## 1. Introduction

In current satellite-based retrievals of ice cloud optical thickness and effective particle size, bulk single-scattering properties of ice clouds are used to simulate the reflectance and transmission characteristics over a range of cloud microphysical conditions. These bulk properties are used to build a static lookup table that is used with satellite observations in the implementation of a retrieval algorithm (Platnick et al. 2003; Minnis et al. 2011). In the forward light scattering computation of the bulk ice cloud optical properties, predefined size and habit (shape) distributions of ice particles are assumed, although some efforts have been carried out to explore the retrieval of ice cloud properties without a priori assumption of the shape/size distribution of ice particles (Kokhanovsky and Nauss 2005). Furthermore, the particles are typically assumed to be randomly oriented for computational and theoretical simplicity.

In environments with relatively gentle updraft velocities, ice particles with certain shapes may become oriented as a result of the balance between gravitational settling and the vertical updraft velocity with relevant aerodynamic effects on a population of particles (Magono 1953; Ono 1969). The orientation of an ice particle depends on its shape, size, and ambient aerodynamic conditions. It is generally recognized that planar and columnar crystals tend to exhibit preferred orientations; in particular, ice plates with maximum dimensions greater than 100 *μ*m are likely to be quasi-horizontally oriented (Sassen 1980). Furthermore, oriented small planar particles tend to have a range of tilt angles between 10° and 20° (Klett 1995). It has been previously shown that oriented ice particles are observed in more than 40% of ice clouds (Chepfer et al. 1999).

However, our understanding of the impact of oriented ice particles on light scattering calculations and subsequent application to satellite-based cloud property retrievals is poor, resulting in a potential significant bias in the inferred properties (Masuda and Ishimoto 2004). The present study is intended to investigate the impact of horizontally oriented ice crystals (HOIC) on the interpretation of lidar backscatter and depolarization signals associated with ice clouds, and furthermore to infer the percentage of HOIC in ice clouds.

Quasi-horizontally oriented hexagonal ice crystals are the most dominant oriented ice crystal habit. As oriented planar particles act like little mirrors, their presence can be inferred in depolarization lidar data from a strong increase in the backscattering signal *γ*′ and a low depolarization ratio *δ*, and occurs when the incident beam points along the local zenith or nadir for a spaceborne or ground-based lidar. With the Facility for Atmospheric Remote Sensing scanning lidar datasets, Noel and Sassen (2005) confirmed the presence of quasi HOIC. Noel and Sassen (2005) also suggested that the derivation angles of horizontally oriented planar crystals are smaller in high-level cold clouds (<−30°C) than in midlevel warmer clouds.

The Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) measurements (Winker et al. 2003) provide an unprecedented opportunity to study oriented plates from a global perspective. When the lidar pointing angle was 0.3° off nadir, as it was originally from the beginning of operations through November 2007, the backscattering signals associated with quasi-horizontally oriented plates were strong and had low depolarization (Hu et al. 2007). By further analyzing the CALIOP depolarization-attenuated backscatter relationship, Noel and Chepfer (2010) estimated the contribution of oriented ice crystals with a simple single-scattering model (Sassen and Benson 2001) and suggested that most horizontally oriented plates could be found in optically thick clouds. However, the single-scattering model used in the previous study is not optimal for the case of optically thick clouds, where multiple scattering contribution dominates.

To more accurately simulate the CALIOP measurements, a 3D Monte Carlo model is developed for clouds containing quasi-horizontally oriented plates in both ice clouds and mixed-phase clouds. This model is able to simulate the lidar signals in both optically thin and thick clouds. The simulated *δ*–*γ*′ relationships are then compared with CALIOP observations, and the percentage of HOIC is inferred.

This paper is organized into four sections. Section 2 describes the datasets and method used in this study. Section 3 presents various sensitivity studies based on numerical simulations. In section 3, we also compare the simulated results with *Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO)* data to estimate the percentage of HOIC. The scientific findings of this study are summarized in section 4.

## 2. Data and methodology

Three instruments are on the *CALIPSO* platform, one of which is the CALIOP (Winker et al. 2003). The CALIOP provides observations at two wavelengths: 532 and 1064 nm. The 532-nm channel has a polarization capability that is critical to the detection of quasi-horizontally oriented plates. We will therefore focus on data at this wavelength in this study, specifically from the version-3 *CALIPSO* level-2 cloud-layer products with a 5-km spatial resolution.

