the size-dependence of the $\beta $, S, and $\delta $ of ice particles over a wide effective size range, as well as of various particle shapes and orientations for application to ATLID data from EarthCARE. We also aimed to determine the relationship between S and $\delta $ of ice particles for particle type classification. The following ice particle types were considered: Voronoi aggregates, droxtals, bullets, hexagonal columns, and hexagonal plates. These particles were assumed to be randomly oriented in three-dimensional space. Several different horizontal orientations were considered for hexagonal columns and plates. Based on the effective radii considered in this study, which ranged from approximately 10 to 2,000 µm, the range of variability in lidar backscattering properties was determined. To match the lidar specifications of ATLID, we considered the wavelength of 355 nm and a laser off-nadir angle (also referred to as a laser tilt angle, hereafter “LT”) of 3°.
The theoretical methods and procedures used in this study are briefly described in Section 2. We consider five ice particle shapes as randomly oriented ice particles (3D ice). In addition, the lidar backscattering properties of horizontally oriented hexagonal plate (2D plate) and hexagonal column (2D column) particles were examined for five effective angles. Size-integrated values of $\beta $, S, and $\delta $ are presented in Section 3. Then, the two-dimensional diagrams of S and $\delta $ for ice particles oriented in the horizontal plane were examined. A summary is provided in Section 4.
2. Ice particle models, computational methods, and lidar observables
2.1 Theoretical procedures
We applied PO [22] and the modified GOIE [17] to calculate lidar backscattering properties for the interpretation of spaceborne and ground-based lidar observations. PO assumes that the scattering field at a particle’s surface is first calculated by GO, where reflection and refraction of the incident beam can be estimated according to Fresnel’s law. Then, scattering in the far zone is calculated using vectorized Fraunhofer diffraction theory [22,23].
In the modified GOIE method, reflected and refracted near-field components of the electric field are calculated using a ray-tracing technique, and far-field scattering is obtained by integrating the near fields over the particle’s surface. In the ray-tracing technique, 32 internal reflections were considered. Prior studies [17,18] had introduced a similar approach that has been described previously [22], in which the integral of the phase shift term is computed using a parallelogram as the fundamental surface area element and the integral of the phase of the wave that is calculated analytically, as with PO. A significant reduction of computing time can be achieved through the implementation of the analytical approach in the modified GOIE [17].
The applicability of PO was evaluated against Finite Difference Time Domain (FDTD) methods [25]. They considered hexagonal plates with diameter D = 10 µm and length L = 5.68 µm at λ = 532 nm, corresponding to ${X_{eq}} = 2\pi {r_{eq}}/(\lambda /1000)$ of approximately 50, where ${r_{eq}}$ denotes the mass equivalent radius. The results of PO agreed with those of FDTD. For the same shape with smaller sizes, i.e., D = 5 µm and L = 2.898 µm, backscattering results agreed well with those of FDTD, although errors in the differential scattering cross section were considered large for side-scattering (${30^\circ } < \theta < {150^\circ }$). The applicability of the modified GOIE was tested against FDTD [17], and good agreement between the two methods was obtained for a column with random 3D orientation when ${X_{eq}}$ = 50.
In this study, we considered ice particles that were randomly oriented in three-dimensional space (hereafter 3D particles) as well as those with quasi-horizontal orientations (2D particles).
The probability distribution functions for particle orientation, $\frac{{dp(\Theta )}}{{d\Theta }}$, are described as follows. To estimate the average backscattering cross section ${\bar{C}_{bk}}$ for 3D particles, a uniform distribution of $\frac{{dp(\Theta )}}{{d\Theta }} = \frac{1}{{4\pi }}$ is used [26,27]:
Lidar backscattering properties are determined through the superposition of many particles in the scattering volume defined by lidar specifications. The lidar backscattering coefficient $\beta $ and extinction coefficient of ice particles can be written as [31]:
Using Eq. (5), the effective radius ${r_{eff}}$ can be defined as:
2.2 Particle models and orientations
We considered five particle shapes: Voronoi aggregates, droxtals, bullets, hexagonal plates, and hexagonal columns as shown in Fig. 1. The backscattering properties of these five particles with random orientations were estimated using PO or the modified GOIE. The Voronoi aggregate model was created using spatial Poisson-Voronoi tessellations as described previously [33]. The cell number was eight throughout the size range, and its mass-size relation is given by:
where mass m is in grams, D is in µm, and the density of solid ice is assumed to be 0.917 g cm-3.
