Ice clouds play an important role in the radiation balance of the Earth's atmospheric system through interaction with solar radiation and infrared emissions (Liou, 1986). However, large uncertainties exist in quantifying the radiative impact of ice clouds. This is because they consist of ice particles with various microphysical characteristics, e.g. a wide range of habits and sizes (C.-Labonnote et al., 2000; Forster et al., 2007; Baran et al., 2007; Cole et al., 2014; Yang et al., 2015). Different ice particle habits have varying single-scattering characteristics, resulting in different radiative properties. Satellite observations are important as a means of inferring the ice clouds' optical properties and monitoring their radiative impact on a global climate system. However, retrieved ice cloud properties highly depend on the assumed ice particle model. In practice, one chooses an ice particle model, which may consist of a single habit or a mixture of habits, and look-up tables (LUTs) for ice cloud reflection and transmission characteristics are computed for a range of input optical properties such as optical thickness, cloud temperature, and effective particle size. The LUTs and a fast radiative transfer model are subsequently used for global operational retrievals. Thus, the choice of an ice particle model for a given satellite mission deserves rigorous investigation. The present study aims to better understand the performance of several ice cloud habit models, in conjunction with applications to the Global Change Observation Mission-Climate (GCOM-C) satellite mission.

Over the past 2 decades, aircraft and balloon in situ observations have contributed greatly to understanding ice cloud microphysical characteristics and radiative properties (Baran et al., 1998, 1999, 2003; Heymsfield et al., 2002; Heymsfield, 2003; Zhang et al., 2009). A variety of ice particle models has been developed based on in situ observations of ice particle habits and their single-scattering properties (e.g. Macke et al., 1996a, b; McFarquhar and Heymsfield, 1996; Yang et al., 2000, 2005, 2013; Um and McFarquhar, 2007, 2009, 2011; Nousiainen et al., 2011; Baum et al., 2005, 2011; Baran and C.-Labonnote, 2007; Ishimoto et al., 2012b; Liu et al., 2014a). Numerous light-scattering computation methods have been employed to calculate the single-scattering properties of the various ice particles, including the finite-difference time-domain (FDTD) method (Yee, 1966; Yang and Liou, 1998a; Sun et al., 1999, Ishimoto et al., 2012a), the T-matrix (Baran et al., 2001; Bi and Yang, 2014a, b), the discrete dipole approximation method (Purcell and Pennypacker, 1973; Draine and Flatau, 1994; Yurkin et al., 2007), the boundary element method (Mano, 2000; Groth et al., 2015), the pseudo-spectral time-domain method (Liu, 1997, 1998; Chen et al., 2008; Liu et al., 2012), the surface-integral equation method (Nakajima et al., 2009), the improved geometric optics method (IGOM) (Yang and Liou, 1996), geometric optics integral equation (GOIE) (Yang and Liou, 1996; Ishimoto et al., 2012a), and the ray-tracing geometric optics method (GOM) (Takano and Liou, 1989, 1993; Macke, 1993; Macke et al., 1996a; Yang and Liou, 1998b; Masuda et al., 2012).

Various ice particle models correspond to different radiative properties. Quantifying optical properties of these ice particle models is computationally expensive, and thus for application purposes it is useful to establish a number of libraries that pre-calculate the single-scattering properties of various ice particle habits. Using hexagonal plates and columns with a random orientation, Hess and Wiegner (1994) developed a single-scattering property database at wavelengths between 0.35 and 3.7 µm. Additionally, Yang et al. (2000) provided a database at wavelengths between 0.2 and 5 µm for six ice particle habits (plates, solid and hollow columns, planar bullet rosettes, spatial bullet rosettes, and aggregates); Yang et al. (2005) further included two more ice habits and extended the database to wavelengths between 3 and 100 µm. Recently, Yang et al. (2013) released a database of a full set of scattering, absorption, and polarisation properties, assuming random orientation for a set of 11 habits at a number of wavelengths, ranging between 0.2 and 100 µm. This database involved the addition of roughness to the particle surfaces. This library is based on the Amsterdam discrete dipole approximation, T-matrix, and IGOM methods. Using this updated library, Baum et al. (2014) developed a new set of bulk scattering and absorption models, with habit mixtures for radiative transfer calculations and remote sensing retrievals of ice clouds.