*δ*and the total-layer-integrated attenuated backscatter

*γ*′, are defined as follows:

*CALIPSO*data used in this study are for two periods: July–December 2006 and July–December 2010.

*D*is the maximum dimension, frequently referred to as the particle size;

*n*(

*D*) is the particle concentration; and

*N*

_{0}is the total number of plate particles in a unit volume. For illustrative purposes, a set of coefficients is chosen for the gamma distribution, namely,

*μ*= 1.026 and

*λ*= 8.7 mm

^{−1}. Note that

*N*

_{0}needs not be specified because this factor cancels out in the simulation of the bulk optical properties involved in this study [see Eqs. (4)–(6) in the following discussion]. Simulations with numerous sets of habit and size distributions for ROIC were performed during the course of this study, with results similar to the one chosen for illustration. For the mixed-phase cloud simulations, the Lorenz–Mie theory is applied to calculate the scattering properties of liquid droplets with an effective radius assumed to be 4

*μ*m.

*θ*, which is obtained by integrating over the PSD:

_{s}*D*

_{max}is the maximum size of the particles,

*D*

_{min}is the minimum size,

*M*is the number of habits,

*f*

_{hb}is the particle fraction of habit hb, and

The calculations for HOIC are more complicated than for ROIC because the phase matrix of oriented particles depends on both the incident direction with respect to the particle and scattering zenith and azimuthal angles. The coordinate systems for HOIC in the case of hexagonal plates are shown in Fig. 1. The particle coordinate system, *O*–*X _{p}*, –

*Y*, –

_{p}*Z*(Fig. 1a), rotates as the particle rotates. The laboratory coordinate system,

_{p}*O*–

*X*, –

_{f}*Y*, –

_{f}*Z*(Fig. 1b), is a fixed coordinate system with its

_{f}*Z*axis pointing in the zenith direction.

*α*,

*β*,

*γ*) are used to describe the orientation of quasi-horizontally oriented ice particles (Fig. 1c). The line of nodes is the intersection line of coordinate planes

*O*–

*X*, –

_{p}*Y*and

_{p}*O*–

*X*, –

_{f}*Y*. Here

_{f}*α*is the angle between the

*O*–

*X*axis and the line of nodes,

_{f}*β*is the angle between axis

*O*–

*Z*and

_{f}*O*–

*Z*, and

_{p}*γ*is the angle between the line of nodes and

*O*–

*Y*axis. The transformation between the particle coordinates and the laboratory coordinates is given by

_{p}*α*and

*γ*follow the uniform distribution from 0 to 2

*π*(note that for a hexagonal particle,

*γ*needs to be considered only for 0–

*π*/3 because of the particles’ symmetry), and

*β*satisfies the normal distribution:

*σ*is the standard derivation of

_{β}*β*,

*N*

_{HOP,0}is a constant, and

*α, β, γ*) are the Euler angles of a particle,

*θ*

_{if}and

*φ*

_{if}are the incident angles in the laboratory coordinates (Fig. 1d),

*θ*and

_{s}*φ*are the scattering zenith and azimuthal angles (Fig. 2), and

_{s}*2a*/

*L*= 0.8038

*a*

^{0.526}based on in situ measurements (Pruppacher and Klett 1997), where

*a*and

*L*are the semiwidth and length of a hexagonal ice crystal. The size distribution of HOIC is the same as that in ROIC, except that only plates with a size greater than 100

*μ*m are considered to be quasi-horizontally oriented since smaller plates can have large tilt angles (Klett 1995). Subsequently, the phase matrix is normalized before being used in the Monte Carlo radiative transfer simulations.

Illustration of the scattering coordinates and scattering angles.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

Illustration of the scattering coordinates and scattering angles.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

Illustration of the scattering coordinates and scattering angles.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

*Z*axis,

_{f}*S*

_{21}and

*S*

_{12}are zero and the extinction matrix can be calculated from (Mishchenko 1991)

*k*

_{1}is the wavenumber in free space; Re and Im denote the real and imaginary part, respectively; and

The absorption cross section of HOIC is integrated similarly as ROIC. With the phase matrices, extinction matrices, and absorption cross section for ROIC and HOIC, the backscattering signals received by the lidar can be simulated with the Monte Carlo model.