Fig. 1. Ice particle shapes used for estimating ${\beta _{tot}}$, $\delta $, and S. (a) Voronoi aggregate, (b) droxtal, (c) bullet, (d) hexagonal column, and (e) hexagonal plate.
The geometry of a droxtal was specified by two angles θ1 = 32.35° and θ2 = 71.81°, along with the diameter of the circumscribing sphere of the droxtal [34]. The bullet shape was defined according to previous reports [35,36] and depends on the relationship between diameter D [µm] and length L [µm] as follows:
This relationship was derived from in situ measurements collected using an aircraft equipped with a CPI (Cloud Particle Imager) sensor. The tip angle of the bullet was set to 28°.The hexagonal column and plate models are defined using D and L [35,37]. The length of the ice column L [µm] is related to its diameter D [µm], which varies with size as follows:
The height L [µm] of the plate is assumed to be related to its diameter D [µm] as follows [37]: The three-dimensional backscattering properties of the randomly oriented ice particles described above were estimated. The refractive index at 355 nm is 1.3249 [38]. In addition, the backscattering properties of 2D columns and 2D plates were estimated for the following five values of ${\Theta _{eff}}$: 0.5°, 1.0°, 2.0°, 3.0°, and 5.0°.First, the individual scattering properties of 3D and 2D particles were calculated for the size ranges summarized in Table 1. The properties of Voronoi aggregates were initially computed using GOIE. The properties of 3D droxtals, 3D bullets, 3D columns, 3D plates, 2D columns and 2D plates were computed using PO.
Table 1. Parameters used in the lidar backscattering calculations
Then, $\overline {{C_{bk,\parallel }}} $, $\overline {{C_{bk, \bot }}} $, and $\overline {{C_{ext}}} $ for the particle shapes and orientations described above were extrapolated from ${r_{eq}}$ = 0.75 to 2,500 µm based on the power law relationship identified previously [24] between backscattering properties of ice particles and size using PO calculations, which can be approximated with a power function for the wavelengths of 355, 532, and 1,064 nm.
Consequently, based on Eqs. (3) and (4), ${\beta _\parallel }$, ${\beta _ \bot }$, and ${\sigma _{ext}}$ were used to estimate S and $\delta $ as the orientation- and size-averaging properties for ${r_{eff}}$ values ranging from 8.5 to 1,938 µm at a wavelength of 355 nm for the particle shapes and orientations discussed in this subsection. It is noted that the results for small sizes may fall outside the applicability range of PO. In this study, results for ${r_{eff}}$> 8.5 µm are considered to meet the criteria of PO and the modified GOIE. Thus, the minimum size parameter corresponding to ${r_{eff}}$ = 8.5 µm is 150.4 for $\lambda $ = 355 nm.
3. Interpretation of observations from spaceborne HSRL
The lidar backscattering properties $\beta $, S, and $\delta $ were analyzed for five ice particle types with random (3D) and quasi-horizontal orientations (2D) for plates and columns to interpret ATLID observations. We first examined the properties of these 3D ice categories in subsection 3.1. The size-dependence of $\beta $, S, and $\delta $ was also examined. Then, we described those of the 2D plate and column categories in subsections 3.2 and 3.3, respectively. Finally, the relationships between S and $\delta $ are examined in subsection 3.4.
3.1 Backscattering properties of 3D ice categories
The dependence of $\beta $ on ${r_{eff}}$ was examined for 3D ice categories in Fig. 2(a). In general, $\beta $ decreased as ${r_{eff}}$ increased at a constant ice water content (IWC) of 1 g/m3. The size dependence was primary determined by the dependence of number concentration on size since the backscattering efficiency ${Q_{bk}}$ had weak dependence on size, similar to that of spherical ice particles at lidar wavelengths [31]. The slope of the curve depended on particle shape. Differences among 3D ice types were approximately one order of magnitude apart at ${r_{eff}}$ = 30 µm and approximately two orders magnitude apart at ${r_{eff}}$ = 1,000 µm.