There is increasing evidence that the ice particle model should contain some degree of surface roughness (Foot, 1988; Baran et al., 2001, 2003; Ottaviani et al., 2012; van Diedenhoven et al., 2012, 2013, 2014; Cole et al., 2013, 2014; Holz et al., 2016). In particular, using an ensemble ice particle model, Baran and C.-Labonnote (2007) and Baran et al. (2014) showed that featureless phase functions best fitted their multi-angle satellite measurements at solar wavelengths. Interestingly, using particle images of convective ice clouds from in situ measurements, Ishimoto et al. (2012b) developed a new habit of complex and highly irregular shapes, called the Voronoi aggregate. The phase function of the Voronoi habit varies smoothly with the scattering angle, which is similar to behaviour found from assuming severe surface roughness, including bubbles within the particle, or a combination of included bubbles and surface roughness. However, use of the Voronoi habit model for retrieval of the ice cloud's optical thickness has not yet been investigated.

Numerous articles have investigated the use of optimal ice particle habits derived from various ice habit models and remote sensing measurements from multiple angles, for use in cloud parameter retrievals (Baran et al., 1998, 1999, 2003, 2007; Chepfer et al., 1998; C.-Labonnote et al., 2000; Chepfer et al., 2001; Masuda et al., 2002; Knap et al., 2005; Sun et al., 2006; Baran and C.-Labonnote, 2006). C.-Labonnote et al. (2000, 2001) and Doutriaux-Boucher et al. (2000) developed models of randomly oriented hexagonal ice particles containing spherical air bubbles (the inhomogeneous hexagonal monocrystal (IHM) model) for use in the ice cloud retrievals of the POLarization and Directionality of the Earth's Reflectances (POLDER) measurements. Spherical albedo difference (SAD) analysis is employed to investigate the capability of the IHM model for retrieving the optical properties of ice clouds. It is illustrated that POLDER multi-angle measurements are sensitive to ice particle habits and roughness, at least for ice clouds having an optical thickness larger than 5. Chepfer et al. (2002) investigated effective ice particle habits using multi-angle and multi-satellite methods derived from visible reflectance satellite measurements.

The Second Generation Global Imager (SGLI) on board the GCOM-C satellite, scheduled for launch in 2017 by the Japan Aerospace Exploration Agency (JAXA), measures radiation at 19 visible and near-infrared wavelengths in order to understand the global radiation budget, carbon cycle mechanism, and climate change (Imaoka et al., 2010). Since retrieving ice cloud properties on a global scale from satellite observations requires knowledge of ice microphysical models, it is crucial to identify an optimal choice of ice habits for SGLI. The objectives of this study are to better understand the performance of existing ice models used in other satellite missions, investigate the potential of the Voronoi model, and provide a recommendation for the GCOM-C.

The paper is organised as follows. In Sect. 2, in order to develop the ice cloud property products of the GCOM-C satellite, we describe the method for calculating single-scattering properties at the SGLI-operated wavelengths for the five ice particle habits, including the Voronoi model. In Sect. 3, we apply the newly calculated ice cloud properties to SAD analysis, using POLDER measurements as an example. In Sect. 4, we describe the results of the SAD analysis. Section 5 presents our conclusions.

Since 1996, three POLDER instruments have been flown to study clouds and aerosols using multiple angles and polarisation capabilities. The POLDER-1 and POLDER-2 instruments aboard JAXA's ADEOS satellite were operated from November 1996 to June 1997 and December 2002 to October 2003, respectively. Both of the POLDER instruments observed intensity from 14 viewing directions, with scattering angles ranging from 60 to 180∘. The spatial resolution of the product derived from POLDER-2 observation data is approximately 20 km, which is composed of 3 × 3 single pixels. POLDER-2 measured the upwelling total and polarised radiances from eight observing channels centred at wavelengths of 0.443, 0.490, 0.565, 0.670, 0.763, 0.765, 0.865, and 0.910 µm (Baran and C.-Labonnote, 2006). POLDER-3 operates aboard the Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar (PARASOL) microsatellite, launched in 2004. POLDER-3 has nine observing channels, three of which had polarisation capabilities. PARASOL/POLDER-3 views a given scene from up to 16 angles as the satellite passes overhead. However, the capabilities of the instrument, such as observing the radiances from multiple viewing angles in several visible channels, are important for investigating the representative ice particle models for retrieving ice cloud properties. In this study, 589 × 246 pixels of the POLDER-3 observation data with a global scale, obtained when flying over oceans on 20–22 March, June, September, and December 2008, were used to retrieve cloud optical thickness and spherical albedo in order to investigate the behaviour of the five ice particle habits.