*F*and the weight of HOIC can be calculated from

_{h}*ds*is the distance,

**J**is the source representing multiple scattering. To adjust the Stokes vector when a photon travels along a path in the medium, we use

*F*is the fraction of HOIC.

_{h}The Monte Carlo simulation begins with the phase matrices of randomly oriented particles *θ _{s}*) and quasi-horizontally oriented plates

*θ*

_{if},

*θ*,

_{s}*φ*), the absorption cross section, and the extinction matrix. Subsequently, the model begins tracing the transmission of a group of photons. The initial state of a new photon is decided by assuming lidar parameters. For CALIOP simulations, the directional vector for a new photon is set to be (

_{s}*θ*,

*φ*)=(

*θ*

_{off-nadir},

*0*), and the Stokes vector for the linearly polarized photons is (

*I*

_{0},

*I*

_{0}, 0, 0).

**r**−

**r**

_{0}is parallel to the direction vector, and

*ξ*is a random number with uniform distribution between 0 and 1. The extinction coefficient

*φ*) is the rotation matrix;

*ω*is the single-scattering albedo (virtually equal to 1 for ice clouds at 532 nm), and ΔΩ is the solid angle of the lidar aperture viewing from the scattering location; Δ

*z*is the vertical distance between the scattering location and the upper surface of the medium;

*θ*and

_{s}*φ*denote the scattering polar and azimuthal angles for the photon entering the lidar aperture after the scattering; and

_{s}*θ*

_{rcv}is the viewing zenith angle of the scattered light. In Eq. (23) the Stokes vector is first rotated from the meridional plane of the incident beam to the scattering plane, where Φ

_{1}is the angle between the two planes. After scattering, the Stokes vector is rotated to the meridional plane of the incident beam by

*π*− Φ

_{2}, and subsequently rotated back to the initial reference coordinates by

*φ*′.

*θ*

_{scat},

*φ*

_{scat}) with the phase function

*θ*

_{scat}is obtained with the random number

*ξ*

_{1}, which has uniform distribution from 0 to 1:

*F*is the accumulative probability function:

*φ*

_{scat}is calculated with a third random number

*γ*′ and

*δ*are calculated from the Stokes vector of the lidar-collected signals.

## 3. Simulation results

Figures 3–5 show three nonzero elements of the phase matrix for horizontally oriented plates (*σ _{β}* = 0). The phase function has a peak at (

*θ*= 180 – 2

_{s}*θ*,

_{i}*φ*= 0) because of direct reflection from the prism facet (Fig. 3). The size parameter of HOIC is very large at 532 nm (>10

_{s}^{3}) so the forward scattering is very strong because of diffraction. There are also many small peaks as a result of multiple reflections. When the incident angle is small,

*P*

_{22}is approximately equal to

*P*

_{11}, and the depolarization of the backscattering signal is close to zero. The backscattering is very strong when the incident angle is zero, but decreases rapidly as the incident angle increases. It is evident from Figs. 3–5 that the phase matrix elements are strongly dependent upon the azimuthal angle of the scattering plane if the incident angle is large.

Phase function of horizontally oriented plates (*σ _{β}* = 0°) for (a)–(f)

*θ*= 0°, 2°, 5°, 10°, 30°, and 60°, respectively.

_{i}Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

Phase function of horizontally oriented plates (*σ _{β}* = 0°) for (a)–(f)

*θ*= 0°, 2°, 5°, 10°, 30°, and 60°, respectively.

_{i}Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

Phase function of horizontally oriented plates (*σ _{β}* = 0°) for (a)–(f)

*θ*= 0°, 2°, 5°, 10°, 30°, and 60°, respectively.