Fig. 2. Lidar backscattering properties of 3D ice categories as a function of effective radius ${r_{eff}}$. The ice water content (IWC) was fixed at 1 g/m3. The wavelength was 355 nm and the laser tilt angle (LT) was 3° off nadir. A 2D plate and 2D column with ${\Theta _{eff}}$ = 1° were also compared. (a) the total backscattering coefficient ${\beta _{tot}}$; (b) the lidar ratio S (sr); and (c) the depolarization ratio $\delta $.
For comparison, 2D columns with ${\Theta _{eff}}$ = 1° and 2D plates with ${\Theta _{eff}}$ = 1° were analyzed, with ${\Theta _{eff}}$ = 1° considered a typical angle in the real atmosphere [27]. A 3D plate and 2D plate with ${\Theta _{eff}}$ = 1° had similar $\beta $ values, although the 3D plate had slightly larger $\beta $ values at ${r_{eff}}$< 800 µm. The differences between 3D columns and 2D columns were much larger at all particle sizes.
Next, we discuss the size dependence of S for 3D ice categories shown in Fig. 2(b). The size dependence of S was generally much weaker than that of $\beta $, as S did not depend on number concentration. The ${r_{eff}}$ dependence of 2D and 3D particles differed. For 3D ice categories, S decreased linearly except for Voronoi particles, which have a local minimum (46 sr) at ${r_{eff}}$ of approximately 60 µm as seen in Fig. 2(b). In contrast to 3D ice, S for 2D particles increased with size; results for a 2D plate and 2D column with ${\Theta _{eff}}$ = 1° are shown in Fig. 2. As expected from the analysis of $\beta $, Voronoi particles produced the largest S values among all particle shapes at all sizes considered in the present study.
The S value for a 3D column was smaller than that for a 2D column with ${\Theta _{eff}}$ = 1° at all sizes considered and was the smallest among all particle types. The S value for a 3D plate was also smaller than that for a 2D plate with ${\Theta _{eff}}$ = 1°. These differences are due to the reduction of the specular component contribution to total backscattering intensities for the non-negligible off nadir angle of LT = 3°. We therefore concluded that S alone is insufficient for distinguishing among particle types and orientations, except for Voronoi aggregates, when the variation of particle size is taken into account. That is, different combinations of particle types and ${r_{eff}}$ can produce the same value of S.
Distinct differences in $\delta $ were found among particle types as seen in Fig. 2(c), especially between the 2D and 3D ice categories. We also found that $\delta $ depended weakly on ${r_{eff}}$ as $\delta $ did not depend on number concentration. The $\delta $ values of all 3D ice categories were greater than 22% for all particle sizes. The $\delta $ values of Voronoi aggregates, the most complex shape considered in this study, were the largest among all ice categories. The 2D plate and 2D column with ${\Theta _{eff}}$ = 1° produced low values of $\delta $ (<10%) at all sizes. That is, $\delta $ of a 2D plate with ${\Theta _{eff}}$ = 1° was close to 0% and that for a 2D column with ${\Theta _{eff}}$ = 1° was larger than that for a 2D plate over the entire size range considered in this study.
3.2 Backscattering properties of 2D plate categories
In this subsection, we examine the backscattering properties for 2D plate particles with various ${\Theta _{eff}}$ shown in Fig. 3. Five values of ${\Theta _{eff}}$ (0.5°, 1.0°, 2.0°, 3.0°, and 5.0°) were considered in the simulations. LT is fixed to 3°, indicating that the angle between the laser incident beam direction and the symmetric axis of the plate particle is 3° when the particle is perfectly oriented in the horizontal plane, i.e., ${\Theta _{eff}}$ = 0°. The $\beta $ for this particle type decreased linearly with increasing ${r_{eff}}$ as seen in Fig. 3(a), similar to results described for 3D ice in the previous subsection. However, $\beta $ was not linearly dependent on ${\Theta _{eff}}$. A 2D plate with ${\Theta _{eff}}$ = 2.0° produced the largest $\beta $ and a 2D plate with ${\Theta _{eff}}$ = 0.5° produced the smallest $\beta $ over the entire ${r_{eff}}$ ranges considered in this study. These properties can be explained as follows. A 2D plate with ${\Theta _{eff}}$ = 2.0° and 3.0° has a greater probability of the incident laser beam entering vertically with respect to the hexagonal plane, so the probability of specular reflection is greater. At ${\Theta _{eff}}$ = 0.5° and 1.0°, the probability of specular reflection is small and $\beta $ is therefore smaller than for ${\Theta _{eff}}$ = 2.0° and 3.0°.