Figure 2a shows the distribution of the number of directional samples used in the SAD analysis. The number of pixels is increased in the scattering angle range of 60 to 160∘ and is decreased in the scattering angle range from 160 to 180∘. There is a peak value of the number of sample pixels in the scattering angle range of 140 to 160∘. Figure 2b indicates the variation of the number of pixels by latitude; the number of pixels changes significantly as a function of latitude and is lowest when the latitude is around 90∘ N and 90∘ S. There are three peaks of the number of pixels in the different latitudes, due to the location of more samples at midlatitude, where storm tracks occur, as well as along the Intertropical Convergence Zone (ITCZ), where there are numerous deep convective clouds. C.-Labonnote et al. (2000) and Baran and C.-Labonnote (2006) proposed the SAD method for testing the phase function of the various ice particle models, using POLDER observational data with multiple viewing angles. For investigating the phase functions (P11) of the different ice crystal models for retrieving the cloud microphysical properties, the cloud spherical albedo as a function of scattering angle is required. For calculating the cloud spherical albedo, bidirectional reflection is first determined by

Rcldμ,μ0,ϕ-ϕ0=πLobs(μμ0ϕ-ϕ0)/μ0F0, where u and u0 are cosines of the satellite and solar zenith angles, ϕ-ϕ0 is the relative azimuth angle between the satellite and the sun, Lobs is the reflected solar radiance observed by the satellite, and F0 is the solar flux density. POLDER usually observes a given Earth target (pixel) under up to 16 different directions. From each of these N observations a so-called “directional cloud optical thickness” is retrieved from Lobs using pre-computed LUTs that provide the bidirectional reflection (Rlcd) of clouds as a function of optical thickness, zenith angles, and relative azimuth angle. The cloud-plane albedo (Ap) and spherical albedo (S) are calculated by integrating over all the zenith and azimuth angles as

Apμ0=∫∫Rcld(μ,μ0,ϕ-ϕ0)μdμdϕ,S=∫Ap(μ0)μ0dμ0. A total of N observation of Lobs are acquired under different viewing geometries hence associated with different scattering angles θ. Those are converted to N directional optical thickness values which in turn can be translated into equivalent direction spherical albedo values using Eqs. (9) to (11). Eventually we obtain N values of cloud spherical albedo S for various θ values. Baran and C.-Labonnote (2006) assumed that if the scattering phase function of the ice particle model is correct, then calculated S(θ) in each direction should be the same and the SAD, as shown in Eq. (13), should be 0. S‾, SAD, and θ are given as S‾=(1/N)∑S(θ),SAD=Sθ-S‾,cosθ=cosπ-u0cosu+sinu0sinucos⁡ϕ-ϕ0, where u0 and u are the solar and satellite zenith angles, respectively.

The steps for applying the SAD analysis to POLDER-3 measurements are as follows:

Calculate spherical albedo from the POLDER-3 measurements with 16 viewing geometries for each of the ice particle models.

Ice particle single-scattering properties were investigated for potential use in the GCOM-C satellite programme. The single-scattering properties of five different ice particle models (plates, columns, droxtals, bullet rosettes, and Voronoi) were developed using the FDTD, GOIE, and GOM methods. The accuracy of the single-scattering property was investigated by comparing the phase function from the FDTD method used in this study with conventional results from ADDA and T-matrix methods. The FDTD phase functions were also compared with computational results from GOIE. Results indicate that the FDTD-based phase functions are consistent with results from the ADDA, T-matrix, and GOIE methods, which suggests that the single-scattering property database developed in this study is reliable for use in radiative transfer simulations and applications in the remote sensing of ice clouds.

The characteristics of the single-scattering property database for five different ice particle models were investigated by analysing the single-scattering albedo, asymmetry factor, and the extinction efficiency. Bulk scattering phase functions for five different ice particle models at the wavelength of 1.05 µm were compared as a function of various effective diameters. It is concluded that phase functions depend on the particle habit and effective diameters. There is a halo peak for middle and large sizes of column, plate, and bullet-rosette habits. For the droxtal particle, variation of the phase function is evident for different effective diameters. The phase function of the Voronoi habit is very smooth, with features similar to those of severely roughened ice particle models.

Furthermore, SAD analysis was performed to determine the optimal ice particle habit for retrieving the optical thickness and cloud spherical albedo using POLDER-3 multi-angle measurements. Retrievals were performed using 589 × 246 pixels of the POLDER-3 observation data on a global scale, recorded over oceans on 20–22 March, June, September, and December 2003. The following conclusions are drawn from the results.

The SADs of the droxtal and column habits show significant variations in scattering angle and effective particle radius.

Data are available upon request.