_{i}Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

As in Fig. 3, but for the −*P*_{12}/*P*_{11} component of phase matrix.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

As in Fig. 3, but for the −*P*_{12}/*P*_{11} component of phase matrix.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

As in Fig. 3, but for the −*P*_{12}/*P*_{11} component of phase matrix.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

As in Fig. 3, but for the *P*_{22}/*P*_{11} component of phase matrix.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

As in Fig. 3, but for the *P*_{22}/*P*_{11} component of phase matrix.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

As in Fig. 3, but for the *P*_{22}/*P*_{11} component of phase matrix.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

*δ*–

*γ*′ relationship is useful for the discrimination of cloud phase (Hu et al. 2007) and for the estimation of the percentage of HOIC. Before carrying out the Monte Carlo simulations, a simple model is implemented to derive a formula for the

*δ*–

*γ*′ relationship of horizontally oriented plates when the incident angle is close to zero. When a small fraction of horizontally oriented plates is present in a cloud composed primarily of randomly oriented particles, the lidar signal can be approximated by

**I**

_{h}is the lidar-received Stokes vector from clouds with only horizontally oriented crystals,

*W*is the weight of the horizontally oriented crystals, and

_{h}**I**

_{r}is for clouds without horizontally oriented crystals.

*P*

_{12}(Fig. 4) and

*P*

_{21}components are equal, and

*P*

_{22}≈

*P*

_{11}when the incident angle is less than 10° (Fig. 5). When the incident angle is close to zero, the backscatter signal is strong and has a small depolarization ratio; thus the relationship between the

*I*and

*Q*components of the Stokes vector is

*δ*–

*γ*′ relationship for clouds with oriented crystals. This simple model also implies that the fraction of oriented crystals and

*γ*′ are linearly related. The Monte Carlo model provides a way to test these relationships. In the Monte Carlo simulations, an ice cloud is assumed to form a homogeneous layer that contains a small fraction of horizontally oriented plates. More than 10 simulations are run to simulate the lidar returns from the ice cloud layer. In each simulation, the ice cloud layer is given a different percentage of oriented plates, and more than 10

^{8}photons are traced.

As ice particles flutter in the atmosphere, the plates will likely have a range of tilt angles depending on the particle size and meteorological conditions. The standard deviation of tilt angle *σ _{β}* for oriented plates is important for backscattering properties. Relative to horizontally oriented plates with

*σ*= 0°, horizontally oriented plates with

_{β}*σ*= 1.5° display weaker backscatter at

_{β}*θ*= 0° and stronger backscatter when the incident angle deviates from zero. The

_{i}*σ*values for the Monte Carlo simulations in this study can be seen in Table 1.

_{β}Input parameters of Monte Carlo simulations (the percentage of quasi-horizontally oriented plates is *W _{h}*).

Figure 6 shows the *δ*–*γ*′ relationship for ice clouds with quasi-horizontally oriented plates. When the off-nadir angle is 0.3°, the backscattering signal for clouds with oriented plates is strong and the depolarization ratio is small relative to ice clouds with solely ROIC. The dashed line shows that the *δ*–*γ*′ relationship agrees very well with Eq. (34). Figure 6b shows the weight of horizontally oriented plates and the value of *γ*′ are approximately linearly related when the weight of oriented plates is small, and the relationship provides a convenient way to estimate the percentage of oriented plates. When the off-nadir angle is 3°, the *δ* and *γ*′ values associated with HOIC are very close to that of ROIC. Figures 6c,d show the relationships for transmissive cloud (*τ* = 1); note that the *δ*–*γ*′ relationship in Eq. (34) also holds.

(a),(c) The *δ*–*γ*′ relationship for ice clouds with HOIC (*σ _{β}* = 0.8°) when the off-nadir angle is 0.3° and 3°. (b),(d) Relationship between the percentage of HOIC and

*γ*′. Optical depths are (top)

*τ*= 4 and (bottom)

*τ*= 1.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

(a),(c) The *δ*–*γ*′ relationship for ice clouds with HOIC (*σ _{β}* = 0.8°) when the off-nadir angle is 0.3° and 3°. (b),(d) Relationship between the percentage of HOIC and

*γ*′. Optical depths are (top)

*τ*= 4 and (bottom)

*τ*= 1.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

(a),(c) The *δ*–*γ*′ relationship for ice clouds with HOIC (*σ _{β}* = 0.8°) when the off-nadir angle is 0.3° and 3°. (b),(d) Relationship between the percentage of HOIC and

*γ*′. Optical depths are (top)

*τ*= 4 and (bottom)

*τ*= 1.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

For mixed-phase clouds, simulations are performed where the clouds are considered to be a homogeneous layer containing water droplets, ROIC, and quasi-horizontally oriented plates. In the first set of simulations (mixed-phase cloud A), the ratio of ROIC to water cloud droplets is fixed, while the percentage of oriented plates varies. In the second and third sets of simulations (mixed-phase clouds B and C), the ratio of ROIC to HOIC is fixed, but the total percentage of ice particles varies (Table 1).