Fig. 3. As described for Fig. 2, but for 2D plates with five different values of ${\Theta _{eff}}$: 0.5°, 1.0°, 2.0°, 3.0°, and 5.0°. (a) the total backscattering coefficient ${\beta _{tot}}$; (b) the lidar ratio S (sr); and (c) the depolarization ratio $\delta $. The wavelength was 355 nm and the laser tilt angle (LT) was 3° off nadir.
S values for 2D plate particles did not generally show strong dependence on ${r_{eff}}$ as seen in Fig. 3(b), except at ${\Theta _{eff}}$ = 0.5°. As expected from the comparison of $\beta $, the 2D plate with ${\Theta _{eff}}$ = 0.5° produced the largest S (>60 sr) and the 2D plate with ${\Theta _{eff}}$ = 2.0° produced the smallest S (∼5 sr). Notably, a small difference in ${\Theta _{eff}}$ between 1.0° and 2.0° produced large differences, up to a factor of six, indicating the high sensitivity of S to orientation.
The $\delta $ values for 2D plates were very small as long as small values of ${\Theta _{eff}}$ were considered as shown in Fig. 3(c). The maximum $\delta $ value was obtained from a 2D plate with ${\Theta _{eff}}$ = 5.0° and $\delta $ = 0.02%. A 2D plate with ${\Theta _{eff}}$ = 2.0° produced the smallest $\delta $ value of approximately 0.001%. Because the errors in $\delta $ for spaceborne lidar are much larger—e.g., 2% for CALIPSO lidar [39], these differences cannot be observed. When ${\Theta _{eff}}$=15° and 20° were considered, $\delta $ became comparable to that of 3D plate.
3.3 Backscattering properties of 2D columns
We then investigated the backscattering properties of the 2D column category. Almost no differences were found among results comparing the five ${\Theta _{eff}}$ values in Fig. 4(a), although the smallest $\beta $ was obtained for ${\Theta _{eff}}$ = 5° and a small ${r_{eff}}$ of < 30 µm. The $\beta $ for 3D columns was much larger than that for 2D columns. Compared with 2D plates, 2D columns generally have a smaller $\beta $ when relatively small ${\Theta _{eff}}$ values were considered, except for the 2D plate with ${\Theta _{eff}}$ = 0.5°, which produced the smallest $\beta $ among all 2D plates and 2D columns.
Fig. 4. As described for Fig. 3, but for 2D columns with five values of ${\Theta _{eff}}$: 0.5°, 1.0°, 2.0°, 3.0°, and 5.0°. (a) the total backscattering coefficient ${\beta _{tot}}$ values; (b) the lidar ratio S (sr); and (c) the depolarization ratio $\delta $. The wavelength was 355 nm and the laser tilt angle (LT) was 3° off nadir.
Similar to 3D ice and 2D plates, the size dependence of S was relatively small for 2D columns as seen in Fig. 4(b). S values increased slightly with increasing ${r_{eff}}$ except at = 5°. The largest S value was obtained for a 2D column with ${\Theta _{eff}}$ = 5° and ${r_{eff}}$<800 µm. The 2D column with ${\Theta _{eff}}$ = 2.0° produced the smallest S throughout the size range. Differences among ${\Theta _{eff}}$ values were larger for small ${r_{eff}}$ than for large ${r_{eff}}$. S values for 2D columns were generally larger than those for 2D plates, as expected based on the analysis of $\beta $, except for the 2D plate with ${\Theta _{eff}}$ = 0.5°, which produced the largest S and smallest $\beta $.
The $\delta $ values of 2D columns were generally smaller than 10% but larger than those of 2D plates as seen in Fig. 4(c). The $\delta $ of 2D columns decreased linearly with ${r_{eff}}$. A larger ${\Theta _{eff}}$ resulted in a larger $\delta $ for the same ${r_{eff}}$, and 3D columns produced larger $\delta $ than 2D columns at all sizes investigated. In summary, 3D ice categories produced $\delta $ with values >20% and 2D pristine ice categories produced $\delta $ with values ≤ 10%. Therefore, $\delta $ might be used to distinguish between the 2D pristine ice and 3D ice categories.
3.4 Relationship between lidar ratio and depolarization ratio
We examined the relationship between S and $\delta $ for 2D plates, 2D columns, and the 3D ice categories by plotting S versus $\delta $ (hereafter, the 2-dimensional diagram). Because these values do not depend on IWC or the number concentration of particles, they are very useful for distinguishing among particle types.
We first examined this relationship for 2D plates in Fig. 5(a). For a given ${\Theta _{eff}}$, different points in the S vs. $\delta $ plot corresponded to different ${r_{eff}}$. As ${\Theta _{eff}}$ increased from 0.5° to 2.0°, both S and $\delta $ decreased. Then, both S and $\delta $ increased as ${\Theta _{eff}}$ increased from 2° to 5°. That is, a 2D plate with ${\Theta _{eff}}$ = 2.0° produced the smallest values of both S and $\delta $. As noted previously, $\delta $ was not practically detectable in observations, therefore S can be used to determine ${\Theta _{eff}}$ among 2D plates.
Fig. 5. The relationship between S and $\delta $ for (a) 2D plates, (b) 2D columns, and (c) 3D ice and 2D ice. The wavelength was 355 nm and the laser tilt angle (LT) was 3° off nadir. ${\Theta _{eff}}$: 0.5°, 1.0°, 2.0°, 3.0°, and 5.0° are indicated in Figs. 5(a) and 5(b).
A similar two-dimensional diagram was plotted for 2D columns in Fig. 5(b). S appeared to be more useful in distinguishing among ${\Theta _{eff}}$ values than $\delta $, although some lines between ${\Theta _{eff}}$ = 1.0 and 3.0° overlapped and became indistinguishable.
Next we examined the relationships in all categories, including 3D ice in Fig. 5(c). In addition to separating 2D pristine ice and 3D ice categories by $\delta $ alone, the 2-dimensional diagram of S and $\delta $ makes it possible to distinguish particle types and the details of each particle’s orientation. The use of S or $\delta $ alone is not ideal for distinguishing among particle types.
S and $\delta $ values reported in this study are also found in ground-based Raman lidar measurements in [10].
In the real atmosphere, the shapes of the horizontally oriented ice particle are not restricted to hexagonal plate or hexagonal column and irregular shape-ice particles exist. We considered aggregate of 8 columns as more complex shape [45]. The S and $\delta $ of the 2D and 3D aggregate of 8 columns are calculated by the PO as shown in Fig. 6. The S of the 2D aggregates of 8 columns with ${\Theta _{eff}}$=1° and LT = 3° are almost comparable to that of the 3D aggregates of 8 columns. The $\delta $ of 2D aggregates of 8 columns did not decrease drastically from that of 3D- aggregates and was larger than that of 2D column. Preliminary calculation of S and $\delta $ of the 2D and 3D Voronoi aggregates also showed similar tendency. Therefore, it is expected that the $\delta $ of the 2D complex ices might not be as small as that of 2D pristine hexagonal columns and S of the 2D and 3D complex ices might be comparable with each other.
Fig. 6. The relationship between S and $\delta $ for 3D aggregate of 8 columns. Results of 2D aggregate of 8 column with ${\Theta _{eff}}$ = 1° were also compared.
[23] showed that the shape distortion of pristine hexagonal column lead to strong increase of S and $\delta $ at 532 nm. That is, both S and $\delta $ of 3D-distorted hexagonal columns tended to increase as distortion increased, and S and $\delta $ were 5 and 2 times larger at maximum compared with those of 3D pristine hexagonal column, respectively. Assuming similar increase of S and $\delta $ at 355 nm, estimated S and $\delta $ values of the 3D distorted hexagonal columns shifted from those of 3D columns towards those values of Voronoi aggregate. This may be understood as follows. The shape of the constituent particle of Voronoi aggregate is somewhat similar to the distorted hexagonal column. As seen in Figs. 5 and 6, the backscattering properties of the 3D aggregate of 8 columns are similar to its constituent particle so that the backscattering properties of the 3D distorted hexagonal column are considered to be similar with those of 3D Voronoi aggregates. Similarly, S and $\delta $ values of distorted bullets and droxtals are expected to shift towards those of 3D Voronoi aggreagtes.