Figure 7a shows the *δ*–*γ*′ relationship of mixed-phase clouds with quasi-horizontally oriented plates. When the components for ROIC are fixed (mixed-phase cloud A), the *δ*–*γ*′ relationship satisfies Eq. (34). Compared to ice clouds with same percentage of oriented plates, the *γ*′ value of mixed-phase clouds is slightly weaker because of the difference in the multiple scattering factor. The forward scattering by large ice particles is much stronger than that by water cloud particles. At the 0.3° off-nadir angle, after being scattered by a randomly oriented particle, a photon propagating in the nadir direction has a greater chance of entering the lidar aperture. Thus, lidar signals associated with ice clouds with oriented plates show slightly stronger backscatter compared with mixed-phase clouds.

As in Fig. 6, but for mixed-phase clouds with HOIC. The optical depth of the cloud layer is 4.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

As in Fig. 6, but for mixed-phase clouds with HOIC. The optical depth of the cloud layer is 4.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

As in Fig. 6, but for mixed-phase clouds with HOIC. The optical depth of the cloud layer is 4.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

Figures 7c–f show the simulation results for mixed-phase clouds B and C, which represent conditions in which water cloud droplets dominate. When compared with mixed-phase cloud B, the *σ _{β}* value of mixed-phase cloud C is much larger and its backscatter at

*θ*

_{off}= 0.3° is much weaker. However, when the off-nadir angle is 3°, the backscattering signal is stronger for clouds with a larger

*σ*value.

_{β}While the high backscatter–low depolarization feature of ice clouds is often ascribed to the presence of platelike ice particles, columns with two prism facets parallel to horizontal plane may also have such an effect. We compared the two effects on backscattering signals from oriented columns with Monte Carlo simulations. For oriented columns, the Euler angle *γ* also satisfies the normal distribution, so they have an additional tilt angle compared with oriented plates. In the simulations for comparison, both *σ _{β}* and

*σ*for HOIC are set to zero.

_{γ}Figure 8a shows the value of *P*_{11} at the backscattering angle for oriented plates and columns. When incident angle is less than 1°, the backscatter from plates is much larger than from columns. Figure 8b shows the simulated *δ*–*γ*′ relationship for optically thick (*τ* = 4) ice clouds with horizontally oriented crystals and the off-nadir angle set to 0.3°. The circles denote simulation results for clouds with horizontally oriented plates and the diamonds are values for clouds with horizontally oriented columns. The effect of oriented columns on the *δ*–*γ*′ relationship is much smaller than for the counterpart of horizontally oriented plates. Therefore, it is expected that the high backscatter–low depolarization signals from CALIOP are generated primarily from platelike particles.

(a) Backscattering *P*_{11} of oriented plates and columns as a function of incident angle. (b) Simulated *δ*–*γ*′ relationship for optically thick ice clouds with horizontally oriented plates and columns. The deviation angles for oriented crystals are set to zero. (c) Relationship between the percentage of HOIC and *γ*′.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

(a) Backscattering *P*_{11} of oriented plates and columns as a function of incident angle. (b) Simulated *δ*–*γ*′ relationship for optically thick ice clouds with horizontally oriented plates and columns. The deviation angles for oriented crystals are set to zero. (c) Relationship between the percentage of HOIC and *γ*′.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

(a) Backscattering *P*_{11} of oriented plates and columns as a function of incident angle. (b) Simulated *δ*–*γ*′ relationship for optically thick ice clouds with horizontally oriented plates and columns. The deviation angles for oriented crystals are set to zero. (c) Relationship between the percentage of HOIC and *γ*′.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

Figure 9 shows the *δ*–*γ*′ relationship of opaque single-layer clouds, where the color of each pixel represents the frequency of occurrence. Figure 9a is the *δ*–*γ*′ relationship for clouds warmer than −20°C when the off-nadir angle is set to 0.3°. The branch with a positive slope represents water clouds with spherical particles while the branch with a negative slope represents clouds with HOIC. The HOIC branch is above the water cloud branch when the off-nadir angle is 0.3°, and the points are much closer to the water cloud region when the off-nadir is 3°, similar to the simulations for mixed-phase clouds. Statistically, the distribution function of the percentage of HOIC should be continuous. Thus, it is concluded that single-layered clouds with HOIC at temperatures warmer than −20°C could reasonably be considered as mixed-phase clouds. This conclusion is consistent with Cho et al. (2008), who also indicate that oriented plates are present in mixed-phase clouds. From the comparison of the *δ*–*γ*′ distribution for HOIC in Fig. 9a with our simulation results, the percentage of quasi-horizontally oriented plates ranges from 0% to 6% in optically thick mixed-phase clouds.