4. Summary
The $\beta $, S, and $\delta $ of ice particles were estimated theoretically for the interpretation of spaceborne lidar data from ATLID on the EarthCARE satellite. The selected wavelength and off-nadir angle of the laser beam direction were 355 nm and 3°, respectively, to match the values of ATLID. The relationship between S and $\delta $ of ice particles was also investigated. We considered effective radii ranging from approximately 9 µm to 2 mm and two particle orientation categories: (1) particles oriented randomly in three-dimensional space (3D ice category), and (2) particles oriented quasi-horizontally with respect to the laser tilt angle (2D ice category). Voronoi aggregates, droxtals, bullets, hexagonal plates, and hexagonal columns with random orientations were included in the 3D ice category. Within the 2D ice category, we considered quasi-horizontally oriented hexagonal columns and plates and five effective angles of ${\Theta _{eff}}$ (0.5°, 1.0°, 2.0°, 3.0°, and 5.0°) following a Gaussian distribution. The major findings are as follows.
- (1) The $\beta $ produced by the 2D plate with ${\Theta _{eff}}$ = 2.0° was the largest among all ice particle types and orientations considered here when results for the same ${r_{eff}}$ and IWC were compared, whereas the 2D plate with ${\Theta _{eff}}$ = 0.5° produced the smallest $\beta $. The 3D column particles exhibited the largest $\beta $ among 3D ice categories. The $\beta $ of Voronoi aggregates was the smallest among 3D ice categories for the same ${r_{eff}}$. The $\beta $ values of 2D columns were smaller than those of 2D plates except for the 2D plate with ${\Theta _{eff}}$ = 0.5°. Differences in $\beta $ among types and orientations exceeded two orders of magnitude.
- (2) The size dependence of S was generally weak. The largest S among all types and orientations was produced by a 2D plate with ${\Theta _{eff}}$ = 0.5°. The smallest S among 3D ice types was produced by a 3D column, and this value was also the smallest among all types and orientations for ${r_{eff}}$>20 µm. Aside from the 2D plate with ${\Theta _{eff}}$ = 0.5°, 2D plates with small ${\Theta _{eff}}$ produced smaller S values compared with 3D ice particles due to their large $\beta $. Voronoi particles produced the largest S among all 3D ices (>45 sr). S was not determined solely by particle type. Different combinations of habit and ${r_{eff}}$ often produced the same S or $\delta $ value.
- (3) The size dependence of $\delta $ was also weak. Its habit dependence was much stronger. The 2D plates produced the smallest $\delta $ values among all types. The smallest $\delta $ value was produced by a 2D plate with ${\Theta _{eff}}$ = 2.0° due to the high probability of specular reflection when the vertical incident laser beam enters the flat hexagonal surface; in this configuration, $\delta $ is negligibly small. The 2D pristine columns produced larger $\delta $ values (<10%), but these values were smaller than those of all 3D ice categories ($\delta $>20%) for all sizes. The $\delta $ of Voronoi particles was the largest among all 3D ice types. We conclude that $\delta $ can be used to separate the 2D pristine ice and 3D ice categories. In general, the use of only $\delta $ or S cannot discriminate among particle types in the atmosphere when variations of ${r_{eff}}$ are considered.
- (4) A two-dimensional diagram of S and $\delta $ was effective for discriminating among ice particle types and orientations. Therefore, both S and $\delta $ are necessary parameters for distinguishing among particle habits and orientations.
Funding
Japan Society for the Promotion of Science (JP17H06139, JP18K03745); Japan Aerospace Exploration Agency; Ministry of Education, Culture, Sports, Science and Technology (The Arctic Challenge for Sustainability project); Research Institute for Applied Mechanics, Kyushu University (Collaborative Research Program).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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