Frequency of occurrence for single-layer opaque clouds as a function of *δ* and *γ*′ observed by *CALIPSO* lidar. Observations are for (top) 0.3° off-nadir angles and (bottom) 3° off-nadir angles with (left) *T* > −20°C, (middle) −35° < *T* < −20°C, and (right) *T* < −35°C.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

Frequency of occurrence for single-layer opaque clouds as a function of *δ* and *γ*′ observed by *CALIPSO* lidar. Observations are for (top) 0.3° off-nadir angles and (bottom) 3° off-nadir angles with (left) *T* > −20°C, (middle) −35° < *T* < −20°C, and (right) *T* < −35°C.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

Frequency of occurrence for single-layer opaque clouds as a function of *δ* and *γ*′ observed by *CALIPSO* lidar. Observations are for (top) 0.3° off-nadir angles and (bottom) 3° off-nadir angles with (left) *T* > −20°C, (middle) −35° < *T* < −20°C, and (right) *T* < −35°C.

Citation: Journal of Applied Meteorology and Climatology 51, 7; 10.1175/JAMC-D-11-0265.1

Figures 9b,e show results for clouds at temperatures between −20° and −35°C as provided in the CALIOP product. The HOIC and water cloud branches overlap when the off-nadir angle is 0.3°. The data tend to concentrate in the region representing ROIC when the off-nadir angle changes to 3°, implying that many of the near-nadir CALIOP measurements were of ice particles rather than water at temperatures between −20° and −35°C. Comparison of the *CALIPSO* products with simulations suggests that the percentage of quasi-horizontally oriented plates in these ice clouds ranges from 0% to 3%.

In Figs. 9c,f, the water cloud branch does not exist, implying the nonexistence of supercooled water clouds at temperatures colder than −35°C. The equivalent percentage of HOIC in these cold clouds ranges from 0% to 0.5%.

*δ*

_{rm}and

From the CALIOP measurements and our simulation results, oriented plates are found most frequently in warm mixed-phase clouds, less frequently in ice clouds at warmer temperatures, and infrequently in very cold ice clouds.

## 4. Summary

In this study, we developed a Monte Carlo radiative transfer model to simulate lidar returns from clouds consisting of ROIC and HOIC, with a full consideration of the extinction matrix. An advantage of this model is in its ability to simulate both optically thin and optically thick clouds. The model is used to simulate the CALIOP backscattering and depolarization signals of water clouds, mixed-phase clouds, and ice clouds.

A series of case studies for ice clouds and mixed-phase clouds with HOIC are investigated. The results of the Monte Carlo simulations are found to be consistent with CALIOP observations. Comparison of the model results and observations shows that most oriented plates exist in mixed-phase clouds warmer than −20°C and are very infrequent in cold high clouds at temperatures below −40°C. Specifically, it is estimated that the percentage of horizontally oriented plates are 0%–6%, 0%–3%, and 0%–0.5% in optically thick mixed-phase clouds, warm ice clouds (>−35°C), and cold ice clouds, respectively. This finding is consistent with previous studies (e.g., Noel and Chepfer 2010).

In addition to horizontally oriented plates, the effect of oriented columns was also investigated, but the effect of oriented columns was found to be much smaller than that of horizontally oriented plates. The distribution of *δ*–*γ*′ is quite different when the off-nadir angle for the CALIOP measurements changes from 0.3° to 3° and suggests the existence of large plates with horizontal orientations (note that small plates tend to be randomly oriented).

## Acknowledgments

This study is supported by NASA Grant NNX10AM27G, and partly by NNX11AF40G and NNX11AK37G. The authors are grateful to Lei Bi and Meng Gao for their help in the light scattering and radiative transfer simulations involved in this study.

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